For each graphically defined function below, state the domain, the range, and the intervals on which the function is increasing, decreasing, or constant.

Domain:
Range:
Increasing:
Decreasing:
Constant Intervals?

Using the monthly payment formula, it is found that the amount he will have to pay is given as follows:

a. $151.73.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

In this problem, the parameters are given as follows:

P = 2513.77, r = 0.1066, n = 1.5 x 12 = 18.

Hence:

r/12 = 0.1066/12 = 0.008883.

[tex]A = 2513.77\frac{0.008883(1 + 0.008883)^{18}}{(1 + 0.008883)^{18} - 1} = 151.73[/tex]

Hence option A is correct.

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Answer:

least to greatest: 149,156,161,164,165,165,165,168,169,172,172,172,178,178,178,180,182,184,184,184,187,189,190,190,215

Greatest to least: 215,190,190,189,187,184,184,184,182,180,178,178,178,172,172,172,169,168,165,165,165,164,161,156,149

Step-by-step explanation:

Answer:

Angle 1 = 63.3

Angle 2 = 37.3

Angle 3 = 63.3

Angle 4 = 142.7

Step-by-step explanation:

When a line intersects two parallel lines the interior angles are equal. So angle 2 = 37.3

Angle 3 = 180 - (79.4 + 37.3) = 63.3 since the sum of the angles on a straight line must be 180

Ange 1 = Angle 3 = 63.3

Angle 4 = 180-37.3 = 142.7

Answer:

answer  in picture

Step-by-step explanation:

Answer:

table 1

Step-by-step explanation:

a table represents a proportional relationship between the number of laptop and desktop computers ,if the ratio of the number of desktop computers to laptops is a constant (doesn’t vary)

Table1 : (does not represent a proportional relationship) because :

11÷10=1,1

46÷42=1.09...

and 1.1 ≠ 1.09

Table2 : (represents a proportional relationship) because :

3÷6=0.5

9÷18=0.5

18÷36=0.5

72÷144=0.5

Table3 : (represents a proportional relationship) because :

18÷12=1.5

36÷24=1.5

54÷36=1.5

108÷72=1.5

Table4 : (represents a proportional relationship) because :

2÷3=0.666666666667

18÷27=0.666666666667

22÷33=0.666666666667

200÷300=0.666666666667

The values of the temperature in degree Celsius (12 and 24) converted to degree Fahrenheit are 53.6°F and 75.2°F respectively.

In this exercise, you're required to convert the value of temperature in degree Celsius to degree Fahrenheit. Thus, we would use the following mathematical expression to do the conversion:

F(t) = 9/5C(t) + 32

When t = 12, we have:

F(t) = (9/5 × 12) + 32

F(t) = 21.6 + 32

F(t) = 53.6°F.

When t = 24, we have:

F(t) = (9⁄5 × 24) + 32

F(t) = 43.2 + 32

F(t) = 75.2°F.

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Answer:

x = -1.5 , y = 5.17

Step-by-step explanation:

Solve the system of equation using ELIMINATION (solve for x)

x + 3y = 14

-x + y = 10

Solution

x + 3y = 14 ------- equation 1  * 1

-x + y = 10 ------- equation 2  * 3

x + 3y = 14 ------- equation 3

-(-3x + 3y = 30)------ equation 4

Using the ELIMINATION METHOD.

x-(-3x) + 3y-3y = 14-30

4x = -6

x = [tex]\frac{-6}{4}[/tex]

x = -1.5

Substuting -1.5 into equation one

x + 3y = 14

-1.5 + 3y = 14

Adding 1.5 to both sides

-1.5 + 1.5 +3y = 14 +1.5

+3y = 15.5

Dividing by the coeffient of y

[tex]\frac{3y}{3} = \frac{15.5}{3}[/tex]

y = 5.166666666666

y =5.17

Therefore x = -1.5 , y = 5.17

Answer:

increase in price = $6664

price of next model = $56664

Step-by-step explanation:

(11.9 ÷ 100 ) x 56000 = $6664

56000 + 6664 = $56664

5 (12 + x)

Step-by-step explanation:

Answer:

5(12+X)

Step-by-step explanation:

Answer:

Step-by-step explanation:

a) the thickness of one ream of paper :

= 0.1 × 500

= 50 mm

b) 12 cm = 12 × 10 = 120 mm

Then

the number of sheets that exist in a pile of papers that has a thickness of 12 cm :

= 120 ÷ 0.1

= 1 200 sheet of paper

Answer:

A

Step-by-step explanation:

to find the y- intercept let x = 0 in the equation and solve for y

y = 5(0)² - 17(0) - 12 = 5(0) - 0 - 12 = 0 - 12 = - 12

then the y- intercept is (0, - 12 )

Answer:

[tex]\huge\boxed{\sf (0,-12)}[/tex]

Step-by-step explanation:

[tex]y=5x^2-17x-12[/tex]

y-intercept is the point where x = 0

Put x = 0 in the above equation.

[tex]y=5(0)^2-17(0)-12\\\\y = 0-0-12\\\\y=-12[/tex]

So, y = -12, when x = 0.

Ordered pair = (x,y) = (0,-12)

[tex]\rule[225]{225}{2}[/tex]

Work Shown:

Volume = length*width*height

Volume = 3*7*5

Volume = 105 cubic feet

length × breadth × height

7 × 3 × 5

105 cubic feet

hope it helps...!!!

Step-by-step explanation:

the square root of x squared is x.

this means the( cube root of x ) to the power of 6 is what we need

Step-by-step explanation:

Select all of the following that are quadratic equations.

x² + 3x - 5 = 0 ✓

x² - x = 3x + 7 ✓

5x - 7 = 0 X

7x² + 14x = 0 ✓

x³ - 3x² + 1 = 0 X

x - 5 = 9x + 7 X

What is quadratic equations?

Quadratic equations is a equation that has a general form like "ax² + bx = c"

For example :

x² + 3x - 5 = 0

x² + 3x = 5

x² → ax²

3x → bx

5 → c

Answer:

41 degrees

Step-by-step explanation:

All of the angles must add up to 360 degrees to form a circle. So we have 22 + b + 297 = 360. Solving for b, we get b = 41.

The system of equations that we need to solve is:

And the solution is x = 49 and y = 101.

Let's define the variables:

We know that the total number of CDs is 150, then:

x + y = 150

And we know that:

y = 2x + 3

Then the two equations that represent the information (and conform a system of equations) are:

x + y = 150

y = 2x + 3

b) The graphs of the two equations can be seen below.

c) To find the solution, we just need to see where the graphs intercept.

We can see that the intercept is (49, 101), this means that:

Isabella has 49 rock music CDs and 101 alternative music CDs.

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Answer:

I believe its C , i took this class

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

2 ^(5+x) = 2^8            (because 256 = 2^8)

 equate the exponents    5+x = 8     then x = 3

1/3 ^(2+x) = 1 / 3^ 6        (because 729 = 3^6 )

  equate the exponents  2+ x = 6    then x = 4

Answer:

a) x = 3

b) x = 4

Step-by-step explanation:

Use the Exponential Power Rule.

[tex]a^x \times a^y = a^{x+y}[/tex]

Also covert the term on the right to the same base as on the left.

If you are allowed to have calculator do [tex]\log_{\text{base}} (\text{number})[/tex] to get the exponent. For example [tex]\log_{2} (256) = 8[/tex], that means [tex]256 = 2^8.[/tex]

Without calculator you can divide with base untill you have it fully factored, then count. For example:

256/2 = 128
128/2 = 64
64/2 = 32
32/2 = 16
16/2 = 8
8/2 = 4
4/2 = 2
2/2 = 1

We had to divide with base two 8 times so 256 = 2⁸.

a)

[tex]2^5 \cdot 2^x = 256\\2^{5+x} = 2^8[/tex]

Now that we have same base we can equate the exponents!

[tex]5 + x = 8\\x = 8 - 5\\x = 3[/tex]

b)

[tex](\frac{1}{3})^2 \cdot (\frac{1}{3})^x = \frac{1}{729}\\\\(\frac{1}{3})^{2+x} = \frac{1}{3^6}\\\\(\frac{1}{3})^{2+x} = (\frac{1}{3})^6[/tex]

[tex]2 + x = 6\\x = 6 - 2\\x = 4[/tex]

Answer:

[tex]\sf X=\dfrac{2345}{9999}[/tex]

Step-by-step explanation:

Given:

[tex]\sf X=0.234523452345...[/tex]

Therefore, X is a recurring decimal (the decimal numbers 2345 repeat forever).

Converting a recurring decimal to a fraction

Let X equal the recurring decimal:

[tex]\implies \sf X=0.234523452345...[/tex]

Create another number with recurring 2345s by multiplying the above expression by 10000:

[tex]\implies \sf 10000X=2345.23452345...[/tex]

To solve these two equations and write X as a fraction, take away X from 10000X to remove all the recurring decimal places:

[tex]\large\begin{array}{r r l}& \sf 10000X & = \sf 2345.23452345... \\- & \sf X & = \sf \quad \:\:\:0.23452345.... \\\cline{2-3} & \sf 9999X & = \sf 2345\end{array}[/tex]

[tex]\implies \sf 9999X=2345[/tex]

Divide both sides by 9999:

[tex]\implies \sf X=\dfrac{2345}{9999}[/tex]

Therefore, 0.23452345... as a fraction is [tex]\sf \dfrac{2345}{9999}[/tex]

If the trigonometric expression is sin θ = -√2/2. Then the value of angle θ will be 5π/4, 7π/4, and 13π/4.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The trigonometric expression is given below.

sin θ = -√2/2

The expression can be written as

sin θ = -1/√2

Then the value of angle θ will be

θ = sin⁻¹ (-1/√2)

θ = 5π/4, 7π/4, and 13π/4.

Thus, the correct options are B, C, and E.

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Answer:

B,C,E

Step-by-step explanation:

Answer:

6.28

Step-by-step explanation:

2×3.14 because this is just simple multiple

Answer:

the answer is $31.80

Step-by-step explanation:

6% of $120.00 is $7.20,

75% off of 127.20= $31.80

Answer:

28

Step-by-step explanation:

DI is a radius

CJ is a diameter

The diameter is twice the radius

CJ = 2 * DI

CJ = 2 * 14

CJ = 28

The volume of the cylindrical jar, considering it's radius and height, is of 923 in³.

The volume of a cylinder of radius r and height h is given by:

[tex]V = \pi r^2h[/tex].

In which problem, we have that r = 4.7 in, h = 13.3 in, hence the volume in cubic inches is given by:

[tex]V = \pi \times 4.7^2 \times 13.3 = 923[/tex]

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Answer:

The amplitude is the maximum displacement/highest peek

Which is in your case = 2

Answer:

its C

Step-by-step explanation:

I used something else for it for it

Answer:

Step-by-step explanation:x=π2,3π2

Explanation:

This can be factored as (x2+a)x2+b).⇒(sin2x+3)(sin2x-1)=0⇒

2

x

=

−

3

and

sin

2

x

=

1

⇒

sin

x

=

√

−

3

and

sin

x

=

√

1

⇒

sin

x

=

∅

and

sin

x

=

±

1

⇒

x

=

π

2

,

3

π

2

Hopefully this helps!