Name:
Date:
2.
5.
Directions: Solve for x
This is a 2-page document
Directions identify the similar triangles in the diagram, then sketch them so the coresponding
sides and angles have the same orientation
1.
52
48
Per
20
9.24 and 32
طلال سلال
kl ma jkk
Jkm-kim
Unit 7: Right Triangles & Trigonometry
Homework 3: Similar Right Triangles
& Geometric Mean
X=4.8
6.
22.4
13.2
26
Directions: Find the geometric mean of each pair of numbers.
7.16 and 27
8. 5 and 36
10.8 and 48

The inverse of the function y-∛x/3 -1 is:

To find the inverse of the given function, we need to express x in terms of y. We can start by swapping the positions of x and y in the original equation:

Now, we can solve for y in terms of x:

Therefore, Therefore, the inverse of the given function is f^-1(x) = 27(x-1)³. This means that if we substitute any value of x into the inverse function, we will get the corresponding value of y that makes the original function true. Similarly, if we substitute any value of y into the original function, we will get the corresponding value of x that makes the inverse function true.

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Therefore , the solution of the given problem of unitary method comes out to be you can purchase 30 sausage and 70 pepperoni pizzas to serve at your birthday party.

To complete the assignment, make use of the tried-and-true fundamental technique, the actual variables, and any insightful knowledge you gain from the general and detailed questions. In response, customers might be given another opportunity to sample the products. We will miss out on substantial expression gains in programming comprehension if these changes don't take place.

Here,

Let's use "p" for the quantity of pepperoni pizzas and "s" for the quantity of sausage pizzas. Finding p and s values that meet the requirements is necessary.

In light of the information provided:

One pepperoni pizza costs $8.

One sausage pizza costs $6.

100 pizzas are required.

Budget total: $740

To reflect the stated conditions, we can construct the following system of equations:

=> p + s = 100 (1)

=> 8p + 6s = 740 (2)

=> 8p + 8s = 800 (3)

=> 8p + 6s - (8p + 8s) = 740 - 800

=> -2s = -60

=> s = (-60)/(-2)

=> s = 30

=> p + 30 = 100

=> p = 100 - 30

=> p = 70

With a $740 budget, you can purchase 30 sausage and 70 pepperoni pizzas to serve at your birthday party.

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Answer:

Step-by-step explanation:

Parallel lines would never intersect no matter how long the lines go on for because they have the same slope. That will always be true.

The perimeter of the new shape is 32 cm + 8 * sqrt(3) cm.

What is perimeter?

Perimeter is a measurement of the distance around a two-dimensional shape. It is the total length of the boundary or outer edge of the shape. In other words, it is the sum of the lengths of all the sides of the shape.

First, let's find the length of each side of the equilateral triangle, which was cut out of the square. Since the triangle was cut from a square, its sides have the same length as the sides of the square. Therefore, each side of the equilateral triangle is 8 cm.

Now, let's find the perimeter of the new shape, which is made by joining two of these shapes together. The new shape consists of two equilateral triangles and a rectangle. The length of the rectangle is the same as the side length of the equilateral triangle, which is 8 cm. The width of the rectangle is the same as the height of the equilateral triangle, which can be found by applying the Pythagorean theorem to one of the triangles:

[tex]height^2 = side^2 - (1/2 * side)^2\\\\height^2 = 8^2 - (1/2 * 8)^2\\\\height^2 = 64 - 16\\\\height^2 = 48\\\\height = \sqrt{(48)}\\\\height = 4 * \sqrt{(3)}[/tex]

Therefore, the width of the rectangle is also [tex]4 * \sqrt{(3)} cm.[/tex]

The perimeter of the new shape can be found by adding up the lengths of all four sides:

Perimeter = 2 * (side of equilateral triangle) + 2 * (length of rectangle + width of rectangle)

[tex]Perimeter = 2 * 8 cm + 2 * (8 cm + 4 * \sqrt{(3)} cm)\\\\Perimeter = 16 cm + 16 cm + 8 * \sqrt{(3)} cm\\\\Perimeter = 32 cm + 8 * \sqrt{(3)} cm[/tex]

Therefore, the perimeter of the new shape is [tex]32 cm + 8 * \sqrt{(3)} cm.[/tex]

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We can set up a proportion using the given ratio:

Weight on Earth : Weight on Planet X = 5 : 12

Let's let x be the weight of the elephant on Planet X. We can substitute the given weight on Earth to solve for x:

3800 : x = 5 : 12

We can cross-multiply to get:

3800 * 12 = 5 * x

Simplifying the right side, we get:

45600 = x * 5

Dividing both sides by 5, we get:

x = 9120

Therefore, the weight of the elephant on Planet X is 9120 pounds.

Answer:

[tex] \frac{468}{14.4} = \frac{d}{16.8} [/tex]

[tex]32.5 = \frac{d}{16.8} [/tex]

[tex]d = 546[/tex]

Wyatt can drive 546 miles on a full tank (16.8 gallons) of gas.

The system has the following solution: [tex]x_1=-4,\ x_2=3,\ x_3=1[/tex]. The vector xequals can be used to represent the answer.

A statement in mathematics demonstrating the equality of two expressions is called an equation. Two phrases with the same value are normally separated by the equals sign (=). Finding the area of a circle and predicting planetary motion are only two examples of the many practical issues that equations are used to address.

The linear system's augmented matrix, which is determined by the matrix equation A x = b is given by:

Aequals

[tex]\left[\begin{array}{ccc}1&-3&4\\2&-3&2\\-3&3&4\\-7&15&-4\end{array}\right][/tex]

Part 2:

Aequals

Write the system's solution as a vector after solving it.

We can use Gaussian Elimination to solve this system.

Step 1:

[tex]\left[\begin{array}{ccc}1&1&0\\2&-1&1\\-3&0&1\\-7&8&3\end{array}\right][/tex]

Step 2:

Aequals

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\3&1&0\\-4&3&1\end{array}\right][/tex]

The system's solution is [tex]x_1=-4,\ x_2=3,\ x_3=1[/tex]. The vector xequals represents the answer.

The matrix is,

[tex]\left[\begin{array}{ccc}-4\\3\\1\end{array}\right][/tex]

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The appropriate domain for the function h(t) = −3t^2 + 9t + 12 is [0, 3.08].

The domain of a function is the set of all possible input values for which the function is defined. In this case, the function h(t) gives the height of the ball above the ground as a function of time t.

The ball is thrown from the tree house at some initial time, and it continues to travel until it hits the ground. The height of the ball is defined for all values of t between the time it is thrown and the time it hits the ground.

To find the domain of h(t), we need to determine the range of values of t for which the function is defined. The ball cannot have a negative height, so the function is undefined for values of t that would make h(t) negative.

To find the time at which the ball hits the ground, we need to set h(t) equal to zero and solve for t:

h(t) = -3t^2 + 9t + 12 = 0

Using the quadratic formula, we get:

t = (-9 ± √(9^2 - 4(-3)(12)))/(2(-3))

t = (-9 ± √(105))/(-6)

t ≈ -0.41 or t ≈ 3.08

Since the ball cannot have a negative height, the domain of the function is the interval [0, 3.08]. Therefore, the appropriate domain for the function h(t) = −3t^2 + 9t + 12 is [0, 3.08].

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Answer:

Okay, let's think through this step-by-step:

• Janelle Monae obtained a $3,500 loan at 8.5% interest for 1 year.

• 8.5% interest for 1 year = 8.5% of $3,500 = $297.50 in interest

• The loan amount ($3,500) plus interest ($297.50) = $3,797.50 total paid back

•Monthly payments = $3,797.50 / 12 months = $285.55

• So the interest amount in the first payment is $297.50 (calculated above as 8.5% of the $3,500 loan amount)

The choices do not match this:

A. $297.50 - This is the correct choice. This is the interest amount paid over the full loan.

B. $291.67 - This is too low. Calculated interest over 1 year at 8.5% is $297.50.

C. $24.79 - This is way too low. The interest amount due is $297.50 per the working.

D. $35.00 - This is also too low and does not make sense based on the loan details provided.

In summary, to find the interest in just the first payment, we calculate:

Interest over full loan ($297.50) / Number of payments (12) = $24.79

So the interest amount in just the first monthly payment is $24.79.

But the total interest paid over the life of the loan (1 year) is $297.50.

Does this help explain the steps and reasoning? Let me know if any part of the working or explanation is unclear. I can also provide additional examples if needed.

Let me know if you have any other questions!

Step-by-step explanation:

Answer: A

Step-by-step explanation: The distance for the ball to travel straight from Jose to Harlan is less than what it would be if she were to pass it to Alma first. You can use the distance formula to find this (find the distance between Jose and Harlan, and compare it to the sum of the distances between Jose and Alma and Alma and Harlan)

Answer:2.86.

Step-by-step explanation:

We can use the geometric distribution to solve this problem. The geometric distribution models the number of trials needed to achieve the first success in a sequence of independent trials with a constant probability of success.In this case, the probability of success (the teacher tripping over the cords) is 0.35. Therefore, the expected value or mean of the geometric distribution is 1/0.35 ≈ 2.86.So, on average, students need to wait for 2.86 periods until the teacher trips over the cords in her classroom.Therefore, the answer is 2.86.

Answer:

We can use the Pythagorean theorem to solve this problem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we know that the two sides have lengths of 2 cm and 6 cm, and we are trying to find the length of the third side, which we'll call x. We also know that the third side is not the hypotenuse, so we can't just assume that it's the longest side.

Using the Pythagorean theorem, we can write:

x^2 + 2^2 = 6^2

Simplifying, we get:

x^2 + 4 = 36

Subtracting 4 from both sides, we get:

x^2 = 32

Taking the square root of both sides, we get:

x = sqrt(32)

Simplifying, we get:

x = 4sqrt(2)

So the length of the third side is 4sqrt(2) centimeters.

Answer:

Step-by-step explanation:

hi

First, dont keep the equation  this way.  

f(x) = 2 (x+2) +4x

f(x) = 2x+4+4x

f (x) =  6x+4

after :

x= 0        f(x) = 4

x= 2            f(x)= 16

x= 10           f(x) = 64

x = 30          f(x) = 94

The area and the perimeter of the given parallelogram are 36.792 mm² and 24.28 mm respectively.

In Euclidean geometry, a parallelogram is a simple quadrilateral having two sets of parallel sides.

The confronting or opposed sides and the opposing angles of a parallelogram are of equal length.

There are four distinct types of parallelograms, including three distinct types.

Rhombuses, parallelograms, squares, and rectangles are the four types.

So, the given image itself tells that the given figure is a parallelogram.

The area of the given parallelogram is:
A = b*h

A = 6.3*5.84

A = 36.792 mm²

The perimeter of the given parallelogram:

P = 2(a+b)

P = 2(6.3+5.84)

P = 24.28 mm

Therefore, the area and the perimeter of the given parallelogram are 36.792 mm² and 24.28 mm respectively.

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Volume of oblique pyramid is 170ft³.

An oblique pyramid is a pyramid in which the apex is not directly above or below the center of the base. It is called "oblique" because it has a slant or tilt to its shape, as opposed to a "right" pyramid where the apex is directly above the center of the base. Oblique pyramids can have different shapes for their bases, such as a square, rectangle, triangle, or any other polygon.

Given

Base area=1/2× 12× 5

height of pyramid=17ft

Volume of oblique pyramid=Base area × height/3

=(1/2× 12× 5 ×17)/3

=170ft³

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Answer:

False

Step-by-step explanation:

The formula for the area of a circle is A = pi • r^2

Answer: False

Step-by-step explanation: A = [tex]\pi[/tex] [tex]r^{2}[/tex]

A function relating these variables is D(x) = 10 + 2x,

D(9) = 28, meaning after 9 hours of snowfall,

An independent variable is a variable that is manipulated or controlled by the researcher in an experiment to observe its effect on the dependent variable. It is the variable that is changed deliberately to see how it affects the outcome of the experiment.

The independent variable, x, represents the number of hours since snow began falling,

and the dependent variable is the total amount of snow on Jace's lawn because the amount of snow depends on the number of hours since it began to snow.

A function relating these variables is D(x) = 10 + 2x, where D(x) is the total amount of snow on Jace's lawn in inches after x hours of snowfall.

So, D(9) = 28, meaning after 9 hours of snowfall, Jace will have a total of 28 inches of snow on his lawn.

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There are no orange M&Ms in the bag, thus there is no probability of picking one.

An event is any subset of the sample space, which is the set of all potential results of a random experiment, according to probability theory. By dividing the number of favourable outcomes by the total number of possible outcomes, the probability of an event is determined.

Classical probability, empirical probability, and subjective likelihood are just a few of the several varieties of probability. Empirical probability is based on actual observations or experiments, as opposed to classical probability, which is predicated on the idea that all events are equally likely. On the other hand, subjective probability is dependent on opinion or conviction.

Picking a yellow M&M has a 4/20 chance, which drops to 1/5.

The likelihood of selecting a blue or green card M&M is the result of adding the odds of selecting a blue and a green:

To reduce to 1/2, 2/20 + 8/20 = 10/20.

The likelihood of choosing an orange M&M is zero because there are no orange M&Ms in the bag.

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The complete question is:

Answer:

y=3+2 to the power of x +1

Step-by-step explanation:

Answer:

142 ft square

Step-by-step explanation:

Face 1: 3(10)=30 ft square

Face 2: 4(10)=40 ft square

Front: 2(6)=12/2=6 ft square

Back: Same as front

bottom: 6(10)=60 ft square

Total: 30+40+6(2)+60=142 ft square

() means multiply in case don't know

Answer: 4

Step-by-step explanation:

The indicated value h(-1)  has a value of 0 when evaluated

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

f(x) = - 2x ^ 2

g(x) = x - 3

h(x) = 2f(x) - g(x)

The indicated value of the function is

h(-1)

This means that

h(-1) = 2f(-1) - g(-1)

Calculate g(-1)

So, we have

g(-1) = -1 - 3

g(-1) = -4

Calculate f(-1)

So, we have

f(-1) = -2 * (-1)^2

f(-1) = -2

Recall that

h(-1) = 2f(-1) - g(-1)

Substitute the known values in the above equation, so, we have the following representation

h(-1) = 2 * -2 + 4

Evaluate

h(-1) = 0

Hence, the value is 0

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In the equation , cost of both companies will be same to rent a car is 6 days.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the deposit for the rent car in Wreck = $30

Cost for renting in Wreck = $15 per day

Cost for renting in Barely = $20 per day.

Here let us take the number of days as x.

Then, Cost for renting in Wreck = 15x+30

Cost for renting in Barely = 20x

To rent a car , if cost of both companies is same then the equation is,

=> 15x+30 = 20x

=> 20x-15x = 30

=> 5x = 30

=> x = 30/5 = 6

Hence We have to rent a car for 6 days  the cost of both companies to be the same.

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The length of AB can be found to be 9. 85 units .

To find the length of AB, we can use the distance formula which is:

d = √ ( ( x2 - x1) ^ 2 + ( y2 - y1) ^2 )

The vertices for AB are:

A - ( 1, 7 )

B - ( 10, 3 )

When the values are plugged into the formula, we get :

d = √ ( ( x2 - x1) ^ 2 + ( y2 - y1) ^2 )

d = √ ( ( 10 - 1 )^ 2 + ( 3  - 7) ^2 )

d = √ ( 81 + 16 )

d = √ 97

d = 9. 85 units

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Answer:

56

Step-by-step explanation:

12110 × 100

21625

=1211000

21625

=56

Answer:

Step-by-step explanation:

For creating a budget for your business, you must include 4 main things.

These are as follows:

1. Transportation and vehicle cost.

2. Your estimated revenue plan

3. Profit margin

4. Spending goals

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Simplifying this equation, we get: PQ ≈ 6.93 and QR ≈ 8.

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. A triangle is defined by its three sides and the three angles formed by those sides.

To find the lengths of PQ and QR in triangle RPQ, we can use the law of sines:

sin(R) / RP = sin(P) / PQ = sin(Q) / QR

We are given R = 30° and P = 60°, so we can find Q:

Q = 180° - R - P

Q = 180° - 30° - 60°

Q = 90°

Now we can use the law of sines:

sin(30°) / 4 = sin(60°) / PQ = sin(90°) / QR

Simplifying this equation, we get:

PQ = (4 * sin(60°)) / sin(30°) ≈ 6.93

QR = (4 * sin(90°)) / sin(30°) = 4 * 2 ≈ 8

Therefore, PQ ≈ 6.93 and QR ≈ 8.

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The quadratic functions that have a graph with x-intercepts of -8 and 2 are:

y = (x + 8)(x - 2)

f(x) = -7(x + 8)(x - 2)

Options A and C are the correct answer.

We have,

To find the quadratic functions that have a graph with x-intercepts of -8 and 2, we can start by using the fact that the x-intercepts occur when y = 0.

We know that the x-intercepts are -8 and 2, so we can set up two equations:

(x + 8) = 0 and (x - 2) = 0

Solving for x in each equation, we get:

x = -8 and x = 2

Therefore, the factors of the quadratic function that has x-intercepts of -8 and 2 are (x + 8) and (x - 2).

Now we can use these factors to determine which quadratic functions have a graph with these x-intercepts.

A.

y = (x + 8)(x - 2)

Expanding this quadratic function gives:

y = x² + 6x - 16

This function has x-intercepts of -8 and 2, so it is a valid option.

B.

y = (x - 8)(x - 2)

Expanding this quadratic function gives:

y = x² - 10x + 16

This function does not have an x-intercept of -8, so it is not a valid option.

C.

f(x) = -7(x + 8)(x - 2)

Expanding this quadratic function gives:

f(x) = -7x² - 42x - 96

This function does have x-intercepts of -8 and 2, so it is a valid option.

D.

f(x) = -2x² - 12x + 32

To find the x-intercepts of this quadratic function, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Plugging in the values from the given function, we get:

x = (-(-12) ± √((-12)² - 4(-2)(32))) / 2(-2)

x = (-(-12) ± √(144 + 256)) / (-4)

x = (6 ± √(100)) / 2

x = 3 ± 5

So the x-intercepts are -2 and 8, which means this function is not a valid option.

E.

y = x² - 5x + 8

To find the x-intercepts of this quadratic function, we can again use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Plugging in the values from the given function, we get:

x = (-(-5) ± √((-5)² - 4(1)(8))) / 2(1)

x = (5 ± √(9)) / 2

x = 4 or x = 1

So the x-intercepts are 4 and 1, which means this function is not a valid option.

F.

f(x) = x² - 8x + 2

To find the x-intercepts of this quadratic function, we can once again use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Plugging in the values from the given function, we get:

x = (-(-8) ± √((-8)² - 4(1)(2))) / 2(1)

x = (8 ± √(60)) / 2

x = 4 ± 2√(15)

So the x-intercepts are 4 + 2 √(15) and 4 - 2 √(15), which means this function is not a valid option.

Therefore,

The quadratic functions that have a graph with x-intercepts of -8 and 2 are:

A. y = (x + 8)(x - 2)

C. f(x) = -7(x + 8)(x - 2)

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