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vampirchik [111]
2 years ago
15

Triangle BED is located at B(1,1),E(3,1), and D(2,5). If the triangle is dilated by 3, what is the new location of E?

Mathematics
1 answer:
Nadya [2.5K]2 years ago
6 0
I’ve attached my work...
Hope it helps!

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A right angle triangle normally relates to Pythagoras Theorem , and this is related to the hypotenuse, the answer maybe the hypotenuse. As the other sides are the opposite and alternative  


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3 years ago
Find the number b such that the line y = b divides the region bounded by the curves y = 36x2 and y = 25 into two regions with eq
Gemiola [76]

Answer:

b = 15.75

Step-by-step explanation:

Lets find the interception points of the curves

36 x² = 25

x² = 25/36 = 0.69444

|x| = √(25/36) = 5/6

thus the interception points are 5/6 and -5/6. By evaluating in 0, we can conclude that the curve y=25 is above the other curve and b should be between 0 and 25 (note that 0 is the smallest value of 36 x²).

The area of the bounded region is given by the integral

\int\limits^{5/6}_{-5/6} {(25-36 \, x^2)} \, dx = (25x - 12 \, x^3)\, |_{x=-5/6}^{x=5/6} = 25*5/6 - 12*(5/6)^3 - (25*(-5/6) - 12*(-5/6)^3) = 250/9

The whole region has an area of 250/9. We need b such as the area of the region below the curve y =b and above y=36x^2 is 125/9. The region would be bounded by the points z and -z, for certain z (this is for the symmetry). Also for the symmetry, this region can be splitted into 2 regions with equal area: between -z and 0, and between 0 and z. The area between 0 and z should be 125/18. Note that 36 z² = b, then z = √b/6.

125/18 = \int\limits^{\sqrt{b}/6}_0 {(b - 36 \, x^2)} \, dx = (bx - 12 \, x^3)\, |_{x = 0}^{x=\sqrt{b}/6} = b^{1.5}/6 - b^{1.5}/18 = b^{1.5}/9

125/18 = b^{1.5}/9

b = (62.5²)^{1/3} = 15.75

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3 years ago
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2 years ago
he mean age of bus drivers in Chicago is greater than 54.4 years. If a hypothesis test is performed, how should you interpret a
Natalka [10]

Answer:

There is not sufficient evidence to support the claim μ > 54.4.

Step-by-step explanation:

1) Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

2) Solution to the problem

On this case we want to test is \mu>54.4 and the system of hypothesi on this case are:

Null Hypothesis: \mu \leq 54.4

Alternative hypothesis:\mu >54.4

On this case is our decision is FAILS to reject the null hypothesis then we can conclude that we don't have enough evidence to support the claim at the significance level provided.  So the correct conclusion would be:

There is not sufficient evidence to support the claim μ > 54.4.

8 0
3 years ago
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