For a project in her Geometry class, Madeline uses a mirror on the ground to measure the height of her school building. She walks a distance of 9.45 meters from the building, then places a mirror flat on the ground, marked with an X at the center. She then walks 2.75 more meters past the mirror, so that when she turns around and looks down at the mirror, she can see the top of the school clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.55 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.

Answers

Answer 1

Madeline's school building model is 5.33 meter.

What are similar triangles?

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, Madeline walks a distance of 9.45 meters from the building, then places a mirror flat on the ground, marked with an X at the center.

Use corresponding parts of similar triangles.

Madeline's eyes height/Madeline's distance from x = Buildings height/Buildings distance from X

1.55/2.75 = x/9.45

2.75x=1.55×9.45

2.75x=14.6475

x=14.6475/2.75

x=5.33

Therefore, Madeline's school building model is 5.33 meter.

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Related Questions

If a dose of 100 milligrams is contained in 4 milliliters, how many milliliters are in 40 milligrams?

Answers

10 - if there is 4 in 100, that means there is 25 for every milliliter.

20 Points


A slice is made perpendicular to the base of a right rectangular prism, as shown.


What is the area of the resulting two-dimensional cross-section?


Drag and drop the answer into the box.

Answers

The area of the resulting two-dimensional cross-section is 480 inch².

What is Area?

The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.

Given:

The Resulting Cross section will Have the Size

= 20 inch by 14 inch

So, Area of two dimensional Cross section

=  20 x 14

= 240 inch²

As prism is Sliced so this cross section will on the face of two prism.

Then, the Total cross section area

= 2 x 240

= 480 inch²

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Factor each expression
1. x² + 3x + 2
2. x² +10x+16
3. X²-10x+24

Answers

The expressions are factorized to;

1.(x + 1)(x + 2)

2.(x + 2) (x + 8)

3. (x -4) (x -6)

How to factorize the expression

Using the factorization method of solving quadratic equations, we have;

1.  x² + 3x + 2

Find the pair factors of 2 that adds up to 3 and  substitute the values, we get

x² + 2x + x + 2

Factorize in pairs

x(x + 2) + 1( x+ 2)

(x + 1)(x + 2)

2. x² +10x+16

Find the pair factors

x² + 8x + 2x + 16

Factorize in pairs

x(x + 8) + 2( x+ 8)

(x + 2) (x + 8)

3. X²-10x+24

Find the pair factors

x² - 6x - 4x + 24

Factor in pairs

x(x -6) - 4(x -6)

(x -4) (x -6)

Hence, use the factorization  method in the expressions

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Question 2(Multiple Choice Worth 2 points)
(02.05 MC)
The following tabl summarizes the percent of U.S. who have diabetes and the accuracy of the current medical tests used to detect the disease.
Test positive Test negative Total
Have diabetes
35%
10%
45%
Do not have diabetes 5%
50%
55%
What is the ratio of false positives to true positives?
O
O
10
7
10
O
117

Answers

Ratio of false positives to true positives is 1/7 .

What is False positive?

In statistics, when performing multiple comparisons, the false positive rate is the probability of incorrectly rejecting the null hypothesis for a particular test.

Given In the table,

Number of patient test positive, but not have diabetes = 5%

Number of false positives = 5%

Number of patient test positive, and have diabetes = 35%

Number of true positive = 35%

Ratio of false positives to true positives

= 5%/35%

= 1/7

Hence, 1/7 is the ratio of false positives to true positives.

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What is the slope of this line?
-8
5
8
6
4
0
15

-8

6
8

Answers

Based on the graph, the slope of this line is equal to 2.

How to calculate the slope of a line?

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided in the graph, we can logically deduce the following data points on the line:

Points on x-axis = (-2, 5).Points on y-axis = (-8, 6).

Substituting the given data points into the slope formula, we have the following;

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (6 + 8)/(5 + 2)

Slope, m = 14/7.

Slope, m = 2.

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Let A be a 3x4 matrix with reduced row echelon form given by
U= 1021
0112
0000
a1= 2
3
1
a2 = -2
3
-3

Answers

In a 3×4 matrix with reduced row echelon form given by U=[1,0,5,1;0,1,1,1;0,0,0,0], where a1=[−1,3,−2], and a2=[2,-3,-1]  is given and the value of a3 = [-5, -1, 1, 0], a4 = [-1, -1, 0, 1] .

Since the reduced row echelon form of A has only two pivot columns, the matrix A can have at most two linearly independent columns. We already know that a1 and a2 are linearly independent (neither is a scalar multiple of the other), so we can use them as a basis for the column space of A.

To find a3 and a4, we need to find two vectors that are linearly independent of a1 and a2 and that span the null space of A (i.e., are solutions to the homogeneous equation Ax=0).

To find a basis for the null space of A, we can set the non-pivot columns of A equal to free variables, and then solve for the corresponding pivot variables in terms of the free variables. In this case, the non-pivot columns are columns 3 and 4, so we set x3=t and x4=s for some scalars t and s, and solve for x1 and x2:

x1 = -5t - s

x2 = -t - s

Thus, the general solution to Ax=0 can be written as a linear combination of the vectors [-5, -1, 1, 0] and [-1, -1, 0, 1]. We can check that these two vectors are linearly independent, so they form a basis for the null space of A. We can use them as a3 and a4:

a3 = [-5, -1, 1, 0]

a4 = [-1, -1, 0, 1]

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____The given question is incorrect, the correct question is given below:

Let A be a 3×4 matrix with reduced row echelon form given by U=[1,0,5,1;0,1,1,1;0,0,0,0]. If a1=[−1,3,−2], and a2=[2,-3,-1] Find a3 and a4


LPQR is a right angle. Find m/PQS and mZSQR. Enter deg after any value that
is in degrees.

Answers

The required measures of the angles ∠PQS and ∠SQR are given as 51 and 49.

What is complementary angles?

Complementary angles are two angles whose measures add up to 90 degrees. In other words, if angle A and angle B are complementary, then A + B = 90 degrees.

Here,
∠PQR is a right angle,
So ∠PQS and ∠SQR are supplementary angles, from the figure.

∠PQR = ∠PQS + ∠SQR
90 = 8x + 131 + 10x + 139
90 = 18x + 270
18x = -180
x = -10

Now,
∠PQS = 8x + 131 = -80 + 131 = 51°
Similarly,
∠SQR = 49°

Thus, the required measure of the angles ∠PQS and ∠SQR are given as 51 and 49.

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write y=d^2-8d-10 in vertex form

Answers

The vertex form of the equation is,

⇒ y = (d - 4)² - 26

What is Quadratic equation?

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The equation is,

⇒ y = d² - 8d - 10

Now, We can change in vertex form as;

⇒ y = d² - 8d - 10

⇒ y = d² - 8d + 16 - 16 - 10

⇒ y = (d - 4)² - 16 - 10

⇒ y = (d - 4)² - 26

Thus, The vertex form of the equation is,

⇒ y = (d - 4)² - 26

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Jake ran 145 meters before lunch and 389 meters after lunch.

How many kilometers did Jake run in all?

Responses

0.00534 km


0.0534 km


0.534 km


5.34 km

Answers

Answer:

.534

Step-by-step explanation:

add, then convert meters to kilometers

What is the approximate area of the geometric figure?
Responses
A 10 square units10 square units
B 8 square units8 square units
C 5 square units5 square units
D 2 square units2 square units
E 3 square units

Answers

Area of figure in the graph is 5 square unit.

Correct option is C.

What is area?

Area is defined as the total space taken up by a flat surface or shape of an object. The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m².

Given, By the graph

Figure consists of one triangle and one rectangule

height of the triangle = 2 unit

length of base of triangle = 3 unit

Area of triangle

= (1/2) × height × base

= (1/2) × 2 × 3

= 3 unit²

Length of rectangle = 2 unit

Width of rectangle = 1 unit

Area of the rectangle

= length × width

= 2 × 1

= 2 unit²

Total area of the figure

= area of triangle + area of rectangle

= 3 + 2

= 5 unit²

Hence, 5 square unit is area of the figure in the graph.

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Solve the system of equations by the addition method. If a system contains decimals, you may want to first clear the equation of decimals.0.9x +0.7y = 16 -0.3x-3.5y = - 71.6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution is (Type an ordered pair. Type an integer or a decimal rounded to one decimal place as needed.)O B. There are infinitely many solutions: {(x,y)|0.9x+0.7y=16) or {(x,y)] -0.3x - 3.5y = -71.6) O C. There is no solution, or Ø

Answers

The solution of the system of equations by adding method is equal to :

option A. Solution is ordered pair (x ,y) = ( 2.00 , 20.3 ) representing decimal rounded to one decimal place.

System of equations are :

0.9x +0.7y  = 16  ___(1)

-0.3x - 3.5y = - 71.6 ___(2)

To get the solution of the system of equations are:

Multiply (2) by 3 and add it to (1)

0.9x  +0.7y  = 16

-0.9x - 10.5y = -214.8

0x - 9.8y = - 198.8

⇒ y = 20.3

⇒ x = 1.9966

⇒ x = 2.00

Therefore, the value of (x, y ) in the system of equations is given by :

option A. Type of solution is written as ordered pair (x ,y) = ( 2.00 , 20.3 ) having decimal rounded to one decimal place.

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Mariene and her parents are baking a large batch of cookies for a fundraiser. There are 150 cookies and 62% of cookie and 62% of the cookies are chocolate chips.How many chocolate chip cookies did they make?

Answers

93 chocolate chip cookies

100 days make how many months? ​

Answers

Answer:

There are 3.28542 months in 100 days.

Step-by-step explanation:

For every 100 days, there are approximately 3.28542 months. To solve for any given number of days, divide the time value by 30.417.

For example, to solve for 200 days:

200 ÷ 30.417 = 6.57534 month

Therefore, 100 days make approximately 3.28542 months.

Answer:

3.28542

Step-by-step explanation:

100 days make how many months? ​

Value in months = value in days × 0.0328542

Value in months = 100 × 0.0328542 = 3.28542 (months)

Find the area A of polygon MNOPQ with the given vertices.
M(0,0), N(2,3), O(2,0), P(1, − 1), Q(−1,−1)
A=
square units

Answers

The area of the given polygon will be 10 square units.

What is surface area?

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

here, we have,

In other meaning, if we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.

Given the polygon with vertices

N(-2,1), P(3, 1),\ Q(3,-1), R(-2,-1)

If we draw the points in coordinate then it will become a rectangle with side lengths 5 and 2.

Area of rectangle = length × width

Area of rectangle = 5 × 2 = 10 square units.

Hence "The area of the given polygon will be 10 square units".

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You are shopping and find the same shirt at two different
stores. Store "A" is selling the shirt for $25 and Store
"B" is selling the shirt for 10% off the original price of
$28. Which is the better buy?
a. The shirt at Store "A".
b. The shirt at Store "B".

Answers

Answer:

A. The shirt at Store "A".

Step-by-step explanation:

How to find 10% of 28.

First, we need to convert 10% into a decimal.

To do that, we just divide the number by 100.

[tex]\frac{10}{100}[/tex] [tex]= 0.1[/tex]

Now, we take the original number (28) and multiply it by the decimal

[tex]28 x 0.1 = 2.8[/tex]

Finally, we subtract.

[tex]28.00 - 2.80 = 25.20[/tex]

[tex]25.20[/tex] > [tex]25.00[/tex]

Therefore, Store "A" Has the cheapest shirt

#14.
The table below shows the value in dollars of a car at
the end of x years.

Answers

The function which represents the value of the car is [tex]y = 11000(0.85)^x[/tex].

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

From the table, we can conclude the function of the car as:-

[tex]y = 11000(0.85)^x[/tex]

At x = 0, the value of y is,

[tex]y = 11000(0.85)^0[/tex].

y = 11000

At x = 1 the value of y is,

[tex]y = 11000(0.85)^1[/tex]

y = 11000 x 0.85

y = 9350

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Help if you know how to do it

Answers

First we multiply 9 and 15, which is 135cm. 100cm = 1m so the plant will grow 1.35m, so the plant is now 9.35m

A recent survey found that 80% of IRSC students plan to go on a vacation after graduation. Suppose 5 IRSC
students are randomly selected and let z be the number of students that plan to go on a vacation after
graduation, out of the sample of 5. Use the binomial probability formula or the binomial probability table
to construct the probability distribution of x. Ao, use the binomial probability formula or the binomial
probability table to construct the cumulative probability distribution of .

Answers

The binomial distribution is solved as

a) The probability that no more than 2 students out of the random 5  plan to go out on vacation is P ( X ≤ 2 ) = 0.0579

b) The probability that more than 2 students out of the random 5  plan to go out on vacation is P ( X > 2 ) = 0.9421

What is a Binomial Distribution?

The binomial distribution is a type of probability distribution that predicts the likelihood of obtaining one of two outcomes given a set of inputs. It summarizes the number of tries where each trial has the equal chance of producing the same result.

The formula for Binomial Distribution is given by

P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ

where

n = number of trials

x = number of successes

p = probability of getting a success in one trial

q = probability of getting a failure in one trial

q = 1 - p

Given data ,

Let the probability be represented as P

Now , the total number of trials = 5

The number of students going for vacation be represented as n

Now , the probability of success p = 0.8

So , the value of q = 0.2

a)

The probability that no more than 2 students out of the random 5  plan to go out on vacation is P ( X ≤ 2 ) = P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ

Substituting the values , we get

The probability that no more than 2 students out of the random 5  plan to go out on vacation is P ( X ≤ 2 ) = 0.0579

The probability that no more than 2 students out of the random 5  plan to go out on vacation is P ( X ≤ 2 ) = 5.79 %

b)

The probability that more than 2 students out of the random 5  plan to go out on vacation is P ( X > 2 ) = P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ

Substituting the values , we get

The probability that more than 2 students out of the random 5  plan to go out on vacation is P ( X > 2 ) = 0.9421

The probability that more than 2 students out of the random 5  plan to go out on vacation is P ( X > 2 ) = 94.21 %

Hence , the binomial distribution is solved

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Find all possible fourth corners if the following three points are corners of a parallelogram:(1,2,3),(3,4,7),(2,1,2)

Answers

All possible fourth corners if  the following three points are corners of a parallelogram:(1,2,3),(3,4,7),(2,1,2) is (2, 3, 5) and  (3, 5/2, 9/2)

Let the corners be A(1,2,3);B(3,4,7);C(2,1,2)

Let the fourth vertex D =(x,y,z)

We know that the diagonals of a parallelogram bisect each other. So, the midpoint of AC is same as the midpoint of BD.

Mid point of two points (x 1,y 1,z1) and (x 2,y 2,z2)​  is calculated by the formula ( x 1+x 2/2 , y 1+y 2/2, z1+z2/2 ).

So, midpoint of AC= Mid point of BD

⇒( 1+3/2, 2+4/2, 3+7/2) =(2, 3, 5)

Hence, D=(2, 3, 5).

Same if,

Mid point of two points (x 1,y 1,z1) and (x 2,y 2,z2)​  is calculated by the formula ( x 1+x 2/2 , y 1+y 2/2, z1+z2/2 ).

So, midpoint of AC= Mid point of BD

⇒( 3+2/2, 4+1/2, 7+2/2) = (3, 5/2, 9/2)

Hence, D=  (3, 5/2, 9/2)

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15 puzzle is a sliding puzzle game with numbered squares arranged in 4x4 grid with one tile missing. the puzzle is solved when the numbers are arranged in order. the actions are defined in terms of direction where empty square can be moved to up (u), down(d), left(l), right(r)

Answers

Despite its age, the 15 puzzle remains a popular game today, and it has been adapted into many different variations, including digital versions and physical puzzles with different grid sizes and configurations.

15 puzzle is a sliding puzzle game with numbered squares arranged in 4x4 grid with one tile missing. the puzzle is solved when the numbers are arranged in order. the actions are defined in terms of direction where empty square can be moved to up (u), down(d), left(l), right(r)

The 15 puzzle is a classic sliding puzzle game that has been popular for over a century. The game was invented in the late 1800s by Noyes Chapman, and it quickly became a favorite pastime of people all over the world. The puzzle is sometimes called the "Gem Puzzle" or the "Boss Puzzle," and it has also been used as a tool for studying permutation groups and artificial intelligence algorithms.

Solving the 15 puzzle requires a combination of strategy, planning, and spatial reasoning. While the game is relatively simple to learn, it can be quite challenging to master, especially if you're trying to solve it in the minimum number of moves. In fact, there are over 1 trillion possible configurations of the 15 puzzle, and only a fraction of those can actually be solved.

Despite its age, the 15 puzzle is still widely played today. It has been transformed into a variety of games, including digital and physical puzzles with various grid sizes and arrangements.

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Which statements are true about the ordered pair (−4, 0) and the system of equations? {2x+y=−8x−y=−4 Select each correct answer. Responses The ordered pair (−4, 0) is a solution to the first equation because it makes the first equation true. The ordered pair , begin ordered pair negative 4 comma 0 end ordered pair, is a solution to the first equation because it makes the first equation true. The ordered pair (−4, 0) is a solution to the second equation because it makes the second equation true. The ordered pair , begin ordered pair negative 4 comma 0 end ordered pair, is a solution to the second equation because it makes the second equation true. The ordered pair (−4, 0) is not a solution to the system because it makes at least one of the equations false. The ordered pair , begin ordered pair negative 4 comma 0 end ordered pair, is not a solution to the system because it makes at least one of the equations false. The ordered pair (−4, 0) is a solution to the system because it makes both equations true. The ordered pair , begin ordered pair negative 4 comma 0 end ordered pair, is a solution to the system because it makes both equations true.

Answers

The correct statement about the ordered pair (-4,0) and the system of equations is given as follows:

The ordered pair (-4,0) is a solution to the system because it makes both equations true.

How to interpret the ordered pair and the system of equations?

The system of equations for this problem is defined as follows:

2x + y = -8.x - y = -4.

The ordered pair (-4,0) means that when x = -4, y = 0.

Hence we verify if the first equation is satisfied, as follows:

2(-4) + 0 = -8

-8 = -8 -> Satisfied.

For the second equation, we have that:

-4 - 0 = -4

-4 = -4 -> Satisfied.

As both equations are satisfied, the ordered pair is a solution for the system of equations.

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1, 2, 3, 4, 5? (b) If one of the children is randomly chosen, what is the probability that child comes from a family having i children, i = 1, 2, 3, 4, 5?

Answers

The probability of having i children, i = 1,2,3,4,5 is 0.2, 0.4, 0.25, 0.1, 0.05 respectively. The probability that a randomly chosen child comes from a family with i children are 0.0741, 0,2963, 0.2773, 0.1481, 0.0926.

The probability that a randomly chosen family has i children is given by the ratio of the number of families with i children to the total number of families. Therefore:

P(1 child) = 4/20 = 0.2

P(2 children) = 8/20 = 0.4

P(3 children) = 5/20 = 0.25

P(4 children) = 2/20 = 0.1

P(5 children) = 1/20 = 0.05

(b) To calculate the probability that a randomly chosen child comes from a family with i children, we need to take into account the different numbers of children in each family. There are a total of 4+8x2+5x3+2x4+1x5=54 children in the community organization. Therefore, the probabilities are:

P(child from 1-child family) = 4/54 ≈ 0.0741

P(child from 2-child family) = 2x8/54 ≈ 0.2963

P(child from 3-child family) = 3x5/54 ≈ 0.2778

P(child from 4-child family) = 4x2/54 ≈ 0.1481

P(child from 5-child family) = 5/54 ≈ 0.0926

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____The given question is incomplete, the complete question is given below:

A small community organization consists of 20 families, of which 4 have one child, 8 have two children, 5 have three children,2 have four children, and 1 has five children.

(a) If one of these families is chosen at random, what is the probability it has i children, i = 1,2,3,4,5?

(b) If one of the children is randomly chosen, what is the probability this child comes from a family having i children, i =1,2,3,4,5?

i need help please!!!

Answers

Yes, the given figure is a parallelogram.

What is a parallelogram?

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Given is a parallelogram as shown in the image.

We have -

S(0, 0), T(3, 0), U(4, 3), V(1, 3)

For the figure to be parallelogram, we will have to prove -

ST = VU   &   SV = TU

We can calculate -

ST = 3

VU = 3

SV = 3.1

TU = 3.1

So -

ST = VU   &   SV = TU

Hence, it is a parallelogram.

Therefore, yes, the given figure is a parallelogram.  

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What is the area, in square units, of triangle DEF?
Triangle DEF, with vertices D(3,-9), E(9,-5), and F(6,-2), is drawn on the coordinate grid below.

Answers

Answer:

Below

Step-by-step explanation:

You COULD calculate the lengths of the three sides and then use Heron's Formula to calculate the area.....

 Here is perhaps an easier way (see image)

  calculate the entire area of the rectangle then subtract the 3 smaller RIGHT triangles from the total

Area of rectangle =   6 x 7 = 42 units^2

  triangles    1/2 ( 3 x 7    +    3 x 3    +    4 x 6 ) = 27 units^2

42 - 27 = 15 units^2   = area of given triangle

Answer:

15 square units

Step-by-step explanation:

i am using Heron's formula for this question

Firstly, lets calculate the lengths of the triangle. We can do this by using the formula:

[tex]length=\sqrt{(y_{2}\\-y_{1}\\)^{2}+(x_{2}\\-x_{1}\\)^{2} }[/tex]

Calculating the length between D (3,-9) and E (9,-5):

[tex]length(A)=\sqrt{(-9-(-5))^{2}+(3-9)^{2} } \\length(A)=2\sqrt{13}[/tex]

Calculating the length between F (6,-2) and E (9,-5):

[tex]length(B)=\sqrt{(-2-(-5))^{2}+(6-9)^{2} }\\length(B)=3\sqrt{2}[/tex]

Calculating the length between D (3,-9) and F (6,-2):

[tex]length(C)=\sqrt{(-9-(-2))^{2}+(3-6)^{2} }\\length(C)=\sqrt{58}[/tex]

Now, we can find the semi-perimeter with the formula:

[tex]s=\frac{A+B+C}{2}[/tex]

where A, B and C are the lengths

The semi-perimeter is:

[tex]s=\frac{2\sqrt{13}+3\sqrt{2}+\sqrt{58} }{2}\\s=9.534758... (store \, the \, full \, value \, in \, your \, calculator)[/tex]

The formula for the area of the triangle:

[tex]A=\sqrt{s(s-A)(s-B)(s-C)}\\A=\sqrt{9.534758...(9.534758...-2\sqrt{3})(9.534758...-3\sqrt{2})(9.534758...-\sqrt{58} ) }\\A=15[/tex]

Here is a graph of F and G.

Answers

Answer: please look at the image for the answer

Step-by-step explanation:

Evaluate: (f+g)(-1)
f(x) = 5x^2 +7 (This reads 5x to the 2nd power plus 7)
g(x) = 3x - 6
Hint: (f+g)(x) = f(x) + g(x)
7
-7
-3
3

Answers

The function (f+g)(-1) is equal to 3.

How to find the value of the function?

We can evaluate (f+g)(-1) by first finding f(-1) and g(-1), and then adding them together.

To find f(-1), we substitute -1 for x in the expression for f(x):

f(-1) = 5(-1)^2 + 7 = 5 + 7 = 12

To find g(-1), we substitute -1 for x in the expression for g(x):

g(-1) = 3(-1) - 6 = -3 - 6 = -9

Now we can add f(-1) and g(-1) together:

(f+g)(-1) = f(-1) + g(-1) = 12 + (-9) = 3

Therefore, (f+g)(-1) is equal to 3.

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PRACTICE IT Use the worked example above to help you solve this problem. parallel-plate capacitor has an area A = 2.50 X 10 m2 and plate separation d 1.40 * 10- m. (a) Find its capacitance_ 1.58e-12 (b) How much charge is on the positive plate if the capacitor Is connected to 3.00 battery? 12000 Your response differs significantly from the correct answer: Rework vour solution from the beginning and check each step carefully: € (c) Calculate the charge density on the positive plate, assuming the density is uniform: Clm (d) Calculate the magnitude of the electric field between the plates. 3.92 Your response differs significantly from the correct answer: Rework vour solution from the beginning and check each step carefully: Vlm

Answers

The capacitance is [tex]1.58*10^{-12} F[/tex], the charge is 12000 e, the charge density is [tex]4.80*10^{7} C/m^{2}[/tex], and the electric field is [tex]3.92*10^{6} N/C[/tex].

Here's how you can solve the above problems:

(a) To find the capacitance of a parallel-plate capacitor, we use the formula:

C = ε0A/d

where ε0 is the vacuum permittivity constant [tex](8.85*10^{-12}F/m )[/tex], A is the area of the plates, and d is the distance between the plates. Substituting the given values, we get:

C =[tex](8.85 * 10^{-12} F/m) (2.50* 10^{-4}m^{2} )/(1.40*10^{-7}m )[/tex]

= [tex]1.58*10^{-12} F[/tex]

(b) To find the amount of charge on the positive plate of the capacitor, we use the formula:

Q = CV

where Q is the charge, C is the capacitance, and V is the voltage across the capacitor. Substituting the values from (a) and the given voltage, we get:

Q = [tex](1.58*10^{-12}F )(3.00 V)[/tex]

= [tex]4.74*10^{-11} C[/tex]

= 12000 e

(c) To find the charge density on the positive plate, assuming the density is uniform, we divide the charge on the plate by the area of the plate:

ρ = Q/A = [tex](12000e)/(2.50*10^{-4}m^{2} )[/tex]

= [tex]4.80*10^{7} C/m^{2}[/tex]

(d) To find the magnitude of the electric field between the plates, we use the formula:

E = V/d

where E is the electric field, V is the voltage across the capacitor, and d is the distance between the plates. Substituting the given values, we get:

E = [tex](3.00 V)/(1.40*10^{-7}m )[/tex]

= [tex]2.14*10^{-7} V/m[/tex]

= [tex]3.92*10^{6} N/C[/tex]

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6.3 A truck is carrying mango juice, tomato juice, and passion fruit juice bottles in a ratio of
4: 4:3. If there are 1020 passion fruit juice bottles, then how many juice bottles in total
are there?

Answers

The total number of juice bottles is given by the equation J = 3400 bottles

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

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

Given data ,

Let the proportion be represented as a : b : c

Now , the ratio of mango juices to tomato juice to passion fruit be 4 : 4 : 3

The total number of mango juice = 4x

The total number of tomato juice = 4x

The total number of passion fruit juice = 3x

The total number of passion fruit juice = 1020

Substituting the values in the equation , we get

3x = 1020

Divide by 3 on both sides of the equation , we get

x = 340 bottles

Now , the total number of bottles = 4x + 3x + 3x = 10x bottles

So , substituting the value of x in the equation , we get

The total number of juice bottles = 340 ( 10 ) = 3400 bottles

Hence , the proportion is 40 : 40 : 30

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An instructor grades on a curve (normal distribution) and your grade for each test is determined by the following where S = your score. A-grade: Su + 20 B-grade: u + OSS< + 20 C-grade: u-OSS<+ D-grade: -20 SS-O F-grade: S

Answers

The formula for a curve grade is based on a normal distribution with the average score being 0.

The formula for each grade is as follows:

A-grade: S + 20

B-grade: S + 10S< + 20

C-grade: S - 10S< + 20

D-grade: S - 20

F-grade: S < 0

The formula  is based on a normal distribution with the average score being 0.

For example, if the average score is 50 and your score is 55, then you would receive an A-grade because your score is 5 points above the average. This can be calculated by adding 20 points to your score of 55 resulting in a grade of[tex]75 (55 + 20 = 75)[/tex]. Similarly, if your score is 40, then you would receive a C-grade because your score is 10 points below the average. This can be calculated by subtracting 10 points from your score of 40 resulting in a grade of 30 (40 - 10 = 30).

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Which equation represents f(x)?
O f(x) = 3√x+6+1
Of(x) = 3√x-6 +1.
O f(x)=3√x+6-1
O f(x)=3√x-6-1

Answers

The equation of the straight line would be -

y = 2x.

What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that a straight line passes through the points (2, 4) and (3, 6).

Refer to the graph of the function attached. We can see that the function that represents the graph is -

[tex]$y=\sqrt[3]{x+6} \;+1[/tex]

Therefore, the function representing the graph is -

[tex]$y=\sqrt[3]{x+6} \;+1[/tex]

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