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vfiekz [6]
3 years ago
7

Which equation is y = –6x2 + 3x + 2 rewritten in vertex form?

Mathematics
2 answers:
slava [35]3 years ago
8 0

we have

y = -6x^{2} + 3x + 2

we know that

the vertex form of the vertical parabola equation is equal to

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

where

(h,k) is the vertex of the parabola

To find the equation rewritten in vertex form let's factor the equation

<u>Factor the leading coefficient </u>

y = -6(x^{2} - 0.5x) + 2

<u>Complete the square. Remember to balance the equation by adding the same constants to each side</u>

y = -6(x^{2} - 0.5x+0.0625-0.0625) + 2

y = -6(x^{2} - 0.5x+0.0625) + 2 +0.375

y = -6(x^{2} - 0.5x+0.0625) + 2.375

<u>Rewrite as perfect squares</u>

y = -6(x-0.25)^{2} + 2.375

therefore

the answer is

y = -6(x-0.25)^{2} + 2.375

Annette [7]3 years ago
4 0
The answer is y = -6( x- \frac{1}{4}) ^{2}+3

Regular form: y = ax² + bx + c
Vertex form: y = a(x - h)² + k
(h, k) - vertex

y = -6 x^{2} +3x+2 \\ y -2=-6 x^{2} +3x \\  y-2+6*=-6* x^{2} +6* \frac{1}{2} x \\  \\ y-2-6* \frac{1}{16} =-6* x^{2} +6* \frac{1}{2} x -6* \frac{1}{16} \\  \\ &#10;y -2 -\frac{6}{16} =-6( x^{2} -\frac{1}{2} x+\frac{1}{16}) \\  \\ &#10;y- \frac{2*16}{16} -\frac{6}{16} =-6( x^{2} -\frac{1}{2} x+(\frac{1}{4})^{2} ) \\  \\ &#10;y -  \frac{32}{16} -\frac{6}{16}  = -6( x- \frac{1}{4}) ^{2}  \\  \\ &#10;y -  \frac{32+6}{16} = -6( x- \frac{1}{4}) ^{2} \\  \\ &#10;y -  \frac{48}{16} =  -6( x- \frac{1}{4}) ^{2} \\  \\

y -  3=  -6( x- \frac{1}{4}) ^{2} \\  \\ &#10;y  =  -6( x- \frac{1}{4}) ^{2}+3&#10;

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mixas84 [53]

Answer:

2/6 or 1/3

Step-by-step explanation:

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3 years ago
A hiker leaves the Visitor Center traveling East-by-North East. She hikes 13 miles before
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both or neither as they are the same distance to rescue her

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Step-by-step explanation:

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3 years ago
A surveyor sights the top of a building with a handheld range finder. the top of the building is 148 feet 2 inches away. the ang
Leokris [45]

see the attached figure to better understand the problem


we know that

in the right triangle ABC

cos 56°=AC/AB

where

AC is the adjacent side to angle 56 degrees------> the distance from the surveyor to the building

AB is the hypotenuse-----> 148 ft 2 in

56 degrees------> is the angle of elevation

so

cos 56°=AC/AB---------> solve for AC

AC=AB*cos 56°

AB=148 ft 2 in

convert 2 in to ft

1 ft -----> 12 in

x ft------> 2 in

x=2/12-----> x=0.17 ft

AB=148 ft 2 in-----> 148 ft+0.17 ft------> AB=148.17 ft


AC=AB*cos 56°----> AC=148.17*cos 56°------> AC=82.86 ft


convert 0.86 ft to in

0.86 ft=0.86*12-----> 10.32 in

distance AB=82 ft 10 in


the answer is

the distance from the surveyor to the building is 82 ft 10 in

8 0
3 years ago
The scientist performs additional analyses and observes that the number of major earthquakes does appear to be decreasing but wo
kifflom [539]

Answer:

Step-by-step explanation:

Hello!

A regression model was determined in order to predict the number of earthquakes above magnitude 7.0 regarding the year.

^Y= 164.67 - 0.07Xi

Y: earthquake above magnitude 7.0

X: year

The researcher wants to test the claim that the regression is statistically significant, i.e. if the year is a good predictor of the number of earthquakes with magnitude above 7.0 If he is correct, you'd expect the slope to be different from zero: β ≠ 0, if the claim is not correct, then the slope will be equal to zero: β = 0

The hypotheses are:

H₀: β = 0

H₁: β ≠ 0

α: 0.05

The statistic for this test is a student's t: t= \frac{b - \beta }{Sb} ~~t_{n-2}

The calculated value is in the regression output t_{H_0}= -3.82

This test is two-tailed, meaning that the rejection region is divided in two and you'll reject the null hypothesis to small values of t or to high values of t, the p-value for this test will also be divided in two.

The p-value is the probability of obtaining a value as extreme as the one calculated under the null hypothesis:

p-value: P(t_{n-2}\leq -3.82) + P(t_{n-2}\geq  3.82)

As you can see to calculate it you need the information of the sample size to determine the degrees of freedom of the distribution.

If you want to use the rejection region approach, the sample size is also needed to determine the critical values.

But since this test is two tailed at α: 0.05 and there was a confidence interval with confidence level 0.95 (which is complementary to the level of significance) you can use it to decide whether to reject the null hypothesis.

Using the CI, the decision rule is as follows:

If the CI includes the "zero", do not reject the null hypothesis.

If the CI doesn't include the "zero", reject the null hypothesis.

The calculated interval for the slope is: [-0.11; -0.04]

As you can see, both limits of the interval are negative and do not include the zero, so the decision is to reject the null hypothesis.

At a 5% significance level, you can conclude that the relationship between the year and the number of earthquakes above magnitude 7.0 is statistically significant.

I hope this helps!

(full output in attachment)

5 0
3 years ago
Convert the decimal into a reduce fraction.
Ivanshal [37]

Answer:

hey i dont really know, but look up calculator soup, it has a ton of different calculators and may be able to help u

Step-by-step explanation:

/

7 0
2 years ago
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