If tanθ= 2/5 find cosθ using identities. This is in quad. 1.

The only common factor between these two numbers will be 1.

Remember that any number can be decomposed as a product of prime numbers. For example for 18 we have:

18 = 2*3*3

There 18 is written as a product of its prime factors.

Now, for our case of p^n and q^m we will have:

p^n = P = p*p*p...*p     n times.

q^m = Q = q*q*q*...*q     m times.

Now, notice that because q and p are primes, there is no common factor in these two decompositions. (and we can't decompose it furthermore). Then we conclude that the only factor that these numbers share is the trivial one, which is 1.

If you want to learn more about prime numbers, you can read:

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Answer:

Shorter leg = 20 cm.

Longer leg = 21cm.

Hypotenuse = 29 cm

Step-by-step explanation:

Let the shorter leg be x cm long

Then longer leg = x + 1 and hypotenuse = x + 9 cm long

So by Pythagoras:

x^2 + (x + 1)^2 = (x + 9)^2

0 = x^2 + 18x + 81 - x^2 - (x^2 + 2x + 1)

x^2 + 18x + 81 - x^2 - x^2 - 2x - 1 = 0

-x^2 + 16x + 80 = 0

x^2 - 16x - 80 = 0

(x - 20)(x + 4) = 0

So x = 20   (we ignore the negative root).

So longer leg = 20 + 1 and hypotenuse = 20 + 9.

Answer:

0.1 percent

Step-by-step explanation:

sorry I don't have an explanation. sorry if it's wrong, at least I tried

Answer:

0.1

Explanation:

It's right

Answer:

804

Step-by-step explanation:

603/9 x 12

67 x 12

804

Answer:

804 miles in 12 hours

Step-by-step explanation:

603/9 which = 67

67*12 which equal 804

don't forget the unit (mph)

Answer:

D

Step-by-step explanation:

[tex]4\sqrt{x2[/tex] means [tex](x^{2})^{\frac{1}{4} }[/tex] so then according to indices rule, the powers will be multiplied. Do the same thing for y and z as well, and you will get the answer

Answer:

B) B

Step-by-step explanation:

   2 times 4 is 8, so in this case the option is option b as none of the other options show this.

    In total,

2 * 4 = 8

60 * 4 = 240

240 + 8 = 248

Given:

[tex]\frac{3}{9}[/tex] and [tex]\frac{1}{2}[/tex]

Finding a common denominator:

9 * 2 = 18

       -> If you need to stop here, a common denominator is 18.

Converting [tex]\frac{3}{9}[/tex]:

[tex]\frac{3}{9}[/tex] = [tex]\frac{3*2}{9*2}[/tex] = [tex]\frac{6}{18}[/tex]

Converting [tex]\frac{1}{2}[/tex]:

[tex]\frac{1}{2}[/tex] = [tex]\frac{1*9}{2*9}[/tex] = [tex]\frac{9}{18}[/tex]

       ->  [tex]\frac{6}{18}[/tex] and  [tex]\frac{9}{18}[/tex]

Answer:

9

Step-by-step explanation:

12ⁿ⁻⁵ = 12⁴

n - 5 = 4

n = 9

Answer:

1. a = 1

2. See explanation below.

Step-by-step explanation:

First Question

Given:

[tex]\displaystyle \large{\log_b a = 0}[/tex]

Convert to exponential:

[tex]\displaystyle \large{\log_b a = c \to b^c = a}[/tex]

Thus [tex]\displaystyle \large{\log_b a = 0 \to b^0 = a}[/tex]

Evaluate:

[tex]\displaystyle \large{b^0 = a}[/tex]

We know that for every values to power of 0 will always result in 1, excluding 0 to power of 0 itself.

Solution:

[tex]\displaystyle \large{a = 1}[/tex]

__________________________________________________________

Second Question

Given:

[tex]\displaystyle \large{log_0 3}[/tex] and [tex]\displaystyle \large{\log_1 3}[/tex]

Let’s convert to an equation:

[tex]\displaystyle \large{\log_0 3 = x}[/tex] and [tex]\displaystyle \large{\log_1 3 = y}[/tex]

The variables represent unknown values of logarithm.

Convert to exponential:

[tex]\displaystyle \large{0^x = 3}[/tex] and [tex]\displaystyle \large{1^y = 3}[/tex]

Notice that none of x-values and y-values will satisfy the equations. No matter what real numbers you put in, these equations will always be false.

Hence, no solutions for x and y.

The balance point of the dataset is the mean of the dataset

The balance point of the dataset is 20

From the dataset, we have the following frequency table

Data (x)     Frequency (f)

15                    2

24                   1

26                  1

The balance point of the dataset is the mean value of the dataset, and the mean is calculated as:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

This gives

[tex]\bar x = \frac{15 * 2 + 24 * 1 + 26 *1}{2 +1+1}[/tex]

Evaluate the sum

[tex]\bar x = \frac{80}{4}[/tex]

Evaluate the quotient

[tex]\bar x = 20[/tex]

Hence, the balance point of the dataset is 20

Read more about mean at:

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Answer:

50,000

Step-by-step explanation:

Just put it in the answer lol :p

Answer:

28,360,000

Step-by-step explanation:

The number after the 6 (the ten thousands is 3, so it rounds down to 28, 360, 000.

please give brainliest!

Answer:

5, -⅓

Step-by-step explanation:

x = 2:

4x + 3y = 23

3y = 23 - 4(2)

3y = 15

y = 5

x = 6:

4x + 3y = 23

3y = 23 - 4(6)

3y = -1

y = -⅓

Answer:

31.4

Step-by-step explanation:

diameter (d) = 10

circumference = (3.14)d

                        = (3.14)10 = 31.4

circumference = 31.4

Answer:

27 boxes.

Step-by-step explanation:

This situation can be represented by the equation:

(112 - 105) + 20 = ?

First we subtract 105 from 112:

112 - 105= 7

Now add 20.

7 + 20 = 27

Natalie has 27 boxes now.

Total swimwear = 76 bikinis + 4 other types = 80 total

divide number of bikinis by total swimwear then multiply by 100:

76/80 = 0.95

0.95 x 100 = 95%

Answer: 95% are bikinis

Answer:

False

Step-by-step explanation:

There are some quadratic equations that cannot be solved using the factoring technique. That is why the quadratic formula exists, to solve equations that cannot be factored.

Answer:

31/10

Step-by-step explanation:

Answer:

28.13

Step-by-step explanation:

62 - (98/4)

62 - 24.5 = 37.5

75% of 37.5 is 28.125, or 28.13.

Answer:

22

Step-by-step explanation:

98/4 = 24.5

62-24.5 = 37.5

75% of 37.5

= about 22

Answer:

5(c+3)=85

divide both sides by 5

c+3=17

taking 3 to the other side gives us -3

c=17-3

c=14

Answer: 6

Step-by-step explanation:

Because you have to multiply then remove the fraction and set equal to 0 and solve for x which I’m pretty sure gives u 6

Answer:

38.5

Step-by-step explanation:

70*(0.55) = 38.5

Answer:

Step-by-step explanation:

To find 55% of 70, we need to write an equation.

this equation will be 55x70/100

now, the answer to 55x70 / 100 is

38.5

We get this answer, because 55x70=3850

and 3850 divided by 100 is 38.5

Answer:

3/1

Step-by-step explanation:

In triangle ABC, the known side is AC, which is equal to 6. The corresponding side to AC from triangle DEF would be FD, which is equal to 2. You divide 6/2 in order to get 3/1.

If the data is not skewed, then the mean is the best measure of center.

This then also includes the standard deviation because the standard deviation relies on the mean.

To get the mean, add up the data values:

5+6+7+7+7+8+8+9+9+9+9+9+10+10+11 = 124

Then divide by the sample size n = 15

124/n = 124/15 = 8.267 approximately

Once you determine the mean, you can then determine the standard deviation which involves a bit more complicated steps. The rough outline is:

Once again, step 1 shows how critical the mean is to finding the standard deviation. The standard deviation measures how far each value is from the mean on average. In other words, it's like a measure of the average distance from the mean.

Use of spreadsheet software is strongly recommended to keep track of everything. You can also use a standard calculator to compute the standard deviation. There are also tons of free online calculators that can help out with that as well.

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If the data was skewed to one side, then the median is the better measure of center because it is not affected by outliers. The IQR (interquartile range) is used instead of the standard deviation for skewed distributions.

The solution set 3 and 7 are the true values of the absolute value equation

The absolute value equation that has a solution set of 3 and 7 is [tex]|x - 5| = 2[/tex]

The solution sets of the absolute value equation are given as:

x = {3, 7}

Calculate the mean of the solutions

[tex]x_1 = \frac{7 +3}{2}[/tex]

[tex]x_1 = 5[/tex]

Calculate the difference of the solutions divided by 2

[tex]x_2 = \frac{7 - 3}{2}[/tex]

[tex]x_2 = 2[/tex]

The absolute value equation is the represented as:

[tex]|x - x_1| - x_2 = 0[/tex]

Substitute known values

[tex]|x - 5| - 2 = 0[/tex]

Add 2 to both sides

[tex]|x - 5| = 2[/tex]

Hence, the absolute value equation that has the a solution set of 3 and 7 is [tex]|x - 5| = 2[/tex]

Read more about absolute value equation at:

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Answer:

$13.86

Step-by-step explanation:

Just multiply 77 by 18 percent as a decimal (.18) to get the answer, which is $13.86

Hopefully this helps- let me know if you have any questions!

Answer:

option c

Step-by-step explanation:

This is the net of square pyramid.

Base of the square pryamid is square and all the other face are triangle.

The length of the radius of the mudel is 9 cm

[tex]By\ the\ topic[/tex]

[tex]The\ volume\ of\ the\ mudel\primes\ is\ 3052.08{\rm cm}^3[/tex]

[tex]Formula\ for\ the\ volume\ of\ the\ sphere\ is[/tex]

[tex]\frac{4}{3}\pi\ r^3[/tex]

[tex]\frac{4}{3}\pi\ r^3=3052.08[/tex]

[tex]\pi\ r^3=\frac{3}{4}\times3052.08=2289.06[/tex]

[tex]\gamma3=2289.06\div\pi[/tex]

[tex]\gamma=\sqrt{\frac{2289.06}{\pi}}\approx\sqrt{\frac{2289.06}{3.14}}+\sqrt{729}[/tex]

[tex]r=9cm[/tex]

[tex]7hus,\ the\ length\ of\ the\ vadius\ of\ eanth[/tex]

[tex]mudel\ is\ 9\ cm[/tex]

[tex]Application\ of\ the\ volume\ of\ the\ spheve?[/tex]

I hope this helps you

:)

The distance, In feet, from the base of the ladder to the base of the wall is 4.2 ft.

He needs to move the ladder 0.1 ft closer to the base of the building.

The situation forms a right angle triangle.

Right angle triangle has one of its angles as 90 degrees. The sides and angle can be found using trigonometric ratios.

The length of the ladder is the hypotenuse of the triangle formed. Therefore, the distance, In feet, from the base of the ladder to the base of the wall can be calculated as follows;

cos 65° = adjacent / hypotenuse

cos 65° = d / 10

d = 10 × 0.42261826174

d = 4.22618261741

d = 4.2 ft

She needs to move the ladder so it reached a window 9.6 feet above the ground. Therefore, the distance from the base of the ladder and the wall is as follows;

cos 65 = d / 9.6

d = 9.6 × 0.42261826174

d = 4.05696

d = 4.1

Therefore, he needs to move the ladder 0.1 ft closer to the building.

learn more on right angle triangle here: https://brainly.com/question/14988069