The image quadrilateral is identical to the original quadrilateral but has been mirrored across the x- and y-axes.
The coordinates W(-2, 1), X(-1, 3), Y(3, 3), and Z(3, 3) can be plotted to form the quadrilateral's graph as follows:
code is as follows:
|
| Y(3,3)
|
|
------Z(3,-3)
------
|
|
|
| X(-1,3)
|
|
|
W(-2,-1)
We may use the following transformation on each vertex to determine the image of this quadrilateral following a 180-degree rotation of the origin:
(x, y) -> (-x, -y) (-x, -y)
As a result, the picture quadrilateral's new vertices are:
W' = (-(-2), -(-1)) = (2, 1) (2, 1)\sX' = (-(-1), -(3)) = (1, -3) (1, -3)\sY' = (-3, -3) = (-3, -3) (-3, -3)\sZ' = (-3, 3) = (3, -3) (3, -3) (3, -3)
To create a quadrilateral image, we can plot these points on the same coordinate plane:
code
|
| Y'(3,-3)
|
|
------
Z'(3,-3)
------
|
|
|
| X'(1,-3)
|
|
|
W'(2,1)
It should be noted that the image quadrilateral is identical to the original quadrilateral but has been mirrored across the x- and y-axes.
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Dilate H using C as the center and a scale factor of 3. H is 40 mm from C.
M angle 3 = 48 degrees
M angle 3 = 112 degrees
M angle 3 = 88 degrees
M angle 3 = 68 degrees
The last
M angle 3 = 68 degrees
Step-by-step explanation:
interior angles between parallel lines
sum =180
A tank is full of water. Find the work required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the density of water. Assume r = 6 m and h = 2 m.)
The work required to pump the water out of the spout is 70.9 * 10⁶ joules which is 71 M Joules approx.
Let the spherical tank be divided into a series of horizontal disks.
Let x be the height of each disk, g = gravity and p = density
Volume of each disk = πr2dx
Where r is the radius of each disk and dx is the thickness
By Pythagoras r² = 6² - x²= 36 -x²
Therefore Volume = π*(36-x²)*dx cubic metres
The distance each disk has to be lifted to escape the top of the spout = 2 + 6-x meters = (8-x)
Work needed to lift each disk to outlet = distance * mass where
mass = volume * density * gravity
= pi(36-x²)*p*g = 9800pi(36-x²)dx
dW = (8-x)* 9800pi(36-x²)dx
Since we have already accounted for the height of the spout, the work required is obtained by integrating the above expression from the bottom of the tank to the top. In other words, - 6 to + 6.
W = ⌠(8-x)*9800pi(36-x2)dx = 9800pi⌠[288 - 36x - 8x² +x³]dx
The odd terms evaluate to zero and we can rewrite the above as 2* I from 0 to 6.
W = 9800pi*2 [288x - 8x³/3] at x = 6 = 1152*19600π Joules = 22579200π joules = 70963200j
Total work required = 70.9 * 10⁶ joules
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In a small rectangular wallet photo, the width is 5 cm less than the length. If the border (perimeter) of the photo is 22 cm, find the length and width
As a result, the length is 8.5 cm and the breadth is 3.5 cm, and the total perimeter is 22 cm.
what is perimeter ?
An enclosed line that surrounds, distinguishes, or incorporates a two-dimensional contour or a three-dimensional length is referred to as a boundary. The edge of an ellipse or circle refers to its broadest area. The perimeter calculation has many useful properties. The rim of a form is its edge's radius. Understand how to determine the perimeter by adding the lengths of such sides of various forms. You can always measure the perimeter of a shape by multiplying its side lengths. The perimeter of an object is the space around it. At your house, any enclosed terrace is one illustration. The border of anything is the area encircling it. For a 50 feet x 50 feet yard, a 200 foot fence is required.
given
let the length of the rectangular wallet be x
the width be x - 5
perimeter = sum of all the sides = 22
x + x - 5 = 22
2x - 5 = 22
2x = 17
x = 8.5
length is 8.5 and width is 8.5 - 5 = 3.5
As a result, the length is 8.5 cm and the breadth is 3.5 cm, and the total perimeter is 22 cm.
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Determine which of the lines are skew
The lines are skew is Lines AD and BF.
Definition of Skew lineSkew lines are two lines that do not intersect, are not parallel, and are not coplanar. This means that the skew lines never cross and are not parallel to each other. For lines to be two-dimensional or coplanar, they can intersect or be parallel. This property does not apply to diagonal lines, which are always non-coplanar and exist in three or more dimensions.
Skew line exampleIn real life, cities have different types of roads, such as highways and overpasses. These streets are supposed to be on different levels. Lines drawn on such roads never intersect, creating skew lines instead of being parallel to each other.
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Solve The Following System Of Equations For Z And For Y: System Of Equations: y= 10+2zy=38-5z
For the system of equations, y = 10 + 2z and y = 38 - 5z the value of y and z are 18 and 4 respectively.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The first equation is : y = 10 + 2z
The second equation is : y = 38 - 5z
Subtract equation (1) and (2) -
y - y = 10 + 2z - (38 - 5z)
0 = 10 + 2z - 38 + 5z
Collect the like terms -
2z + 5z = -10 + 38
7z = 28
z = 28/7
z = 4
Substitute the value of z in equation (1) -
y = 10 + 2(4)
y = 10 + 8
y = 18
Therefore, the value of y = 18 and z = 4.
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Translate this sentence into an equation. The sun of 15 and Delia’s age is 65. Use the variable d to represent Delia’s age
The translation of the sentence 'The sum of 15 and Delia’s age is 65'
is 15 + d = 65.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let, The age of Delia be 'd'.
Therefore, The equation for the statement 'The sum of 15 and Delia’s age is 65' can be expressed as,'
15 + d = 65.
d = 65 - 15.
d = 50.
So, The age of Delia is 50 years.
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Which of the following problems would NOT have a solution? Group of answer choices 10 divided by 2. 10 divided by 5. 10 divided by 0. 0 divided by 10.
10 divided by 0 problem would NOT have a solution.
Given:
a. 10 divided by 2
b. 10 divided by 5
c. 10 divided by 0
d. 0 divided by 10
We know that ,
Integer divided by an integer is an integer
Therefore (a) and (b) will have a proper solution
We also know that ,
Zero divided by anything is Zero
Therefore (d) also have a unique answer that is zero
Now , We know that
Any numeric value divided by Zero tends to infinity .
Hence, 10 divided by 0 problem would NOT have a solution.
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Five years ago, a father was six times as old as his son. Two years hence, the age of the father will be 1 year more the three times then age of his son. Find their present ages.
Answer:
84
Step-by-step explanation:
Let's call the father's present age "F" and the son's present age "S".
Five years ago, the father's age was F - 5 and the son's age was S - 5.
According to the first statement, F - 5 = 6(S - 5), so F = 6S - 35.
Two years in the future, the father's age will be F + 2 and the son's age will be S + 2.
According to the second statement, F + 2 = 3(S + 2) + 1, so F = 3S + 7.
We can now substitute the first equation into the second:
3S + 7 = 6S - 28,
3S - 6S = -35 - 7 = -42,
-3S = -42,
S = 14.
Finally, the father's present age is F = 6S - 35 = 84.
Answer:
The dad is 35 and the son is 10
Step-by-step explanation:
Let f = the father's age
let s - the son's age
In the equations f-5 and s-5 represents the father and son's ages 5 years ago. f + 2 and s +2 represent the father and son's ages two years in the future.
Deandre rented some movies and video games last month. He did the same this month. The table below shows the number of movies and video games he
rented each month. It also shows the total cost (in dollars).
A) the picture…
B)How much did it cost(in dollars) to rent each movie and each video game?
Rental cost for each movie:?
Rental cost for each video game:?
Answer:
Step-by-step explanation:
We can find the rental cost for each movie and each video game by dividing the total cost by the number of movies and video games rented, respectively.
For the movies:
Rental cost for each movie = Total cost of movies rented / Number of movies rented
= $33 + $24 = $57
= $57 / 6 = $9.50 per movie
For the video games:
Rental cost for each video game = Total cost of video games rented / Number of video games rented
= $18 + $24 = $42
= $42 / 4 = $10.50 per video game.
7. For a dropped object, the function t(h)=√ h/16 can be used to find the distance, h, in feet,
that the object has fallen after a time, t, in seconds. How far has the object fallen after 1.6
seconds?
Answer: To find the distance fallen after 1.6 seconds, we simply plug this value into the function and solve for h:
h = t^2 * 16
h = 1.6^2 * 16
h = 2.56 * 16
h = 40.96 feet
So, the object has fallen 40.96 feet after 1.6 seconds.
Step-by-step explanation:
The circumference of a circular glazed donut with rainbow sprinkles is 9.42 inches. What is the diameter and radius of the circular donut?
The formula for the circumference of a circle is given by 2 * pi * r, where r is the radius. If the circumference is 9.42 inches, then we can write the equation:
9.42 = 2 * pi * r
Solving for r, we get:
r = 9.42 / (2 * pi)
The diameter of the circle is equal to 2 * r, so:
d = 2 * r = 2 * (9.42 / (2 * pi)) = 9.42 / pi
So, the radius of the circular donut is approximately 3 inches, and the diameter is approximately 9.42 inches.
The effect of the time of day a science class is taught on test scores is being
studied in an experiment. Which of these is most likely to be an extraneous
factor that could also affect test scores?
O A. Color of the school hallways
B. Principal of the school
OC. Difficulty of test questions
OD. Student clothing
In linear equation, The effect of the time of day a science class is taught on test scores being studied in an experiment will be the length of the class period.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
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suppose that a is an upper bound for the set S and that there is a sequence of elements xn that exists in S such that xn-->a. Prove that a is the least upper bound.
a must be the least upper bound of S because it satisfies both conditions: it is an upper bound of S, and any other upper bound b for S must be greater than or equal to a.
What is the difference between the least upper bound and upper bound?
An upper bound of a set S of real numbers is any real number that is greater or equal to all numbers in S. A lower bound is any which is less than or equal to all numbers in S. A least upper bound is an upper bound that is less than or equal to all upper bounds.
To prove that a is the least upper bound (LUB) of the set S, we need to show that a satisfies two conditions:
a is an upper bound of S, meaning that for every element x in S, x <= a.
If there is another upper bound b for S, then a <= b.
First, we already know that a is an upper bound of S because it is given that a is an upper bound of the set S.
Next, suppose there is another upper bound b for S such that b > a. Then, since the sequence xₙ converges to a, there exists a positive integer N such that for all n >= N, xₙ is arbitrarily close to a, meaning that |xₙ - a| < (b - a)/2. This means that xₙ < b for all n >= N, which contradicts the assumption that b is an upper bound of S, since xₙ is an element of S and xₙ < b.
Therefore, a must be the least upper bound of S because it satisfies both conditions: it is an upper bound of S, and any other upper bound b for S must be greater than or equal to a.
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Answer the questions below
The triangle is congruent by the Angle side Angle property.
What is congruency?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.
The Angle side Angle Congruence Theorem (ASA) defines two triangles to be congruent to each other if the included two angles and one side of one are congruent to the included angle and corresponding two sides of the other triangle.
The three parameters that are congruent are:-
BV ≅ BV ( common side)
∠1 ≅ ∠2 ( Bisector)
∠3 ≅ ∠4 ( Bisector)
Hence, the two triangles are congruent with each other.
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Write the inverse of f(x) = 3x - 1
f -1(x) =
log 3 x + 1
log 3 ( x - 1)
log 3 x - 1
Answer:
see below
Step-by-step explanation:
we need to write the inverse of ,
[tex]\longrightarrow f(x) = 3x -1 \\[/tex]
Substitute [tex] f(x)=y[/tex] ,
[tex]\longrightarrow y = 3x-1 \\[/tex]
Interchange x and y ,
[tex]\longrightarrow x = 3y -1 \\[/tex]
now solve for y ,
[tex]\longrightarrow 3y = x + 1 \\[/tex]
[tex]\longrightarrow y =\dfrac{x+1}{3} \\[/tex]
replace [tex] y[/tex] with [tex] f^{-1}(x)[/tex] as ,
[tex]\longrightarrow \underline{\underline{ f^{-1}(x) =\dfrac{x+1}{3}}}\\[/tex]
And we are done!
Answer:
[tex]f^{-1}(x)=\log_3(x)+1[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=3^{x-1}[/tex]
To find the inverse of the given function, swap y and x:
[tex]\implies x=3^{y-1}[/tex]
Take the log base 3 of each side of the equation:
[tex]\implies \log_3(x)=\log_{3}3^{y-1}[/tex]
[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies \log_3(x)=(y-1)\log_{3}3[/tex]
[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]
[tex]\implies \log_3(x)=(y-1)(1)[/tex]
[tex]\implies \log_3(x)=y-1[/tex]
Add 1 to both sides of the equation:
[tex]\implies \log_3(x)+1=y[/tex]
[tex]\implies y=\log_3(x)+1[/tex]
Replace y for f⁻¹(x):
[tex]\implies f^{-1}(x)=\log_3(x)+1[/tex]
How can you help me with that please also my homework math please
1. Given the image of the circle, identify the length of the radius, diameter, and circumference. Also, find the area. Make sure to show work (area and circumference) to receive credit. Choose a number for the diameter.
Answer:
Radius = 5 units
Diameter = 10 units
Circumference = 10π units
Area = 25π square units.
Step-by-step explanation:
i choose diameter.
Let's say the diameter of the circle is 10 units.
The radius of the circle can be found by dividing the diameter by 2:
Radius = Diameter / 2 = 10 / 2 = 5 units
The circumference of the circle can be found using the formula:
Circumference = 2πr = 2π * 5 = 10π units
The area of the circle can be found using the formula:
Area = πr^2 = π * 5^2 = 25π square units.
So, for a circle with a diameter of 10 units:
Radius = 5 units
Diameter = 10 units
Circumference = 10π units
Area = 25π square units.
For each equation draw a tape diagram and find unknown value
The solutions are:
a. x = 7
b. x = 7
The tape diagrams are given in the image below.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Two equations,
a. x + 9 = 16
b. 4x = 28
Solving the first equation,
x + 9 = 16
x = 7
Solving the second equation,
4x = 28
x = 7
The tape diagrams are given in the image below.
Hence, all the unknown values are given above.
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The digit in the units place of a 2 digit number is 4 times the digit in the tens place. The number obtained by reversing the digits exceeds the given number by 54. Find the given number.
A. 28B. 32C. 15D. 25
The number in question is 28.
To make solving this problem easier, we need to consider the number.
Let the number is ab.
So that,
4 × a = b
4a = b
We spread the numbers on the options.
28
(4 × 2 = 8) → True
32
(4 × 3 = 2) → False
15
(4 × 1 = 5) → False
25
(4 × 2 = 5) → False
We prove what number of 28 is when the digits is reversed to be greater than 54.
28 ⇄ 82
It is proved that the number 82 is greater than the number 54.
So, the number in question is 28.
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A company makes computer chips from square wafers of silicon. It wants to keep the side length of a wafer very close to 15 mm and it wants to know how the area A(x) of a wafer changes when the side length x changes. Find A` (15) and explain its meaning in this situation.
A'(15) = 2 * 15 = 30.The meaning of A'(15) in this situation is that if the side length of the wafer changes by 1 mm, the area will change by 30 mm^2 when the side length is 15 mm.
The area A(x) of a square wafer is given by A(x) = x², where x is the side length of the wafer. The derivative of A(x) with respect to x, denoted A'(x), represents the rate of change of the area with respect to the side length. To find A'(15), we need to find the derivative of A(x) at x = 15.
A'(x) = 2x
Therefore, A'(15) = 2 * 15 = 30.
The meaning of A'(15) in this situation is that if the side length of the wafer changes by 1 mm, the area will change by 30 mm² when the side length is 15 mm. This means that for every 1 mm increase in the side length, the area of the wafer will increase by 30 mm², and for every 1 mm decrease in the side length, the area of the wafer will decrease by 30 mm².
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the domain of the function given below is the set of all real numbers greater than 1/2.
F(x) =(1/2)^x
A. True
B. false
Answer:
B. False
Step-by-step explanation:
The domain is the set of values of x.
There is no restriction on the value of x.
x can be any real number.
Answer: B. False
Cooking time 35 minutes to be ready for lunch at 13:00, calculate what time the item should be put in the oven.
Answer:
he item should be put in the oven at 12:25 (in 24-hour format) to be ready for lunch at 13:00.
Step-by-step explanation:
To calculate what time the item should be put in the oven, you need to work backwards from the desired serving time of 13:00 and subtract the cooking time of 35 minutes. Here's how you can do it:
Convert the serving time to 24-hour format: 13:00 is the same as 1:00 PM in 12-hour format. In 24-hour format, it is 13:00.
Subtract the cooking time: Subtract 35 minutes from the serving time of 13:00 to get the time when the item should be put in the oven.
13:00 - 00:35 = 12:25
So, the item should be put in the oven at 12:25 (in 24-hour format) to be ready for lunch at 13:00.
On Friday, Thomas the clown sells 16 balloons at the circus. Due to demand, Thomas charges three dollars more per balloon on Saturday. On Saturday, he sells 40 balloons. Let f represent the price of a balloon on Friday and let t represent the total amount he earns on both days combined.
a Write an equation to describe the relationship between the price of a balloon on Friday and the total amount earned.
b Determine the price of a balloon on Saturday if Thomas earns 400 dollars on Friday and Saturday.
The relationship between the price of balloons and the amount earned is 56f + 120 dollars
The price of the balloons if 400 dollars is earned on friday and saturday is 5 dollars on friday and 8 dollars on saturday
How to solve for the pricea) If f is the price of a balloon on Friday, then the price of a balloon on Saturday would be f + 3 dollars. The total amount Thomas earns on Friday would be 16 balloons * f dollars/balloon = 16f dollars. The total amount Thomas earns on Saturday would be 40 balloons * (f + 3 dollars/balloon) = 40f + 120 dollars. Hence, the total amount earned on Friday and Saturday would be 16f + 40f + 120 dollars = 56f + 120 dollars.
Therefore, the equation to describe the relationship between the price of a balloon on Friday and the total amount earned is: t = 56f + 120 dollars.
b) We are given that Thomas earns 400 dollars on Friday and Saturday, so we can set t = 400 dollars in the equation derived above:
400 = 56f + 120
Solving for f, we have:
280 = 56f
f = 5 dollars
The price of a balloon on Friday is $5, and the price of a balloon on Saturday would be f + 3 = 5 + 3 = $8.
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why did brainly get me so up someone help
Answer:
we on top
Step-by-step explanation:
Answer:
Step-by-step explanation:
you gotta be kidding me right now b r u h. Aint no way bro is posting this hahahha get it i guess
how many 3/5 are in two as a tape diagram
The number of the 3 / 5 in a tape diagram is 3.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator. Any number of equal parts is represented by a fraction, which also represents a portion of a whole.
A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated.
Given that the fraction is 3 / 5. When we add the fraction three times we will get the value that is closest to 2.
E = 3 / 5 + 3 / 5 + 3 / 5
E = ( 3 + 3 + 3 ) / 5
E = 9 / 5
E = 1.8 ≅ 2
Hence, in a tape diagram, the 3/5 is represented by the number 3.
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Consider a set of data in which the sample mean is 83.3 and the sample standard deviation is 6.3. Calculate the z-score given that x = 79.8. Round your answer to two decimal places.
For a set of data in which the sample mean is 83.3 and the sample standard deviation is 6.3 the z-score given that x = 79.8 would be -0.555
We know that the formula for calculating a z-score is :
z = (x - μ) / σ
where z is the standard z - score
x is the observed value
μ is the mean of the sample
σis the standard deviation of the sample
here, set of data in which the sample mean is 83.3 and the sample standard deviation is 6.3
i.e., μ = 83.3, σ = 6.3
We calculate the z-score for x = 79.8
Using above formula,
z = (x - μ) / σ
z = (79.8 - 83.3) / (6.3)
z = (-3.5) / (6.3)
z = -0.555
Therefore, the z-score is: -0.555
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From 15 men and 11 women how many committees of 10 persons can be chosen is each committee is to have exactly 8 men
There are 353925 committees of 10 persons that can be chosen with exactly 8 men.
How to determine the number of waysFrom the question, we have the following parameters that can be used in our computation:
People = 15 men and 11 women
Committee = 10 persons (8 men)
The number of ways is then calculated as
Ways = Men * Women
So, we have
Ways = C(15, 8) * C(11, 2)
Evaluate the products
Ways = 353925
Hence, the number of committee is 353925
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the data set shows the january 1 noon temperatures in degrees Fahrenheit for a particular day in each of the past six years. 28 34 27 42 52 15 the five number summary of the data set is15 27 28 34 42 52 the mean of the data set is 33 what is the sum of the squares of the differences between each data value and the mean? use the table to organize your work
The sum of the squares of the differences between each data value and the mean is given as follows:
828.
How to obtain the sum of the squares?The mean of the data-set in this problem is given as follows:
33.
The data-set is given as follows:
28, 34, 27, 42, 52 and 15.
Hence the sum of the squares of the differences between each data value and the mean is obtained as follows:
(28 - 33)² + (34 - 33)² + (27 - 33)² + (42 - 33)² + (52 - 33)² + (15 - 33)² = 828.
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Practice
Solve for x.
1.x³ = 64
2.x² = 49
3.x³ =25
4.x²=125
The solutions for all the equations are:
1) x = 4
2) x = ±7
3) x = 5²´³
4) x = ±5³´²
How to solve the equations for x?The first equation is:
x³ = 64
If we apply the cubic root in both sides we will get:
∛x³ = ∛64
x = ∛64 = 4
2) now we have:
x² = 49
If we apply the square root:
√x² = ± √49
(remember the plus minus sign when you use a even degree root)
x = ±7
In this case we have two solutions.
3) x³ =25
Like in the first case:
x = ∛25 = ∛5² = 5²´³
Now we can't simplify this, so we leave it in this way.
4) x² = 125
Remember that 125 = 5³, then:
x² = 5³
x = ±√5³ = ±5³´²
These are all the solutions.
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