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2 years ago

Geometry!!

Mathematics

1 answer:

MrMuchimi2 years ago

5 0

The length of line JL which has endpoints J(8,10) and L(20,5) is; JL = 13.

According to the question, we are required to determine the length of line JL.

However, the coordinates of the end points of line JL are given as;

Point J; (8,10)

Point L; (20,5).

The length of line JL is given by Pythagoras theorem as;

JL = √(20-8)² + (5-10)²

JL = √ 12² + (-5)²

JL = √ 144 + 25

JL = √169

JL = 13.

Therefore, the length of line JL which has endpoints J(8,10) and L(20,5) is; JL = 13.

Read more:

brainly.com/question/13502098

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Solve: 12 + (-13) - 12 - 5 A: 14 B: -12 C: -18 D: 45

Drupady [299]

Answer:

-18

(i think this is right, sorry if i'm wrong)

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3 years ago

Write in standard notation 6.12 x 10 to the 3rd power

Gemiola [76]

First, we find out what 10^3 is.
10 * 10 * 10 is 1,000

Now take 1000 and multiply that by 6.12.

1000 * 6.12 = 6120

Your answer would be 6120.

Hope this helps!

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4 years ago

Find an exact value.

Westkost [7]

Answer:

$\displaystyle \cos\left(-\frac{7\,\pi}{12}\right) = \frac{\sqrt{2} - \sqrt{6}}{4}$ .

Step-by-step explanation:

Convert the angle $\displaystyle \left(-\frac{7\, \pi}{12}\right)$ to degrees:

$\displaystyle \left(-\frac{7\, \pi}{12}\right) = \left(-\frac{7\, \pi}{12}\right) \times \frac{180^\circ}{\pi} = -105^\circ$ .

Note, that $\left(-105^\circ\right)$ is the sum of two common angles: $\left(-45^\circ\right)$ and $\left(-60^\circ\right)$ .

$\displaystyle \cos\left(-45^\circ\right) = \cos\left(45^\circ\right) = \frac{\sqrt{2}}{2}$ .
$\displaystyle \cos\left(-60^\circ\right) = \cos\left(60^\circ\right) = \frac{1}{2}$ .

$\displaystyle \sin\left(-45^\circ\right) = -\sin\left(45^\circ\right) = -\frac{\sqrt{2}}{2}$ .
$\displaystyle \sin\left(-60^\circ\right) = -\sin\left(60^\circ\right) = -\frac{\sqrt{3}}{2}$ .

By the sum-angle identity of cosine:

$\cos(A + B) = \cos(A)\cdot \cos(B) - \sin(A) \cdot \sin(B)$ .

Apply the sum formula for cosine to find the exact value of $\cos\left(-105^\circ \right)$ .

$\begin{aligned}\cos\left(-105^\circ \right) &= \cos\left(\left(-45^\circ\right) + \left(-60^\circ\right)\right) \\ &= \cos\left(-45^\circ\right) \cdot \cos\left(-60^\circ\right)\right) - \sin\left(-45^\circ\right) \cdot \sin\left(-60^\circ\right)\right) \\ &= \frac{\sqrt{2}}{2} \times \frac{1}{2} - \left(-\frac{\sqrt{2}}{2}\right)\times \left(-\frac{\sqrt{3}}{2}\right) = \frac{\sqrt{2} - \sqrt{6}}{4}\end{aligned}$ .

$\displaystyle \left(-\frac{7\, \pi}{12}\right) = \left(-\frac{7\, \pi}{12}\right) \times \frac{180^\circ}{\pi} = -105^\circ$ . In other words, $\displaystyle \left(-\frac{7\, \pi}{12}\right)$ and $\left(-105^\circ\right)$ correspond to the same angle. Therefore, the cosine of $\displaystyle \left(-\frac{7\, \pi}{12}\right)\!$ would be equal to the cosine of $\left(-105^\circ\right)\!$ .

$\displaystyle \cos\left(-\frac{7\,\pi}{12}\right) = \cos\left(-105^\circ\right) = \frac{\sqrt{2} - \sqrt{6}}{4}$ .

3 0

3 years ago

It is believed that the average starting salary for a 21-25 year old college grad exceeds $52,000 per year. Hence, it is desired

gregori [183]

Answer:

The significance level α is 0.02.

Step-by-step explanation:

A hypothesis test for single mean can be performed to determine whether the average starting salary for a 21-25 year old college grad exceeds $52,000 per year.

The hypothesis is defined as follows:

H₀: The average starting salary for a 21-25 year old college grad does not exceeds $52,000 per year, i.e. µ ≤ 52,000.

Hₐ: The average starting salary for a 21-25 year old college grad exceeds $52,000 per year, i.e. µ > 52,000.

The information provided is:

σ = $5,745

n = 65

Also, if $\bar X>\$53,460$ then the null hypothesis will be rejected.

Here, we need to compute the value of significance level α, the type I error probability.

A type I error occurs when we reject a true null hypothesis (H₀).

That is:

α = P (type I error)

α = P (Rejecting H₀| H₀ is true)

$=P(\bar X>53460|\mu \leq 52000)$

$=P[\frac{\bar X-\mu_{0}}{\sigma/\sqrt{n}}>\frac{53460-52000}{5745/\sqrt{65}}]$

$=P(Z>2.05)\\=1-P(Z$

*Use a z-table for the probability.

Thus, the significance level α is 0.02.

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4 years ago

Which equation represents a line which is parallel to the line 3x-4y=283x−4y=28?

Fed [463]

Answer:

Step-by-step explanation:in standard form y= ax+b

-4y = -3x+28

4y =3x-28

or y= 3/4 x -7

So a= 3/4 = slope and -7 is y intercept ( parallel lines have same slope)

Equation 3 is

y= 3/4x-2

which also has slope = 3/4 and y intercept = -2

Parallel lines have same slope

Similarly a perpendicular line will have slope of - 1/a

For equation

y= ax+b

Perpendicular line is

y=( -1/a) x +c

5 0

3 years ago