Describe how the graph of the function g(x)=1/4|x|-2 can be obtained from the basic graph. Then graph the function.Start with the graph of h(x)=|x|. Then [__] it vertically by a factor of [__]. Finally, shift it [___] units.

30pq=3p×5q=15pq×2=30pq

Answer:

y = 1/10x + 9/10

Step-by-step explanation:

Find slope intercept form: –2x = –20y + 18

slope intercept form: y = mx + b

_______________________________

–2x = –20y + 18

add 20y to both sides:

–2x + 20y = –20y + 18 + 20y

–2x + 20y = 18

add 2x to both sides:

–2x + 20y + 2x = 18 + 2x

20y = 18 + 2x

divide all terms by 20:

20y/20 = 18/20 + 2x/20

y = 9/10 + 1/10x

reorder terms for slope intercept form:

y = 1/10x + 9/10

Answer:

[tex]y=\dfrac{1}{10}x+\dfrac{9}{10}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Given equation:

[tex]-2x=-20y+18[/tex]

To write the given equation in slope-intercept form, make y the subject.

Add 20y to both sides:

[tex]\implies 20y-2x=-20y+18+20y[/tex]

[tex]\implies 20y-2x=18[/tex]

Add 2x to both sides:

[tex]\implies 20y-2x+2x=2x+18[/tex]

[tex]\implies 20y=2x+18[/tex]

Divide both sides by 20:

[tex]\implies \dfrac{20y}{20}=\dfrac{2x+18}{20}[/tex]

[tex]\implies \dfrac{20y}{20}=\dfrac{2x}{20}+\dfrac{18}{20}[/tex]

[tex]\implies y=\dfrac{1}{10}x+\dfrac{9}{10}[/tex]

Therefore, the given equation in slope-intercept form is:

[tex]\boxed{y=\dfrac{1}{10}x+\dfrac{9}{10}}[/tex]

The value of x in the equation given is x = -4/7.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The information given will be illustrated as:

9 - (9x - 6) - 9 = 3(4x + 6)

9 - 9x + 6 - 9 = 12x + 18

Collect like terms

-9x + 6 = 12x + 18

-9x - 12x = 18 - 6

-21x = 12

Divide

x = 12/-21

x = -4/7

This illustrates the concept of equations.

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SOLUTION

We want to identify the equation that represents the data in the table.

Let's put the first values for x and y from the table, that is x = -2 and y = 11 and see if it works for the first option

This becomes

Since we didn't get y = 11, but we got y = 3, then the first option is wrong.

Let's try the next one

This becomes

So, we got y = 11, this option should be the correct answer, but let us confirm with the next values of x and y which are (0, 5).

So we will put x = 0, if we get y = 5, then the option is correct, so

Since we got y = 5, this option is correct.

Hence, the answer is the 2nd option.

We have the following:

The first thing is to calculate the volume of the cone

where r is the radius and h is the height

the radius is half the diameter, like this

The radius is 5 cm.

Now, for the height, we calculate it by means of the Pythagorean theorem that says the following

The height is 12 cm

The volume is:

The water bottle has a total of 500 cubic centimeters, while the cone is 314 cubic centimeters, therefore it cannot pour out all the water and it would overflow

Answer:

22 feet

Explanation:

The area of a triangle can be calculated using the following equation:

Where b is the base and h is the height.

We know that the area is 330 square feet and the base is 30 ft, so we can replace these values to get:

Now, we can solve the equation for h. First, multiply both sides by 2:

Then, divide both sides by 30:

Therefore, the height of the triangle is 22 feet.

Given:

A graph

To determine the Mean, Median, and Mode based on the given graph, we first get the data set as shown below:

2,5,5,5,5,6,9,11,12,13,14,15,18,20

Next, we find the Mean by getting the average:

Then, we get the Median by getting the average of the two middle values since there is an even number of data values:

Now, we get the Mode by finding the number that appears most frequently. Hence, the Mode is 5.

Therefore, the answer is:

Mean:10, Median:10, Mode:5

The normal price for the CD player is $117.30

Since the normal prices are reduced by 15%, the percentage for the normal price will be:

= 100% + 15%

= 115%

Also, the sale price of a CD player is £102.

Therefore, the normal price will be:

= Percentage for normal price × Price

= 115% × $102

= 1.15 × $102

= $117.30

The price is $117.30.

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If f(x) is a linear function and gives f(3) = 3 and f(9) = -2

Part a

The slope of the line = -5/6

Part b

The y-intercept = 11/2

Part c

f(x) = (-5/6)x + 11/2

The values of

f(3) = 3

f(9) = -2

The points are (3,3) and (9,-2)

Part a

The slope of the line is the change in y coordinate with respect to the change in x coordinate.
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

= [tex]\frac{-2-3}{9-3}[/tex]

=-5/6

Part b

The slope intercept form of the line

y = mx+b

b is the y intercept

Substitute the values in the equation

3 = (-5/6)×3 + b

3= -5/2 + b

b = 11/2

Part c

Then the linear function f(x) = (-5/6)x + 11/2

Hence, if f(x) is a linear function and gives f(3) = 3 and f(9) = -2

Part a

The slope of the line = -5/6

Part b

The y-intercept = 11/2

Part c

f(x) = (-5/6)x + 11/2

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the probability is 1 whole number 1 over 2

A rational number

The perimeter of a rectangle is given by the formula:

Perimeter = 2(Length + Width)

The Length = 6 units

Perimeter = 2 (6 + Width)

Perimeter = 12 - 2 Width

2 Width = 12 - Perimeter

Width = (12 - Perimeter)/2

Note that a rational number is a number that can be written as a fraction of two integers.

Since the perimeter is said to be a rational number, any rational number substituted into the formula equation for the width above will give a rational number.

The width of the rectangle is therefore a rational number

Answer:120 inches per second

Step-by-step explanation:120 inches per second this is because 1 ft= 12 inches so you can multiply 10 x 12 which is 120 inches.

The Solution.

Monday's sales is $3459.00

The food cost for Monday is

Tuesday's sales is $2976.81

The food cost for Tuesday is

Wednesday's sales is $3185.32

The food cost for Wednesday is

Thursday's sales is $3562.91

The food cost for Thursday is

Friday's sales is $4582.13

The food cost for Friday is

Saturday's sales is $4820.36

The food cost for Saturday is

ANSWER

z = 1.88

EXPLANATION

We have to find z such that the area under the normal curve to the right of that value is 0.03,

This is the same as finding z such that the area to the left of that value is 1 minus 0.03,

These are the values that z-score tables show. So, we have to find a z-score where the value in the table is 0.97,

The z-score whose area to its left is closest to 0.97 is z = 1.88.

Hence, for z = 1.88, the area under the curve to its right is 0.03.

Answer: x 0 1 2 3

p(x) 0.011 0.170 0.279 0.539

Given that the values of x =

Television 0 1 2 3

Household 30 443 727 1401

Let television be = x

Household = frequency = distribution

Firstly, we need to find the interval of x

The interval of x = Range between two numbers

1 - 0 = 1

2 -1 = 1

3 - 2 = 1

Hence, the interval is 1

Where N = total frequency

w = interval

Total frequency = 30 + 443 + 727 + 1401

Total frequency = 2601

when x = 1

When x = 2

when x = 3

Therefore,

x 0 1 2 3

p(x) 0.011 0.170 0.279 0.539

Answer:

She buys 24 pints of milk

Step-by-step explanation:

The conversion rule for a pint to the gallon is represented:

Then, we can make a proportional relationship to determine how many pints of milk she buys:

Answer:

B. the cost to enroll in the file-sharing service

Explanation:

The y-intercept is the cost when x = 0. It means that it is the cost of the service when the customer uploads 0 Mb, so it should represent the cost to enroll in the file-sharing service.

Answer:

Step-by-step explanation:

Here, we have two congruent triangles.

Given:

ST = 3x - 1 XY = 4x - 5

SW = 3x + 1 XZ = 4x - 3

TW = 2x + 1 YZ = x + 5

Since triangle STW and triangle XYZ are congruent, they have exactly the same corresponding sides.

To find the value of x, equate the corresponding sides and evaluate.

ST = XY

SW = XZ

TW = YZ

Take one of the corresponding sides.

We have:

ST = XY

3x - 1 = 4x - 5

Subtract 4x from both sides:

3x - 4x - 1 = 4x - 4x - 5

-x - 1 = -5

Add 1 to both sides:

-x - 1 + 1 = -5 + 1

-x = -4

Divide both sides by -1:

Therefore, the value of x that makes ΔSTW ≅ ΔXYZ is 4

ANSWER:

x = 4

A graph of the proportional relationship is given by: D. graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 30.

A graph can be defined as a type of chart that's commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate.

Mathematically, a proportional relationship can be modeled by the following linear equation:

y = kx

Where:

Furthermore, the graph of any proportional relationship is characterized by a straight line with data points passing through the origin (0, 0) because as the values on the x-coordinate (x-axis) decreases or increases, the values on the y-coordinate (y-axis) decreases or increases simultaneously.

In this context, we can reasonably infer and logically deduce that the relationship between the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of this graph is proportional and given by this equation:

y = 3x

Where:

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Answer:

A graph of the proportional relationship is given by: D. graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 30.

Step-by-step explanation:

Firstly, we need to know the number of boxes they both filled per hour.

From the question, we are told that 126 boxes were filled in six hours; thus in an hour, the number of boxes filled will be 126/26 = 21 boxes

Now in an hour, Nicholas filled 9 boxes; the number of boxes that will be filled is clearly the remainder of the 21 boxes.

The number of boxes filled by Jack is thus; 21 - 9 = 12 boxes

Jack fills 12 boxes in an hour

Answer:

The 3 angles are 22.5, 67.5 and 90 degrees.

Step-by-step explanation:

Let the smallest angle be x degrees.

Then the other angles = 3x and 2x + 45.

x + 3x + 2x + 45 = 180

6x = 180 - 45

6x = 135

x = 135/6 = 22.5 degrees

3x = 67.5 degrees

2x+45 = 90 degrees.

Given,

The amount of liquid hold by measuring cup is 2 cups.

The number of times measuring cup used to fill the pitcher.

Required:

The amount of liquid pitcher hold.

The amount of liquid hold by the pitcher is,

Substituting the values.

Hence, the pitcher can hold 15 cups.

The required system of equation is x+y+z=18, z=5x, x+2z=22 and the required values of x=2, y=6 and z=10 by using the substitution method of solving equations and according to given conditions: The sum of three numbers is 18. The largest is 5 times the smallest, while the sum of the smallest and twice the largest is 22. .

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the other equation in this method, as the name implies.

x+y+z=18

z=5x

x+2z=22

x+10x=22

x=2

y=6

z=10

The required system of equations is x+y+z=18, z=5x, x+2z=22, with the required values of x=2, y=6, and z=10 when solving equations using the substitution method under the conditions stated: Three numbers added together equal 18. The sum of the smallest and twice-largest numbers is 22, while the largest is five times the smallest.

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x=-4, y=1 and z=-5 are solutions of x+y+2z=-5" 5x+4y-4z=4 x-3y-2z=3

Two or more expressions with an Equal sign is called as Equation.

The given three equations are

-x+y+2z=-5.....(1)

5x+4y-4z=4....(2)

x-3y-2z=3....(3)

Add equations (1) and (3)

-x+y+2z+x-3y-2z=-5+3

Add the like terms

-2y=-2

y=1

Now put value of y in equations (1) and (2)

-x+2z=-6..(4)

5x-4z=0...(5)

Multiply with 5 on equation 4 and add with equation 5

-5x+10z+5x-4z=-30

6z=-30

z=-5

Now put y and z values in equation (1)

-x+1+2(-5)=-5

-x+1-10=-5

-x-9=-5

-x=4

x=-4

Hence x=-4, y=1 and z=-5 are solutions of x+y+2z=-5" 5x+4y-4z=4 x-3y-2z=3

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Answer

Domain is all real numbers except x ≠ 0, -4, and 4

Vertical asymptote at x = 0, -4, and 4

Explanation

Given function:

Note: The domain of a function is a set of input or argument values for which the function is real and defined.

For the function to be real; the denominator must not be equal zero, i.e.

Hence, the domain is all real numbers except x ≠ 0, -4, and 4.

Note: A vertical asymptote with a rational function occurs when there is division by zero.

Hence, the vertical asymptote at x = 0, -4, and 4

Givens.

• The total number of laps is 14.

• The total distance is 30.8 miles.

First, divide the total distance by the number of laps.

Each lap length is 2.2 miles.

Let's transform it to yards using the conversion factor 1 mile = 1760 yards.

Therefore, each lap length is 3872 yards.

Answer:

Step by step explanation:

Linear functions represent situations that have a constant rate of change, and they are represented by:

We can calculate the constant rate of change with the following formula:

Then, the function that describes the relationship between x, the number of net earnings, and y, the self-employment tax would be:

Answer: undefined

The slope of this graph is undefined because it does not run on the horizontal

Since, slope = y2 - y1 / x2 - x1

Therefore, x2 - x1 = 0

Slope = y2 - y1 / 0 = undefined