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Jet001 [13]
3 years ago
13

The base of a triangle is 3 cm longer than its altitude. The area of the triangle is 35cm^2. Find the altitude. (Hint: use the a

rea of a triangle. 1/2 * base * altitude.)
Mathematics
1 answer:
klemol [59]3 years ago
7 0
The base is 3+(x), altitude is x so substitute. Now we know the area of a triangle is base X height X 1/2. Substitute again! 1/2 (3+x)(x)=35. Multiply both sides by 2 to cancel out the 1/2. Now you have (x)(x+3)=70 and you have to foil out the left side x^2+3x=70. Subtract 70 on both sides x^2+3x-70=0. Find two numbers that multiply to -70 and add to 3. Solve (x+10)(x-7)=0. the x value is 7. since you can't have negative length values. Substitute 7 into 3+x for the base so you know the base is 10 and the height is 7.

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The Environmental Protection Agency (EPA) publishes fuel economy values that are known to be good estimates of the fuel economy
r-ruslan [8.4K]

Answer:

The 90% confidence interval for the mean combined fuel economy for Ford Explorers is between 22.95 and 23.63 mpg.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 16 - 1 = 15

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 15 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.9}{2} = 0.95. So we have T = 1.7531

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 1.7531\frac{0.78}{\sqrt{16}} = 0.34

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 23.29 - 0.34 = 22.95 mpg

The upper end of the interval is the sample mean added to M. So it is 23.29 + 0.34 = 23.63 mpg

The 90% confidence interval for the mean combined fuel economy for Ford Explorers is between 22.95 and 23.63 mpg.

7 0
2 years ago
A circle has a circumference of 125.6 centimeters. what is the diameter of the circle to the nearest centimeter?what is the radi
natali 33 [55]
You divide 125.6 by 3.14 which = 68.66
That's the diameter. so the nearest cm is 69cm
The radius is half of the diameter so to the nearest cm it is 34cm
5 0
3 years ago
What is the<br> slope of<br> (-3, 1) and (2, -1)
solmaris [256]

Answer:

the slope is -2/5

Step-by-step explanation:

you do y2-y1 on top of the division sign and x2-x1 on the bottom.

8 0
3 years ago
3a b2 b3 4b2 4 5a what is the answer
Otrada [13]
Is there a piece of paper that comes with the questions? Or do I just pick one? If there is a piece of paper attached, please add it to your question. Thank you!
7 0
3 years ago
The length of a rectangle is 3 meter shorter than3 times its width.Find the length and width if the perimeter is 210 meters
Shkiper50 [21]

Answer:

length = 78 m , width = 27 m

Step-by-step explanation:

let w represent width then length l = 3w - 3

the perimeter (P) is calculated as

P = 2l + 2w = 210 , substitute values

2(3w - 3) + 2w = 210 ← distribute parenthesis and simplify left side

6w - 6 + 2w = 210

8w - 6 = 210 ( add 6 to both sides )

8w = 216 ( divide both sides by 8 )

w = 27 and l = 3(27) - 3 = 81 - 3 = 78

Then length = 78 m and width = 27 m

8 0
3 years ago
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