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3 years ago

Given the equation 7x-6=5(x+4) solve for variable and explain each step and justify your process

Mathematics

2 answers:

LekaFEV [45]3 years ago

4 0

7x-6=5(x+4)

7x-6=5x+20
-5x -5x

2x-6=20
+6 +6

2x=26
/2 /2

X=13

nlexa [21]3 years ago

4 0

Solve for x so we get the problem 7x-6=5(x+4) first parentheses solve 5(x=4) turns into 7x-6=5x+20 we need x on one side only 7x is greater so will add 6 to the -6 and do the same to the other side to get the new problem 7x=5x+26 the positive 6 gets rid of the 6 on the 7x side and adds 6 to 20 to make 26. last we get rid of 5x so subtract it from both sides and you get 2x=26 x has to be by its self so last thing to do is divide 2x by itself and 2x divided by 26 for the final problem (x=13 answer)

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Show with work please.

kolbaska11 [484]

Answer:

$\csc \left(\theta-\frac{\pi }{2}\right)=0.73$

Step-by-step explanation:

The identity you will use is:

$\csc \left(x\right)=\frac{1}{\sin \left(x\right)}$

So,

$\csc \left(\theta-\frac{\pi }{2}\right)$

$\csc \left(\theta-\frac{\pi }{2}\right)=\frac{1}{\sin \left(-\frac{\pi }{2}+\theta\right)}$

Now, using the difference of sin

Note: state that $\text{sin}(\alpha\pm \beta)=\text{sin}(\alpha) \text{cos}(\beta) \pm \text{cos}(\alpha) \text{sin}(\beta)$

$\csc \left(\theta-\frac{\pi }{2}\right)=\frac{1}{-\cos \left(\theta\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(\theta\right)}$

Solving the difference of sin:

$-\cos \left(\theta\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(\theta\right)$

$-\cos \left(\theta\right) \cdot 1+0\cdot \sin \left(\theta\right)$

$-\text{cos} \left(\theta\right)$

Then,

$\csc \left(\theta-\frac{\pi }{2}\right)=-\frac{1}{\cos \left(\theta\right)}$

Once

$\text{sec}(-\theta)=\text{sec}(\theta)$

And, $\text{sec}(\theta)=-0.73$

$-\frac{1}{\cos \left(\theta\right)}=-\text{sec}(\theta)$

$-\frac{1}{\cos \left(\theta\right)}=-(-0.73)$

$-\frac{1}{\cos \left(\theta\right)}=0.73$

Therefore,

$\csc \left(\theta-\frac{\pi }{2}\right)=0.73$

3 0

3 years ago

You previously found the mean of this data set. Use that in answering the question. 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25,

kicyunya [14]

Answer:

Sum of squares of differences = 11239.74

Step-by-step explanation:

We are given the following data set:

63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79

We have to calculate the sum of square of the data set.

Formula:

$\text{Sum of square of differences} = \sum (x_i -\bar{x})^2$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{962}{15} = 64.13$

Sum of squares of differences =

1.284444444 + 618.3511113 + 776.5511113 + 78.61777778 + 221.0177779 + 61.88444445 + 908.0177776 + 791.4844443 + 892.017778 + 1860.484444 + 1531.417778 + 833.2844446 + 1775.217777 + 669.0844446 + 221.0177779

= 11239.74

3 0

3 years ago

John’s mathematics teacher drew a triangle that had a 70° angle and a 20° angle. What is the measure of the third angle in the t

kari74 [83]

All triangles interior angles equal 180
So these 3 angles = 180

7 0

3 years ago

What does a closed circle on a number line indicate? Is it the solution does not include that number?

Lilit [14]

No, a closed circle does include that number.

Closed circles are used for greater than or equal to or less than or equal to
Open circles are only used for greater than or less than

3 0

3 years ago

Consider the function, f(x) = 3x - 3. Determine the asymptote for the function f(x).

Natali [406]

Answer:

Y= 1

Step-by-step explanation:

Given the expression f(x) = 3x - 3.

To solve for the asymptote y

Firstly we need to solve for x

3x-3=0

3x=3

x= 3/3

x=1

Hence the asymptote of the function y=1

5 0

3 years ago