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3 years ago

point a is at (-7 5) and point c is at (5 -1). find the coordinates of point b on line ab such that ab is 5 times as long as bc

Mathematics

1 answer:

WARRIOR [948]3 years ago

5 0

Step-by-step explanation:

Let the coordinates of point b be (x,y).

Given the coordinates of a (-7,5) and c(5,-1)

Now according to question

ab = 5bc

using distance formula

$\sqrt{(x+7)^2+(y-5)^2} =5\sqrt{(5-x)^2+(-1-y)^2}$

Solving we can get

$x=-\frac{-11+\sqrt{-4y^2-10y+25}}{2},\:x=\frac{\sqrt{-4y^2-10y+25}+11}{2}$ '

However, we do need either x or y coordinate of point b to find the other.

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Point M is the midpoint of segment QR. If QM = 16 + x and MR = 2(x + 2), find the length of QR. QR = 12 QR = -12 QR = 28 QR = 56

vfiekz [6]

The midpoint divided a segment into two congruent lengths/segments.

So, QM = MR.

Set up the equation.

16 + x = 2(x+ 2)

16 + x = 2x + 4

12 + x = 2x

12 = x

Now, that you have the value of x, substitute it for the two equations.

QM = 16 + x

QM = 16 + 12

QM = 28

MR = 2(12+ 2)

MR = 2(14)

MR = 28

Find the whole length by of the line by adding the two segments. 28 × 2 = 56.

QR = 56

6 0

3 years ago

the graph below shows how many gallons of gas are used by a boat when it travels. how many gallons of gas would the boat use to

Sindrei [870]

The boat uses 4 gallons to travel 6 miles. Traveling 4 times as far is expected to require 4 times the gas.

4 gallons = 6 miles
Multiply by 4.
16 gallons = 24 miles

⇒ 16 gallons

3 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:

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

5 0

2 years ago

Please help, i can't figure this out and im ready to pull my hair out!!!

Nat2105 [25]

Answer:

I'm sorry I don't know the equation, but she walks 3 mph.

Step-by-step explanation:

We know that the answer is asking for speed, which needs both distance and time, so we also need both. Which is where the 9 mph is used. 9 mph means its a difference. b means biking mph, w means walking mph, sooo ----->>> b=w+9, and the difference in the 1st equation is 36, which means the first equation is 4 times larger than the b=w+9, so she walked 48 miles, as well as walked 12 miles in 4 hours. Divide then distances by 4, and you get 12 miles and 3 miles in one hour. Or 12 mph & 3 mph, which fits into 12=3+9. So she walks 3 miles per hour.

5 0

2 years ago

Find the coordinates of the midpoint of a segment with the given

galben [10]

Answer:

(9,5.5)

Step-by-step explanation:

6 0

3 years ago