Can someone please help me look at the picture

How do you solve for x in this problem 21=6-1x-4x

suter [353]

You first combine like terms -1x and -4x to make the equation 21=6-5x then subtract 6 from itself to cancel it out and from 21, 15=5x where x= 3

5 0

3 years ago

Read 2 more answers

I don’t know how to solve this

Lady_Fox [76]

Answer:

$\theta =2\pi k,\ \ k\in Z\ \\\text{or}\ \\\theta=-\dfrac{2\pi}{3}+2\pi k,\ \ k\in Z$

Step-by-step explanation:

Given:

$\cos \theta-\sqrt{3}\sin \theta=1$

Divide this equation by 2:

$\dfrac{1}{2}\cos \theta-\dfrac{\sqrt{3}}{2}\sin \theta=\dfrac{1}{2}$

Note that

$\cos \dfrac{\pi }{3}=\dfrac{1}{2}\\ \\\sin \dfrac{\pi }{3}=\dfrac{\sqrt{3}}{2}$

So, the previous equation is

$\cos \dfrac{\pi}{3}\cdot \cos \theta-\sin \dfrac{\pi}{3}\cdot \sin \theta=\dfrac{1}{2}$

Remind that

$\cos x\cos y-\sin x\sin y=\cos (x+y),$

then

$\cos \left(\dfrac{\pi}{3}+\theta\right)=\dfrac{1}{2}$

The solution of this equation is

$\dfrac{\pi}{3}+\theta=\pm \arccos \dfrac{1}{2}+2\pi k,\ \ k\in Z\\ \\\dfrac{\pi}{3}+\theta=\pm \dfrac{\pi}{3}+2\pi k,\ \ k\in Z\\ \\\theta =2\pi k,\ \ k\in Z\ \text{or}\ \theta=-\dfrac{2\pi}{3}+2\pi k,\ \ k\in Z$

8 0

3 years ago

The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard deviation

Paraphin [41]

Answer:

0.13% of students have scored less than 45 points

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 60, \sigma = 5$

About what percent of students have scored less than 45 points?

This is the pvalue of Z when X = 45. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{45 - 60}{5}$

$Z = -3$

$Z = -3$ has a pvalue of 0.0013

0.13% of students have scored less than 45 points

3 0

4 years ago

Please help me i would really appreciate it

inna [77]

So the first thing that happens here is that the triangle is rotated 90 degrees clockwise. This can be seen because it is rotated, then you also notice that the triangle is reflected across the y axis.

8 0

4 years ago

Find the height in centimeters of a triangular prism with a volume of 72 cm3 and a base area of 12 cm2

nikitadnepr [17]

Answer:

Socratic app

Step-by-step explanation:

it will help you

6 0

3 years ago