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)

Pi([tex]\pi[/tex]) is the ratio of circumference to diameter for any circle.

Perimeter is the distance around a circle.

Circumference of circle [tex]C = \pi d[/tex].

Perimeter of circle [tex]= 2 \pi r[/tex]

What is circle ?

A circle is a spherical shape without boundaries or edges.

A circle is a closed, curved object with two dimensions in geometry.

Consider two small arcs AB and CD of two circles of radii x and y units, both of which make an angle of measure θ at the centers P and Q respectively.

For smaller values of θ, the arc length AB is almost equal to the length of the line segment [tex]\bar{AB}[/tex]. Similarly, arc CD ≅ [tex]\bar{CD}[/tex].

Using the SAS rule of triangle similarity, we can say that APB and CQD are similar triangles because their angles are the same and their ratios are AP: PB = CQ: QD = 1: 1. So, it stands to reason that AB: AP = CD: CQ.

Circumference = [tex]\pi \times[/tex] diameter or circumference = 2[tex]\pi \times[/tex] radius if this constant equals some value.

So it was proved.

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Answer:

44.24

Step-by-step explanation:

The 2 in the thousandths place is lower than 5 therefore it does not round the 4 to a 5

Answer:

44.24

Step-by-step explanation:

hopes this helps please mark brainliest

Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

y = 180 -71 = 109

x = 360 - (81+100+71)

x = 360 -252

x = 108

answer is B

x = 108 and y = 109

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The value of X is 108 and the value of y is 109. The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division.

Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

y = 180 -71 = 109

x = 360 - (81+100+71)

x = 360 -252

x = 108

Therefore the value of x and y is x = 108 and y = 109

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The value of k for the expression, 3 (2− k) = −3k + 2, does not exist.

According to the question,

We have the following expression:

3 (2− k) = −3k + 2

Now, we will multiply 3 into the bracket:

6-3k = -3k+2

Now, moving -3k from the left hand side to the right hand side will result in the change of the sign from minus to plus:

6-3k+3k = 2

Now, 3k will get subtracted from 3k. So, we do not have any variable left for this equation.

Hence, the value of k  for the expression, 3 (2− k) = −3k + 2, does not exist.

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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{70\% of 30}}{\left( \cfrac{70}{100} \right)30}\implies 21[/tex]

Answer: 21

Step-by-step explanation:

70% of 30 students is 21

Hope this helped :)

Answer:

80

Step-by-step explanation:

Answer:

x = -2 ; x = 6/5

Step-by-step explanation:

5x + 2 >=0

5x >= -2

5/5 x >= -2/5

x >= -2/5

if x >= -2/5

5x +2 = 8

5x = 8 -2

5x = 6

5/5 x = 6/5

x = 6/5

if x < -2/5

-5x -2 = 8

-5x = 8+2

-5x = 10

-5/-5 x = 10/-5

x = -2

The total 18 numbers such  that n<150 exist, if the sum of the numbers of factors of N and N^2 is 34

Let me give you an example. 12. Both 2- 2 times and 3- 1 times are factors of 12.

Factors in total (2+1)*(1+1)=6

It will have 2- 4 times and 3-2 times for 122.

15 total factors of 5*3

Situation 1: N = xy

attempting a reverse strategy for N*N Factors in 35=5*7 are x-4 times and y-6 times.

Regarding N-x-2 and Y-3 timings.

There are a total of (2+1)*(3+1)=12 factors.

Situation 2

Since N2 has 34 factors if N2 is raised to the power of 34, there are 17 factors for N.

Consequently, 17+1 = 18 factors in total.

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Answer:

15-p

Step-by-step explanation:

15-p

Answer:

thats correct

Step-by-step explanation:

If a baseball diamond is a square that measures 90ft on each side. The  expression for the distance from 2nd base to home plate in square root form isc =√ (90)² + (90)²   and the distance is 127ft.

Using the Pythagoreans theorem formula

c= √ a²+b²

Where:

c = length of hypotenuse

a and b =  length of the sides of the right triangle

Let plug in the formula

c =√ (90)² + (90)²

c =√ 8100 +8100

c =√16200

c = 127.3

c = 127 ft (Approximately)

Therefore the distance is 127ft.

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Answer:

x = 12

Step-by-step explanation:

Angles in a triangle add up to 180 degrees.

This means that 6x - 19 + 3x + 7 + 84 = 180

6x - 19 + 3x + 7 + 84 = 180

==> combine like terms

9x + 72 = 180

==> subtract 72 from both sides

9x = 108

==> divide both sides by 9

x = 12

The time at which Liz will catch up with Mandy is 1 pm.

Here we have to find the time when Mandy and Liz meet.

Let t be the time taken by Liz to meet Mandy

Given:

Speed of Mandy = 30mile/hr

Speed of Liz = 36 miles/hr

Formula:

Speed = Distance/ time

Distance by Mandy = 30t

Distance by Liz = 36( t - 20/60)

As the distance covered by both is the same. So we have

30t = 36( t - 1/3)

6t = 12

t = 2

2 hours past 11 am is 1 pm.

Therefore Liz catch Mandy at 1 pm.

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The probability that a compact car's randomly chosen mpg would be higher than 30 is 0.797.

Given data;

A certain compact car's mpg (miles per gallon) has a mean of 31 and a standard deviation of 1.2 and is regularly distributed.

We need to get the probability that the mpg for a randomly selected compact car would be more than 30.

Therefore;

Mean = μ = 31

Standard deviation = σ = 1.2

Let;

P(X > 30) = P(X - 31/1.2 > 30 - 31/1.2)

               = P(Z > -0.833)

               = 0.797

Hence, the probability that the mpg for a randomly selected compact car would be more than 30 is 0.797.

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It a because i told the tese

The equation of the straight lines are:

For m = 6 and (x1, y1) = (2, 8)  => y = 6x - 4

For m = 7 and (x1, y1) = (2, 10) => y = 7x - 4

We know that the equation of a line with gradient m and y-intercept is:

y = mx + c.

We need to find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.

We know the point-slope form of equation of line,

(y - y1) = m(x - x1)

For m = 6 and (x1, y1) = (2, 8)

(y - 8) = 6(x - 2)

y - 8 = 6x - 12

y = 6x - 4

For m = 7 and (x1, y1) = (2, 10)

(y - 10) = 7(x - 2)

y - 10 = 7x - 14

y = 7x - 4

Therefore,  the equation of the straight lines are:

For m = 6 and (x1, y1) = (2, 8)  => y = 6x - 4

For m = 7 and (x1, y1) = (2, 10) => y = 7x - 4

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In 2267 year, this population would be 400000.

From the question, we have

population is growing as  Pn = 200*(1.03)n

substituting the value, we get

400000 = 200*(1.03)n

2000 = 1.03n

ln(2000) = n*ln(1.03)

n = ln(20000) / ln(1.03)

n = 257.15

2010 + 257.15 = 2267 year , this population would be 400000.

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Answer: the square root of twenty-four would be plotted (A) between 4 and 5, but closer to 5 on a number line.

Step-by-step explanation:

The probability of at least 15% of 100 Indianapolis residents supporting the patriots in gaint match Super Bowl XLVI is 0.293.

By using the normal distribution method, a mean u and standard deviation σ,

The ratio of people who wants the Giants to eat patriots is p = 0.90,

The assumed sample size denoted by n is 100,

and their distribution's mean is u = 0.90,

by using the standard deviation formula is

σ = √(p(1 - p) ÷ n),

σ = √(0.90(1 - 0.90) ÷ 100),

σ = 0.03,

we get that the standard deviation is σ = 0.03

Here the probability that at least 15% of 100 Indianapolis residents encouraged the Patriots in the gaint match  Super Bowl XLVI is

P(X > 0.15) = 1 - P((X - u) ÷ σ) > (0.90 - 0.15) ÷ 0.03))

The significant value of X,

X - u ÷ σ = Z

we get,

P(X > 0.75) = (Z<5)-1

P(X < 0.75) = 1.293 - 1

P(X < 0.75) = 0.293

By solving we get, The probability of at least 15% of 100 Indianapolis residents supporting the patriots in gaint match Super Bowl XLVI is 0.293.

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(i) Relative growth rate, k = 48 million people/ year

(ii) Population in 2020 is given by 5920 million people.

Given that in 1950, the population of world was 2560 million.

In 1960, the population of world was 3040 million people.

Also it is mentioned that,  world population grows in constant relative proportion.

So, the difference between time = 1960 – 1950 = 10 years

The growth in population = 3040 mil – 2560 mil = 480 million

So the relative growth rate of population is = 480/10 = 48 million/year

Now N be the new population, k be the relative population growth rate, all figures in millions. And t be the time in years passes since 1950.

Then the mathematical model is,

N = 2560 + kt

So for 2020, t = 2020-1950 = 70

k = 48

So, N = 2560+48*70 = 5920

So the population in 2020 is 5920 million people.

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Answer: yes, because -2 is the opposite of the leading coefficient

Step-by-step explanation:

The standard error for the sample was 0.13 when "for the 25 students, the standard deviation of grade points was 0.65 and the mean was 2.89."

The standard deviation of a statistic's sampling distribution, or an estimate of that standard deviation, is the statistic's standard error. The term "standard error of the mean" is used when referring to a statistic that is the sample mean. By dividing the standard deviation by the square root of the sample size, the standard error is determined. By taking into account the sample-to-sample variability of the sample means, it provides the precision of a sample mean.

Here,

The standard error=standard deviation/√number of samples

=0.65/√25

=0.65/5

=0.13

When "for the 25 students, the standard deviation of grade points was 0.65 and the mean was 2.89," the standard error for the sample was 0.13.

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Answer:

16(2z-3) or GCF: 16

Step-by-step explanation:

32z-48 has a GFC of 16

16(2z-3)

Answer:

$16(2z-3)

Step-by-step explanation:

Prime factorization:

32: 2*2*2*2*2

48: 2*2*2*2*3

Notice any similarities:

2*2*2*2=16

$32z-$48 = $16(2z-3)

Answer:

One number is 19 and the other is 6

Step-by-step explanation:

25 = x + (x- 13)

25 = x + x - 13

38 = 2x

19 = x

x = 19

25 - 19 = 6

Answer:

(a-5)(a+4)

Step-by-step explanation:

[tex]a^{2}[/tex]-a-20

[tex]a^{2}[/tex]+4a-5a-20

a(a+4) -5(a+4)

(a-5)(a+4)

Answer:

A and D

Step-by-step explanation:

8(6) means 8x6 so that's 48

and 12(4) is the same as 4(12) so that should be simple enough

The probability that the dart lands in centre is = √2-1.

acc to our question-,

hence,The probability that the dart lands in centre is = √2-1.

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