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Neko [114]
3 years ago
8

What is the y-value if the vertex of 4x^2 + 8x - 8

Mathematics
2 answers:
Levart [38]3 years ago
6 0

The x-value is -b/(2a) = -8/(2·4) = -1.

The corresponding y-value is ...

... 4(-1)² +8(-1) -8 = 4 -8 -8 = -12

The y-value of the vertex is -12.

djverab [1.8K]3 years ago
5 0

Answer:

The y-value of the vertex is -12

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

f(x)=a(x-h)^{2}+k

where

(h,k) is the vertex of the parabola

In this problem we have

f(x)=4x^{2}+8x-8 -----> this a vertical parabola open upward

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

f(x)+8=4x^{2}+8x

Factor the leading coefficient

f(x)+8=4(x^{2}+2x)

Complete the square. Remember to balance the equation by adding the same constants to each side

f(x)+8+4=4(x^{2}+2x+1)

f(x)+12=4(x^{2}+2x+1)

Rewrite as perfect squares

f(x)+12=4(x+1)^{2}

f(x)=4(x+1)^{2}-12

The vertex is the point (-1,-12)

The y-value of the vertex is -12


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Answer: 64.2^{\circ}

Step-by-step explanation:

According to the cosine rule

\cos C=\dfrac{a^2+b^2-c^2}{2ab}

Here, a=83, b=111, c=165,\ C=180^{\circ}-\theta

Putting values

\Rightarrow \cos (180^{\circ}-\theta)=\dfrac{83^2+111^2-165^2}{2\times 83\times 111}\\\\\Rightarrow \cos(180^{\circ}-\theta)=\dfrac{6889+12321-27225}{18426}\\\\\Rightarrow \cos(180^{\circ}-\theta)=\dfrac{-8015}{18426}=-0.4349\\\\\Rightarrow 180^{\circ}-\theta=\cos^{-1}(-0.4349)=115.77^{\circ}\\\Rightarrow \theta=64.23\approx 64.2^{\circ}

So, the ship turns by 64.2^{\circ} north of west

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3 years ago
A taxi service charges a $10 flat fee plus $3 per mile traveled. If an equation is made to calculate the total cost of a taxi ri
sertanlavr [38]
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3 years ago
In the triangle below, b = _____. If necessary, round your answer to two decimal places.
lara [203]
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frez [133]

Answer:

surface area of the smaller figure ≈ 1474.64 m²

Step-by-step explanation:

The figures are similar base on the question . The surface area and the volume of the larger figure is given while only the figure of the smaller figure is given.

To find the surface area of the smaller figure we simply use the ratios. That is the scale factors.

Therefore, they are similar figure the scale factor  can be represented as a:b.

The scale factor for volume is cubed.

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a/b = 16.5535451/13.7946209

Note that for two similar solid with scale factor a:b the surface area ratio is a²: b² (the scale factor is square)

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x ≈ 1474.64 m²

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