What is the slope of the line?

The figure that is a dilation of figure E is the figure F

Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.

The graph represents the given parameter

From the figure, we have the original shape to be figure E

The center point of figure E is the origin

This means that a line drawn from the origin that passes through point E must pass through the same point on the shape

From the figure, the line passes through the same point on figure E and F

Hence, figure F is a dilation of figure

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Answer:

As addition: -13+(-7)=-20

The equation of line having a slope of 1/4 which passes through point (8,-3) is y = (1/4)x - 5.

The equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the data in the question;

Point (8, -3 )

Determine the y-intercept 'b'.

Substitute the point and slope into the equation of line formula and solve for b.

y = mx + b

-3 = (1/4)(8) + b

-3 = 8/4 + b

-3 = 2 + b

b = -3 - 2

b = -5

Now, substitute slope and y-intercept into y = mx + b to determine the equation of the line.

y = mx + b

y = (1/4)x + (-5)

y = (1/4)x - 5

Therefore, the equation of the line is y = (1/4)x - 5.

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Answer:

Credit (C) = $45.50 - 0.10x

Step-by-step explanation:

Since you are wanting the credit (C) that is the y variable.

The prepaid phone card starts off with a balance of $45.50.

Every minute a call is made $0.10 is deducted (subtracted) from the card.

The unknown number or 'x' represents the number of minutes the calls lasted.

The answers are as follows -

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

Given are the following relations -

3y = x

{(2,6),(3,9),(5,15)}

{(1,16),(2,8),(4,4)}

We can write -

x = 3y

as

y = (1/3)x

m = 1/3

Relation 3y=x represents direct variation.

For the relation - {(2,6),(3,9),(5,15)}, we can write -

We can write it as -

y = 3x

Relation {(2,6),(3,9),(5,15)} represents direct variation.

For the relation - {(1,16),(2,8),(4,4)} , as [x] increases, [y] decreases, so it is a inverse relation.

Therefore -

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Answer:

Domain: {-2, 0, 3, 5}

Step-by-step explanation:

The domain is the list of possible inputs

Using simplification, the equations that are equivalent to [tex]\frac{(6x+2)}{3} =2-(3x+14)[/tex] are [tex]\frac{(6x+2)}{3 } = -3x-12[/tex] and 6x + 2 = -9x - 36

Two systems of equations are equivalent if they have the same solution(s)

In a simpler term, two equations are equivalent if they have the same solution.

Therefore, let's simplify the equation to find the equivalent solutions.

[tex]\frac{(6x+2)}{3} =2-(3x+14)[/tex]

let's open the brackets of the right side of the equation.

[tex]\frac{(6x+2)}{3}=2-(3x+14)[/tex]

[tex]\frac{(6x+2)}{3} = 2-3x-14[/tex]

[tex]\frac{(6x+2)}{3 } = -3x-12[/tex]

Therefore, let's cross multiply

6x + 2 = 3(-3x - 12)

6x + 2 = -9x - 36

Therefore, the equivalent equation are as follows:

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Answer:

14

Step-by-step explanation:

Final answer: 3[tex]b^{2}[/tex] + 8b + 2

12(3y + 6) = 12 x 3(y + 2) // Factor out 12 = 36(y + 2) // Simplify the multiplication Final answer: 36(y + 2)

An equation is a statement that two mathematical expressions are equal. It consists of two expressions separated by an equal sign (=), where one expression is on the left side and the other expression is on the right side of the equal sign. An equation represents a balance or equivalence between the two expressions, and it can be solved for the unknown variable(s) by applying mathematical operations to both sides of the equation.

Given by the question.

3b (b+4) - 4 (b-5)

= 3[tex]b^{2}[/tex] + 12b - 4b + 20 // Distribute the terms.

= 3[tex]b^{2}[/tex] + 8b + 20 // Simplify the like terms.

Final answer: 3[tex]b^{2}[/tex]+ 8b + 20

12(3y + 6)

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The distance around the triangle is equivalent to 13x/12.

A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

The sum of two sides of a triangle is greater then the third side. Mathematically -

a + b > c

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given are the sides of triangle as x/2, x/3, x/4

The distance around the triangle is equivalent to perimeter of triangle. We can write perimeter as -

P = x/2 + x/3 + x/4

P = (6x + 4x + 3x)/12

P = 13x/12

Therefore, the distance around the triangle is equivalent to 13x/12.

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Answer:

x^3 + 64 + 11x - 20bxy - 80by

(if I am wrong, apologies)

Answer:

x^2+4x-5

Step-by-step explanation:

x^3+8x^2+11x-20/x+4=x^2+4x-5

Using the distance formula, the order of each line segment from longest to shortest is b→c→a→e→f→d.

Distance Formula: d = √[(x₂ - x₁)² - (y₂ - y₁)²]

Now, calculate the distance using the distance formula as follows:

(A) The distance between A and B is:

(B) The distance between C and D is:

(C) The distance between E and F is:

(D) The distance between G and H is 2.

(E) The distance between J and K is:

(F) The distance between L and M is:

Hence, the distance using the distance formula is:

Therefore, using the distance formula, the order of each line segment from longest to shortest is b→c→a→e→f→d.

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The probability that a randomly chosen bolt has a width between 942 and 959 mm is 0.647.

The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities. Information about the possibility that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes.

Given,

The width of bolts of fabric is normally distributed with mean 951 mm (millimeters) and standard deviation 10 mm.

Z = X - 951/10 ≈ N(0.1)

P(942 ≤ X ≤ 959)

P(942 - 951/10 ≤ X - 951/10 ≤ 959- 951/10)

P( -0.9 ≤ Z ≤ 0.8)

P(Z ≤ 0.8) - P(Z ≤ -0.9)

∅(0.8) - (1 - ∅(0.9))

∅(0.8) + ∅(0.9) - 1

0.788 + 0.859 - 1

0.647

The probability that a randomly chosen bolt has a width between 942 and 959 mm is 0.647.

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Answer:

Step-by-step explanation:

so you just have to round where it came from

The equation that models the function is y = 8/3(x) - 5/3.

Given:

The graph of a linear function passes through the point (-2, -7).

When the input increases by 3 the value of the function increases by 8.

(x,y) = (x+3,y+8)

(-2,-7) = (-2+3,-7+8)

= (1,1)

slope between (1,1) and (-2,-7) is m = -7-1/-2-1

= -8/-3

m = 8/3.

substitute m in y = mx + c

y = 8/3(x)+c

substitute (-2,-7)

-7 = 8/3(-2) + c

-7*3 = -16 + 3c

-21+16 = 3c

-5 = 3c

c = -5/3

y = 8/3(x) - 5/3.

Therefore the equation that models the function is y = 8/3(x) - 5/3.

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a) The new principal (principal + capitalized interest) when Rich begins making loan payments will be $9,425.10.

b) The total interest that Rich will pay over the life of the loan is $4,914.20.

The interest on student loans is based on simple interest.

The only interest capitalized is the interest during the non-payment period if the student does not pay the interest.

Some students elect to pay the interest during the non-payment period to reduce the capitalized interest and principal during the payment period.

Capitalization refers to the addition of interest to the principal amount.

Period of student loan = 10 years

The amount of the federal unsubsidized student loan = $7,900

Interest rate = 4.29%

Capitalized interest during the non-payment time = $1,525.10 ($7,900 x 4.29% x 4.5)

New principal when Rich begins making loan payments = $9,425.10 ($7,900 + $1,525.10)

Total interest for loan = $4,914.20 ($7,900 x 4.29% x 14.5)

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Miguel drove at a speed of 60 mph in the first part of the trip and at a speed of 50 mph in the second part of the trip.

Let the speed while dropping his son to college be x mph

Therefore speed while returning is (x - 10) mph

The distance is 300 mi

Speed = Distance/Tie

or, Time = Distance/Speed

Hence the time taken during the first part of the journey = 300/x hrs

and,

Time taken for the next part of the journey

= 300/(x - 10) hrs

It is given that the total time taken was 11 hrs

Hence we get

300/x + 300/(x - 10) = 11

or, (300x - 3000 + 300x) / x(x - 10) = 11

or, (600x - 3000) / (x² - 10x) = 11

or, 600x - 3000 = 11x² - 110x

or, 11x² -710x + 3000 = 0

Applying the shreedharacharya rule gives us

x =  (710 ± √(710² -132000)/22)

x = 50/11 or x = 60

If x = 50/11 then x - 10 will be negative.

hence x = 60

Therefore Miguel drove at a speed of 60 mph in first half and 50 mph in second half.

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The Piecewise Function be

                      25x                                 when x < 40

y =

                   1000+32(x-40)                   when x > 40

Given, an engineering technician makes $25 an hour for the first 40 hours she works.

and $32 an hour for each hour over 40 hours.

Let the number of hours be x and her total weekly pay in dollars be, y

then the piecewise function,

                      25x                                 when x < 40

y =

                   1000+32(x-40)                   when x > 40

Hence, the piecewise function be

                      25x                                 when x < 40

y =

                   1000+32(x-40)                   when x > 40

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Answer:

143.75

Step-by-step explanation:

11/4+110+15+16 1/2=143.75

Answer:

Hello _____,

You are a pig, a fatty, a dunce, and a monkey. Also, you smell like a diseased pustule on the butt of a wildebeest.

Cordially,

_____

Step-by-step explanation:

Answer:

Assuming the bags sold were for 1 week period.

1.  $659.20 for 1 week and 380 bags of peanuts

2. 890 bags

Step-by-step explanation:

The equation is missing the variable, n (the number of bags sold).  I'll take the liberty to add it after the $0.84/bag term, where it belongs:

    P = 0.84n + 340

The 340 is $340/week.  n must be in units of "bags/week."

1.  How much will Ibram be paid if he sells 380 bags of peanuts?

   P = $0.84n + $340

n = 380 bags (we will assume in 1 week).

   P = $0.84n + $340

   P = $0.84(380) + $340

   P = $659.20

2.  How many bags of peanuts did Ibram sell if he earned $1,087.60?

  P = $0.84n + $340

   P = $1087.60

   $1087.60 = $0.84n + $340

      $1087.60 - $340 = $0.84n

      $0.84n =  $1087.60 - $340

      $0.84n =  $747.60

 n = 890 bags  ( ! - I'm impressed)

Then the equation that represents the total rent will be y = 5x + 7. Then the correct option is C.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The table is given below.

Number of Days Rented               Rental Cost ($)

                   1                                          12

                  2                                          17

                  3                                          22

                  4                                          27

At x = 1, the value of y is 12.

12 = m + c                      ...1

At x = 2, the value of y is 17.

17 = 2m + c                      ...2

Subtraction equation 1 from equation 1, then we have

2m - m = 17 - 12

m = 5

Then the value of 'c' is given as,

17 = 2 x 5 + c

17 = 10 + c

c = 7

Then the equation that represents the total rent will be y = 5x + 7. Then the correct option is C.

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Using the concept of linear equation in one variable, it is concluded that the total number of students who will go on the trip are 40.

An equation that contains only one variable and has its degree one is called a linear equation in one variable. The general form of linear equation in one variable is ax + b = 0, where a and b are real numbers and a ≠ 0.

Given that food and lodging charge per student = $ 60

Charge per student for bus = $ 40

And the amount paid for the cleaning fee for the bus = $ 30

Let the total number of students who are going on the trip = x

Now, the Total charge for food and lodging = $60x

The total charge for bus fare = $ 40x

Given that total cost paid = $ 4030

Hence, $60x + $40x + $30 = $4030

$100X = $4030 - $30

$100X = $4000

x = 40

Hence, the total number of students who will go on a trip is 40.

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Answer:

see explanation

Step-by-step explanation:

m + 20 and 100 are vertically opposite angles and are congruent , then

m + 20 = 100 ( subtract 20 from both sides )

m = 80

The angles are vertically opposite angles and value of m is 80°

Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

Given two angles which are Vertically opposite to each others,

We know Vertically opposite angles are equal to each other, so,

m + 20° = 100°

m = 100° - 20°

m = 80°

Hence, the value of m is 80°

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In 139.4 [tex]\pi[/tex] [tex]ft^2[/tex]sec rapidly is area of enclosed by the ripple increasing at the end of 6.4 seconds.

What is area of circle?

 For measuring the area occupied by a circular field or plot, use the area of a circle formula. The area formula will allow us to determine how much fabric is required to completely cover a circular table, for example. We can determine the boundary length, or the circle's circumference, using the area formula.

Here area of circle

=> A= π[tex]r^2[/tex]--------> 1

Differentiating 1 with respect to to time then

=> [tex]\frac{dA}{dt}= 2\pi r\frac{dr}{dt}[/tex]

If the radius is  increasing at a constant rate 3.3ft/sec then after 6.4 seconds, radius is

=> 6.4*3.3=21.12 ft.

We know [tex]\frac{dr}{dt}= \frac{3.3ft}{sec}[/tex] and so ,

=> [tex]\frac{dA}{dt}[/tex] = 2*[tex]\pi[/tex]*21.12*3.3=139.4 [tex]\pi[/tex] [tex]ft^2[/tex]sec.

Hence In 139.4 [tex]\pi[/tex] [tex]ft^2[/tex]sec rapidly is area of enclosed by the ripple increasing at the end of 6.4 seconds.

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The linear programming model for this problem is Max 1000F + 1000T

Given that,

If the quantity of flip top pens to be produced is f and the quantity of tiptop pens to be produced is t, then

Number of lots of Flip top pens to produce = F

Number of lots of Tip top pens to produce = T

Therefore, The linear programming formulation is given by:

Max 1000F + 1000T

s.t.

Plastic: 3F + 4T <= 39

Ink Assembly:  5F + 4T <= 45

Molding time: 5F + 2T <= 37

F, P >= 0

Hence, the linear programming model for this problem is Max 1000F + 1000P

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Mr. Fitzpatrick bought 9 adult tickets and 13 children's tickets.

It is given that Mr. Fitzpatrick bought 22 tickets

The tickets collectively cost him $265

The student tickets cost $10 while adult tickets cost $15

Let the no. of adult tickets sold be x

Let the no. of children's tickets sold be y

Therefore we get the equations

x + y = 22                      [1]

15x + 10y = 265                      [2]

or, 5x + 10x + 10y = 265

or, 5x + 10(x + y) = 265

from equation [1] we get

5x + 220 = 265

or, 5x = 265 - 220

or, 5x = 45

or, x = 9

Therefore,

y = 22 - 9

= 13

Therefore he bought 9 adult tickets and 13 children tickets.

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