On the coordinate plane, plot the following points. Then, connect the points in order from A to E then back to A to form a figure. what is the area of the figure?
A (1, 2) B (1, 7) C (9, 7)
D (9, 3) E (6, 5)

Aisha and Jordan need 63 carpet tiles to cover the maximum amount of floor with the whole tiles.

To find the area of the greatest amount of floor that can be covered with carpet tiles, we need to figure out how many tiles can fit in that area. Since each tile has a side length of 1.5 feet, we can divide the grid into squares with side lengths of 1.5 feet to see how many tiles can fit.

Dividing the grid in this way, we can see that the area of each square is 2.25 square feet (1.5 ft x 1.5 ft). To find the maximum area that can be covered with whole tiles, we need to find the dimensions of the largest rectangle that can be formed using these squares.

In the grid, the longest side that can be formed using whole tiles is 9 squares long (13.5 feet), and the shortest side that can be formed using whole tiles is 7 squares long (10.5 feet). Therefore, the maximum area that can be covered with whole tiles is:

Area = Length x Width = 13.5 ft x 10.5 ft = 141.75 square feet

To find out how many tiles are needed to cover this area, we need to divide the area by the area of each tile:

Number of tiles = Area / Area of each tile = 141.75 sq ft / 2.25 sq ft per tile = 63 tiles

Therefore, Aisha and Jordan need 63 carpet tiles to cover the maximum amount of floor with the whole tiles.

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Answer :

Step-by-step explanation :

It's given that :

The volume of a cylinder is 180π cubic meters. The height of the cylinder is 11.25 meters.

Formula of volume of cylinder = πr²h

where,

By substituting the values of values of height and volume in the above formula we'll get the required value of the radius.

[tex]:\implies [/tex] 180π = πr² 11.25

[tex]:\implies [/tex] 180π = r² × 11.25 π

[tex]:\implies [/tex] 180π/11.25 π = r²

[tex]:\implies [/tex] 16 = r²

[tex]:\implies [/tex] r² = √16

[tex]:\implies [/tex] r = 4

Hence, Radius of the cylinder is 4 meters.

The area of the region in this problem is given as follows:

A = 1 square unit.

The curve represented in this problem is given as follows:

y = sin(x).

The bounds of the region are given as follows:

Hence the area of the region is represented by the definite integral presented as follows:

[tex]\int_{0}^{\frac{\pi}{2}} \sin{x} dx[/tex]

The integral of the sine is the negative cosine, hence the area is:

A = -cos(x), from x = 0 to x = π/2.

Applying the Fundamental Theorem of Calculus, we have that the area is given as follows:

A = -cos(π/2) + cos(0)

A = -0 + 1

A = 1 square unit.

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The correct answer is,

C. 60(x - 3) = 45x.

This equation is based on the information that the 45 expensive wood costs $3.00 more than the 60 cheap wood. In other words, if the price of the 60 cheap wood is x, the price of the 45 expensive wood is x + 3.

Since,  Algebra involves working with numbers, equations, and variables to solve real-world problems and understand abstract relationships.

Now, To solve this equation, we must use algebra and solve for x.

First, we multiply both sides of the equation by 4/5. This gives us:

48x + 36 = 45x

-36 = 3x

Finally, we divide left side of the equation by 3, giving us the final solution:

x = -12

Therefore, the price of the 60 cheap wood is $12, and the price of the 45 expensive wood is $15.

that is, 60 (x - 3) = 45x

This equation shows the correct relationship between the two types of wood that the contractor purchased.

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In the right triangle, the value of x is approximately 64°

From the question, we are to set up an equation for x and then solve for the value of x.

To determine the value of x, we will use SOH CAH TOA

sin (angle) = Opposite / Hypotenuse

cos (angle) = Adjacent / Hypotenuse

tan (angle) = Opposite / Adjacent

In the given diagram,

x is the included angle

Adjacent = 12

Opposite = 25

Thus,

We can write that

tan (x) = 25/12

tan (x) = 2.0833

x = tan⁻¹ (2.0833)

x = 64.3586

x ≈ 64° (to the nearest degree)

Hence,

The value of x is approximately 64°

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Answer: 2b.[tex]\frac{1}{a^{18} }[/tex]

The length QT of the given chords is determined as 14.5.

The length QT is calculated by applying the following formula for intersecting chord theorem.

QS x QT  = OR x TR

Substitute the given values;

10.5QT = 10(OR)

We don't know the length of the radius, so we are going to form another equation.

Since O is the center, angle QRT is a right angle, and we will apply Pythagoras theorem do determine the length QT.

Also, QS = QR

QT² = TR² + QR²

QT² = 10² + 10.5²

QT = √ (10² + 10.5²)

QT = 14.5

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve this problem, we can use the multiplication principle of counting, which states that if there are k choices for one task and m choices for a second task, then there are k x m choices for both tasks combined.

In this case, we can apply this principle to each shelf of books, as there are different numbers of books on each shelf. For the first shelf, there are 12 choices, for the second shelf there are 18 choices, for the third shelf there are 25 choices, and for the fourth shelf there are 30 choices.

To choose one book from each shelf, we need to multiply the number of choices for each shelf together, which gives us:

12 x 18 x 25 x 30 = 16,200,000

Therefore, there are 16,200,000 ways to choose three books, one from each shelf, in the library.

The total number of ways of choosing three books , one from each shelf is given by A = 162,000 ways

The number of ways of selecting r objects from n unlike objects is given by combinations

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

There are 12 ways to choose a book from the first shelf, 18 ways to choose a book from the second shelf, 25 ways to choose a book from the third shelf, and 30 ways to choose a book from the fourth shelf

So , the total number of ways = 12 x 18 x 25 x 30

A = 162,000 ways

Hence , the combination is solved and there are 162,000 ways

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The equation of tangent line related to the parametric equations is equal to y = 3 · x - 22.

In this question we find the case of two parametric equations evaluated at t = - 1, whose tangent line equation must be found. Equation of the tangent line is introduced below:

y = m · x + b

Where:

First, determine the slope of the tangent line:

dx / dt = 1 + 2 · t

dx / dt = 1 - 2

dx / dt = - 1

dy / dt = 2 · t - 1

dy / dt = - 2 - 1

dy / dt = - 3

m = (dy / dt) / (dx / dt)

m = (- 3) / (- 1)

m = 3

Second, evaluate the parametric functions at t = - 1:

x = - 1 + (- 1)² + 8

x = 8

y = (- 1)² - (- 1)

y = 2

Third, determine the intercept of the tangent line:

b = y - m · x

(m = 3, x = 8, y = 2)

b = 2 - 3 · 8

b = 2 - 24

b = - 22

Fourth, write the equation of the tangent line:

y = 3 · x - 22

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The length of the indicated segments are determined as:

17. VX = 6      18. SU = 15

Based on the side-splitter theorem, the sides that are intercepted are divided proportionally. Using this theorem, we will find the length of the indicated segments below:

17. 8/20 = VX/15

Cross multiply:

VX * 20 = 8 * 15

VX * 20 = 120

VX = 120/20

VX = 6

18. SU/10 = 12/8

Cross multiply:

SU = 120/8

SU = 15

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Answer:

C

Step-by-step explanation:

The time it will take for him to have enough money for the project is given as follows:

t = 8.5 years.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The parameters for this problem are given as follows:

P = 4000, r = 0.062, n = 2, A(t) = 6720.

Hence the time needed is obtained as follows:

[tex]4000\left(1 + \frac{0.062}{2}\right)^{2t} = 6720[/tex]

(1.031)^2t = 672/400

(1.031)^2t = 1.68

2tlog(1.031) = log(1.68)

t = log(1.68)/[2 x log(1.031)]

t = 8.5 years.

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We can see here that filling up the remaining spaces:

AB ≅ CD: Opposite sides are congruent.

∠ABC and ∠BCD are supplementary: Consecutive angles are supplementary.

An angle is actually known to be a geometric figure that is formed by the joining together of two rays or endpoints which are known as vertex.

The sides or legs of the angle are known to be make up the rays.

Angles are actually known to be measured in degrees, with a full circle containing 360 degrees.

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Results:

The equivalent pairs are:

A. 5.80; 5+0.08,

C. 6.050; six and five thousandths, and

E. nine and nine-tenths; 9.9

A. 5.80; 5+0.08

The two are equivalent expressions because they both represent the same decimal number. 5.80 can be interpreted as 5 units and 0.80 units, which is the same as 5 units and 0.08 units. So 5.80 is equal to 5+0.08.

C. 6.050; six and five thousandths

The two expressions describe the same decimal number. 6.050 means 6 whole units, 5 hundredths, and 0.005 thousandths, while "six and five thousandths" means the same thing - 6 whole units, 5 hundredths, and 0.005 thousandths.

E. nine and nine tenths; 9.9

They are also equivalent. Nine and nine-tenths mean 9 whole units and 9 tenths, while 9.9 means the same thing - 9 whole units and 9 tenths.

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Step-by-step explanation:

( 11 * x ) + 2     where 'x' is a number

The probability of picking L and another A with replacement is: 2/49

Probability of picking A and then another A with replacement is:  1/49

We are given the letter DALLAS.

There are a total of 7 letters. Thus, the probability of picking L is:

2/7

Probability of picking A after that with replacement is: 1/7

Thus, probability of picking L and another A with replacement is:

(2/7) * (1/7) = 2/49

Probability of picking A and then another A with replacement is:

(1/7) * (1/7) = 1/49

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Answer:

[tex]6x + 5y = - 30[/tex]

[tex]5y = - 6x - 30[/tex]

[tex]y = - \frac{6}{5} x - 6[/tex]

Since the slope of this line is -6/5, the slope of a perpendicular line is 5/6. The slopes of perpendicular lines are negative reciprocals.

The large jar has better value for money than the smaller one.

To see which jar is the best value for the money, we need to take the quotient between the cost of each jar and the size. The smaller that value gets, the best value we have.

For the first jar we have:

q = £4.10/540 = 0.0075

For the second jar we have:

q' = £2.81/360 = 0.0078

Then we can see that the large jar has the best value for money.

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Answer: graphed and attached

Step-by-step explanation:

to graph a y intercept and slope, first find the y intercept on the graph and place your point. here the y intercept is 3, so (0, 3) because x=0 at a y intercept.

next use slope to find your next point. slope of -2 is the same as -2/1 or down -2 and right +1. so from your y intercept of 3, go down -2 and right 1 and place your point (1, 1). do this again for a 3rd point at (2, -1).

graph is attached.

A graph of this function d = 45t is shown in the image below.

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

d = kt

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 45/1 = 90/45

Constant of proportionality, k = 45.

Therefore, the required linear equation or function is given by;

d = kt

d = 45t

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The values of θ for different conditions were calculated with the help of trigonometric functions.

Given that;

The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function,

f (θ) = 2 sin θ + √ 2

Hence, We can simplify as;

A) Function is,

f (θ) = 2 sin θ + √ 2

f (θ) = 2 sin θ + √ 2 = 0

2 sin θ + √ 2 = 0

2 sin θ = -  √ 2

sin θ = - 1/√2

θ = nπ ± π/4

Where, n = 1, 3, 5, 7, ...

So, At θ = nπ ± π/4 pogo stick's spring will be equal to its non compressed length.

2) If the angle was doubled, the function will look like this,

f (θ) = 2 sin 2θ + √ 2

f (θ) = 2 sin 2θ + √ 2 = 0

2 sin 2θ + √ 2 = 0

2 sin 2θ = -  √ 2

sin 2θ = - 1/√2

θ = nπ/2 + π/8

Where, n = 1, 3, 5, 7, ...

n = 1;

θ = π/2 + π/8

θ = 5π/8

n = 2;

θ = π + π//8

θ = 9π/8

Hence, Solutions are, 5π/8, 9π/8, ...

3) g (θ) = 1 - cos²θ + √2

g (θ) = sin²θ + √2

sin²θ + √2 = 2 sinθ + √2

sin²θ - 2 sinθ= 0

sinθ (sinθ - 2) = 0

sinθ = 0

θ = nπ

Where, n = 1, 3, 5, 7, ..

So, θ = nπ , the lengths of springs from the original pogo stick and the toddler's pogo stick are equal.

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The value of the product of the rational expressions is,

⇒ (4x - 32) (x² - 36)

We have to given that;

The rational expressions is,

⇒ 4x/(x+6) times (x-8) / (x-6)

Now, We can multiply as;

⇒ 4x/(x+6) times (x-8) / (x-6)

⇒ 4x/(x+6) × (x-8) / (x-6)

⇒ 4 (x - 8) / (x + 6) (x - 6)

⇒ (4x -32) / (x² - 6²)

⇒ (4x - 32) (x² - 36)

Thus, The value of the product of the rational expressions is,

⇒ (4x - 32) (x² - 36)

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Answer:

Step-by-step explanation:

1. $4,076.92

2. Assets = Liabilities + Equity

3. They can be used to make online purchases.

4. by using an emergency fund for this unplanned expense

5. a fund with a minimum investment that tracks the value of cash (This question)

6. 1930s

7. Banks because they are highly regulated by the government, so the loan terms will not be predatory.

8. their vacation cabin

9. You should shop around for the best overall deal.

10. If you use a credit card, it is easy to run up huge debts.

11. They are tied directly to your bank account.

12. preventative care

13. $100,000 per person bodily injury, $300,000 per incident for bodily injury, $50,000 for property damage

14. how long the coverage lasts, how much the premium costs, and the cash value

15. 1-year renewable group term life

16. Identity thieves can intercept unencrypted data being sent to Wi-Fi hot spots.

17. Wells Fargo employees were opening unauthorized deposit and credit accounts for its customers.

18. 2 year in state community college degree

19. tuition assistance

20. -a sundae, -movie tickets

Explanation: All of these answers are correct!

Personal Finance Semester Exam

5/11/2023

The single formulas for f and g so that both compositions hold true are f(x) = 3sin(x) and g(x) = π/4(x − 1)

From the question, we have the following parameters that can be used in our computation:

f(g(x)) = 3sin (pi/4(x − 1))

g(f(x)) = pi/4(3 sin(x) − 1)

Express pi as π

So, we have

f(g(x)) = 3sin (π/4(x − 1))

g(f(x)) = π/4(3 sin(x) − 1)

In f(g(x)) = 3sin (π/4(x − 1)), replace the expression in bracket with g(x)

So, we have

f(g(x)) = 3sin (g(x))

This means that

f(x) = 3sin(x) and also, it means

g(x) = π/4(x − 1)

Hence, the single formulas that both compositions hold true are f(x) = 3sin(x) and g(x) = π/4(x − 1)

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From the given value of z = 3(cos pi/2 + isin pi/2),  the exact value of z⁷ is -2187i.

Given z = 3(cos pi/2 + isin pi/2)

which can be represented as 3sin(pi/2) in polar form.

Now, by applying De-Moivre's theorem,

z⁷  = (3cis(pi/2))⁷

      =   3⁷cis(7pi/2)

      = 3⁷cis(3pi/2)                   [7pi/2 --- 3pi/2 ]

To write it in complex form,

z⁷  = 3⁷(cos(3pi/2) + isin(3pi/2))

z⁷  = 3⁷(0-i)                                    [cos(3pi/2) = 0 and sin(3pi/2) = -1]

z⁷  = 3⁷(-i)

z⁷  = -2187i

From the above explanation, we can conclude that the value of  z⁷ is -2187i.

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Answer:

Rational

Step-by-step explanation:

Improper fractions are always rational.

The total area of all six sides that will be painted on the wooden cube is 96 square centimeters.

First, we need to understand that each cube has six faces or sides, which are all squares of the same size. When we paint the cube, we will be painting all six sides of it. Therefore, we need to find the total area of all six sides that will be painted.

To calculate the area of each side, we need to know the length of the side. You mentioned that the wooden blocks are cubes, so each side will have the same length. Let's say the length of each side is 4 cm.

Now, we can calculate the area of one side of the cube by squaring the length of the side. In this case, the area of one side will be:

Area of one side = (length of side)²

= (4 cm)²

= 16 cm²

Since there are six sides to each cube, we can find the total area of all six sides by multiplying the area of one side by six:

Total painted area = 6 x Area of one side

= 6 x 16 cm²

= 96 cm²

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