Which statement must be true if APQR = ASTU?

Answers

Answer 1

Answer:

(a) [tex]PQ \sim ST[/tex]

Step-by-step explanation:

Given

See attachment

Required

Which must be true

[tex]\triangle PQR \simeq \triangle STU[/tex] implies that:

The following sides are corresponding

[tex]PQ \sim ST[/tex]

[tex]PR \sim SU[/tex]

[tex]QR \sim TU[/tex]

The following angles are corresponding

[tex]\angle P \sim \angle S[/tex]

[tex]\angle Q \sim \angle T[/tex]

[tex]\angle R \sim \angle U[/tex]

From the given options, only option (a) is true because:

[tex]PQ \sim ST[/tex]

Which Statement Must Be True If APQR = ASTU?

Related Questions

Find area and perimeter of shaded regions below

Answers

Answer:

Step-by-step explanation:

ABCD is a square.

side = 24 cm

Area of square = side  * side = 24 * 24 = 576 cm²

Semicircle:

d = 24 cm

r = 24/2 = 12 cm

Area of semi circle =πr²

                               = 3.14 * 12 * 12

                               = 452.16 cm²

Area of shaded region = area of square - area of semicircle  + area of semicircle

  = 576  - 452.16 + 452.16

  = 576 cm²

Perimeter:

Circumference of semicircle = 2πr

               = 2 * 3.14 * 12

               = 75.36

Perimeter = 2* circumference of semicircle + 24 + 24

                = 2 * 75.36 + 24 + 24

                = 150.72 + 24 + 24

                 = 198.72 cm

Is 3.6 a integer or a whole number?

Answers

36 is a whole number.

Answer:

The number 3.6 is a rational number.

All numbers that can be represented as fractions made of two integers (whole numbers) are considered to be

When it was built, the given stadium held 31,080 fans per game. Today, it holds 86,047. How many more fans could attend per year (12 games) compared to the year it was built?

Answers

Answer:

659604 students

Step-by-step explanation:

86047-31080=54967 more students per game

54967 students per game x 12 games = 659,604 students

It used to take 20 hours to get to Los Angeles, now it takes 12 hours, how much shorter was it?​

Answers

Step-by-step explanation:

It takes 20 Hours to get to Los Angeles

Now it takes 12 hours....

Therefore we subtract 20 from 12

which becomes

20 - 12= 8.

So it's 8 hours shorter

I’m the triangle shown we can find the angle theta as follows.

Answers

Answer:

sin = opp/hyp

cos = adj/hyp

tan = opp/adj

log, (x + y)=log, y, log, x .
Solve for question D only

Answers

Answer:

4.

Step-by-step explanation:

Change of base formula is

logb x = loga x / loga b

So logx 25 = log5 25 /log5 x

Now log5 25 = log5 5^2 = 2, so:

logx 25 = 2 / log5 x

So log5 x^2 * logx 25

= log5 x^2 * 2 /log5 x

= 2 log5 x * 2 / log5 x

= 4.

Put 1.09, 1.0, 1.9, 1.19, 1.1 on a number line in order?

Answers

Answer:

1.0, 1.09, 1.1, 1.19, 1.9

Step-by-step explanation:

Basic ordering of decimals

For each of the following angles, assume that the terminal ray of the angle opens up in the counter-clockwise direction. A circle with a radius 7 cm long is centered at Angle A's vertex, and Angle A subtends an arc length of 9.8 cm along this circle. The subtended arc is how many times as long as the circle's radius

Answers

9514 1404 393

Answer:

  1.4

Step-by-step explanation:

We want to find the multiplier n such that ...

  arc length = n × radius

  n = arc length / radius = (9.8 cm)/(7 cm)

  n = 1.4

The subtended arc is 1.4 times as long as the circle's radius.

Jordan buys sandals and sunglasses for a trip to the beach. The sunglasses cost $6. The sandals cost 3 times as much as the sunglasses. How much do the sandals cost?

Answers

We know that the sunglasses cost $6, and the sandals are 3 times as much. We can multiply 6*3 to get 18. The sandals cost $18.

Answer:

18 dollars

Step-by-step explanation:

sunglasses = 6 dollars

sandals = 3 * sunglasses

             = 3 * 6 dollars

             = 18 dollars

Which line segment has the same measure as ST?

RX
TX
SR
XS

Answers

Answer:

The answer is Line Segment SR.

Graph the equation
y = 5x
Use the graphing tool to graph the line.

Answers

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

You want a line that goes through (0, 0) and has a slope of 5. That means it will also go through (1, 5) and (2, 10), for example. I like the attached graphing tool because it will draw the graph directly from the equation.

The weight of an object above the surface of the Earth varies inversely with the square of the
distance from the center of the Earth. If a body weighs 50 pounds when it is 3,960 miles from
Earth's center, what would it weigh if it were 4,015 miles from Earth's center?

Answers

Answer:

weight =48.71228786pounds

Step-by-step explanation:

[tex]w = \frac{k}{ {d}^{2} } \\ 50 = \frac{k}{ {3960}^{2} } \\ \\ k = 50 \times {3960}^{2} \\ k = 50 \times 15681600 \\ k = 784080000 \\ \\ w = \frac{784080000}{ {d}^{2} } \\ w = \frac{784080000}{16120225} \\ \\ w = 48.71228786 \\ w = 48.7pounds[/tex]

If a body weighs 50 pounds when it is 3,960 miles from Earth's center, it would weigh approximately 48.547 pounds if it were 4,015 miles from Earth's center, according to the inverse square law formula.

We know the inverse square law formula:

W₁ / W₂ = D²₂ / D²₁

Where W₁ is the weight of the body at the initial distance D₁, and W₂ is the weight at the final distance D₂.

So we have,

W₁ = 50

D₁  = 3,960

D₂  = 4015

We know that the body weighs 50 pounds when it is 3,960 miles from Earth's center,

So we can plug in those values as follows:

50 / W₂ = (4,015)²/ (3,960)²

To solve for W₂, we can cross-multiply and simplify as follows:

W₂ = 50 x (3,960)² / (4,015)²

W₂ = 50 x 15,681,600 / 16,120,225

W₂ = 48.547 pounds (rounded to three decimal places)

Therefore, if the body were 4,015 miles from Earth's center, it would weigh approximately 48.547 pounds.

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Consider the probability that no more than 28 out of 304 students will not graduate on time. Choose the best description of the area under the normal curve that would be used to approximate binomial probability.

a. Area to the right of 27.5
b. Area to the right of 28.5
c. Area to the left of 27.5
d. Area to the left of 28.5
e. Area between 27.5 and 28.5

Answers

Solution :

Here the probability that exactly 28 out of 304 students will not graduate on time. That is

P (x = 28)

By using the normal approximation of binomial probability,

[tex]$P(x=a) = P(a-1/2 \leq x \leq a+1/2)$[/tex]

∴ [tex]$P(x=28) = P(28-1/2 \leq x \leq 28+1/2)$[/tex]

                   [tex]$=P(27.5 \leq x \leq 28.5)$[/tex]

That is the area between 27.5 and 28.5

Therefore, the correct option is (e). Area between 27.5 and 28.5

Complete the equation describing how
x and y are related.
5
1 2 3 4
8 13 18
-2
3
23
28
y = 5x + [?]
Enter the answer that belongs in [?].

Answers

Answer:

y=5x+3

Step-by-step explanation:

The equation of line is y=5x+3 since the y intercept is 3

Which statements can be used to compare the characteristics of the functions? Select three options.

Answers

Answer:

Step-by-step explanation:

g(x) has the smallest minimum value. All three functions share the same domain and the y-intercept is also the same for all three thus options (C),(D), and (E) is correct.

What is a graph?

A graph is a diametrical representation of any function between the dependent and independent variables.

For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.

As per the given table,

The minimum value among all functions is -204 which is for g(x).

The domain is the set of x since all function defines the same x thus they have the same domain.

At y-intercept x = 0

Since at x = 0 all function is 3 thus all three will have the same y-intercept.

Hence "The smallest minimal value is for g(x). The y-intercept for all three functions is the same, and all three functions have the same domain".

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Please Help!
Use the function f(x) to answer the questions

f(x) = 5x^2 + 2x - 3

Part A: What are the x-intercepts of the graph of f(x)? Show your work (5 points)

Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show

your work (5 points)

Part 2: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph (5 points)

Answers

9514 1404 393

Answer:

  A: -1, 3/5

  B: (-1/5, -3 1/5)

  2: plot the given points and draw a curve through them.

Step-by-step explanation:

Part A

The x-intercepts are most easily found from a graph of the function. I like the Desmos graphing calculator for this purpose. The x-intercepts are -1 and 3/5.

You can also find the x-intercepts by factoring the function.

  f(x) = 5x^2 +5x -3x -3 = 5x(x +1) -3(x +1) = (5x -3)(x +1)

The x-intercepts are the values of x that make the factors zero:

  5x -3 = 0   ⇒   x = 3/5

  x +1 = 0   ⇒   x = -1

__

Part B

The vertex is on the axis of symmetry, which is the vertical line at the value of x halfway between the zeros. (-1 +3/5)/2 = (-2/5)/2 = -1/5

The value of f(x) there is ...

  f(-1/5) = (5(-1/5) +2)(-1/5) -3 = (-1 +2)(-1/5) -3 = -1/5 -3 = -3 1/5

The vertex is (-1/5, -3 1/5).

__

Part 2

The easiest step to take to graph the function is to type it into a graphing calculator (see attached).

If you're graphing this by hand, the three points given in parts A and B will be on the graph. The leading coefficient in the function is 3, so the x^2 parent function is vertically stretched by a factor of 3. This can make it a little more difficult to find points that lie on the graph.

Recognizing that the vertex form equation is ...

  f(x) = 3(x +1/5) -3 1/5

I might choose x-values that are -1/5 ± 1/2 to get y-values that are -3 1/5 + 3/4. And, x = -1/5 ± 1 ⇒ y = -3 1/5 +3.

A cone and a pyramid have equal heights and volumes. If the base area of the pyramid is 154cm^2, find the radius of the cone

Answers

Answer:

√154/π

Step-by-step explanation:

thể tích nón = thể tích hình chóp

1/3πr².h=1/3S.h

πr²=154(rút gọn h và 1/3)

=> r=√154/π

The radius of the cone is 7 cm if the cone and a pyramid have equal heights and volumes.

What is a cone?

It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.

[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]

We have:

A cone and a pyramid have equal heights and volumes.

154 = πr²

π = 22/7

r = 7 cm

Thus, the radius of the cone is 7 cm if the cone and a pyramid have equal heights and volumes.

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I really need the help please and thank you

Answers

Asnwer: C

-------------------------------------

Which graph represents the solution set for the quadratic inequality x2 + 2x + 1 > 0?

Answers

You need to sole for o and you will get x4 and the graph

howdy!!

yr answer is the third graph!

I need help in understanding and solving quadratic equations using the quadratic formula

x^2+8x+1=0​

Answers

Answer:

Exact Form: -4⊥√15

Decimal Form:

0.12701665

7.87298334

Form a polynomial whose zeros and degree are given.
Zeros: - 2, 2, 6; degree: 3
Type a polynomial with intéger coefficients and a leading coefficient of 1 in the box below.
f(x)=(Simplify your answer.)

Answers

Answer:

[tex]f(x) = (x + 2)(x - 2)(x - 6)[/tex]

[tex]f(x) = ({x}^{2} + 4)(x - 6)[/tex]

[tex]f(x) = {x}^{3} - 6 {x}^{2} + 4x - 24[/tex]

Step-by-step explanation:

Multiply factors.

Given the function f(x) = 3x - 1, explain how to find the average rate of change between x = 1 and x = 4.

Answers

Step-by-step explanation:

f(1) = 3×1 - 1 = 2

f(4) = 3×4 - 1 = 12-1 = 11

so, the functional value changes 11-2=9 units on an x interval of 4-1=3 units length.

the average change rate is the total change across the x interval relative to the interval length.

that is

9/3 = 3

which is the slope (= the factor of x) in the line equation.

for a line its change rate for any point is the same constant. and that is therefore automatically also the average change rate across an interval of x values.

if the change rate would be different for different parts of the function, it would not be a straight line.

Answer:

3

Step-by-step explanation:

The average rate of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Here [ a, b ] = [ 1, 4 ] , then

f(b) = f(4) = 3(4) - 1 = 12 - 1 = 11

f(a) = f(1) = 3(1) - 1 = 3 - 1 = 2

average rate of change = [tex]\frac{11-2}{4-1}[/tex] = [tex]\frac{9}{3}[/tex] = 3

Find the other endpoint of the line segment with the given endpoint (-2, -2) and midpoint (3,10)

Answers

9514 1404 393

Answer:

  (8, 22)

Step-by-step explanation:

For endpoints A and B, and midpoint M, the relationship of interest is ...

  B = 2M -A

  B = 2(3, 10) -(-2, -2) = (6+2, 20+2)

  B = (8, 22)

The other end point is (8, 22).

What does 1.20 mean in this situation?

Answers

Answer:

hshsjzhzzoazuhsox9 hzbskznzjzbziznzkalajhzisjshaoianajs9zjgz

A: the costumer bought 1.20kg of lettuce

2x + 5y = 10 into slope- intercept form

Answers

Answer:

y=-2x+10

Step-by-step explanation

Hope this helped

a farmer produced 47581 2 oranges of one kind and 651 65 oranges of another kind He mixed these oranges and packed in 296 boxes how many oranges did he pack in a box?​

Answers

Step-by-step explanation:

I am not sure the scanning of the text went well, as this has some strange gaps in the numbers.

I understand that we have 475812 oranges of one type and 65165 oranges of another type.

we have no information, if these types of oranges have significantly different sizes or weight. so, we have to assume that they are reasonably equal to each other.

therefore, the "different type" statement is just to confuse us. the text could have also said that these were 2 different truck loads of the same type.

we only need to deal with the total number of oranges.

so,

475812 + 65165 = 540977 total oranges

he packs them into 296 boxes.

that makes

540977 / 296 = 1827.625 oranges per box.

these are many oranges for one box in real life.

and it is not a round number, which is strange for a home work or test question if this type.

if the farmer truly put only the same number of oranges in every box, he would have

540977 - 1827×296 = 540977 - 540792 = 185

oranges left over.

in any case, these are all signs that there was probably something wrong with the text. but you see the principle up there. please do the same thing with the real numbers.

Numbers of one kind oranges=475812

No of other kind oranges=65165

Total oranges

[tex]\\ \sf\longmapsto 475812+65165=540977[/tex]

Total boxes=296

Oranges per box:-

[tex]\\ \sf\longmapsto \dfrac{540977}{296}=1827.6[/tex]

[tex]\\ \sf\longmapsto 1827(Approx)[/tex]

Một cuộc điều tra tại một đô thị cho kết quả: 20% dân số dùng một loại sản phẩm A, 50% dân số
dùng một loại sản phẩm B, 15% dân số dùng cả hai loại A và B. Chọn ngẫu nhiên một người dân
trong đô thị đó, tìm xác suất để:
a. Người đó dùng sản phẩm A hoặc B.
b. Người đó không dùng sản phẩm A cũng không dùng sản phẩm B.
c. Người đó chỉ dùng đúng một trong hai loại sản phẩm A hoặc B.
d. Người đó chỉ dùng duy nhất sản phẩm A.

Answers

A, and make it more clearer.some people can’t read it

multiply 725base 9× 367base 9​

Answers

Answer:

Hello,

Answer 303028

Step-by-step explanation:

Multiplication in base 9

[tex]\begin{array}{cccccc}9^5&9^4&9^3&9^2&9^1&9^0\\--&--&--&--&--&--\\&&&7&2&5\\&&&3&6&7\\--&--&--&--&--&--\\&&5&5&8&8\\&4&7&6&3&\\2&3&7&6&&\\--&--&--&--&--&--\\3&0&3&0&2&8\end{array}[/tex]


rewrite -4<x<-1 using absolute value sign​

Answers

[tex] - | 4 | < x < - |1| [/tex]

dunno if that's the desired form tough, but it states the same definition

The given inequality rewritten using absolute value sign​ as |-4|<x<|-1|.

What are inequalities?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is -4<x<-1.

An absolute value inequality is an expression with absolute functions as well as inequality signs.

Here, using absolute value sign​ we get

|-4|<x<|-1|

Therefore, the given inequality rewritten using absolute value sign​ as |-4|<x<|-1|.

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1km make how many cm​

Answers

Answer:

100000

Step-by-step explanation:

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