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2 years ago

What is the factor to dilate triangle ABC to get A'B'C'? (Write your answer below. Show your work for partial credit.)

Mathematics

1 answer:

marusya05 [52]2 years ago

6 0

Answer:

The Factor is 1.5

Step-by-step explanation:

5.1(which is B'C') divided by 3.4(which is BC) = 1.5

3.6(A'C') divided by divided by 2.4(AC) = 1.5

2.7(A'B') divided by 1.8(AB) = 1.5

Henceforth the factor is 1.5

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andrey2020 [161]

First observe that if $a+b>0$ ,

$(a + b)^2 = a^2 + 2ab + b^2 \\\\ \implies a + b = \sqrt{a^2 + 2ab + b^2} = \sqrt{a^2 + ab + b(a + b)} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}$

Let $a=0$ and $b=x$ . It follows that

$a+b = x = \sqrt{x \sqrt{x \sqrt{x \sqrt{\cdots}}}}$

Now let $b=1$ , so $a^2+a=4x$ . Solving for $a$ ,

$a^2 + a - 4x = 0 \implies a = \dfrac{-1 + \sqrt{1+16x}}2$

which means

$a+b = \dfrac{1 + \sqrt{1+16x}}2 = \sqrt{4x + \sqrt{4x + \sqrt{4x + \sqrt{\cdots}}}}$

Now solve for $x$ .

$x = \dfrac{1 + \sqrt{1 + 16x}}2 \\\\ 2x = 1 + \sqrt{1 + 16x} \\\\ 2x - 1 = \sqrt{1 + 16x} \\\\ (2x-1)^2 = \left(\sqrt{1 + 16x}\right)^2$

(note that we assume $2x-1\ge0$ )

$4x^2 - 4x + 1 = 1 + 16x \\\\ 4x^2 - 20x = 0 \\\\ 4x (x - 5) = 0 \\\\ 4x = 0 \text{ or } x - 5 = 0 \\\\ \implies x = 0 \text{ or } \boxed{x = 5}$

(we omit $x=0$ since $2\cdot0-1=-1\ge0$ is not true)

3 0

1 year ago

HELP HELP HELP HELP

Harrizon [31]

Answer:

62.8cubic units

Step-by-step explanation:

volume of a cylinder isπ×radius×radius×height.hope it helps.

4 0

2 years ago

Which relation is a direct variation that contains the ordered pair (2, 7)?

Tasya [4]

Lets write equation of a function:

y = kx + n

Direct variation in simple is equation of a line which has n=0 or in other words which y to x ratio is k.

First option gets 7=7 but it isnt direct variation because n is not equal to 0

third option is indeed correct. once we implement coordinates (2,7) we get 7=7

Answer is
y = 7/2x

8 0

2 years ago

What is the lowest common denominator of the following set of fractions: 1/6 , 13/27 , 4/5 , 3/10 , 2/5 ?

Serga [27]

Answer:

LCD = 270

Equivalent Fractions with the LCD

1/6 = 45/270

13/27 = 130/270

4/5 = 216/270

3/10 = 81/270

2/5 = 108/270

3 0

2 years ago

Round 48.079 to the nearest tenth. A:48.08 B:48.8 C:50 D:48.1

tatiyna

Answer:

48.1

Step-by-step explanation:

Seven rounds up.

Hope this helped! :)

3 0

2 years ago

Read 2 more answers