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3 years ago

How did the Punic Wars change the population of the cities of Rome?

1 answer:

6 0

People moved to the cities to escape war. Some people had left the countryside to work in the arms industry and some had left for Rome looking for subsistence. Rome became the most populous city in Europe and West Asia.

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Triangle ABC was dilated by 50%. What is the relationship between AC and A'C'?

Elina [12.6K]

Answer:

The length of segment AC is two times the length of segment A'C'

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Let

z ----> the scale factor

A'C' ----> the length of segment A'C'

AC ----> the length of segment AC

$z=\frac{A'C'}{AC}$

we have that

$z=50\%=50/100=\frac{1}{2}$ ---> the dilation is a reduction, because the scale factor is less than 1 and greater than zero

substitute

$\frac{1}{2}=\frac{A'C'}{AC}$

$AC=2A'C'$

therefore

The length of segment AC is two times the length of segment A'C'

5 0

3 years ago

Read 2 more answers

(-3c+6) + (-c+8) simplify with a step by step please

mel-nik [20]

Step-by-step explanation:

$= ( - 3c + 6) + ( - c + 8)$

$= - 3c + 6 - c + 8$

$= - 3c - c + 6 + 8$

= -4c + 14

hence -4c + 14 is the answer ...

hope it helped !!

6 0

2 years ago

Write 3x^2-18x-6 in vertex form

Vedmedyk [2.9K]

The standard form of a quadratic equation is $\displaystyle{ y=ax^2+bx+c$ , while the vertex form is:

$y=a(x-h)^2+k$ , where (h, k) is the vertex of the parabola.

What we want is to write $\displaystyle{ y=3x^2-18x-6$ as $y=a(x-h)^2+k$

First, we note that all the three terms have a factor of 3, so we factorize it and write:

$\displaystyle{ y=3(x^2-6x-2)$ .

Second, we notice that $x^2-6x$ are the terms produced by $(x-3)^2=x^2-6x+9$ , without the 9. So we can write:

$x^2-6x=(x-3)^2-9$ , and substituting in $\displaystyle{ y=3(x^2-6x-2)$ we have:

$\displaystyle{ y=3(x^2-6x-2)=3[(x-3)^2-9-2]=3[(x-3)^2-11]$ .

Finally, distributing 3 over the two terms in the brackets we have:

$y=3[x-3]^2-33$ .

Answer: $y=3(x-3)^2-33$