There are 114 pencils in the drawer. Jessica placed 117 more pencils in the drawer. How many pencils are now there in all?

A country's population in 1995 was 65 million. In 1998 it was 69 million. Estimate the population in 2006 using the exponential

LenKa [72]

80 million. 2001= 73 million. 2004=77 billion. 2007=81 million. Take away a year, maybe take away one million.

3 0

3 years ago

Read 2 more answers

Find the equation of the line that passes through (0, -3) and is parallel to

Tresset [83]

Hey there!

$\\$

Answer:

$\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}$

$\\$

Explanation:

To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.

Let the line that we are trying to determine its equation be $\: \sf{d_1} \:$ and the line that is parallel to $\: \sf{d_1} \:$ be $\: \sf{d_2} \:$ .

$\sf{d_2} \:$ passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:

$\sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}}$

$\\$

⇒Subtitute the values :

$\sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )}$

$\implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}$

$\sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}}$ .

Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:

Slope-Intercept Form:

$\sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \: the \: line \: and \: b \: is \: the \: y-intercept.}$

$\implies \sf{y = \bold{\dfrac{7}{6}}x + b}$ $\\$

We know that the coordinates of the point (0 , -3) verify the equation since it is on the line $\: \sf{d_1} \:$ . Now, replace y with -3 and x with 0:

$\implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Therefore, the equation of the line $\: \bold{d_1} \:$ is $\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}$

$\\$

▪️Learn more about finding the equation of a line that is parallel to another one here:

↣brainly.com/question/27497166

8 0

2 years ago

Read 2 more answers

Bernard typically runs x km/hour. While he was sick, he only ran 41. 5 km/hour. What equation represents that the difference in

dedylja [7]

Oh man this is complicated

6 0

3 years ago

Read 2 more answers

Is c^5 - 49 a difference of squares? <br> a. yes<br> b. no

gogolik [260]

No. Since we cannot factor,

$c^5-49$ .

Hope this helps.

r3t40

4 0

3 years ago

Sarah is making flower bouquets that she will put in 10 vases. She will put 15 roses and some lilies in each vase. Which express

lesya [120]

Let, the number of Lilies in each vase = x
Then, expression would be: 10(15+x)
150+10x

So, final answer is 150+10x
Where, x = number of lilies.

Hope this helps!

4 0

3 years ago

Read 2 more answers