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Tema [17]
3 years ago
10

Find the exact value tan^-1(tan(3pi))

Mathematics
1 answer:
bearhunter [10]3 years ago
6 0
The answer is 0
(According to the radical stuffs)
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8. The sum of two numbers is 8 less than twice the first number. Their difference is 4 less than twice
Delicious77 [7]

Answer:

14 and 6

Step-by-step explanation:

Let's start by naming the first number x.

We can name the second number y.

We can set up equations to model our situation.

x+y=2x-8

x-y=2y-4

Let's simplify the equations.

x+y=2x-8

Subtract 2x from both sides

-x+y=-8

__________

x-y=2y-4

Subtract 2y from both sides.

x-3y=-4

Add the two equations together to eliminate x.

x-3y=-4

-x+y=-8

________

0x-2y=-12

-2y=-12

Divide both sides by -2.

y=6

The second number is 6.

Plug that back in.

x+6=2x-8

Subtract x from both sides

6=x-8

Add 8 to both sides

x=14

The first number is 14

7 0
3 years ago
What is 28- 12.5% decrease???
OLEGan [10]
Ok so I assume
28 and decreased by 12.5%

percent means partst out of 100 so
12.5%=12.5/100=0.125
first find 12.5% of 28 then subtract
0.125 times 28=3.5
decrease
28-3.5=24.5

answer is 24.5
3 0
3 years ago
What is the value of x and the length of segment DE?
Mandarinka [93]

Answer:

Part 1) x=6.6\ units

Part 2) DE=16.2\ units

Step-by-step explanation:

Part 1) Find the value of x

we know that

Triangles CDF and FDE are similar

therefore

The ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

CD/FD=FD/DE

\frac{5}{9}=\frac{9}{2x+3} \\ \\5*(2x+3)=9*9\\ \\10x+15=81\\ \\10x= 81-15\\ \\10x=66\\ \\ x=6.6\ units

Part 2) Find the length of DE

DE=2x+3

substitute the value of x

DE=2(6.6)+3=16.2\ units

8 0
2 years ago
Read 2 more answers
Rewrite the equation x = 65 - 60p by factoring the side that contains the variable p.
grigory [225]

Answer: x=5(13-12p)


Step-by-step explanation:

Given equation: x=65-60p

\\\Rightarrowx=(5\times13)-(5\times12)p

Since 5 is the greatest common factor of 65 and 60 in the given expression.

Therefore, the above expression can be written as

x=5(13-12p)

Hence, by factoring the side that contains the variable p we have the expression x=5(13-12p).




7 0
3 years ago
The least-squares regression model y =−3.4+5.2x and correlation coefficient r=−0.66 were calculated for a set of bivariate data
Makovka662 [10]

Answer:

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}  

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

r^2 = (-0.66)^2 = 0.4356

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

Step-by-step explanation:

For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

\bar x= \frac{\sum x_i}{n}

\bar y= \frac{\sum y_i}{n}

And we can find the intercept using this:

b=\bar y -m \bar x

And the model obtained for this case is:

y = -3.4 +5.2 x

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:  

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}  

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

r^2 = (-0.66)^2 = 0.4356

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

8 0
2 years ago
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