Mr.Williams drew
△
A
B
C
on a coordinate grid and asked his students to determine the transformations that will result in a transformed figure
△
A
`
B
`
C
`
such that
△
A
`
B
`
C
`
is similar but NOT congruent to
△
A
B
C
.
Two student responses are shown below.



Student 1: Reflect
△
A
B
C
across the y-axis and then dilate it by a scale factor of 1 with the center of dilation at the origin.

Student 2: Dilate
△
A
B
C
by a scale factor of 2 and the center of dilation at the origin and then reflect it across the x-axis.



Which statement is true?

A.
Neither student 1 nor student 2, because dilations and reflections preserve both side lengths and angle measures.

B.
Both student 1 and student 2, because dilations and reflections preserve angle measures but not side lengths.

C.
Only student 2, because dilations preserve angle measures and side lengths are proportional.

D.
Only student 1, because this dilation preserves angle measures and side lengths.

Answer:

70

Step-by-step explanation:

she burns 250 calories per hour .to burn 3500 calories and shed 1 pound she has to work 14 hours and to shed 5 pounds she has to work 14×5=70 hours

Hope this helps!! :)))))))

Answer:

[tex]6 \sqrt{5} [/tex]

Step-by-step explanation:

Take out Square root 5 as common and then add numbers

[tex]4 \sqrt{5} + 2 \sqrt{5} \\ 6 \sqrt{5} [/tex]

Answer:

We reach at 8.

Step-by-step explanation:

The starting point is 2 .

Jump at the six places, the final point reaches at 8, so the point is 8.

A survey is conducted in order to collect a piece of specific information. The number of people that can be considered as a sample for the given population is 320.

A survey is conducted in order to collect a piece of specific information from a group of people chosen from the entire population who denotes the entire population for those questions.

Given the population consist of 3200 people, therefore, the number of people that can be considered as a sample for the given population is 320.

Learn more about Survey:

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Answer:

i)

Odd numbers:

P(odd and odd) = 3/6*3/6 = 1/4

ii)

Total outcomes:

Sum of 8:

Sum of 12:

P(8 or 12) = 5/36 + 1/36 = 6/36 = 1/6

iii)

Prime numbers:

Odd numbers:

P(prime or odd) = 3/6*3/6 + 3/6*3/6 = 1/4 + 1/4 = 1/2

Answer:

20×10=200mm

70:200

70/10=7

200/10=20

7:20 is your answer in it's simplest form

Answer:

D   (0, 3)

Step-by-step explanation:

To go from B (8, 3) to C (3, 8)

subtract 5 from x, add 5 to y

A (5, -2)

subtract 5 from x,   x = 0

add 5 to y,   y = 3

D (0, 3)

Answer:

Area = 97.4 cm²

Step-by-step explanation:

a = 15 cm

        [tex]Area = \frac{ \sqrt 3}{4} a^2\\[/tex]

                 [tex]=\frac{\sqrt 3}{ 4 } \times 15^2\\\\=\frac{\sqrt 3}{ 4 } \times 225\\\\= 97.4 \ cm^2[/tex]

Answer:

[tex] { ({x}^{2}. {y}^{6} )}^{ \frac{1}{8} } \\ {x}^{2 \times \frac{1}{8} } . {y}^{6 \times \frac{1}{8} } \\ = {x}^{ \frac{2}{8} } . {y}^{ \frac{6}{8} } \\ = {x}^{ \frac{1}{4} } . {y}^{ \frac{3}{4} } [/tex]

It has been shown that [tex]3P_{n} =T_{3n-1}[/tex], [tex]3P_{n} =T_{3n-1}[/tex] and hence [tex]3P_{n} =T_{3n-1}[/tex].

Given: [tex]T_{n}[/tex] is the nth triangular number. [tex]Q_{n}[/tex] is the nth square number. [tex]P_{n}[/tex] is the nth pentagonal number.

To show:

Triangular numbers are numbers formed by addition of consecutive natural numbers starting from 1. Square numbers are numbers formed by squaring natural numbers. Pentagonal numbers are numbers formed by distinct dots in a pattern of dots consisting of the outlines of regular pentagons with sides up to n dots, when the pentagons are overlaid so that they share one vertex.

The formula for each of them is given by:

[tex]T_{n}=\frac{n(n+1)}{2}[/tex]

[tex]Q_{n}=n^{2}[/tex]

[tex]P_{n}=\frac{3n^{2}-n}{2}[/tex]

(a).

Now, put [tex]n=3n-1[/tex] in [tex]T_{n}=\frac{n(n+1)}{2}[/tex] to get,

[tex]T_{3n-1}=\frac{(3n-1)(3n)}{2}[/tex]

[tex]T_{3n-1}=3\frac{n(3n-1)}{2}[/tex]

[tex]T_{3n-1}=3\frac{3n^{2}-n}{2}[/tex]

Put [tex]P_{n}=\frac{3n^{2}-n}{2}[/tex] in [tex]T_{3n-1}=3\frac{3n^{2}-n}{2}[/tex] to get,

[tex]T_{3n-1}=3P_{n}[/tex]

So, [tex]3P_{n}=T_{3n-1}[/tex]

(b).

Now,

[tex]P_{n}-Q_{n}=\frac{3n^{2}-n}{2}-n^{2}[/tex]

[tex]P_{n}-Q_{n}=\frac{3n^{2}-n-2n^{2}}{2}[/tex]

[tex]P_{n}-Q_{n}=\frac{n^{2}-n}{2}[/tex]

Put [tex]n=n-1[/tex] in [tex]T_{n}=\frac{n(n+1)}{2}[/tex] to get,

[tex]T_{n-1}=\frac{(n-1)(n-1+1)}{2}[/tex]

[tex]T_{n-1}=\frac{(n-1)n}{2}[/tex]

[tex]T_{n-1}=\frac{n^{2}-n}{2}[/tex]

Comparing [tex]P_{n}-Q_{n}=\frac{n^{2}-n}{2}[/tex] and [tex]T_{n-1}=\frac{n^{2}-n}{2}[/tex], we get,

[tex]P_{n}-Q_{n}=T_{n-1}[/tex]

Now, put [tex]n=3n[/tex] in [tex]P_{n}-Q_{n}=T_{n-1}[/tex] to get,

[tex]P_{3n}-Q_{3n}=T_{3n-1}[/tex]

As shown in part (a), [tex]T_{3n-1}=3P_{n}[/tex]

Put [tex]T_{3n-1}=3P_{n}[/tex] in [tex]P_{3n}-Q_{3n}=T_{3n-1}[/tex] to get,

[tex]P_{3n}-Q_{3n}=3P_{n}[/tex]

[tex]P_{3n}-3P_{n}=Q_{3n}[/tex]

So, [tex]P_{n}-Q_{n}=T_{n-1}[/tex] and hence [tex]P_{3n}-3P_{n}=Q_{3n}[/tex]

Learn more about these kinds of numbers here:

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Answer:

[tex]a_{n}[/tex] = 2n + 5

Step-by-step explanation:

There is a common difference between consecutive terms, that is

9 - 7 = 11 - 9 = 13 - 11 = 15 - 13 = 2

This indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 7 and d = 2 , then

[tex]a_{n}[/tex] = 7 + 2(n - 1) = 7 + 2n - 2 = 2n + 5

Answer:

Step-by-step explanation:

The diagonals of a rhombus divides it into four congruent right triangles.  Each triangle is a mirror image of the adjacent.

Therefore angle 2 is the alternate interior angle of 57°, and angle 3 is the mirror image, so also 57°.

Angles 1 is the complement of angle 3, and angle 4 is equal to the complement of angle 2 , so both equal 90-57 = 33°.

To summarize,

angle 1 = 33°

angle 2 = 57°

angle 3 = 57°

angle 4 = 33°

Answer:

90=30+(x+10). remove blanket

90=30+x+10. correct like terms

90=30+10+x

90=40+x. 40 will cross the = and change from +ve to -ve sign

90-40=x.

therefore

x=40

Answer:

x = 50

Step-by-step explanation:

The 2 angles sum to 90° , that is

x + 10 + 30 = 90

x + 40 = 90 ( subtract 40 from both sides )

x = 50

Answer:

5/7 or 0.71 is the answer

Answer:

40

Step-by-step explanation:

The first step is to calculate the base area of the prism

= 15×30

= 450

The volume is then calculated as follows

= 450×h

= 450h

The capacity is 18 liters

= 18×1000

= 18,000

Therefore the height of the rectangular prism can be calculated as follows

450h= 18,000

h= 18,000/450

= 40

Hence the height is 40 cm

Answer:i honestly dont know just trying to get points

Step-by-step explanation:

Answer:

your will becanswer $95.00

Answer:

105

Step-by-step explanation:

instalment time 10 months

so from 1050÷10

105 ans

Answer:

positive charge...............

Answer: one solution

this is all i know

Answer:

D

Step-by-step explanation:

Given

1 - [tex]\frac{1}{2}[/tex] (6x - 4) = 3(1 - x) ← distribute parenthesis on both sides

1 - 3x + 2 = 3 - 3x

3 - 3x = 3 - 3x

Since both sides of the equation are the same , then

This indicates the equation has infinitely many solutions.

Answer:

5 dollors i just tookthe test 4

Step-by-step explanation:

Arianna bought 0 bags of oranges. It's possible that she may have bought other items along with the oranges or there might be a pricing discrepancy.

To find out how many oranges Arianna bought, we can use the given price of a bag of 4 oranges and the total amount she spent on oranges.

Let's set up a proportion:

Price of a bag of 4 oranges = $2.84

Amount Arianna spent on oranges = $3.55

Let "x" be the number of bags of oranges Arianna bought.

Since each bag contains 4 oranges, the total number of oranges she bought is 4 times the number of bags (4x).

Now, we can set up the proportion:

(Price of a bag of 4 oranges) / (Amount spent on oranges) = (Number of bags bought) / 4x

$2.84 / $3.55 = 1 / 4x

To solve for "x," cross-multiply:

$2.84 * 4x = $3.55 * 1

11.36x = 3.55

Now, solve for "x":

x = 3.55 / 11.36

x ≈ 0.3125

Since we can't buy a fraction of a bag, we round the value of "x" to the nearest whole number:

x ≈ 0 (rounded to the nearest whole number)

So, Arianna bought 0 bags of oranges. It's possible that she may have bought other items along with the oranges or there might be a pricing discrepancy.

To know more about oranges:

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Answer:

Y is equal to 2

Step-by-step explanation:

X equals -8

So,

4(-8) + 9y = -14

-32 + 9y = -14

-32 + 32 + 9y = -14 + 32

9y = 18

1/9 × 9y = 18 × 1/9

y = 2

Answer:

$27.00

Step-by-step explanation:

We first have to start at the base value of $45.00, as without that, we have nothing to go off of. We can work right to left because we start at the rightmost point of the problem.

Therefore, we start with finding 9/10 of 45.00 . This is as simple as multiplying 9/10 with 45.00, resulting in 40.5

To figure out a percentage relative to real numbers, we first have to turn that percentage into a fraction or decimal. To turn it into a decimal, we simply divide by 100, and 66 2/3 divided by 100 is roughly 0.6666 , or 2/3 . Multiplying our result of 40.5 by this, we get $27.00 as our answer.

Answer:

D

Step-by-step explanation:

Answer:

295/72

Step-by-step explanation:

Answer:

use the pythagorean theorem

Step-by-step explanation:

a²+b²=c²

Hope this may help you ☺

Answer:

3.78 × [tex]10^{2}[/tex] = 378

Step-by-step explanation:

Answer:

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