Which represents the solution(s) of this system of equations?

(4, 4)
(–4, –12)
(4, 4) and (–4, 12)
(–4, 4) and (4, 12)

========================================================

Explanation:

Focus on the bottom most triangle. The upper angle of this triangle is 360/5 = 72 degrees. This is because the regular pentagon is split into five congruent (aka identical) triangles.

Each of the triangles are isosceles. Let x be the measure of the base angles.

Use the rule that adding the three angles of a triangle gets us 180

angle1+angle2+angle3 = 180

x+x+72 = 180

2x+72 = 180

2x = 180-72

2x = 108

x = 108/2

x = 54 is the answer

----------------------

Another way to get the answer:

i = interior angle of a regular polygon with n sides

i = 180(n-2)/n

i = 180(5-2)/5

i = 180(3)/5

i = 540/5

i = 108

Each interior angle of a regular pentagon is 108 degrees.

Angle x marked in blue is half that, so it is 108/2 = 54 degrees

----------------------

A third method:

E = exterior angle of a regular polygon with n sides

E = 360/n

E = 360/5

E = 72 degrees is the measure of each exterior angle

i = 180 - E

i = 180-72

i = 108 is the measure of each interior angle.

To wrap things up, we follow the same exact steps at the end of the 2nd section to get 108/2 = 54 as our answer.

Answer:

The Answer Above The Image

The solution to x^2 - 4x = 5 is x = -1 or 5

The equation is given as:

x^2 - 4x = 5

Take the coefficient of x

k = -4

Divide by 2

k/2 = -2

Square both sides

(k/2)^2 = 4

Add this value to the sides of the equation

x^2 - 4x + 4= 5 + 4

Express as a difference of two squares

(x - 2)^2 = 9

Take the square root of both sides

x - 2 = ±3

Add 2 to both sides

x = 2 ± 3

Evaluate

x = -1 or 5

Hence, the solution to x^2 - 4x = 5 is x = -1 or 5

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Answer:

C. 5/12

Step-by-step explanation:

Finding the missing side :

Taking the tan ratio :

Answer:

25 : 1

Step-by-step explanation:

125 : 5. divide by 5 we get

25 : 1

Answer:

Step-by-step explanation:

(x² − 8x + 20) ÷ (x − 4)

x - x²/4 - 8 - 8x/4 + 20/x - 20/5

x - x²/4 - 8 - 2x + 20/x - 4

-x - x²/4 + 20/x -12

...don't know, keep going

Answer:

the answer to a is 70

the answer to b is 55

the answer to c is 15

The probability that Hope performs any of the activities each day of the week can be expressed in the tree diagram.

A tree diagram is a term for a graphical tool that shows the possible outcomes of an experiment. To build a tree diagram, start by putting a branch for each of the possibilities.

The tree diagram of Hope's activities must include all the days of the week and on each day there must be three branches for each of the possible activities that she is going to do (play tennis, swim or play soccer).

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The equivalent expression of [tex]\log_c(\frac{x^2 - 1}{5x})[/tex] is [tex]\log_c(x^2 - 1) - \log_c(5x)[/tex]

The logarithmic expression is given as:

[tex]\log_c(\frac{x^2 - 1}{5x})[/tex]

The law of logarithm states that:

log(a) - log(b) = log(a/b)

This means that the expression can be split as:

[tex]\log_c(\frac{x^2 - 1}{5x}) = \log_c(x^2 - 1) - \log_c(5x)[/tex]

Hence, the equivalent expression of [tex]\log_c(\frac{x^2 - 1}{5x})[/tex] is [tex]\log_c(x^2 - 1) - \log_c(5x)[/tex]

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Answer: 192?

Step-by-step explanation:

i just think that that is the answer. you get the surface area by multiplying all of them just how you get area

Answer:

the volume is about 84.8 in³

Step-by-step explanation:

Let b be the base of the cone

and h be the height of the cone

Formula :

Consider the cone with base b and height h

The volume = (1/3)×b×h

………………………………………………………

In our example:

b = 3.14×3^2 = 28.26

h = 9

Therefore

The volume = (1÷3)×(28.26)×9 = 84.78

The arithmetic sequence that has a common difference of -5 from the options given is: A. 8, 3, -2, -7...

The common difference of an arithmetic sequence is determined as: a term - previous term.

For the sequence, 8, 3, -2, -7,.. the common difference is:

-7 - 2 = -2 - 3 = 3 - 8 = -5.

Therefore, the arithmetic sequence with a common difference of -5 is: A. 8, 3, -2, -7...

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The factored form of the quadratic equation  x² - 2x - 3 = 0 is (x - 3)(x + 1)

The quadratic equation can be factored as follows;

x² - 2x - 3 = 0

Therefore, let's find the numbers we can multiply to get -3 and add to get -2.

x² + x - 3x - 3

x(x + 1) - 3(x + 1)

Therefore,

(x - 3)(x + 1)

Therefore, the factored form of x² - 2x - 3 = 0 is (x - 3)(x + 1)

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Answer: y = -4

Step-by-step explanation:

4 (6) + y = 20

24 + y = 20

-24 -24

y = -4

Answer:

x = 6

y = -4

Step-by-step explanation:

Comment

You have 2 equations

x = 6

4x + y = 20

You already know what x is from the first equation.

All you need do is put 6 in for x in the second equation.

Solution

x = 6

4*6 + y = 20               Combine what you can on the left

24 + y = 20                Subtract 24 from both sides

24-24+ y = 20-24      Combine

y = - 4

Answer:

13,12,25

Step-by-step explanation:

Square root of 169 is 13.

Square root of 144 is 12

Square root of 625 is 25.

Answer:

[tex]\sqrt{169} = 13\\\\\sqrt{144} = 12\\\\\sqrt{625} = 25[/tex]

Step-by-step explanation:

[tex]\sqrt{169} = \left(13^2 \right)^{\tfrac 12} = 13^{\tfrac 22} = 13^1 = 13\\\\\sqrt{144} = \left( 12^2\right)^{\tfrac 12} = 12^{\tfrac 22} = 12^1 = 12\\\\\sqrt{625}= \left(25^2 \right)^{\tfrac 12} = 25^{\tfrac 22} = 25^1 = 25[/tex]

Answer:

Step-by-step explanation:

3x - 10 = 2x + 30

x - 10 = 30

x = 40

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The two lines shown in the figure intersects each other ~

Therefore,

[ by vertical opposite angle property ]

Now let's solve for x :

[tex]\qquad \sf  \dashrightarrow \:3x - 10 = 2x + 30[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3x - 2x = 30 + 10[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 40[/tex]

Answer:

9: 50

10: 90

11: 60

12: 25 and 115

13: 130 and 40

Thats all i can do, im sorry but i hope this helps ^^

The solids have the same volume.

Volume is the measure of the capacity that an object holds.

Volume of triangular prism be

= Base area * height

= 12*10

=120 cm³

Volume of rectangular prism be,

=10*3*4

=120 cm³      

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Answer:

33 1/3

Step-by-step explanation:

divide 2/3 which is 0.66... then multiply that by 5 which is 3.33...

then multiply 6 times 5 which is 30, then add 30 and 3.33... which is 33.33...

in fraction form that is 33 1/3

Answer:

  a.  y = -1/2x - 2

Step-by-step explanation:

The correct answer choice can be determined by finding the slope of the line. The slope is the ratio of rise to run.

__

The x-intercept is 4 units left of the y-axis. As the line "runs" those 4 units, it "rises" -2 units to intercept the y-axis at -2. The slope of the line is ...

  m = rise/run = -2/4 = -1/2

In the slope-intercept form of the equation of a line, the slope is the coefficient of x. This information is sufficient to let us choose the first answer choice.

__

The slope-intercept equation is ...

  y = mx +b . . . . . . . slope m, y-intercept b

We know the slope is -1/2, and the y-intercept is where x=0, at y=-2. Then the equation is ...

  y = -1/2x -2 . . . . . matches choice A

_____

Additional comment

When answering multiple-choice questions, you only need to do enough work to tell which answers are not viable.

When we plot the points, we see that the line has negative slope. (eliminates choice C). The slope is shallow, rather than steep (the x-intercept is farther from the origin than the y-intercept), so the magnitude of the slope is less than 1 and choices B and D are eliminated.

Answer:

see the attachment photo!

Answer:

Step-by-step explanation:

Givens

sin(theta) = - 8/17

cos(theta)= 15/17

Tan(theta) = ?

Comment

Without using the Pythagorean Theorem, you could simply use tan(theta) = Sin(theta) / cos(theta)

Tan(theta) = sin(theta) / cos(theta)

Tan(theta) =[tex]\dfrac{\dfrac{-8}{17} }{\dfrac{15}{17} }[/tex]

Now turn  the bottom fraction upside down and multiply.

Tan(theta) = [tex]\dfrac{-8}{17}*\dfrac{17}{15} = \dfrac{-8}{15}[/tex]

Answer Tan(theta) = -8/15

Answer:

Transitive

If x = 2y and 2y = 8, then x = 4.

The residuals of the linear regression equation are 0.329, -0.346, 0.064, -0.326,  0.049, -0.286,  -0.161, 0.214, 0.429 and 0.059

The regression equation is given as:

y = 0.005x + 3.111

Next, we calculate the predicted values (y) at the corresponding x values.

So, we have:

y = 0.005 * 4 + 3.111 = 3.131

y = 0.005 * 3 + 3.111 = 3.126

y = 0.005 * 5 + 3.111 = 3.136

y = 0.005 * 3 + 3.111 = 3.126

y = 0.005 * 8 + 3.111 = 3.151

y = 0.005 * 15 + 3.111 = 3.186

y = 0.005 * 10 + 3.111 = 3.161

y = 0.005 * 15 + 3.111 = 3.186

y = 0.005 * 6 + 3.111 = 3.141

y = 0.005 * 6 + 3.111 = 3.141

The residuals are then calculated using:

Residual = Actual value - Predicted value

So, we have:

y = 3.46 - 3.131 = 0.329

y = 2.78 - 3.126 = -0.346

y = 3.2 - 3.136 = 0.064

y = 2.8 - 3.126 = -0.326

y = 3.2 - 3.151 = 0.049

y = 2.9 - 3.186 = -0.286

y = 3 - 3.161 = --0.161

y = 3.4 - 3.186 = 0.214

y = 3.57 - 3.141 = 0.429

y = 3.2 - 3.141 = 0.059

Hence, the residuals of the linear regression equation are 0.329, -0.346, 0.064, -0.326,  0.049, -0.286,  -0.161, 0.214, 0.429 and 0.059

See attachment for the residual plot.

The residual plot shows that the linear model from the regression calculator is a good model because the points are not on a straight line

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Answer:

C = 3

Step-by-step explanation:

By using the distributive property, we multiply 1 and 6c inside the brackets by -2. This gives us 3 -2 - 12c = -35. Next, we subtract 2 from 3, giving us 1 - 12c = -35. We will now subtract 1 from both sides, leaving us with -12c = -36, or simply 12c = 36. Finally, we divide by 12, giving us C = 3. I hope this helps!

Answer:

-31/8

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Answer: The answer is 40 there are 40 favorable outcomes of people who made a purchase.

Step-by-step explanation: