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Mathematics

1 answer:

koban [17]3 years ago

7 0

Answer:

the last one

Step-by-step explanation:

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What is an equation of the line that is perpendicular to y+1=-3(x-5) and passes through the point 4,-6

Oliga [24]

Answer:

$y=\frac{1}{3}x-\frac{16}{3}$

Step-by-step explanation:

Arranging the given equation in slope-intercept form ( y = mx + b ):

$y+1=-3(x-5)\\y+1=-3x+15\\y=-3x+15-1\\y=-3x+14$

<em>We know that the perpendicular line would have a slope (m) that is </em><em>negative reciprocal </em><em>of this ( $\frac{1}{3}$ ). Thus we can write the perpendicular line's equation as $y=\frac{1}{3}x+b$ . </em>

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<em>Now putting x = 4 and y = -6 into the equation, we can solve for b:</em>

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Thus, the equation of the perpendicular line is $y=\frac{1}{3}x-\frac{16}{3}$

6 0

3 years ago

Read 2 more answers

4. Find the lateral area and surface area of the given prism.

scoundrel [369]

Answer:

Step-by-step explanation:

$\bold{Q4}\\\text{We have}\\\text{two right triangles with legs a = 4m and b = 7m}\\\text{three rectangles}\ 7m\ \times 38m,\ 8.06m\ \times\ 38m\ \text{and}\ 4m\ \times\ 38m\\\\\text{The formula of an area of a right triangle:}\\\\A=\dfrac{ab}{2}\\\\\text{substitute:}\\\\A_1=\dfrac{(4)(7)}{2}=\dfrac{28}{2}=14\ m^2\\\\\text{The formula of an area of a rectangle}\ l\ \times w:\\\\A=lw\\\\\text{substitute:}\\\\A_2=(7)(38)=266\ m^2\\A_3=(8.06)(38)=306.28\ m^2\\A_4=(4)(38)=152\ m^2\\\\\text{The Surface Area:}$

$S.A.=2A_1+A_2+A_3+A_4\\\\S.A.=2(14)+266+306.28+152=752.28\ m^2$

$\bold{Q11}\\(look\ at\ the\ picture)\\\\\text{The formula of a volume of a pyramid:}\\\\V=\dfrac{1}{3}BH\\\\B-\text{area of a base}\\H-\text{height}\\\\\text{In the base we have the square. The formula of an area of a square with side a:}\\\\A=a^2\\\\\text{We have}\ a=12ft.\ \text{Substitute:}\\\\B=12^2=144\ ft^2\\\\\text{For}\ H\ \text{we need use the Pythagorean theorem:}\\\\H^2+6^2=10^2\\\\H^2+36=100\qquad\text{subtract 36 from both sides}\\\\H^2=64\to H=\sqrt{64}\\\\H=8\ m$