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3 years ago

PLS HELP I'll mark brainlest! i need the process too!

Mathematics

1 answer:

Phoenix [80]3 years ago

7 0

Answer:

19. 1400 ft^2

20. 1680 + 112pi m^3

For 20, a decimal answer would be 2031.86

Step-by-step explanation:

19. Lateral surface area refers to the area without including any horizontal planes(the tops and the bottoms - hence the name lateral). The lateral surface area of this prism is simply 5 equivalent rectangles. Each rectangle has an area of 280(14*20). Thus, the answer is 280*5 = 1400 $ft^{2}$

20. The volume of a shape such as this(where the horizontal planes are always the same shape) can be calculated by the area of the base times the height. In this case, the area of the base is the semi circle (area of $\frac{4*4*\pi}{2}$ ). The area of the rectangle is 15 * 8 = 120. Adding these together gets you 120 + 8pi. Multiplying this by the height of 14 gets you 1680 + 112 $\pi$ $m^3$

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victus00 [196]

Answer:

x-intercepts: (-1, 0) and (2, 0)

x-intercept: (-3, 0)

Step-by-step explanation:

Given quadratic function:

$f(x)=-4x^2+4x+8$

The x-intercepts of a quadratic function are the points at which the curve crosses the x-axis ⇒ when y = 0

Therefore, to find the x-intercepts of the given function, set the function to zero:

$\implies -4x^2+4x+8=0$

Factor out -4:

$\implies -4(x^2-x-2)=0$

Divide both sides by -4

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Factor the first two terms and the last two terms separately:

$\implies x(x-2)+1(x-2)=0$

Factor out the common term (x - 2):

$\implies (x+1)(x-2)=0$

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Using the Zero Product Property, set each factor equal to zero and solve for x (if possible):

$\begin{aligned}(x+1) & = 0 & \quad \textsf{ or } \quad \quad (x-2) & = 0\\\implies x & = -1 & \implies x & = 2\end{aligned}$

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---------------------------------------------------------------------------------------

Given quadratic equation:

$-9 = x^2 + 6x$

Add 9 to both sides:

$\implies x^2+6x+9=0$

Rewrite the middle term as 3x + 3x:

$\implies x^2+3x+3x+9$

Factor the first two terms and the last two terms separately:

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Therefore, the x-intercept is (-3, 0).

As the function has a repeated factor (multiplicity of two), the curve will touch the x-axis at (-3, 0) and bounce off.

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