A cell phone company charges its customers $40 each month for owning a cell phone plan and $0.25 for
each minute the customer talks on the phone. These costs are modeled by the following equation:
C=25m +40, where Crepresents the total cost of the bill and m represents the number of minutes the
customer talked on the phone that month. Given this equation, how many minutes would the customer
have to talk on the phone for their monthly bill to be $84.25? (Hint: plug in 84.25 for the total cost, C, and
solve for the unknown, m).

The linear function f(x) with a slope of -8 and that f(1) = 2 is f(x) = 10 -8x

From the question, we are find a linear function with slope of -8 and that f(1) = 2

If f(1) = 2, then the line passes through the point (1, 2)

Using the point-slope form of the equation of a straight line

y - y₁ = m(x - x₁)

Where m is the slope

Then,

y - 2 = -8(x - 1)

Simplify

y - 2 = -8x + 8

y = -8x + 8 + 2

y = -8x + 10

∴ f(x) = -8x + 10

f(x) = 10 - 8x

Hence, the linear function is f(x) = 10 -8x

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Answer: Emily's in total journey is 15.045 kilometers.

Step-by-step explanation:

Given data,

Emily traveled a certain distance on a horse = 10.98 kilometers

Emily traveled a certain distance on a bike = 4.06 kilometers

The overall distance traveled by Emily on her horse and bike needs to be determined.

For "Total Distance" , we will use addition operation:

So, Total distance covered by Emily's journey is given by equal to

Emily traveled a certain distance on a horse + Emily traveled a certain distance on a bike

Let us assume,

Total distance covered by Emily's journey is represented by 'x'

Then we can write,

                          x = 10.981 kilometers + 4.064 kilometers

                          x = 15.045 kilometers

Therefore, Emily's in total journey is 15.045 kilometers.

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Answer:

y20=225x or y225+x20 ir can be

The percent error is 56. 9%

Percent error is defined as the difference between the estimated value and the actual value in comparison to the actual value.

The formula for percent error is expressed as;

Percent error = [tex]\frac{|VA - VE|}{VE}[/tex] × 100/1

Where;

Substitute the values

Percent error = | 612 - 390| / 390 × 100/ 1

Percent error = 222/ 390 × 100/ 1

Percent error = 0. 56 × 100

Percent error = 56. 9%

Thus, the percent error is 56. 9%

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Answer:

Step-by-step explanation:

Answer: f(x) and g(x) both represent y of the equations

Step-by-step explanation: f(x) and  g(x) both represent the y of the equation for example f(x)=mx+b or g(x)+mx+b both would be to find y of that specific equation and that would also make them inverses because you could use the table to label the inverses on a graph.

Answer: f(-2) = - 4

Step-by-step explanation:

Answer:

C and B

Step-by-step explanation:

Evaluate g(5) then substitute the value obtained into f(x)

g(5) = [tex]\sqrt{5-1}[/tex] = [tex]\sqrt{4}[/tex] = 2 , then

f(2) = 3(2) + 1 = 6 + 1 = 7

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

f(x) = [tex]\frac{x^2+3}{(x-4)(x+8)}[/tex]

the denominator of f(x) cannot be zero as this would make f(x) undefined.

equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.

(x - 4)(x + 8) = 0

equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 8 = 0 ⇒ x = - 8

the vertical asymptotes are x = 4 and x = - 8

Answer:

the answer is 1

Step-by-step explanation:

trust mehhhh

Here is the two-way table :

Felt tired        Did not feel tired               Total

Ate breakfast                    0.0714                0.7142                           0.7857

Did not eat breakfast        0.0714                0.1428                          0.2143                                  

Total                                  0.1428                 0.8572                                   1  

A two-way table represents the frequency of dataset by arranging the dataset into a table made up of rows and columns. A conditional relative frequency is the ratio of the frequency of a class to the total frequency.  

People who ate breakfast and did not feel tired = 110 - 10 = 100

People who did not breakfast and did not feel tired = 30 - 10 = 20

                                              Felt tired        Did not feel tired               Total

Ate breakfast                          10                     100                                    110

Did not eat breakfast              10                      20                                     30

Total                                          20                    130                                     140

                                       Felt tired        Did not feel tired           Total

Ate breakfast                   10 / 140           100 / 140                       110 / 140

Did not eat breakfast      10  / 140          20 / 140                         30 / 140

Total                                20 / 140            130 / 140                         140 / 140

                                         Felt tired        Did not feel tired               Total

Ate breakfast                    0.0714                0.7142                           0.7857

Did not eat breakfast        0.0714                0.1428                          0.2143                                  

Total                                  0.1428                 0.8572                                   1  

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The domain of the relation: {0, 1, 2, 3, and 4}

The range of the relation: {0, -1, -4, -9, -16}

The graph for the relation is in the attachment.

A domain of a relation can be defined as the set of x-values or inputs of a relation.

The set of all output or y-values that correspond to the x-values in a set of ordered pairs.

Given the relation, {(0, 0), (1, -1),(2, -4), (3,-9), (4, -16)}

The domain of the relation is: {0, 1, 2, 3, and 4} (these are all the input of the relation)

The range of the relation is: {0, -1, -4, -9, -16} (these are all the output of the relation)

The graph for the relation is in the attachment.

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No extraneous solution to the equation.

The equation is

[tex](x + 5)^{1/2}[/tex] - [tex](5 - 2x)^{1/4}[/tex] = 0

To know whether the equation is an extraneous solution we first need to find the value of x.

So we have,

[tex](x + 5)^{1/2} = (5 - 2x)^{1/4}[/tex]

Multiply both sides with the power of 4, then we have

[tex]((x+ 5)^{1/2})^{4}[/tex] = [tex]((5 - 2x)^{1/4} )^{4}[/tex]

[tex](x+ 5)^{2}[/tex] = 5 - 2x

[tex]x^{2}[/tex] + 10x + 25 = 5-2x

[tex]x^{2}[/tex] + 12x + 20= 0

[tex]x^{2}[/tex] + 10x + 2x + 20 = 0

x(x + 10 ) + 2(x + 10) = 0

(x + 10)(x+2) = 0

x = -10, -2

Now we have to put the value of x in the equation

x = -10

[tex](-10 + 5 )^{1/2}[/tex]-[tex](5 - 2 * -10)^{1/4}[/tex] = 0

[tex](-5)^{1/2}[/tex] - [tex]25^{1/4}[/tex]= 0

[tex](-5)^{1/2}[/tex] - [tex]5^{1/2}[/tex] = 0

Which has not possible as we don't have negative number in the square root.

x = -2

[tex](-2 + 5)^{1/2}[/tex] -[tex](5-2*-2)^{1/4}[/tex]=0

[tex]3^{1/2}[/tex]- [tex]9^{1/4}[/tex]=0

[tex]3^{1/2}[/tex]- [tex]3^{1/2}[/tex]=0

0 = 0

Therefore there is no extraneous solution to the equation

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The points A(-3, 7), B(4, 9), and C(0, -2) is translated 2 units up and 7 units right to get A'(4, 9), B'(11, 11), and C'(7, 0)

Transformation is the movement of a point around the coordinate plane. Types of transformations are rotation, translation, reflection and dilation.

Dilation is a transformation that affects the size of a figure.

The points A(-3, 7), B(4, 9), and C(0, -2) is translated 2 units up and 7 units right to get A'(4, 9), B'(11, 11), and C'(7, 0)

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The transformation of pentagon Q to pentagon Q' is a clockwise rotation of 180° about the origin.

A transformation is a general term for four specific ways to manipulate the shape or position of a point, a line, or a geometric figure.

We have,

Coordinates of a pentagon Q.

(2, 4), (3, 7), (7, 5), (5,4), and (4,2).

Coordinates of pentagon Q'.

(-2, -4), (-3, -7), (-7, -5), (-5,-4), and (-4,-2).

We see that the coordinates of each point of the pentagon Q have changed their position as negative coordinates in pentagon Q'

The coordinates of pentagon Q are in (x, y) which can be assumed to be in the first quadrant of the coordinate plane.

The coordinates of pentagon Q' are in (-x, -y) which is in the 3rd quadrant.

From the first quadrant to 3rd quadrant there is a rotation of 180°.

Thus the transformation of pentagon Q to pentagon Q' is a clockwise rotation of 180° about the origin.

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Answer: 2169 rounded to the nearest hundred is 2200

Step-by-step explanation: Since 6 in the tenth place is greater than 5 the number in the hundred place which is 1 goes up to 2. That is how you get 2200

The given expression can be written in its simplest form by solving the exponents.

There are two types of exponent rules that will be applied to the expression. First, we will solve the negative exponent then we will multiply the exponents.

According to the negative exponent rule: x^-n=1/x^n.

Hence, applying the rule to the base term in the denominator, 1/y^⁻³/₄= y^³/₄

Therefore, x^¹/₄ / y^⁻³/₄= x^¹/₄ y^³/₄

According to the multiplication of exponent rule: (x^n)^m=x^nm

Hence, applying the rule to the expression,

(x^¹/₄ y^³/₄)^12=x^¹/₄*12 y^³/₄*12

Multiplying the powers and simplifying,

x^¹/₄*12 y^³/₄*12=x^3y^9

The simplest form of the expression (x^¹/₄/y^⁻³/₄)^12 is x^3y^9.

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The function model will be -

Divide the cost by the number of pupils to split it, and you'll get the function C=1200 / n.

1200/N ≤ 7.50

1200 / 7.50 ≤ N

N ≥ 1200/7.5

N ≥ 160

To keep the price per kid to no more than $7.50, there must be more than 160 participants.

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Devon will be able to cover 71.25 ft² of flower bed.

The number of bags of soil Devon has = [tex]4\frac{3}{4}[/tex]

Converting mixed fraction to fraction

Number of bags of soil = (4×4+3)/4

Performing multiplication and addition in numerator to find the number of bags of soil with Devon

Number of bags of soil = 19/4

Now, it is stated that area covered by 1 bag = 15 ft²

So, 19/4 bags will cover area = 15×(19/4)

Performing multiplication and division to find the area covered by the bags of soil

Area covered by bags of soil Devon has = 71.25 ft²

Hence, the area covered by bags of soil Devon has is 71.25 ft²

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The complete question is -

Devon has 4 3/4 bags of soil to put in his flower bed. Each bag will cover 15 ft2. How many square feet will he be able to cover?

the logarithm function ( log ₂ 4 ) is not a common logarithm function as it does not have a base 10.

In mathematics, the common logarithm is the logarithm with base 10.

It is also known as the decadic logarithm and as the decimal logarithm function.

Here, we have the logarithm function as:

( log ₂ 4 )

Now, we can see that:

It has a base of 2.

So, it will not be a common logarithm function as having base 10 is an important characteristic of a common logarithm function.

Therefore, we get that, the logarithm function ( log ₂ 4 ) is not a common logarithm function as it does not have a base 10.

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The truth value of the conditional statement is false

The conditional statement is given as

“If a number is greater than -500, then the number is greater than 500.”

The above conditional statement is false

This is so because

Not all numbers greater than -500 are greater than 500

Take for instance 499 is greater than -500, but less than 500

Hence, the truth value of the conditional statement is false

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20 people likes movies, such that  12 of these also like music, then the probability is just the quotient between:

Q = 12/20 = 0.6

The probability that a person likes music given that he/she lies movies is 0.6 or 60%

Notice that there are 5 + 7 common elements between movies and music, and a total of 20 people likes movies, such that 5 + 7 = 12 of these also like music, then the probability is just the quotient between the numbers of total people that likes movies which we know is 20, and the people that likes movies and also music.

So the quotient between 12 and 20, that will gave us the probability we want to find.

The probability that a person likes music given that he/she lies movies is 0.6 or 60%

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We know that the measures of dispersion tend to see how numbers are scattered around the mean. In this case, we are asked to find three of the measures of dispersion which are; range, variance and standard deviation.

We first have to arrange the data in the proper order as follows;

20.1, 21.7, 23.2, 24.0, 30.9, 33.5, 58.4, 60.0, 74.8, 110.8

It is now easier for us to find the range of the data set as the difference between the largest and the smallest value; 110.8 – 20.1 = 90.7

The mean of the dataset is = 20.1 +  21.7+  23.2 + 24.0 + 30.9 + 33.5 + 58.4 + 60.0 + 74.8 + 110.8/10

= 45.74

Now;

Variance = (20.1 - 45.74)^2 + (21.7 - 45.74)^2 + (23.2 - 45.74)^2 + (24.0 - 45.74)^2 + (30.9 - 45.74)^2 + (33.5 - 45.74)^2 + (58.4 - 45.74)^2 + (60.0 - 45.74)^2 + (74.8 - 45.74)^2 + (110.8 - 45.74)^2/10

= 657.4 + 577.9 + 508.1 + 472.6 + 220.2 +149.8 + 160.3 + 203.3 + 844.5 + 4233/10

= 802.71

Standard deviation = √variance = √802.71

= 8.96

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Value for (g⁰g)(1) = 17

Now, (g⁰g)(x) = g[g(x)]

let g(x) = 3x + 2

(g⁰g)(x) = g(3x + 2)

(g⁰g)(1) = g(5)

(g⁰g)(1) = 3(5) + 2

(g⁰g)(1) = 17

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The range of the function represented by y = 15x + 20, where y is Kim's daily earnings and x is the number of bikes she assembles, is $20 ≤ y ≤ $110.

The range of a function is the set of values of y possible values of the dependent variable after substituting values for the independent variable(domain).

The total amount she earns can be represented by

y = 15x + 20

where y is her daily earnings and x is the number of bikes she assembles

If Kim's boss daily goal is to assemble no more than 6 bicycles a day, then the value of x will only range from 0 to 6(whole number).

domain : {x| 0 ≤ x ≤ 6}

where x is a whole number

Substituting the minimum and maximum value of x in the function.

y = 15(0) + 20     when x = 0

y = 20

y = 15(6) + 20     when x = 6

y = 110

range : $20 ≤ y ≤ $110

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47576777...................

[tex]25^{2x+1}=144[/tex] => x = 0.272, by properties of logarithm.

Given: [tex]25^{2x+1}=144[/tex]

Taking logarithm on both sides:

log ([tex]25^{2x+1}[/tex]) = log (144)

=> (2x + 1) log (25) = log (144) (As [tex]log_b(a)^m = m (log_b(a))[/tex])

=> 2x + 1 = [tex]\frac{log144}{log25}[/tex]

=> 2x + 1 = [tex]\frac{2.158}{1.397}[/tex]

=> 2x + 1 = 1.544

=> 2x = 0.544

=> x = 0.272

Hence, [tex]25^{2x+1}=144[/tex] => x = 0.272, by properties of logarithm.

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7/4 miles distance  does that person walk.

What is distance?

We can use a ratio to solve

1 mile           x miles

----------------= ---------------

1 hour           1 3/4 hours

Changing to improper fractions

1 mile           x miles

----------------= ---------------

1 hour         7/4 hours

Using cross products

1 * 7/4 = 1 * x

7/4 = x

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The solution to the equation √x+4=√3 x is x = 2(1 + √3) or x = 2(1 - √3).

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] is called a quadratic equation.

The formula for the roots of the quadratic equation is found by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

It is given that:

The equation is:

√x + 4 = √3 x

√x = √3 x - 4

Squaring both sides:

x = (√3 x - 4)²

x = 3x² - 8√3 x + 16

2x² - 8√3 x + 16 = 0

x² - 4√3 x + 8 = 0

After solving with the quadratic formula:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\rm x = \dfrac{-(-4\sqrt3) \pm\sqrt{(-4\sqrt3)^2-4(1)(8)}}{2(1)}[/tex]

x = 2(1 + √3) or x = 2(1 - √3)

Thus, the solution to the equation √x+4=√3 x is x = 2(1 + √3) or x = 2(1 - √3).

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The simplest form of the following are -

a) 4/7 / (1 3/4) = 16/49

b) 5 3/5 / (2 2/3) = 21/10

The word simplify means to make something easier to do or understand. So, reducing or simplifying fractions means we make the fraction as simple as possible. We do this by dividing the numerator and the denominator by the largest number that can divide into both numbers exactly.

We have been given that

a) 4/7 / (1 3/4)

Rewrite as -

= (4/7) / (1× 3/4)

= (4/7) / (7/4)

= (4/7) × (4/7)

= 16/49

b) 5 3/5 / (2 2/3)

Rewrite as -

= (5× 3/5) / (2× 2/3)

= (5× 3/5) / (8/3)

= (28/5) / (8/3)

= (28/5) × (3/8)

= 7/5 × 3/2

= 21/10

= 2.1

Thus , the following are in order of simplicity:

a) 4/7 / (1 3/4) = 16/49

b) 5 3/5 / (2 2/3) = 21/10

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