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Talja [164]
3 years ago
12

Two parallel lines are cut by a transversal as shown below

Mathematics
1 answer:
labwork [276]3 years ago
4 0

Answer:

<2 and <4 = 74 degrees

Step-by-step explanation:

<7=<1, alt exterior angles

<1=<3, opposite angles

<1+<2= 180

since angle one is 106 just subtract 106 from 180 and you get 74= <2

<2 and <4 are opposite angles so they are congruent

therefore, <2 and <4 = 74 degrees.

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<img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csec%5Cleft%28x%5Cright%29%7D%7B%5Ccos%5Cleft%28x%5Cright%29%7D-%5Cfrac%7B%5Csin%5
DanielleElmas [232]

Answer:

1

Step-by-step explanation:

First, convert all the secants and cosecants to cosine and sine, respectively. Recall that csc(x)=1/sin(x) and sec(x)=1/cos(x).

Thus:

\frac{sec(x)}{cos(x)} -\frac{sin(x)}{csc(x)cos^2(x)}

=\frac{\frac{1}{cos(x)} }{cos(x)} -\frac{sin(x)}{\frac{1}{sin(x)}cos^2(x) }

Let's do the first part first: (Recall how to divide fractions)

\frac{\frac{1}{cos(x)} }{cos(x)}=\frac{1}{cos(x)} \cdot \frac{1}{cos(x)}=\frac{1}{cos^2(x)}

For the second term:

\frac{sin(x)}{\frac{cos^2(x)}{sin(x)} } =\frac{sin(x)}{1} \cdot\frac{sin(x)}{cos^2(x)}=\frac{sin^2(x)}{cos^2(x)}

So, all together: (same denominator; combine terms)

\frac{1}{cos^2(x)}-\frac{sin^2(x)}{cos^2(x)}=\frac{1-sin^2(x)}{cos^2(x)}

Note the numerator; it can be derived from the Pythagorean Identity:

sin^2(x)+cos^2(x)=1; cos^2(x)=1-sin^2(x)

Thus, we can substitute the numerator:

\frac{1-sin^2(x)}{cos^2(x)}=\frac{cos^2(x)}{cos^2(x)}=1

Everything simplifies to 1.

7 0
3 years ago
Find the slope. Please reply if you can help
aliina [53]

Answer:

1/1 because you go up 1 and over 1

7 0
3 years ago
Read 2 more answers
I need help graphing this
uranmaximum [27]

Answer: y=4/3x-2

Y-Intercept: -2

Slope: 4/3

Step-by-step explanation:

On the Y-Axis put -2 because thats the Y-intercept.

And for slope graph a slope of 4/3

7 0
3 years ago
Consider this population data set: 4,6,7, 11, 12, 18, 26, 23, 14, 31, 22, and 12. The values 11, 31, 22, and 12 constitute a ran
Andrej [43]

Answer:

The population mean is the sum of the 12 data set values divided by 12:

4 + 6 + 7 + 11 + 12 + 18 + 26 + 23 + 14 + 31 + 22 + 12 = 186.

Therefore the population mean = 186/12 = 15.5.

The sample mean is the sum of the 4 sample values divided by 4:

11 + 31 + 22 + 12 = 76.

Therefore the sample mean = 76/4 = 19.

The sample mean is more than the population mean by 19 - 15.5 = 3.5.

hope it helped

Step-by-step explanation:

6 0
4 years ago
How many times can 38 go into 192 using long division
pshichka [43]

Answer: 5.0526

Step-by-step explanation:

Step 1:

Start by setting it up with the divisor 38 on the left side and the dividend 192 on the right side like this:

           

 3 8 ⟌ 1 9 2

Step 2:

The divisor (38) goes into the first digit of the dividend (1), 0 time(s). Therefore, put 0 on top:

       0    

 3 8 ⟌ 1 9 2

Step 3:

Multiply the divisor by the result in the previous step (38 x 0 = 0) and write that answer below the dividend.

       0    

 3 8 ⟌ 1 9 2

      0    

Step 4:

Subtract the result in the previous step from the first digit of the dividend (1 - 0 = 1) and write the answer below.

       0    

 3 8 ⟌ 1 9 2

     - 0    

       1    

Step 5:

Move down the 2nd digit of the dividend (9) like this:

       0    

 3 8 ⟌ 1 9 2

     - 0    

       1 9  

Step 6:

The divisor (38) goes into the bottom number (19), 0 time(s). Therefore, put 0 on top:

       0 0  

 3 8 ⟌ 1 9 2

     - 0    

       1 9  

Step 7:

Multiply the divisor by the result in the previous step (38 x 0 = 0) and write that answer at the bottom:

       0 0  

 3 8 ⟌ 1 9 2

     - 0    

       1 9  

         0  

Step 8:

Subtract the result in the previous step from the number written above it. (19 - 0 = 19) and write the answer at the bottom.

       0 0  

 3 8 ⟌ 1 9 2

     - 0    

       1 9  

     -   0  

       1 9  

Step 9:

Move down the last digit of the dividend (2) like this:

       0 0  

 3 8 ⟌ 1 9 2

     - 0    

       1 9  

     -   0  

       1 9 2

Step 10:

The divisor (38) goes into the bottom number (192), 5 time(s). Therefore put 5 on top:

       0 0 5

 3 8 ⟌ 1 9 2

     - 0    

       1 9  

     -   0  

       1 9 2

Step 11:

Multiply the divisor by the result in the previous step (38 x 5 = 190) and write the answer at the bottom:

       0 0 5

 3 8 ⟌ 1 9 2

     - 0    

       1 9  

     -   0  

       1 9 2

       1 9 0

Step 12:

Subtract the result in the previous step from the number written above it. (192 - 190 = 2) and write the answer at the bottom.

       0 0 5

 3 8 ⟌ 1 9 2

     - 0    

       1 9  

     -   0  

       1 9 2

     - 1 9 0

           2

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 192 divided by 38 calculated using Long Division is: 5.0526

6 0
3 years ago
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