Name: Date: Writing Linear Equations from Word Problems (Page 2) 5) You are planning a class pool party and have reserved the pool for $625. It will cost an additional $11 per person for food. Write a linear equation to represent the total cost of the pool party based on the number of people that will attend. a) If 26 people end up coming to the pool party how much will it cost you?

The value of the length of the segment SR is; 12 units.

A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).

According to the diagram at point it makes the angle of 90° with both triangles, thus;

SR = SQ

2x + 8 = 8x - 4

And to find the value of x, we will find the value of  line segment SR

8x -2x = 8+4

6x = 12

x = 12/6

x = 2

Then we will put the value of x in SR ;

SR = 2x + 8 = 2(2) + 8 = 4 + 8 = 12

SR = 12

Hence, The value of the length of the segment SR is; 12 units.

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The solution for the given equation is x = -5 and x = 3.

How to solve a quadratic equation by substitution?
The equation is first transformed into a more familiar form. Replace the substitutions with the original variables after factoring the problem. The difference of squares equation is used to finish the factorization and locate the answers for x.

Given, the equation for solving is: (x + 2)² - 2(x + 2) - 15 = 0 --(i)
Let in the equation, y = x + 2 --(ii)
Equating (i) and (ii), we get:
y² - 2y - 15 = 0 ⇒ y² - 5y + 3y - 15 = 0 ⇒ y(y - 5) + 3(y - 5) = 0
⇒ (y + 3)(y - 5) = 0 ⇒ y = -3, 5 (by solving the equations)
Thus, from (ii) and value of y obtained above, we get,
x + 2 = -3 ⇒ x = -3 -2 = -5 and x + 2 = 5 ⇒ x = 5 - 2 = 3
Thus, (b) x = -5 and x = 3 is the correct answer.

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Solution

Houe Call = $55

Workdone call per hour = $40

Let h denotes the number of hours used

Total charges on the call

The client can spend no more than $250 for the call to the mechanic

The inequality is

Using Pythagoras's theorem, the length of the third side of the right triangle is 3 units.

The length of the third side of the right triangle can be found using Pythagoras's theorem.

The Pythagoras's theorem can be represented as follows:

c² = a² + b²

where

Therefore, the missing side of the right triangle is the other legs.

b²  = (3√5)² - 6²

b² = 45 - 36

b = √9

b = 3

Therefore,

third side of the right triangle = 3 units

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By using Pythagoras' theorem the length of the third side is 3 units

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

Given, the hypotenuse is 3√5 units and one of the legs is 6 units and assuming the length is x units.

∴ x² = (3√5)² - 6².

x² = 9×5 - 36.

x² = 45 - 36.

x² = 9.

x = ± 3.

As length can not be negative the appropriate value for x is + 3.

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The only way to check which one is the correct answer is to perform each set of transformations and check which one is the correct one. First, note that the initial position of the smiley face is the third quadrant. So, we will first apply vaguely the transformations to check to which one is the smiley face located in the first quadrant once we are done with the transformations.

So, let us analyze each set of transformations separately.

Option A

After reflexing over the x axis, the smiley face position would be

so, once rotated 270° counterclockwise, the position of the smiley face would be

so option A is not the correct answer

Option B

if we rotate 270° counterclockwise, the smiley face's position would be

and by translating 8 units to the right, it would be

so option B is the correct answer

Given the functions:

1. (h/g)(x)

We substitute the functions and solve:

Factor the common term 8:

And we have:

The average rate of change of the function f(x) = x² + 8x from x₁ = 1 to x₂ = 2. is 16

The average rate of change expresses how frequently one quantity changes in relation to another. It provides an idea of the amount the function changed per unit throughout the specified time period. In order to calculate the rate of change, one simply divides the amount of change in one thing by the comparable amount of change in another.

The average rate of change of a continuous function,

f(x) , on a closed interval [a,b] is given by

F(x)=[tex]\frac{F(b)-F(a)}{b-a}[/tex]

[tex]\frac{25 -9}{1}\\ \frac{16}{1}\\ =16[/tex]

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For the ending account balances, these are the solution

a. The ending account if it is compounded monthly is $12,708.68

b. If it is compounded daily = $12712.374

c. If it is continuous = $12712.49

d. The graphs are in the attachment

e. The answers are not similar

This is the data that we can use to solve the problem

Principal = $10000

Time = 8 years

Rate = 3 percent

The ending balance when compounded monthly

= number of months n

= 12

A = P (1 + r/n)^nt

= 10000 (1 + 0.03/12)⁸*¹²

= 10000 (1.0025)⁹⁶

= 100000 X 1.270868

= 12,708.68

The amount that would be the ending account if it is compounded monthly is $12,708.68

b. If it is compounded daily

total number of days in a year n = 365

10000 (1 + 0.03/365)⁸*³⁶⁵

10000 x 1.2712374

= $12712.374

c. The endind account if the interest is compounding continuously

[tex]A = Pe^r^t\\\\A = 10000 *e ^0^.^0^3^*^8[/tex]

= $12712.49

e. The answers are not similar here due to the fact that all of the accounting periods that we used are not the same for the problems that we have here.

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We can generate congruent shapes by combining the three types of transformations: rotations, reflections, and translations. Actually, using a combination of one or more of these three transformations, any pairs of congruent shapes can be matched to one another.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given Data

We now understand that the size and shape of the figures are preserved during stiff transformations (reflections, translations, and rotations). Pre-image and image are always congruent with one another.

Series of transformation Matt can perform:

Reflection (Flip)

Because the equivalent points from the pre-image to the image remain at the same distance from the line of reflection, a reflection maintains its original shape.

Rotations as a Transformation of Congruence

A rotation is when a figure turns. Although the figure is the same size and shape, it appears to have fallen over. A clock is a fantastic example of a rotation in the real world. Every hour or every day, the connecting arms of a clock revolve around its central point. The degree of rotation is used to characterize a rotation; popular rotations include 90 degrees, 180 degrees, and 270 degrees. The figure returns to its original position after a full 360-degree spin. A rotation must additionally include the direction, either clockwise or counterclockwise. A rotation's degree amount and direction can be computed using this information.

Congruence transformation through translation

When we move an object or shape from one location to another without changing its size, shape, or orientation, we call that movement a translation. A translation, often known as a slide, involves moving each point on an object or shape by the same amount and in the same direction.

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If the length of a side of cube is "s", then total edge length (E = 12s), total surface area (A = 6s²) and Volume (V = s³).

As per the question statement, the length of a side of cube is "s".

We are required to write down the equations for total edge length "E", total surface area "A" and Volume "V" of the cube with respect to "s".

To solve this question, we need to know a couple of basic structural properties of a cube, that is,

There are 12 edges in a cube, all of equal length,

And, there are 6 faces in a cube, all of equal surface area.

[A reference image is attached hereby for better understanding;

The 12 edges of the cube are: AB, BC, CD, AD, CG, DH, BF, AE, EF, FG, GH and EH,

And, the 6 Faces of the cube are: ABCD, ABEF, CDGH, BCFG, ADEH and EFGH]

Therefore, total edge length (E) = (12 * s) = 12s,

Or, (E = 12s)

Total surface area (A) = [6 * (s)²] = 6s²,

Or, (A = 6s²)

[Since, area of a square of edge length "s" = s², and every face of a cube is a square]

Finally, Volume (V) of the cube = [s * s * s] = s³,

Or, (V = s³).

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Area of shaded region = 168.56  [tex]m^2[/tex]

What is area of square and semicircle?

Area of square is the total space taken by the square.

If the side of square is a units, then area of square is calculated by

Area of square = [tex]a \times a[/tex] sq units

Area of semicircle is the total space taken by the semicircle

If the radius of semicircle is r units, then area of semicircle is calculated by

Area of semicircle = [tex]\frac{1}{2}\times \pi \times r^2[/tex] sq units

Here,

Side of square = 28 m

Area of square = [tex]28 \times 28 = 784 m^2[/tex]

Radius of circle = [tex]\frac{28}{2} = 14 m[/tex]

Area of two semicircles =

                                         [tex]2 \times \pi \times r^2 \times \frac{1}{2}\\3.14 \times 14 \times 14\\615.44 m^2[/tex]

Area of shaded region = [tex](784 - 615.44) m^2[/tex]

                                      = 168.56 [tex]m^2[/tex]

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Complete Question

The figure has been attached here.

The probability is 0.9204 that exactly 3 of them say job applicants should follow up within two weeks.

Binomial probability distribution

P(X = x) = [tex]C_{n,x}[/tex] . [tex]p^{x}[/tex] .[tex](1-p)^{n-x}[/tex]

[tex]C_{n,x}[/tex]= n!/ x!(n - x)!

The parameters are:

n is the number of trails.

x is the number of successes.

p is the probability of success on a single trial.

In this problem:

43% say job applicants should follow up within two weeks, thus p = 0.43

6 managers are selected, thus n= 6.

The probability that at least 3 of them say job applicants should follow up within two weeks is P(X≥ 3), which is given by:

P(X ≥3) = 1 -P(X < 3)

In which:

P(X < 3 ) = P(X = 0) + P(X = 1) + P(X = 2)

Then:

P(X = x) = [tex]C_{n,x}[/tex]. [tex]p^{x}[/tex]. [tex](1-p)^{n-x}[/tex]

P(X = 0) = [tex]C_{6,0}[/tex] [tex](0.43)^{0}[/tex]. [tex](0.57)^{6}[/tex] = 0.0342

P(X = 1) = [tex]C_{6,1}[/tex](0.43) . [tex](0.57)^{5}[/tex] = 0.0259

P(X = 2) = [tex]C_{6,2}[/tex](0.43)² [tex](0.57)^{4}[/tex] =0.0195

P(X<3) = P(X = 0) + P(X = 1) + P(X =2) = 0.0342 + 0.0259 + 0.0195

                                                             = 0.0796

P(X≥3) = 1 - P(X<3) = 1- 0.0796 = 0.9204

0.9204 is the probability that at least 3 of them say job applications should follow up within two weeks.

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Answer: Europe quit buying crops which left the united states with a surplus of crops

hope i helped

Step-by-step explanation:

the probability of both is the one they share

Answer:

Step-by-step explanation:

point of intersection of the equations: (4,6)

The line parallel to the given line would be y = -x + k

the line passes through (4,6)

putting the values, we get, 6 = -4 + k ⇒ k = 10

Required equation⇒ y = -x + 10

If a bicycle has a listed price of $522.95  before tax and the sales tax is 7.75%, then the total cost of the bicycle with sales tax included is $563.47

The listed price of bicycle = $522.95

The sales tax percentage = 7.75%

We know

C = p(t×p)

Where C is the total cost

p is the listed price

t is the sales tax percentage

Substitute the values in the equation

C = 522.95+((7.75/100)×522.95)
= 522.95+40.53

= $563.47

Hence, if a bicycle has a listed price of $522.95  before tax and the sales tax is 7.75%, then the total cost of the bicycle with sales tax included is $563.47

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Answer:

  (c)  corresponding angles

Step-by-step explanation:

You want to know the description of the marked angles in the given diagram.

Interior angles are between the "parallel" lines. Angle 5 is interior, but angle 1 is not, so they cannot be described as interior angles.

Exterior angles are both outside the "parallel" lines. Angle 1 is exterior, but angle 5 is not, so they cannot be described as exterior angles.

Corresponding angles are both in the same direction from the point of intersection of the "parallel" lines with the transversal. Here, both angles 1 and 5 are "northwest" of the intersection point, so are corresponding angles.

Alternate angles are on opposite sides of the transversal. Consecutive, or same-side, angles are on the same side of the transversal. Angles 1 and 5 are not alternate angles, as they are both on the same side of the transversal.

We know that

• The dimensions of the pool are 26 meters by 12 meters.

• The uniform surrounding path has a width of ,x, meters.

To find a function of x to express the whole area, we have to define the width and length including the path.

The width would be-

The length is

The total area is

We use the distributive property to show the function in the simplest form.

Then, we reduce like terms. So, the function is

Given the expression:

The answer = 3

The word problem for the given expression will be:

What is the 18 divided by 6?

A point that belongs to the solution region of this system of inequalities is (0, 4).

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):

A graph refers a type of chart that's generally used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In this scenario, a graph which represent the solution to the given system of inequalities is shown in the image attached below.

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The numbers written in correct scientific notation format are-

7 x 10⁻⁹

3 x 10⁻⁶

0.1 x 10⁻⁸

Scientific notation is a techniques of writing a large number or small number in a simple form. It involves expressing a number by the multiplication of 10 raise to the specific exponent.

Given are the set of numbers.

In order to classify the given numbers based on the correct syntax of scientific notation, it is necessary to understand the rules for writing the correct syntax.

Based on the above rules, we can classify the correct scientific notation as -

7 x 10⁻⁹

3 x 10⁻⁶

0.1 x 10⁻⁸

Therefore, the numbers written in correct scientific notation format are-

7 x 10⁻⁹

3 x 10⁻⁶

0.1 x 10⁻⁸

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Answer: you can get the full fraction by multiplying 6x3 which is 18 so then you add 18 and 2 and you get 20 so now the fraction is 20/3

and you need 11/3 for a batch so now you have 1 whole batch and 9/3 so you just make the 11 a percentage which is 81%

so the answer is 1 whole batch and 81% of another

or 1 9/3

Answer:

b. $0.21

Step-by-step explanation:

(7·49.95 + 162.38)/2465 = 0.2077

Answer:  72.4

Step-by-step explanation:

soh-cah-toa

cos(25)= adjacent/hypotenuse

cos(25)= adjacent/48

adjacent= 48 * cos(25)

tan(59) = opposite/adjacent

tan(59) = x / 48 * cos(25)

x = 72.4

There is a mound of 2000 pounds of gravel in a quarry

Quantity of gravel added in the mound throughout the day = 400 pounds

Quantity of orders sold from the mound = 600*2 = 1200 pounds

Quantity of gravel left in the mound at the end of the day = 1200 pounds

Let g represent the pounds of gravel in the quarry

Formulating the equation we get the following:

Mounds of gravel in the quarry + Gravel added in the mound - Gravel sold from the mound = Gravel left at the end of the day

g + 400 - 600(2) = 1200

g + 400 - 1200 = 1200

g = 2000

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To calculate (f g)(-1), we use the definition:

This is true if x is defined for f and g. Now, for our problem:

Answer: [tex]y=-2x+3[/tex]

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocal slopes, so the slope of the line we want to find is -2.

The y-intercept is given to be 3, so the equation is [tex]y=-2x+3[/tex].

Given:

The number of people = 150,000,000.

The amount of water used in town = 310 × 109 cubic meters.

Required:

We need to find the amount of water (in cubic meters) used per person each year.

Explanation:

Substitute the number of people = 150,000,000 and the amount of water used in town = 310 × 109 cubic meters in the equation.

Final answer:

Step-by-step explanation:

You have found a used car and your parents have agreed to pay the first $750 for you. You have a summer job mowing yards for $25 per yard. Write and inequality that will calculate the number of yards (y) you will have to mow to get to at least the cost (C) of the car.

25y + 750 = C

If the car cost a total of $4500 how many yards will you have to mow?

25y + 750 = 4,500

subtract 750 from both sides:

25y + 750 - 750 = 4,500 - 750

25y = 3,750

divide both sides by 25:

25y/25 = 3,750/25

y = 150

Must mow 150 yards.

check:

25(150) + 750 = 4,500

3,750 + 750 = 4,500

4,500 = 4,500