Question 4 (10 points)
(02.07 MC)

The figure shows triangle PQR and line segment AB, which is parallel to QR:

Triangle PQR has a point A on side PQ and point B on side PR. The line AB is parallel to the line QR.
Part A: Is triangle PQR similar to triangle PAB? Explain using what you know about triangle similarity. (5 points)

Part B: Which line segment on triangle PAB corresponds to line segment QR? Explain your answer. (3 points)

Part C: Which angle on triangle PAB corresponds to angle Q? Explain your answer. (2 points)

Amoli is Correct, where distributive property is used to multiply two expressions.

What is Distributive property?

The Distributive Property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.

What is Associative property?

A mathematical principle known as the associative property states that grouping the factors in a multiplication problem does not affect the solution.

Step-by-step explanation:

According to distributive property:

= (125 * (1/2y)) +( y * (1/2y))

= 125/2y + 1/2

Here, Associative property does not held.

Hence, Distributive property should be used.

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The correct way by using the power of a power property we can write as;

⇒ x¹⁵ = (x³)⁵

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ x¹⁵

Now,

Since, The expression is,

⇒ x¹⁵

We can write the expression as by using the power of a power property as;

⇒ x¹⁵ = (x³)⁵

Thus, The correct way by using the power of a power property we can write as;

⇒ x¹⁵ = (x³)⁵

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The value of z is given by (b) z = 63.

According to Angle Sum Property, the sum of interior angles of a triangle is 180 degree.

So for left hand triangle, interior angles are 31, 61 and x. So,

31 + 61 + x = 180

92 + x = 180

x = 180-92

x = 88

Now x and y are the linear angles so their sum is 180 degree too.

x + y = 180

88 + y = 180

y = 180-88 = 92

Again for right hand triangle the interior angles are 25, y, z. So again by Angle Sum Property,

25 + y + z = 180

25 + 92 + z = 180

117 + z = 180

z = 180-117 = 63

Hence the value of z is 63.

So the correct option is (b).

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Answer:

Step-by-step explanation:

they will sprint 75 yard in total

Answer:

1870

Step-by-step explanation:

10 x 2 = 20

25 x 2 = 50

50 x 2 = 100

20 + 50 + 100 = 170

170 x 11 = 1870

I cried over this problem so you dont have to :)

The number of ride tickets that were sold are 8 and the number of food tickets that were sold  are 24  .

In the question ,

it is given that

total number of tickets bought by the family at carnival = 32 tickets

total amount spent by the family of tickets = $90

let the number of ride tickets be [tex]=[/tex] x

let the number of food tickets be [tex]=[/tex] y

So , x + y = 32

x = 32 - y

cost of 1 ride ticket = $1.50

cost of 1 food ticket = $3.25

So the total cost is 1.25x + 3.25y = 90

Substituting x = 32 - y in the equation 1.5x + 3.25y = 90 ,

we get ,

1.5(32 - y) + 3.25y = 90

48 - 1.50y + 3.25y = 90

1.75y = 90 - 48

1.75y = 42

y = 24

So , x = 32 - 24 = 8

Therefore , The number of ride tickets that were sold are 8 and the number of food tickets that were sold  are 24  .

The given question is incomplete , the complete question is

A family buys a total of 32 tickets at a carnival. Ride tickets cost $1.50 each and food tickets cost $3.25 each. The family pays a total of $90 for the tickets store. How many of each type of ticket were sold ?

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Step-by-step explanation:

the picture is very blurry.

I understand we need the y-intercept in every case and then move the pictures into the empty frames based on sorting these numbers from lowest to highest.

the y-intercept is the point, where a function/curve intersects the y-axis.

in other words, it is the y-value of the point, where x = 0.

so,

1. 0

2. -6

3. looks like -2 (again, very blurry)

4. looks like +2

5. +6

6. +4

sorting these gives us

2. -6 3. -2 1. 0 4. +2 6. +4 5. +6

therefore the 6 frames need to receive the original pictures in that sequence.

Answer:

x = 7

Step-by-step explanation:

(10x+30)° and (17x-19)° are

EQUAL TO EACH OTHER

10x+30 = 17x-19

7x = 49

x = 7

desmos

Answer:

provide context

Step-by-step explanation:

The area of the circle on the paper is 4.5 cm when traced around the edge of the quarter on a sheet of paper.

The area of the circle is equal to the product of the square of the radius of the circle and pi.

A = πr²

where 'r' is the radius of the circle

The diameter of a quarter is 2.4 cm. You trace around the edge of the quarter on a sheet of paper.

The area of the circle on the paper = πr²

Here r = (diameter of a quarter)/2 = 2.4/2 = 1.2 cm

The area of the circle on the paper = π(1.2)²

The area of the circle on the paper = π × 1.44

The area of the circle on the paper = 4.5238

Round the answer to the nearest tenth.

The area of the circle on the paper = 4.5 cm

Thus, the area of the circle on the paper is 4.5 cm

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Answer:its 4.5

Step-by-step explanation:

The examples of some integers whose product is negative include:

-4 × 3 = -12

10 × (-2) = -20

An integer is a number that has no decimal or fractional part and can be negative or positive, including zero.

A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.

Integer examples include -5, 1, 5, 8, 97, and 3,043. Numbers that are not integers include: -1.43, 1 3/4, 3.14, and

In this case, the example has been given above. It should be noted that the product of a negative and positive number is a negative number.

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You cannot solve it because you do not know what x and y are for the parallel line. which is the correct answer would be option (B).

We have to find out the y-intercept of the line that is parallel to y = 0.5x - 2,

As per the given options,

Since the parallel line goes through point (3, 0) substitute 3 for x and 0 for y and solves for b, the y-intercept.

This is not the correct answer.

You cannot solve it because you do not know what x and y are for the parallel line.

This is the correct answer.

Since the parallel line goes through the point (3, 0) substitute 0 for x and 3 for y and solve for b, the y-intercept.

This is not the correct answer.

Therefore, You can't solve it since you don't know what the parallel line's x and y coordinates are.

Hence, the correct answer would be option (B).

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Answer:

the answer is £15

Step-by-step explanation:

Carly works 6 hours for four days 6x4= 24

so she worked for 24 hours we know that she makes  £360 per week.

so we divide 360 by 24 which gives us the total of

£15 per hour

The height of building has shadow 47.75m long is 95.5m

The angle of elevation is defined as the angle which is formed by angle between horizontal line of sight and object.

let the height of building be h. we have given height of another building is 3.2m and shadow is 1.6m long.

we know that

tan(∅) = perpendicular/base = 3.2/1.6 =2

As question says at same time, another building of height h and shadow is 47.75m long.then angle will be same.

⇒ tan(∅) = perpendicular/base = h/47.75

⇒ h/47.75 = 2

⇒ h = 2(47.75) = 95.5m

Thus, required height of building is 95.5.

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Answer:

5/9

Step-by-step explanation:

The result of a spin is either an odd number or an even number.  The two outcomes are complements.

If the probability of getting an odd number is 4/9, the probability of getting an even number is  1 - 4/9 = 5/9.

Answer:

11 - 2i

Step-by-step explanation:

Given expression:

[tex](4-3i)(2+i)[/tex]

Expand:

[tex]\implies 4(2+i)-3i(2+i)[/tex]

[tex]\implies 8+4i-6i-3i^2[/tex]

[tex]\implies 8-2i-3i^2[/tex]

Apply the imaginary number rule  i² = -1 :

[tex]\implies 8-2i-3(-1)[/tex]

Simplify:

[tex]\implies 8-2i+3[/tex]

[tex]\implies 11-2i[/tex]

Step-by-step explanation:

well, when 2 summed teens are multiplied, every part of one term is multiplied with every part of the other term :

(4 - 3i)(2 + i) = 8 + 4i - 6i - 3i² = 8 - 2i + 3 = 11 - 2i

Total pre-split Market Capitalization is $1,08,125,000.

In mathematics, Multiplication operations perform Multiplying values on either side of the operator.

For example 4×2 = 8

Williams and Co. is splitting their stock at a ratio of 3:1. The pre-split price is $43.25 and the pre-split number of shares is 2.5 million.

Total Value of Shares = $43.25 Share Price × 2.5 × 10⁶ Shares

Total Value of Shares = $1,08,125,000

Let’s say the company’s board decides to approve a 3-for-1 split.

Total Shares = 2.5 × 10⁶ × 3 = 75,00,000

Share Price = $43.25 ÷ 3 = $14.416

Total Value of Shares = $14.416 Share Price × 75,00,000 Shares

Apply the multiplication operation,

Total Value of Shares = $1,08,120,000

Thus, the total pre-split Market Capitalization is $1,08,125,000.

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The number of possible license plates that can be issued using this system is 1757600. Therefore, option B is the correct answer.

Given that, a state offers specialty license plates that contain 3 letters followed by 2 numbers.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

The number of possible license plates

= 26×26×26×10×10

= 1757600

The number of possible license plates that can be issued using this system is 1757600. Therefore, option B is the correct answer.

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The quadratic inequality that will represent the parabola will be

y ≤ 2[tex]x^{2}[/tex] - 8x + 3

The given graph is a parabola where the mouth is open upwards. So from here we can clearly say that the coefficient of [tex]x^{2}[/tex] will be positive.

The vertex of the parabola  is given as (2 , -5) in the graph.

So let us put value of x in the inequations given to us.

first option is

y ≤ 2[tex]x^{2}[/tex] - 8x + 3

y ≤ 2*[tex]2^{2}[/tex] - 8*2 + 3

y ≤ 8 - 16 + 3

y ≤ -5

Therefore the quadratic inequality that will represent the parabola will be

y ≤ 2[tex]x^{2}[/tex] - 8x + 3

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There will be infinite number of states and paths when the state space is (x,y) as the state space (i.e., a set of possible locations for the robot) consists of all possible positions (x, y) in the plane.

The collection of every possible setup for a system is its state space. It is a common abstraction in the study of artificial intelligence and game theory because it can be used to reason about the behavior of a specific system. A state space is typically introduced into a system description without being given any thought to its precise physical meaning. However, it is well known that choosing an appropriate state space representation makes it simpler for us to comprehend or control a system's property.

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Answer:

Step-by-step explanation: I think it could be 5,0000

It a because i told the tese

Answer:

4x+3y=12

Step-by-step explanation:

y=mx+b

m=-4/3,b=4

y=mx+b

y=-4/3x+4

3(y=-4/3x+4)

3y=-4x+12

4x+3y=12

please rate it,thanks.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The final expression of (-2/9)x² - (1/9)x² is (-1/3)x².

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(-2/9)x² - (1/9)x²

Taking out the common.

(-1/9) (2x² + x²)

Adding the like terms.

(-1/9)3x²

-1/9 x (3x²)

(-1/3)x²

Thus,

The final expression of (-2/9)x² - (1/9)x² is (-1/3)x².

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Answer:

125=16t², t²=125/16=√7.8125=2.7951 ,hence t=3secounds

The equation of the line in the slope intercept form is y = (-1/2)x + 60

From the given graph,

Choose two points

(0, 60) and (40, 40)

The slope of the line the change in y coordinates with respect to the change in x coordinate of the function

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the value in the equation

= [tex]\frac{40-60}{40-0}[/tex]

= -20/40

= -1/2

From the graph we can say that,

y intercept of the line = 60

The slope intercept form is

y = mx + b

where m is the slope of the line

b is the y intercept

y = (-1/2)x + 60

Hence, the equation of the line in the slope intercept form is y = (-1/2)x + 60

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By using the rule of 3 we wills ee that the percentage of students who play the trumpet is 20%

We know that there are 150 students in the marching band, that will be our 100% in this case, and we know that 30 of them play the trumpet.

These 30 students represent a percentage X that we want to find, so we can write a little system of equations and use the rule of 3.

30  = X

150 = 100%

Taking the quotient between the two equations we get:

(30/150) = X/100%

Solving for X we get:

(30/150)*100% = X = 20%

So we can say that 20% of the students play the trumpet.

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Answer:

x=2/11 + (1/11) (√15) or 2/11 - (1/11) (√15)

Step-by-step explanation:

Plug it into the quadratic formula

The values of x are 9/11 and -5/11.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

To use the quadratic formula to solve 11x² - 4x = 1.

We first need to rewrite the equation in the form ax² + bx + c = 0.

So,

11x² - 4x - 1 = 0

Now,

We can use the quadratic formula, which states that the solutions for the equation ax² + bx + c = 0.

x = (-b ± √(b² - 4ac)) / 2a

Now,

In our case,

a = 11, b = -4, and c = -1.

Substituting these values into the formula, we get:

x = (-(-4) ± √((-4)² - 4(11)(-1))) / 2(11)

x = (4 ± √(196)) / 22

x = (4 ± 14) / 22

So,

The solutions for the equation 11x² - 4x = 1

x = (4 + 14) / 22 = 9/11

x = (4 - 14) / 22 = -5/11

Therefore,

The values of x are 9/11 and -5/11.

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Answer:

Step-by-step explanation:

Let's say your consecutive numbers are A and B with A+2=B. Using the information we have been given, we can get the linear equation; AB=3B+22. A=B-2, so we can replace A with B-2 to get (B-2)(B)=3(B+22). Multiplying this out, we get B^2-2B=3B+66. Simplifying, we get B^2-5B-66=0. This is a quadratic equation. Using the quadratic formula, we get B=11,-6. B has to be positive, so B=11. A+2=11, so A=9