$C(0,3) \\
x_1=0 \\
y_1=3 \\ \\
D(4,7) \\
x_2=4 \\
y_2=7 \\ \\
\overset{\underline{\ \ \ \ }}{CD} =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(4-0)^2+(7-3)^2}= \\
=\sqrt{4^2+4^2}=\sqrt{16+16}=\sqrt{16 \times 2}=4\sqrt{2} \\ \\
\boxed{\overset{\underline{\ \ \ \ }}{CD} = 4\sqrt{2}}$

7 0

3 years ago

Write an equation of the line that passes through (2,-4) and (0,-4)

Arte-miy333 [17]

y = mx + b

To find the slope(m), you use the slope formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

You plug in the points into the equation.

$m = \frac{-4 - (-4)}{0 - 2}$

$m = \frac{-4+4}{0-2} = \frac{0}{-2} =0$

The slope is 0

y = 0x + b

Any number multiplied by 0 is 0. So:

y = b

To find b, you plug in the y value of either of the points.

-4 = b

Your equation is:

y = -4 (This is a horizontal line)

5 0

3 years ago

Which of the following expressions is equivalent to a3 + b3?

lubasha [3.4K]

ANSWER
${a}^{3} + {b}^{3} = (a + b)( {a}^{2 } - ab + {b}^{2} )$

EXPLANATION

To find the expression that is equivalent to
${a}^{3} + {b}^{3}$
we must first expand
${(a + b)}^{3}$
Then we rearrange to find the required expression.

So let's get started.

${(a + b)}^{3} = (a + b) {(a + b)}^{2}$

We expand the parenthesis on the right hand side to get,

${(a + b)}^{3} = (a + b) ( {a}^{2} + 2ab + {b}^{2} )$

We expand again to obtain,

${(a + b)}^{3} = {a}^{3} + 3 {a}^{2}b + 3a {b}^{2} + {b}^{3}$

Let us group the cubed terms on the right hand side to get,

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3 {a}^{2}b + 3a {b}^{2}$

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab (a+ b)$

We make the cubed terms the subject,

${(a + b)}^{3} - 3ab (a+ b) = {a}^{3} + {b}^{3}$

We factor to get,

$(a + b)({(a + b)}^{2} - 3ab ) = {a}^{3} + {b}^{3}$

We expand the bracket on the left hand side to get,

$(a + b)( {a}^{2} + 2ab + {b}^{2} - 3ab ) = {a}^{3} + {b}^{3}$

We finally simplify to get,

$(a + b)( {a}^{2} - ab + {b}^{2} ) = {a}^{3} + {b}^{3}$

5 0

3 years ago

Read 2 more answers

First five common multiples of 7and 20

gulaghasi [49]

The first 5 Multiples of 7 are 35, 70, 105, 140, 175
The first 5 Multiples of 20 are: 20, 40, 60, 80, 100

4 0

3 years ago