All categories

3 years ago

What is the first step when rewriting y = 6x2 + 18x + 14 in the form y = a(x – h)2 + k?

2 answers:

6 0

The first step in rewriting the equation given to the vertex form is to transpose first the constant term to the other side to simplify the procedure. It is done as follows:

y - 14= 6x² + 18x )

Hope this answer the question.

Tatiana [17]3 years ago

5 0

Answer:

y = 6(x -(-3/2))^2 - 13/12

Step-by-step explanation:

Given: $6x^2 +18x + 14$

We have to write in vertex form y = a(x -h)^2 + k

Step 1: In the given function y = 6x^2 + 18x + 14, the coefficient of x^2 is 6, we need to make it 1, so we take out 6 and factor it.

y = 6(x^2 + 3x + 7/6)

x^2 + 3x + 7/6, the value of b = 3, now divided 3 by 2, then square it.

(3/2)^2 = 9/4

Now add and subtract 9/4

y = 6(x^2 + 3x +9/4 -9/4 + 7/6)

y = 6(x +3/2)^2 -9/4+ 7/6

y = 6(x -(-3/2))^2 + $(\frac{-27 + 14}{24} )$

Here we simplified -9/4 + 7/6 taking the LCD as 12

$y = 6(x - (-\frac{3}{2}))^2 +(\frac{-13}{12} )$ .

This can be written as

$y = 6(x -(-\frac{3}{2} )^2 -\frac{13}{12}$

You might be interested in

Hey guys! Can you simplify this? Be sure to show your work so i know you aren't guessing! Also remember when you answer a questi

Svetlanka [38]

Answer:

x≤−11

Step-by-step explanation:

−99≥18x−9x

−99≥9x

−

≥x

−11≥x

x≤−11

5 0

3 years ago

If the distance from Haley’s house to school is 2.5 cm on the map and the actual distance is 3 miles. What is the scale for the

Brrunno [24]

To find your answer you divide 3 by 2.5 to get 1.2. The scale for the map is 1.2.

Hope this helps,
♥Nikki♥
(P.S. I'm not completely sure about this so you might want to get a second opinion on this particular question.)

7 0

3 years ago

42 deliveries in 3 hours = deliveries per hour

DochEvi [55]

Answer:

14 deliveries per hour

Step-by-step explanation:

42/3

The person makes 14 deliveries per hour

8 0

3 years ago

Read 2 more answers

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than ex

Olenka [21]

Answer:

The 90% confidence interval that estimate the true proportion of students who receive financial aid is

$0.533 < p < 0.64$

$n = 1789$

Step-by-step explanation:

Considering question a

From the question we are told that

The sample size is n = 200

The number of student that receives financial aid is $k = 118$

Generally the sample proportion is

$\^ p = \frac{k}{n}$

=> $\^ p = \frac{118}{200}$

=> $\^ p = 0.59$

From the question we are told the confidence level is 90% , hence the level of significance is

$\alpha = (100 - 90 ) \%$

=> $\alpha = 0.10$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} }$

=> $E = 1.645 * \sqrt{\frac{0.59 (1- 0.59)}{200} }$

=> $E = 0.057$

Generally 90% confidence interval is mathematically represented as

$\^ p -E < p < \^ p +E$

=> $0.533 < p < 0.64$

Considering question b

From the question we are told that

The margin of error is E = 0.03

From the question we are told the confidence level is 99% , hence the level of significance is

$\alpha = (100 - 99 ) \%$

=> $\alpha = 0.01$

Generally from the normal distribution table the critical value of is

$Z_{\frac{\alpha }{2} } = 2.58$

Generally the sample size is mathematically represented as

$[\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p )$

=> $n = [\frac{2.58}{0.03} ]^2 * 0.59 (1 - 0.59 )$

=> $n = 1789$

8 0

3 years ago

Find the volume of a sphere that has a surface area of 16 sq. in.

Vaselesa [24]

Given the surface area of the sphere, for us to obtain the volume we need to get the value of the radius. The surface area of the sphere is given by:
S.A=4πr^2
hence the radius can be calculated as follows;
16=4πr^2
4=πr^2
r=(4/π)^(1/2)
volume of a sphere is given by:
V=4/3πr^3
=4/3*π*(4/π)^(1/2))^3
=32/3 cubic inches

4 0

3 years ago

Read 2 more answers