What type of triangle is formed by joining the points D(7, 3), E(8, 1), and F(4, -1)?

Answers

Answer 1

Answer: $D(7,3) \nE(8,1) \nF(4,-1)$

The lengths of the sides of the triangle:
$\overline{DE}=√((8-7)^2+(1-3)^2)=√(1^2+(-2)^2)=√(1+4)=√(5) \n \n\overline{DF}=√((4-7)^2+(-1-3)^2)=√((-3)^2+(-4)^2)=√(9+16)=√(25)=5 \n \n\overline{EF}=√((4-8)^2+(-1-1)^2)=√((-4)^2+(-2)^2)=√(16+4)=√(20)= \n=√(4 * 5)=2√(5)$

No sides are equal to each other, so it's a scalene triangle.

Check if the sides satisfy the Pythagorean theorem:
$(√(5))^2 + (2√(5))^2=5^2 \n5+20=25 \n25=25 \ntrue$
They do, so it's a right triangle.

The triangle is a right scalene triangle.

Answer 2

Answer: Have a nice day :)
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A triangle has an area of 20 cm2. If its base is 40% of its height, what is its height to the nearest tenth of a centimeter?

Answers

Answer:

10cm

Step-by-step explanation:

Let's call the base a and the height h
a.h/2 = 20
a.h = 40
2/5h.h = 40 (because a = 40%h)
h^2 = 100
h = 10
a = 4

Find the simplified form of (t^4/10y^4)^-4

Answers

The answer is [(10,000*y^16)/t^16]. At first, you have to distribute the exponent -4 to the numerator and denominator by virtue of the law of exponent, (a/b)^n = [(a^n)/(b^n)]. After distribution, you get (t^-16)/[(10^-4)*(y^-16)]. To simplify the negative exponent, follow the law of exponent: a^-m = 1/a^m. Thus, you now have [(10^4)*(y^16)]/(t^16). Hence, the answer is [(10,000*y^16)/t^16].

A real estate agent is working for a developer who claims that the average commute time to downtown is 20 minutes with a standard deviation of 7 minutes. Stephon is an independent real estate agent and wants to check the times for his client. He took a random sample of 15 commute times and found an average of 26 minutes. He did hypothesis testing using a significance level of 5%. Which conclusion could he make?

Answers

To calculate the z-statistic, we must first calculate the standard error.

Standard error is standard deviation divided by the square root of the population. In this case, it is equal to 1.81.

The z-score is defined the distance from the sample to the population mean in units of standard error.

z = (26 – 20)/1.81 = 3.31

at this z-score = 0.0005 which is less than 5%

the answer is C. the z- statistic is 3.32, so the null hypothesis should be rejected.

Solve: The quantity 3 x minus 15 divided by 2 = 4x11

6

−3

−15

Answers

−3

(3x - 15) / 2 = 4x
3x - 15 = 8x
-15 = 5x
x=-3

Final answer:

To solve the equation (3x - 15) / 2 = 4x, we start by multiplying both sides by 2. Then, we subtract 3x from both sides. Finally, we divide both sides by 5 to find that x = -3.

Explanation:

Your question is to solve the equation (3x - 15) / 2 = 4x. We can start solving this equation by following steps:

First, multiply both sides of the equation by 2 to get rid of the denominator. This will give us the equation: 3x - 15 = 8x.
Second, subtract 3x from both sides to gather the x terms on one side of the equation. This will result in: -15 = 8x - 3x, which simplifies to -15 = 5x.
Finally, divide both sides of the equation by 5. This will yield the solution: x = -15 / 5, which simplifies to x = -3.

So, the solution to the equation is x = -3.

Learn more about Solving Equations here:

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Robert makes $4.00 an hour when he works overtime.how much does he for 3 1/4 hours of overtime work?

Answers

Okay, to find that out, ignore the 3 in the 3 1/4 for now. So 1/4 right? Is 25% right? Out of four, 4/4 is? One. So bring back the three, do 3*4=12, so it equals: 13$ . not a good job right?

Planes have edges true or false

Answers

False planes do not have edges.

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