The slope of a line is 2/3 . What is the slope of a line that is perpendicular to this line?

What is f(x) = –4x2 + 24x + 13 written in vertex form? f(x) = –4(x – 6)2 + 23 f(x) = –4(x – 6)2 + 7 f(x) = –4(x – 3)2 + 4 f(x) =

nika2105 [10]

We have that
f(x) = –4x² + 24x + 13

we know that

The vertex form for a parabola that opens up or down is:

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

in the given equation, a=-4, therefore we add zero to the original equation in the form of 4h²−4h²
f(x) = –4x² + 24x + 4h²−4h² +13
Factor 4 out of the first 3 terms and group them
f(x) = –4*(x² -6x +h²) +4h² +13
We can find the value of h by setting the middle term equal to -2hx
−2hx=−6x
h=3 and 4h²=36
f(x) = –4*(x² -6x +9) +36 +13

we know that the term (x² -6x +9) is equals to------> (x-3)²
so
f(x) = –4*(x-3)² +49

the answer is
f(x) = –4*(x-3)² +49

4 0

3 years ago

You read 9.75 pages in your science book and 24.5pages of a play for English class. It takes you 1.2minutes to read each page of

drek231 [11]

Answer:

the number of time spend in reading is 31.3 minutes

Step-by-step explanation:

The computation of the number of time spend in reading is as follows:

= 9.75 pages in science book × 1.2 minutes + 24.5 pages in english class × 0.8 minutes

= 11.7 minutes + 19.6 minutes

= 31.3 minutes

Hence, the number of time spend in reading is 31.3 minutes

The same is relevant and considered

6 0

3 years ago

Several years ago, 50% of parents who had children in grades K-12 were satisfied with the quality of education the students r

galina1969 [7]

Answer:

The 95% confidence interval for the proportion of parents that are satisfied with their children's education is (0.4118, 0.4618). 0.5 is not part of the confidence interval, so this represents evidence that parents' attitudes toward the quality of education have changed.

Step-by-step explanation:

We have to see if 50% = 0.5 is part of the confidence interval.

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 1095, \pi = \frac{478}{1095} = 0.4365$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4365 - 1.96\sqrt{\frac{0.4365*0.5635}{1095}} = 0.4118$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4365 + 1.96\sqrt{\frac{0.4365*0.5635}{1095}} = 0.4612$

The 95% confidence interval for the proportion of parents that are satisfied with their children's education is (0.4118, 0.4618). 0.5 is not part of the confidence interval, so this represents evidence that parents' attitudes toward the quality of education have changed.

5 0

3 years ago

I GIVE BRAINLIEST!!!

Doss [256]

Answer: I'm sorry I don't know but il try and calculate the answer for you

Step-by-step explanation:

8 0

3 years ago

A manager at a shipping company will purchase boxes in the shape of right rectangular prisms. He wants the volume of each box to

Archy [21]

Answer:

Step-by-step explanation:

Ok so if u are shipping boxes in a right rectangular prism u will need to either divide or multiply. if he wants to make each box to be exactly 98 cubic feet then he will need to divide so when u do the u will need to find the first part of the answer then u will divide it by 98 cubic feet :> hope u get what i meant

6 0

3 years ago