15. A rectangular wooden gate with two diagonal boards across the front

Write an equation in standard form. Y+2=2/3(x+4)

Alina [70]

$Standard\ form:Ax+By=C\\\\y+2=\frac{2}{3}(x+4)\ \ \ \ |multiply\ both\ sides\ by\ 3\\\\3y+6=2(x+4)\\3y+6=2(x)+2(4)\\3y+6=2x+8 \ \ \ |subtract\ 6\ from\ both\ sides\\3y=2x+2\ \ \ \ |subtract\ 2x\ from\ both\ sides\\-2x+3y=2\ \ \ \ \ |change\ the\ signs\\\boxed{2x-3y=-2}$

4 0

4 years ago

Adam is building birdhouses that requires 1/2-ft-long boards. How many pieces that are exactly 1/2 ft long can be made from a bo

Julli [10]

Answer:

16

Step-by-step explanation:

Adam is building birdhouses that requires $\frac{1}{2}$ i.e 0.5 feet long boards.

Now, he has an $8\dfrac{1}{4}$ i.e. 8.25 feet longboard and wants to cut each 0.5 feet longboards.

We have to calculate the number of pieces of exactly 0.5 feet length that can be made from this 8.25 feet longboard.

Now, $\frac{8.25}{0.5}= 16.5$

So, there can be 16 whole board of exact length 0.5 feet. (Answer)

4 0

3 years ago

Find the x and y-intercepts of the following:

svet-max [94.6K]

Answer:

x-intercept (-3,0); y-intercept (0,12)

Step-by-step explanation:

To find the x-intercept --> y should equal 0

8x-2(0)=-24 substitute

8x=-24 divide

x=-3 (-3,0)

To find they-intercept --> x should equal 0

8(0)-2y=-24 substitute

-2y=-24 divide

y=12 (0,12)

5 0

3 years ago

1. Find the slope of the line passing through (-3,-4) and (-6,-2).

r-ruslan [8.4K]

Answer:

slope = - $\frac{2}{3}$

Step-by-step explanation:

Calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (- 3, - 4) and (x₂, y₂ ) = (- 6, - 2)

m = $\frac{-2+4}{-6+3}$ = $\frac{2}{-3}$ = - $\frac{2}{3}$

8 0

4 years ago

Read 2 more answers

Question #12 Please help

julia-pushkina [17]

$\bf \textit{logarithm of factors}\\\\
log_a(xy)\implies log_a(x)+log_a(y)
\\\\\\
\textit{Logarithm of rationals}\\\\
log_a\left( \frac{x}{y}\right)\implies log_a(x)-log_a(y)
\\\\\\
\textit{Logarithm of exponentials}\\\\
log_a\left( x^ b \right)\implies b\cdot log_a(x)\\\\
-------------------------------\\\\
$

$\bf a)\\\\
log_9\left( \sqrt[3]{y^2+y} \right)\implies log_9\left[ (y^2+y)^{\frac{1}{3}} \right]\implies \cfrac{1}{3}log_9(y^2+y)
\\\\\\
\cfrac{1}{3}log_9[y(y+1)]\implies \cfrac{1}{3}\left[~log_9(y)~+~log_9(y+1) ~ \right]
\\\\\\
\cfrac{1}{3}log_9(y)~~+~~\cfrac{1}{3}log_9(y+1)$

$\bf b)\\\\
log_4\left( \frac{a^2b}{\sqrt{c}} \right)\implies log_4(a^2b)~-~log_4(\sqrt{c})\implies log_4(a^2b)~-~log_4(c^{\frac{1}{2}})
\\\\\\\
[~log_4(a^2)~+log_4(b)~]~~-~~\cfrac{1}{2}log_4(c)\\\\\\ log_4(a^2)+log_4(b)-\cfrac{1}{2}log_4(c)$

7 0

4 years ago