Show your work (?) please

What are the coordinates of the point on the directed line segment from (-4,1) to (1,6) that partitions the segment into a ratio

Aleksandr [31]

Answer:

a segment is partitioned at a ratio of 1:3, then the point is one-fourth of the distance from (-4,-1) to (2,7).

To compute the x-coordinate of that point, you will need to compute one-fourth of the x-distance between 2 and -4 then add it to -4: (2--4)/4 = 1.5; 1.5 + -4 = -2.5.

To compute the y-coordinate of that point, you will need to compute one-fourth of the y-distance between 7 and -1 then add it to -1: (7--1)/4 = 2; 2 + -1 = 1.

The point is (-2.5,1)

3 0

2 years ago

Write the equation for a parabola with a focus at (6,-4) and a directrix at y= -7

shtirl [24]

Given:

The focus of the parabola is at (6,-4).

Directrix at y=-7.

To find:

The equation of the parabola.

Solution:

The general equation of a parabola is:

$y=\dfrac{1}{4p}(x-h)^2+k$ ...(i)

Where, (h,k) is vertex, (h,k+p) is the focus and y=k-p is the directrix.

The focus of the parabola is at (6,-4).

$(h,k+p)=(6,-4)$

On comparing both sides, we get

$h=6$

$k+p=-4$ ...(ii)

Directrix at y=-7. So,

$k-p=-7$ ...(iii)

Adding (ii) and (iii), we get

$2k=-11$

$k=\dfrac{-11}{2}$

$k=-5.5$

Putting $k=-5.5$ in (ii), we get

$-5.5+p=-4$

$p=-4+5.5$

$p=1.5$

Putting $h=6, k=-5.5,p=1.5$ in (i), we get

$y=\dfrac{1}{4(1.5)}(x-6)^2+(-5.5)$

$y=\dfrac{1}{6}(x-6)^2-5.5$

Therefore, the equation of the parabola is $y=\dfrac{1}{6}(x-6)^2-5.5$ .

4 0

2 years ago

the ortiz will travel fron indianapolis to denver this summer.The driving distance between the two cities is 1058 miles. They ne

Sladkaya [172]

Answer:

a. 2116 miles

b. 105.8 gallons

c. $305.76

d. cost per gallon = total cost / number of gallons = total cost/105.8

Step-by-step explanation:

The round-trip distance is the sum of the distances there and back. It is double the one-way distance.

round-trip distance = 2 × one-way distance

round-trip distance = 2 × 1058 miles = 2116 miles

__

The gas used will be the distance divided by miles per gallon.

gas used = round-trip distance / miles-per-gallon

gas used = (2116 mi)/(20 mi/gal) = 105.8 gal

__

The cost of gas will be the product of cost per gallon and number of gallons.

cost of gas = cost-per-gallon × gallons

cost of gas = $2.89/gal × 105.8 gal = $305.762 ≈ $305.76

__

The relation used in the previous step can be used to find the cost per gallon. Divide that equation by gallons to get ...

(cost of gas)/gallons = cost-per-gallon

For the same trip, the number of gallons is 105.8, so the equation becomes ...

cost-per-gallon = (cost of gas)/105.8

3 0

2 years ago

Last question of today<br> 20pts/brainliest//thx

ziro4ka [17]

Answer is 32 square feet

7 0

2 years ago

Read 2 more answers

H 0 : μ ≥ 25 H 1 : μ < 25 Your sample consists of 28 subjects, with a mean of 23.2 and standard deviation of 8.6. Calculate t

kykrilka [37]

Answer:

The test statistic would be given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

And replacing we got:

$t=\frac{23.2-25}{\frac{8.6}{\sqrt{28}}}=-1.11$

Step-by-step explanation:

Information given

$\bar X=23.6$ represent the sample mean

$s=8.6$ represent the sample standard deviation

$n=28$ sample size

$\mu_o =25$ represent the value that we want to test

t would represent the statistic

System of hypothesis

We want to test if the true mean is lower than 25, the system of hypothesis would be:

Null hypothesis: $\mu \geq 25$

Alternative hypothesis: $\mu < 25$

The test statistic would be given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

And replacing we got:

$t=\frac{23.2-25}{\frac{8.6}{\sqrt{28}}}=-1.11$

7 0

3 years ago