Hi! I need Help With The Bottom Answers Someone Already Answered The Top So Just The Bottom Questions!

Answers

Answer 1
Answer:
f. 4 + 4 = 8
f. 23 + 8 + 4 = 35
h. 53 + 3 + 28 = 84
i. 11 + 17+ 93 = 121
j. 24 + 8 + 3 = 35

Step-by-step explanation:
f. 4.112 rounded to the nearest whole number is
rounded to the nearest whole number is 4 because 1 doesn't round up the number. 3.89 rounded to the nearest whole number is 4 because any number equal to or greater than 5 rounds up the number in front of itself. 4 + 4 = 8

g. 23.14 rounded to the nearest whole number is 23 because 1 doesn't round up the number. 7.6 rounded to the nearest whole number is 8 because any number equal to or greater than 5 rounds up the number in front of itself. 3.67 rounded to the nearest whole number is 4 because any number equal to or greater than 5 rounds up the number in front of itself. 23 + 8 + 4 = 35.

h. 53.2 rounded to the nearest whole number is 53 because 2 doesn't round up a number. 3.08 rounded to the nearest whole number is 3 because 0 doesn't round up a number. 27.51 rounded to the nearest whole number is 28 because any number equal to or greater than 5 rounds up the number in front of itself. 53 + 3 + 28 = 84.

i. 11.08 rounded to the nearest whole number is 11 because 0 doesn't round up a number. 17.28 rounded to the nearest whole number is 17 because 2 doesn't round up a number. 92.6 rounded to the nearest whole number is 93 because any number equal to or greater than 5 rounds up the number in front of itself. 11 + 17+ 93 = 121

j. 24.08 rounded to the nearest whole number is 24 because 0 doesn't round up a number. 7.9 rounded to the nearest whole number is 8 because any number equal to or greater than 5 rounds up the number in front of itself. 3.06 rounded to the nearest whole number is 3 because 0 doesn't round up a number. 24 + 8 + 3 = 35.

Answer 2

F:4+4=8

A:23+8+4=35

H:53+3+28=84

I:11+17+93=121

I:24+8+3=35

I think that is all correct


Related Questions

A baker places 4 muffins in each box. Which is the total number of muffins in 8 boxes?

Answers

Answer: 32

Step-by-step explanation: 4 x 8 = 32 . I am concerned how simple this is ;-;

Answer:

32

Step-by-step explanation:

each boxes have 4 muffins

so,in 8 boxes

by question

8×4=32

The question is in the picture I would appreciate if you could explain how to get the answer thank you.

Answers

Answer: the cost for Internet increase by 5/4 per minute

Step-by-step explanation:

Help please radicals

Answers

Answer:

5√2

Step-by-step explanation:

Hello!

To simplify the radical, we can identify perfect square factors in the radicand or the number inside the square root.

We know that 50 is 25 times 2, so we can expand the radical like this...

[tex]\sqrt{50[/tex][tex]\sqrt{25*2}[/tex][tex]\sqrt{25} * \sqrt2[/tex]

Now we can simplify each radical:

[tex]\sqrt{25} * \sqrt2[/tex][tex]5\sqrt2[/tex]

The simplified form is 5√2.

CANN SOEMOEN PLS HELP ME PLS. I DONT KNOW WHAT TO DO AND THIS IS ALREADY A WEEK LATE.

Answers

Answer:

y = 72 and x = 36

Step-by-step explanation:

So firstly, the outside angle is 108, right? And the total of all angles in a triangle is 180 degrees. So:
180 - 108 = 72
Then the other angle, angle x, is also 72 degrees. That's because they are supplementary angles.
Now that we know x = 72 degrees. To find the y angle, you add 72 and 72 together. Which is 144.
Then you do 180 - 144. Which is 36. So, x = 72 and y = 36

I hope it helped you!

What is a 69 sided shape called?

Answers

A 69 sided shape called"Hexacontakaienneagon".

Naming a polygon by its number of sides requires that we know the appropriate:

3=tri, 4=tetra, 5=penta, 6=Hexa, 7=hepta, 8=octa, 9=Nona or ennea, 10=deca,11=hendeca,12=dodeca,13=triskaideca,14=tetradeca,15=pentadeca,16=hexadeca,17=heptadeca,18=octadeca,19=enneadeca,20=icosa

For polygons with 3 through 20 sides, simply add "gon" to the prefixes at the left.

For more than 20 sides, we "construct" the name by using so-called combining prefixes:

For Tens Digit:

20=icosi,30=triaconta,40=tetraconta,50=pentaconta,60=hexaconta,70=heptaconta,80=octaconta,90=enneaconta

for One's Digit:

1=hena,2=di,3=tri,4=tetra,5=penta,6=hexa,7=hepta,8=octa,9=ennea

60                and      9    

hexaconta    kai     ennea

As per the given information, 69 is defined as "Hexacontakaienneagon".

To know more about Naming Polygons:

https://brainly.com/question/26583264

#SPJ4

Señor Ochoa is planting a garden in the corner of his yard. Before he does any planting, however, he wants to make a

scale drawing showing where he wants each vegetable and fruit to go. So far, he has drawn the perimeter of his garden.

The actual length of the vertical and horizontal legs of his triangular garden is 3 meters.

6 cm

6 cm

8. 5 cm

After making his drawing, he decides that his scale is way too small. Instead, he wants the vertical and horizontal legs of

the triangle on his drawing to be 18 centimeters. Make a new scale drawing with the new dimensions of the scale

drawing. Make sure to label all three sides of the garden and include the new scale.

Answers

Señor Ochoa draws the perimeter of the garden with actual length of the vertical and horizontal legs of his triangular garden 3 meters as 6cm in his initial drawing with 18.5cm third side. Then new drawing with the vertical and horizontal legs of 18 cm

A scale drawing is a representation of an object or space that is reduced or enlarged in proportion to the actual size. To make a new scale drawing of Señor Ochoa's garden with the new dimensions of 18 centimeters for the vertical and horizontal legs of the triangle, you would need to apply a scale factor of 18/6 = 3 to the original drawing.

So, you would multiply each original dimension by 3 to get the new dimensions for the scale drawing.

The new scale drawing would be:

6cm × 3 = 18cm

6cm × 3 = 18cm

8.5cm × 3 = 25.5cm

The new scale is

= scale dimension/ original dimension

= 18cm/ 3m

= 18cm/ 300cm

= 3/ 50

It is also worth noting that as you are changing the scale, the measurement of the hypotenuse of the triangle would be affected, which is the square root of 3 meters, that would be approximately 25.5cm, which is the same as the original measurement on the original drawing.

To know more on scale drawing

https://brainly.com/question/17388747

#SPJ4

PLEASE HELP PICTURE ATTACHED!!

IF m /3 = (9x + 14) and m/5 = (14x - 1), find m/28.

Answers

Answer:

∠8 = 139°

Step-by-step explanation:

Before we start solving, let's identify the figure to understand the problem.

We are given two parallel lines that are cut by a transversal.

Two lines are parallel if they have the same arrow head marking.

If two parallel lines are cut by a transversal, the following angles are created:

alternate interior anglesalternate exterior anglesvertical anglesadjacent anglescorresponding angles

I have attached an image of the different types of angles to this response.

Thus, we can use the types of angles to solve for ∠8.

3 and 5 are corresponding angles. Therefore, they have the same measure.

Set up the equation to solve for x:

∠3 = ∠5

9x + 14 = 14x - 1 . . . . . . substitute the values

14 = 5x - 1 . . . . . . . . subtract 9x from the LHS and RHS

15 = 5x . . . . . . . . . . add 1  to the LHS and RHS

∴ 3 = x . . . . . . . . . . . . divide the LHS and RHS by 5 to isolate x

Now that we know what x is, we can substitute it into the value of ∠3.

∠3 = 9x + 14

∠3 = 9(3) + 14 . . . . substitute the values

∠3 = 27 + 14 . . . . . compute

∴ ∠3 = 41

∠3 and ∠8 are adjacent angles. Therefore, they add up to 180°.

Set up the equation to solve for ∠8:

∠8 + ∠3 = 180

∠8 + 41 = 180 . . . . substitute the known values

∴ ∠8 = 139° . . . . . subtract 41 from the LHS and RHS to isolate ∠8

⭐if this response helped you, please mark it the "brainliest"!⭐

Answer:

Step-by-step explanation:

180-54=139 so 8 equals 139

How do you find the parent function of a line?

Answers

The parent function of a line (usually of the form y = ax + b) is y = x.

The most basic form of a function is a parent function. Its essential shape is not changed in any manner. In mathematics, some graphs are frequently seen. Because of this, the graphs of quadratic functions, square roots, absolute values, cubics, and cube roots are among the original, widespread functions that are referred to as parent graphs.

For instance, you should still be able to identify the parabola that has undergone various transformations when you view a u-shaped graph that has been inverted and stretched vertically.

Linear Function

Linear functions have x as the term with the highest degree and a general form of y = a + bx. All linear functions have a straight line as a graph. The parent function of linear functions is y = x, and it passes through the origin. The domain and range of all linear functions are all real numbers.

These functions represent relationships between two objects that are linearly proportional to each other.

Therefore, the parent function of a line (usually of the form y = ax + b) is y = x.

To learn more about parent functions, visit the link:

brainly.com/question/20333814

#SPJ4

Here is a piece of cake each piece of cake has the same number of candles how old is rongopai

Answers

Rongopai's age is equal to the total number of candles on the cake, thus I need to determine what that is.

How to estimate Rongopai's age?

What I need to figure out because I am aware that Rongopai's age is equal to the total number of candles on the cake.

The number of pieces the cake was sliced into must first be determined. A quarter has a specific appearance to me. This is how it would seem (the teacher traces a quarter shape on the circle). There must have been more than four pieces since this one seems a little smaller.

Each cut's location may be identified using my finger. Given that all the pieces must be the same size, I'm predicting the locations of each line using the first piece as a reference.

Here would be the approximate location of the first line, followed by here and here (the teacher draws a line with her finger) (tracing two more lines). the third line. In my mind, the lines and parts are somewhat "visible." Four "invisible" pieces plus the one drawn in are present when I count backward.

The complete question is:

A teacher wants a student to see how visualising the size of a share (in this case, a piece of cake) can be used to work out how many shares are needed to make a whole:

“Here is a piece of Rongopai’s birthday cake. Each piece of cake has the same number of candles. How old is Rongopai?”

To learn more about quarter shape refer to:

https://brainly.com/question/20333097

#SPJ4

Age of Rongopai is 20 years.

What means one fifth of a circle?

One fifth of a circle means if a circle can be divided into five equal parts, then one fifth is one of them.

How old is Rongopai?

As per the figure given, there is shown a 1 fifth of a circular birthday cake.

As all the piece of cake is equal in size so the total number of cake piece is five.

the number of candles in each piece is four.

the total number of candles present in the whole cake is = 5 × 4

the total number of candles = 20

Therefore, Rongopai is 20 years old.

To know more about a circle visit:

https://brainly.com/question/11833983

#SPJ4

Find the approximate number of grams of milk fat in a 200-gram serving of whole milk.

Answers

The answer is :6.5g

The newest streaming service costs $9.24 per month with
tax. If tax is 5%, how much is the streaming service before
tax and how much does a year of the service cost?

Answers

Tax = 5%
Total = $9.24

Tax = 9.24 x 0.05 = 0.462

Answers:
Total before tax = 9.24 - 0.462 = $8.778
Year of service = 8.778 x 12 = $105.336

Have a good day ^^

Tobias is constructing barriers to prevent cars from driving on a bike path. He can make conical pylons using the dimensions shown. If he used the
same amount concrete to construct a spherical barrier, how tall would it be? Express your answer in terms of π?

Is it:
A)1 2/3 π
B)3 2/3 π
C)4 1/3 π
D)5 π

Answers

The volume of the cone is (2/3)π cubic feet. And the radius of the spherical barrier would be 0.8 ft. and the height would be 2r = 2(0.8) = 1.6 ft. The correct option is A.

What is volume?

Space occupied by an object in three-dimensional space is called as volume of an object. In simple words, space is taken by object.

Given:

Tobias is constructing barriers to prevent cars from driving on a bike path. He can make conical pylons using the dimensions shown.

He used the same amount of concrete to construct a spherical barrier.

According to the information  given in the exercise, the height and the radius of the pylons are the following:

Height h = 2 ft

Radius r = 1 ft

So, the volume of the cone,

= (1/3)πr²h

= (1/3)π(1)²(2)

= (2/3)π cubic feet.

And the volume of the sphere is twice the volume of the cone.

So, the volume of the sphere,

4πr³/3 = 2π/3

2r³ = 1

r³ = 1/2 = 0.5

r = ∛0.5 = 0.8 ft.

Therefore, the radius of the spherical barrier would be 0.8 ft. and the height would be 2r = 2(0.8) = 1.6 ft.

To learn more about the volume;

https://brainly.com/question/23477586

#SPJ1

Pls help question 9,10 and 11. And can u explain or show how u make the equation ?

Answers

Answers
9) $2.00 ÷ 5 oranges = .40 per orange
.40 x 24 oranges = $9.60 cost of 24 oranges

An equation would be
2.00 /5 = x/24
Cross multiply
5x = 48
X = 9.60

10) $180 ÷ 3 days rent = $60 per day rent
$60 x 7 days (1 week) = $420 rent for 1 week

An equation would be

$180/3 = x/ 7
Cross multiply
3x = 1260
X = $420

11) 32 km ÷ 2L gas = 16 km per L gas
78 km ÷ 16 km = 4.875 L gas to drive 78 km

An equation would be

32 / 2 = 78 / x
Cross multiply
32x = 156
X = 4.875



Step by step

Proportions are the same as rate. Rate is found using division to find the amount per unit. Proportional equations will equal each other. I showed you common sense math and also an equation to find the answers.

If y varies inversely as x and y=3 when x=4, then y=12 when x=15
Please select the best answer from the choices provided
T
F

Answers

Answer:

F.

Step-by-step explanation:

y = k/x where k is a constant

given that x = 4 when y = 3, we have:

3 = k/4

So, k =12.

The equation of variation is:

y = 12/x

When x = 15

y = 12/15 = 4/5.

So not 12 so this is False,

Which is not a polynomial a 4x2 2x 1 by 3 YC x3 1 D y2 5y 1?

Answers

2) y+ 3÷y is the equation that is not a polynomial. Using addition, subtraction, multiplication, and division of numbers .

what is polynomial ?

Using just the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables, a polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients. Using addition, subtraction, multiplication, and division of numbers, a polynomial is an equation that combines variables, constants, and exponents (No division operation by a variable).

given

An algebraic mathematical equation known as a polynomial might have two components. coefficients and parameters

You can combine the solutions to these algebraic equations to achieve the result.

It follows the general formula as follows:

a + a1 + a+ …

2)y+ 3y is the equation that deviates from the formula above.

So, 2)y+ 3y is the equation that is not a polynomial.

To know more about polynomial visit :-

brainly.com/question/11536910

#SPJ4

A school administrator asks each student if they participate in a sport and if they participate in a club. The results are shown below.

Participates in a Sport
Yes No Total
Participates in a Club Yes 620 450 1070
No 325 535 860
Total 945 985 1930
What percentage of students do not participate in a sport?

27.7%
44.6%
51.0%
62.2%.


answer is 51.1

Answers

The percentage of students who do not participate in a sport is C. 51.0%.

How to calculate the percentage?

To find the percentage of students who do not participate in a sport, we can use the following formula:

(Number of students who do not participate in a sport) / (Total number of students) * 100%

From the table, we can see that the number of students who do not participate in a sport is 985, and the total number of students is 1930. So, plugging these values into the formula gives us:

= 985 / 1930 * 100%

= 51.03%

So, about 51.03% of students do not participate in a sport.

Learn more about Percentage on:

https://brainly.com/question/24304697

#SPJ1

What is the solution to the system of equations 3x 2y 7 and Y 3x 11?

Answers

The solution of the given system of equations is x = -7/3 and y = 7.

The given system of equations is given as,

3x + 2y = 7

y = 3x + 11

To solve this system of equations, we need to eliminate one of the variables. We can eliminate y by subtracting the second equation from the first.

3x + 2y = 7

y = 3x + 11

⇒ 3x + 2y - y = 7 - 11

⇒ 3x + 2y - 3x - 11 = -4

⇒ 2y - 11 = -4

⇒ 2y = -4 + 11

⇒ 2y = 7

Now, substitute the value of y in the first equation to find the value of x.

3x + 2(7) = 7

⇒ 3x + 14 = 7

⇒ 3x = 7 - 14

⇒ 3x = -7

⇒ x = -7/3

Therefore, the solution of the given system of equations is x = -7/3 and y = 7.

Learn more about equations here:

https://brainly.com/question/29657983

#SPJ4

A dumpster is shaped like a rectangular prism. It has a width of 8 feet, a height of 5 feet, and a volume of 880 cubic feet. What is the length of the dumpster

Answers

The volume of a rectangular prism is found via the following formula:

V=l•w•h, where V is volume, l is length, w is width, and h is height.

So, we can input the known values into the formula and solve for the unknown values since we already have the volume.

(880)=l•(8)•(5)

Simplify:

880=l•40

l•40 = 40l

880=40l

Solve for l:

Divide both sides by 40:

880/40=l

22=l

Apply the symmetric property:

l=22

Now, let’s plug the length back into the volume formula and check that it is correct:

880=(22)•8•5

880=880

So, our answer is correct.


Answer: the length is 22 feet.

Aisha bought 15 apples and oranges for $9.00. each orange costs $0.50, and each apple costs $0.65. let x represent the number of oranges and y represent the number of apples. which system can be used to find the number of apples and oranges aisha bought? x y = 15. 0.5 x 0.65 y = 9.00 x = y. 0.5 x 0.65 y = 9.00 x y = 9. 0.5 x 0.65 y = 15.00 x = y. 0.5 x 0.65 y = 15.00

Answers

Both (x + y = 15) and (0.5x + 0.65y = 9.00) make up the equation system.

What is an equation ?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

The statement is not an equation if there is no "equal to" sign in it

According to our question-

x is the quantity of oranges.

y is the quantity of apples.

Oranges plus apples equal 15, or x plus y equals 15, so Aisha purchased 15 pieces of fruit.

Apples cost $0.65 and oranges cost $0.50. The fruit cost Aisha $9.00.

0.5x (the total cost of the oranges) + 0.65y (the total cost of the apples) equals 9.00 (the total cost of the fruit).

x + y = 15

0.5x + 0.65y = 9.00

As a result, the system of equations is (0.5x + 0.65y = 9.00) and (x + y = 15).

learn more about equation click here:

brainly.com/question/2972832

#SPJ4

Find the radius of a circle that has a sector area of 165.6 cm2 and an angle measure of 129*. Round your answer to the nearest tenth.

Answers

To find the radius of a circle given the area of a sector and the measure of the central angle of the sector, we can use the formula:

radius = sector area / (central angle measure / 360)

In this case, the sector area is 165.6 cm2 and the central angle measure is 129*. Plugging these values into the formula gives us:

radius = 165.6 / (129 / 360)

= 165.6 / (129 / 360)

= 165.6 / (0.3583)

= 462.9 cm

Rounding this value to the nearest tenth gives us a radius of approximately 463 cm.

How do you find the value of x in a two step equation?

Answers

Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One results from multiplying a number by its reciprocal, or inverse.

Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One results from multiplying a number by its reciprocal, or inverse.

To know more about Inverse operations visit :

https://brainly.com/question/26204160?referrer=searchResults

#SPJ4

How do you plot the point 3?

Answers

Here the point 3 can be taken as (3,0) or (0, 3) ; For first, move right 3 units along the x-axis. No vertical component is there , as the y-coordinate is 0 here; For second, move 3 units along the y-axis. Since the x-coordinate is 0, there is no horizontal component.

A point is marked in a coordinate plane using its coordinates when it is plotted in a coordinate system.

The intersection of the x-axis, a horizontal number line, and the y-axis, a vertical number line, creates a 2D coordinate plane.

At the coordinate plane's origin, where the two axes (plural for axis) intersect, four right angles are formed. On a coordinate plane, a grid is frequently drawn to make it simpler to plot points.

In a 2D coordinate plane, a point's location is represented by an ordered pair of numbers (x, y). An ordered pair of numbers is used to represent the location of a point in a 2D coordinate plane (x, y). The first number in the pair represents the point's location along the x-axis, and the second number represents its location vertically (y-axis).

Count x squares from the origin along the x-axis, then count y squares in the direction of the y-axis to plot the point (x, y) in the coordinate plane.

Here the point 3 can be taken as (3,0) or (0, 3) ; For first, move right 3 units along the x-axis. No vertical component is there , as the y-coordinate is 0 here; For second, move 3 units along the y-axis. Since the x-coordinate is 0, there is no horizontal component.

To know more about Graph plotting here:

https://brainly.com/question/11616742#

#SPJ4

maddox has $12.25 to spend on sports drinks. Each drink costs $1.75. Use the guess, check, and revise strategy to solve the equation 1.75d=12.25 to find d, the number of drinks Maddox can buy.

Answers

First you divide 12.25 by 1.75 then your answer will be 7 so therefor (D = 7)

h=?ft
what is the correct answer

Answers

Answer:

h = 4 ft

Step-by-step explanation:

the area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

here b = 8 and h = 3 , then

A = 8 × 3 = 24 ft²

Now consider the other base b = 6 with perpendicular height h , then

6h = 24 ( divide both sides by 6 )

h = 4

Graph the image of square KLMN after a translation 6 units left and 4 units up.

Answers

The coordinates of the image of the square KLMN are:

K = (0, -1)

L = (2, -1)

M = (2, 1)

N = (0, 1)

The graph of the image is given below.

What are coordinates in a graph?

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The coordinates of the square KLMN are:

K = (6, -5)

L = (8, -5)

M = (8, -3)

N = (6, -3)

Now,

Translation of 6 units left and 4 units up.

This means,

K = (6 - 6, -5 + 4) = (0, -1)

L = (8 - 6, -5 + 4) = (2, -1)

M = (8 - 6, -3 + 4) = (2, 1)

N = (6 - 6, -3 + 4) = (0, 1)

Thus,

The image of the square KLMN will be on the following coordinates.

K = (0, -1)

L = (2, -1)

M = (2, 1)

N = (0, 1)

Learn more about coordinates here:

https://brainly.com/question/13118993

#SPJ1

Find the area of the fairway between two streams on a golf course.



Area =

yd2



Question 2

Explain how the fairway could be separated into figures whose areas you can find using formulas.

You could separate the figure into a trapezoid and a _____

A. Triangle

B. Square


Please do a step by step explanation

Answers

Question 1

The area of the fairway between two streams on a golf course cannot be determined without additional details such as the dimensions or measurements of the fairway and the streams.

Question 2

A. Triangle

THE FAIRWAY

To find the area of the fairway, you could separate it into figures whose areas you can find using formulas.

Step 1: Draw a diagram of the fairway, including the two streams and any other relevant features such as bunkers or trees.

Step 2: Divide the fairway into two sections, one on either side of the streams.

Step 3: Measure the width and length of each section of the fairway.

Step 4: Use the formula for the area of a rectangle to find the area of each section. (Area = width x length)

Step 5: Add the areas of the two sections together to find the total area of the fairway between the two streams.

THE TRAPEZOID

The base of the trapezoid would be the width of the fairway and the width of the stream, and the height would be the distance between the fairway and the stream. The area of a trapezoid is (a+b)h÷2, where a and b are the lengths of the bases and h is the height. The triangle would be formed by the side of the trapezoid that is the distance between the fairway and the stream, and the width of the stream. The area of a triangle is base×height÷2.

Learn more about trapezoid here:

https://brainly.com/question/8643562

#SPJ4

Point lies on the diagonal of square with . Let and be the circumcenters of triangles and respectively. Given that and , then , where and are positive integers. Find .

Answers

Point P lies on the diagonal AC of square ABCD with AP > CP. Let [tex]$O_1$[/tex] and [tex]$O_2$[/tex] be the circumcenters of [tex]$\triangle \mathrm{ABP}$[/tex] and [tex]$\triangle \mathrm{CDP}$[/tex] respectively. Given that AB = 12 and [tex]$\angle \mathrm{O}_1 \mathrm{PO}_2=120^{\circ}$[/tex], then [tex]$\mathrm{AP}=\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}$[/tex],

where a and b are positive integers.

The value of a + b is 96.

Let mid-point of DC be E and mid-point of AB be F.

Since [tex]$\mathrm{O}_1$[/tex] and [tex]$\mathrm{O}_2$[/tex] are circumcenters, therefore both lie on the perpendicular bisectors of DC and AB passing through E and F.

Now, [tex]$\mathrm{O}_1 \mathrm{P}=\mathrm{O}_1 \mathrm{~B}$[/tex] and [tex]$\mathrm{O}_2 \mathrm{P}=\mathrm{O}_2 \mathrm{D}$[/tex]

Also [tex]$\angle \mathrm{CAB}=\angle \mathrm{ACD}=45^{\circ}$[/tex]

Therefore [tex]\angle \mathrm{BO}_1 \mathrm{P}=2 \times 45^{\circ}=90^{\circ}=\angle \mathrm{DO}_2 \mathrm{P}$[/tex]

Angle subtended by an arc of a circle at its center = 2 × the angle subtended at its circumference

Therefore [tex]\angle \mathrm{O}_1 \mathrm{~PB}$[/tex] and [tex]$\angle \mathrm{O}_2 \mathrm{PD}$[/tex] are isosceles right triangles.

Using the above information and symmetry,

[tex]$\angle \mathrm{DPB}=120^{\circ}$[/tex]

Also, [tex]$\triangle[/tex]ABP is congruent to [tex]$\triangle[/tex]ADP (SAS)

and [tex]$\triangle[/tex]CPB is congruent to [tex]$\triangle[/tex]CPD (SAS)

Therefore [tex]\angle \mathrm{APB}=\angle \mathrm{APD}=60^{\circ}[/tex]

And [tex]\angle \mathrm{CPB}=\angle \mathrm{CPD}=120^{\circ}[/tex]

Now, [tex]$\angle \mathrm{ABP}=(180-60-45)^{\circ}=75^{\circ}$[/tex]

[tex]\Rightarrow \angle \mathrm{O}_1 \mathrm{BF}=30^{\circ}[/tex]

And [tex]$\angle \mathrm{PDC}=(180-120-45)^{\circ}=15^{\circ}$[/tex]

[tex]\Rightarrow \angle \mathrm{O}_2 \mathrm{DE}=30^{\circ}[/tex]

Therefore [tex]\triangle \mathrm{O}_1 \mathrm{BF}$[/tex] and [tex]$\triangle \mathrm{O}_2 \mathrm{DE}$[/tex] are right angled triangles.

BF = DE = [tex]\frac{12}{2}[/tex] = 6

[tex]\Rightarrow O_1 B=O_2 D=4 \sqrt{3}[/tex]

And  PB = PD = [tex]\frac{4 \sqrt{3}}{\cos 45^{\circ}}=4 \sqrt{6}[/tex]

Now, Let x = AP

Using law of cosine on [tex]$\triangle[/tex]ABP, we have

[tex]& 96=x^2+144-24 x \times \frac{1}{\sqrt{2}} \\[/tex]

[tex]& \Rightarrow x^2-12 \sqrt{2} x+48=0 \\[/tex]

[tex]& \Rightarrow x=\sqrt{72} \pm \sqrt{24}[/tex]

Taking the positive root, AP = [tex]\sqrt{72}+\sqrt{24}$[/tex]

Therefore a + b = 72 + 24 = 96

For more questions on square

https://brainly.com/question/21327969

#SPJ4

Point P lies on the diagonal AC of square ABCD with AP > CP. Let [tex]$O_1$[/tex] and [tex]$O_2$[/tex] be the circumcenters of [tex]$\triangle \mathrm{ABP}$[/tex] and [tex]$\triangle \mathrm{CDP}$[/tex] respectively. Given that AB = 12 and [tex]$\angle \mathrm{O}_1 \mathrm{PO}_2=120^{\circ}$[/tex], then [tex]$\mathrm{AP}=\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}$[/tex], where a and b are positive integers. Find a + b. (correct answer +5, wrong answer 0 )

Drag each label to the correct location on the net. Each label can be used more than once, but not all labels will be used.
Identify the dimensions of the net that will give a surface area of 48 sq cm. The area of each part of the net is shown in the figure.

Answers

As a result, the response to the query that the area provided With interiors of 32 and 44 square feet, respectively, the future complex will consist of a 60.1-foot circular.

Describe the Area.

Finding out how big a rectangle or rectangle is is the simplest (and most used) method. Divide the width by the altitude to find the area of a rectangle. Since all sides of a square are equal in length, determining the area of unit only requires knowledge of the size of one of its sides.

Here,

Here is the formula for area:

The area formula is length times width.

=> 8 × 4

= >32ft²

Following space will be on the trapezoid:

=>(14 + 18)/2 × 4

=> 44ft²

By multiplying the measurement by two, the perimeter will indeed be determined. Knowing this,

= 2(8 + 4) + (14 + 8 + 4 + 5.6 + 4.5)

= 24 + 36.1

= 60.1 ft

In light of this, the answer to the area-related question is

For the specified polygon, 60.1 square feet.

To know more about area , visit

brainly.com/question/27683633

#SPJ1

A car that travels 20 miles in 1/2 hour at consent speed travels at the same rate as a car that travels 30 miles in 3/4 hour at a constant speed.

Answers

Explain how the Distributive Property can be used to solve the equation 3(x+4)=36. Multiply the first term in the parentheses by 3, then add 3 to the second term in the parentheses. Then solve the equation using inverse operations.

Salma's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Salma $5.60 per pound, and type B coffee costs $4.40 per pound. This month's blend used three times as many pounds of type B coffee as type A, for a total cost of $451.20. How many pounds of type A coffee were used?

Answers

Answer: hi

11,28 pound / usd

Step-by-step explanation:

Other Questions
3. As a result of Bismarck's leadership, Prussia FIRST fought with Austria to gain land in __________.a. Franceb. Denmarkc. Africad. Russia Evaluating Linear Functions Do you think observation of anatomical similarities should be used alone to group organisms, or should DNA and/or amino acid comparisons also be taken into account? Which method do you think is more effective at establishing evolutionary relationships? Explain your answer A client reads the nutritional chart and follows it accurately. The nurse also notes that the client understands the need for a balanced diet and its relationship with a quick recovery. In which domain is the client demonstrating successful learning A couple's home has an assessed value of $40,000 and a market value of $100,000. What will the tax be if a rate of 5 mills is used Failing to see the big picture and acting only in regard to single firm in the supply chain can be referred to as: . What does overstep its bounds mean in Madison drafted the Bill of Rights to ensure the government didnt overstep its bounds?. What does overstep its bounds mean in Madison drafted the Bill of Rights to ensure the government didnt overstep its bounds? Which of these groups is not related to security and cannot have permissions assigned to it?a. Universal groupsb. Global groupsc. Domain local groupsd. Distribution groups The statements below refer to the design and operation of the power sub-system on a spacecraft. Select all those statements that are correct. What is the value of x? Show your work in arriving at your answer. A new car loan has a term of loan from 2 - 6 years and the interest rate is between 4% and 8%. what is the longest amount of time you could take to pay off the loan? what is the best interest rate you could get? Given right triangle JKM, which correctly describes the locations of the sides in relation to J? what is k if 1 1/3k=1/3 Zasha spent $6 on packages of gum. How many more packages of gum that cost $1.20 each can she buy if she has a $20 bill? What did John Locke say about natural rights ? Why is it important to have a flexibility assessment? Is there a difference in diversity between the two sites if you looked at only the number of species CANT DO IT i neeeed herlp For numbers 14a-14d, tell which expressions require you to rename mixed numbers before you can subtract. 14a. LaTeX: 5\frac{2}{5}-2\frac{1}{4}5 2 5 2 1 4 [ Select ] 14b. LaTeX: 5\:-\:2\frac{7}{8}5 2 7 8 [ Select ] 14c. LaTeX: 7\frac{2}{3}\:\:-\:6\frac{1}{8}7 2 3 6 1 8 [ Select ] 14d. LaTeX: 9\frac{1}{6}-5\frac{2}{3}9 1 6 5 2 3 [ Select ] Mason takes an achievement test. Researchers later looked at the even and odd questions and discovered that the correlation betweencorrectly answered questions on the odd and even questions was extremely high. This shows that the achievement test had which of thefollowing?O high predictive validityO high split-half reliabilityO high test-retest reliabilityhigh content validityO high criterion validity What is the slope of the line that passes through the points (-5, 8)(5,8) and (-5, 4)(5,4)?