Mathematical induction​

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

Learn more about Functions here https://brainly.com/question/22340031

#SPJ9

option D, y=x^2-2x+1 , 2x-y=2 represents system of equations .

Given:

points (1,0) and (3,4)

line equation is y - y1 = m(x-x1)

y - 0 = 4-0/3-1(x - 1)

y = 2(x-1)

y = 2x - 2

2x - y =2.

The vertex of the given upward parabola is in the first quadrant so the coefficient of [tex]x^{2}[/tex]  must have positive values.

so y = [tex]x^{2} -2x+1[/tex]

Therefore option D y=x^2-2x+1 , 2x-y=2 is correct.

Learn more about the system of equations here:

https://brainly.com/question/12895249

#SPJ1

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)

Learn more about the student loan and interest payments at https://brainly.com/question/29172183

#SPJ1

The equation of the relation x and y is y = 4x  - 4

The relation follows a linear pattern. Therefore, the relationship is linear.

A linear relationship can be represented in different form such as slope intercept form and point slope form.

Let's represent the equation in slope intercept form.

y = mx + b

where

Therefore,

m = 4 - 0 / 2 - 1

m = 4 / 1

m = 4

Therefore, let's find the y-intercept using (1, 0)

y = 4x + b

0 = 4(1) + b

b = -4

Therefore, the equation is y = 4x - 4

learn more on equation here: https://brainly.com/question/6358267

#SPJ1

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:

a) y = 0

Step-by-step explanation:

Given equation,

→ 3y - 7(y + 5) = y - 35

Now the value of y will be,

→ 3y - 7(y + 5) = y - 35

→ 3y - 7y - 35 = y - 35

→ -4y - y = -35 + 35

→ -5y = 0

→ y = 0/-5

→ [ y = 0 ]

Hence, the value of y is 0.

Answer:

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

Step-by-step explanation:

The domain is the list of possible inputs

Answer:

3.87

Step-by-step explanation:

b =

[tex] \sqrt{8 ^{2} -7 ^{2}} [/tex]

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.

To learn more about probability, visit:

https://brainly.com/question/11234923

#SPJ4

Answer:

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

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°

For more references on Vertically opposite angles, click;

https://brainly.com/question/18045519

#SPJ2

The total length of the sari Divya make is 6 yards, so option A is correct.

Four sides, four corners, and four right angles (90°) make up the enclosed 2-D shape known as a rectangle. A rectangle has opposite sides that are parallel and equal. A rectangle has length and width because it is a two-dimensional form. The length of a rectangle is its longer side; its breadth is its shorter side.

Given:

The length of saris Divya can make = 6 yards,

As the graph is showing,  to make a sari Divya required 6 yards of fabric,

Therefore, the total length of the sari Divya make is 6 yards.

To know more about Rectangle:

https://brainly.com/question/15238546

#SPJ1

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.

Learn more about the equation and function here:

https://brainly.com/question/22964920

#SPJ1

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.

To know more about linear equation one variable, visit:

https://brainly.com/question/28773343

#SPJ4

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:

learn more on equivalent equation here: https://brainly.com/question/10522819

#SPJ1

The quadratic inequality that will represent the parabola will be

y ≤ 2[tex]x^{2}[/tex] - 8x + 3

The given graph is a parabola where the mouth is open upwards. So from here we can clearly say that the coefficient of [tex]x^{2}[/tex] will be positive.

The vertex of the parabola  is given as (2 , -5) in the graph.

So let us put value of x in the inequations given to us.

first option is

y ≤ 2[tex]x^{2}[/tex] - 8x + 3

y ≤ 2*[tex]2^{2}[/tex] - 8*2 + 3

y ≤ 8 - 16 + 3

y ≤ -5

Therefore the quadratic inequality that will represent the parabola will be

y ≤ 2[tex]x^{2}[/tex] - 8x + 3

For more question related to parabola

https://brainly.com/question/16180199

#SPJ1

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.

Know more about distance here:

https://brainly.com/question/26046491

#SPJ13

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

Answer:

A and C

Step-by-step explanation:

For every x value, there should be at most 1 y value.

B and D violate that constraint.

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

Read more about dilation at

https://brainly.com/question/3457976

#SPJ1

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.

To solve more questions on triangles, visit the link below-

brainly.com/question/25950519

#SPJ1

Answer:

1, 3, 7 (<5 is also congruent to <5, but this is not a choice.)

Step-by-step explanation:

The angles congruent to <5 are:

<1 by corresponding angles.

<3 by alternate interior angles.

<7 by vertical angles.

<5 by the theorem: congruence of angles is reflexive.

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.

To learn more about Linear equations visit

https://brainly.com/question/12825068

#SPJ4

Answer:

34

Step-by-step explanation:

Absolute value means the distance from 0. So the absolute value of 34 is just 34.

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)

To learn more about equation:

https://brainly.com/question/29657992

#SPJ1

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)

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.

Learn more about equation of line here: brainly.com/question/2564656

#SPJ1