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3 years ago

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Can someone pls help me with this? I got everything else I just don't really understand PI I know it's the last one because PI i

s approximately 22/7 can you just help me with the rest? It multiple choices too. Thank you soo much! 20 points!

2 answers:

ANEK [815]3 years ago

8 0

Answer: C, D and E are correct :D

Step-by-step explanation:

salantis [7]3 years ago

5 0

Answer:

C, D, and E

Step-by-step explanation:

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Find area of the isosceles triangle formed by the vertex and the x-intercepts of parabola y=x2+4x−12.

xz_007 [3.2K]

The area of the isosceles triangle is 64 sq units.

<u>Solution:</u>

Part 1: x-intercepts

The x-intercepts occur at the points on the function where y=0

So, we need to solve

$x^2-4x-12=0$

The left side factors fairly easily into:

$(x-6)(x+2)=0$

So solution occur when

$x-6=0\rightarrow x=6$

and

$x+2=0\rightarrow x=(-2)$

So the x-intercepts are at (0,6) and (0,−2)

Part 2: vertex of the parabola

The vertex of a simple quadratic parabola occurs when the derivative of the quadratic is equal to 0.

The derivative of the given quadratic is

$\frac{dy}{dx}=2x-4$

By observation, this is equal to 0 when x=2

When x=2 the original equation becomes

$y=(2)^2-4(2)-12$

$y=-16$

Therefore the vertex of this parabola is at (2,−16)

The endpoints of the base of the isosceles triangle are (-6, 0) and (2, 0)

$\Rightarrow$ so its base is 8

The height of the triangle reaches from the midpoint of the base (-2, 0) and the vertex (2, -16)

$\Rightarrow$ so its height is 16

The area is $\frac{1}{2}\times \text { base }\times \text { height }=\frac{1}{2}\times8\times16=64 \text{ sq units }$

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3 years ago

The area of the base of the oblique pentagonal pyramid is 50 cm2 and the distance from the apex to the center of the pentagon is

kirza4 [7]

Answer:

$\text{Height is }6\sqrt2cm$

$\text{The volume is }100\sqrt2cm^3$

Step-by-step explanation:

Given the area of the base of the oblique pentagonal pyramid is $50 cm^2$ and the distance from the apex to the center of the pentagon is 6 cm. The measure of ∠ACB is 45°.

we know that

ABC is a right triangle

∠ACB=45°

AC=hypotenuse------> 6 cm

$\sin 45^{\circ}=\frac{AB}{AC}$

$AB=AC\times \sin 45$

$AB=\frac{6}{\sqrt2}$

$AB=3\sqrt2$

$\text{Height is }6\sqrt2cm$

Now, volume of pyramid

$\text{Volume of the pyramid=}\frac{1}{3}\times \text{Area of the base}\times height$

Area of the base=50 cm²

$Height=6\sqrt2 cm$

so, $\text{volume of the pyramid=}\frac{1}{3}\times 50\times 6\sqrt2=100\sqrt2cm^3$

$\text{the volume is }100\sqrt2cm^3$

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3 years ago

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Granite counter tops cost $40 for every square foot. The base pay to install the counter top is $750. Set up a Linear Model repr

vladimir1956 [14]

Answer:

31.5 square feet of counter top

Step-by-step explanation:

x represents the number of square feet

40x + 750 = 2010 subtract 750 from both sides

40x = 1260 divide both sides by 40

x = 31.5

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3 years ago

The questions below walk through the use of kNN to predict the value of Y for a new point with (X1, X2)=(4, 4). Distance is calc

Nady [450]

Answer:

The Euclidean distance between the two given points is $\sqrt{2}\text{ units}$ .

Step-by-step explanation:

K-NN is used to predict the variable y for a new point with $(X_1,X_2) = (4,4)$

Distance is calculated in the Euclidean sense.

The Euclidean distance between two points is given by the formula:

$\text{Points: }(X_1, X_2), (x_1,x_2)\\\\D = \sqrt{{(x_2-X_2)}^2 + (x_1-X_1)^2}$

The point is $(x_1,x_2) = (3,5)$

The Euclidean distance between the two points is given by:

$D = \sqrt{(5-4)^2 + (3-4)^2} = \sqrt{2}\text{ units}$

Thus, the Euclidean distance between the two given points is $\sqrt{2}\text{ units}$ .

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3 years ago

Which figure shows that

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It’s either Option 1 or 4

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