Graph the equation 4x−5y=1 by plotting points.

The width of the original rectangular slate is 14 inches.

A rectangle is an object that has four sides. The opposite sides are of equal length. A rectangle has two diagonals that are of equal length that bisect each other at right angles.

The area of a rectangle = length x width

Area of the new rectangular slate = (16 - 2) x (w - 2) = (16 x w) - 56

Area of the new rectangular slate = 14 x (w - 2) = 16w - 56

Area of the new rectangular slate = 14w - 28 = 16w - 56

In order to determine the value of w, take the following steps:

Combine similar terms together: 56 - 28 = 16w - 14w

Add similar terms together: 28 = 2w

Divide both sides of the equation by 2 : w = 28 / 2

w = 14

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According to the sum of the given supplementary angles, we find out that the value of x is 30.

It is given that ∠A and ∠B are supplementary where,

∠A = (4x + 30)° and,

∠B = (2x - 30)°

We have to find out the value of x.

We know that two supplementary angles add up to 180°.

Since ∠A and ∠B are supplementary angles, therefore

∠A + ∠B = 180°

=> (4x + 30) + (2x - 30) = 180°

=> 6x = 180°

=> x = 30

Thus, for the given supplementary angles, the value of x is 30.

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**According to the sum of the given supplementary angles, we find out that the value of x is 30.

It is given that ∠A and ∠B are supplementary where,

∠A = (4x + 30)° and,

∠B = (2x - 30)°

We have to find out the value of x.

We know that two supplementary angles add up to 180°.

Since ∠A and ∠B are supplementary angles, therefore

∠A + ∠B = 180°

=> (4x + 30) + (2x - 30) = 180°

=> 6x = 180°

=> x = 30 **

If one item is chosen at random, the probability that it is less than 13.1 inches long is equal to 0.4176.

First of all, we would determine the z-score of this data set. Mathematically, the z-score of a given sample score in a normal distribution can be calculated by using this formula:

Z-score = (x - μ)/σ

Where:

Substituting the given parameters into the formula, we have;

Z-score, z = (13.1 - 13.6)/(2.4)

Z-score, z = -0.5/2.4

Z-score, z = -0.208

If one item is chosen randomly, the probability that it would be less than 13.1 inches long is given by this mathematical expression:

P(x < 13.1) = P(z < -0.208)

P(z < -0.2083) = 0.4176.

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A graph of the given set of functions has been plotted and shown in the image attached below.

In Mathematics, a function simply refers to a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable to an output variable.

In Mathematics, a graph is a type of chart that is typically used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).

By critically observing the graph of this set of functions (see attachment), we can reasonably infer and logically deduce that they both represent parallel lines, with function f(x) being transformed to produce function h(x).

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Based on the number of members in the Westview Journalism Club, the amount that each student should raise on average to meet the goal is $40.

The amount that the students would have to raise is the amount that is remaining from the amount already raised. This can be found as:

= Amount that club needs to raise - Amount already raised

= 2, 100 - 1, 180

= $920

The average amount that each student has to raised to meet the target would then be based on the number of students in the club which is 23 members.

The average amount is therefore:

= Amount that still needs to be raised / Number of students in the Westview Journalism Club

= 920 / 23

= $40

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Answer:

Avi

$21.61

Step-by-step explanation:

I = Prt

Sari: I = Prt = $1230 × 0.045 × 4 = $221.40

Avi: I = Prt = $1105 × 0.055 × 4 = $243.01

$243.01 - $221.40 = $21.61

Answer:

Avi

$21.61

The customer will rent 4 bikes per dollar

Keller's bike deal with renting of bikes

At the Keller's bike rentals it costs $16 to rent a bike for 4 hours

Therefore the number of bikes per dollar can be calculated as follows

16= 4

x= 1

Cross multiply

4x= 16

x= 16/4

x= 4

Hence it costs a customer 1 dollar to get 4 bikes

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The probability that at least one envelope is red envelope is 2/7.

Given:

A collection of envelopes consisting of two red envelopes three blue envelopes one green envelope and one yellow envelope if two envelopes are selected at random with replacement.

Total = 2 + 3 + 1 + 1

= 5 + 2

= 7

Number of possible outcomes = 7

Number of favorable outcomes = 2

Probability that at least one envelope is red envelope is = 2/7

= 0.2857

Therefore the probability that at least one envelope is red envelope is 2/7.

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Answer:

choose 2nd option

Step-by-step explanation:

The accumulated amount in the annuity if $80 is invested for 40 years at 6% is $25,709.04.

An annuity is when a series of payment is made over a specified period of time. An annuity can either be an ordinary annuity or a beginning annuity. An ordinary annuity is when the series of payment is made at the end of the period. A beginning annuity is when the annuity payment is made at the beginning of the period.

In this question, the annuity would last for 40 years and payments would be made twice a year.

The formula that can be used to determine the accumulated amount is:

Accumulated amount = annuity factor x payment

Annuity factor = {[(1+r)^n] - 1} / r

Where:

Accumulated amount = $80 x [{(1.03^80) - 1} / 0.03]

Accumulated amount = $80 x 321.36302

Accumulated amount = $25,709.04

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The other points (7.3, 2.2) are on a line that includes points (-5, 4) and (4, 1).

What is the equation of a line?

The equation of a line is written as axe + by + c = 0, which is its conventional form. In this equation, the variables x and y are the constant term, while the coefficients a and b are the coefficients. It is a first-order equation with the variables x and y.

Slope using the formula:

[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

We have two points, (-5, 4) and (4, 1).

m = (1 - 4) ÷ (4 - (-5))

m = −1/3

m = -0.3

Line Equations with Slope : y - y1 = m(x - x1)

Using the coordinates of one of the points on the line, insert the values in the x1 and y1 spots to get an equation of a line in point-slope form.

Let's use a point from the original example above  (4, 1). and the slope we calculated as -0.3. Put those values in the point-slope format to get an equation of that line in the point-slope form:

y - 1 = -0.3(x - 4)

y = -0.3x + 2.2

Using the equation y = -0.3x + 2.2, set x=0 to find the y-intercept.

y = -0.3(0) + 2.2

y = 2.2

The y-intercept is 2.2

Using the equation y = -0.3x + 2.2, set y=0 to find the x-intercept.

0 = 3x - 6

0 = -0.3x + 2.2

0.3x  = 2.2

x = 7.3

The x-intercept is 7.3.

Hence, the other points (7.3, 2.2) are on a line that includes the points (-5, 4) and (4, 1).

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Answer: 930$ and the expression is 1000$ - 70$ = 930$

Step-by-step explanation:

if she has under 100 dollars in her bank account every month for 10 months therefore multiplying it by 10 giving you 1000 but we cant forget about the 7$ monthly fee.  7 times 10 = 70   1000- 70 = 930$

Answer:

Step-by-step explanation:

The number of kilometers that Brett and Julian would have run at the 3 / 5 point are:

Brett is running the 5k race at the Memorial Day race which means that when he runs 3 / 5 of the race, he would have ran a total of :
= Distance on Brett's race x Proportion ran

= 5 x 3 / 5

= 15 / 3

= 3 km

Julian on the other hand, is in the 10 k race which means that when they get to 3 / 5 of the race, they would have ran:

= 10 x 3 / 5

= 30 / 5

= 6 km

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Answer:

Step-by-step explanation:

1=205

2=63

3=45

4=5

Answer:

I think 72,000 because since the weightlifter is lifting 72 and it is kg. It is turned into grams. multiplied by 1000 so 72000

3 11/20

Step-by-step explanation:

1 3/4+1 4/5=

7/4+9/5=

7/4x5/5=35/20

9/5x4/4=36/20

35/20+36/20=71/20=3 11/20

The component form of the vector that translates C to D is <7, -3>

A translation is a movement in a straight line.

In order to determine the component form of the vector that translates C to D, we have to subtract the coordinate values of point C from the coordinate values of the image C:  

(x, y) = D - C  

The movement from C to D on the x-axis is 7 units to the right (positive 7) while movement on the y-axis is 3 units down (negative -3). Thus:

(x, y)  = (7, -3)

In vector form, <x, y> = <7, -3>

Therefore, the vector that translates C to D is <7, -3>

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Answer:

4/8 and 8/16

Step-by-step explanation:

Multiply 1/2 and 3/4 to find a common fraction between them (4/8) then multiply that fraction by any number greater than 1 to find another fraction equivalent

Answer:

Step-by-step explanation:

You have segment RT of length 77 with point S on it dividing it into segments RS=6y+3 and ST=5y+8. You want to know the value of y and the lengths of segments RS and ST.

The segment sum theorem tells you the whole is the sum of the parts:

  RS +ST = RT

  (6y +3) +(5y +8) = 77 . . . . . use given values

  11y +11 = 77 . . . . . . . . . . . . collect terms

  y +1 = 7 . . . . . . . . . . . . . . . divide by 11

  y = 6 . . . . . . . . . . . . . . . . . subtract 1

The lengths of the parts are ...

  RS = 6y +3 = 6(6) +3 = 39

  ST = 5y +8 = 5(6) +8 = 38

The equation that represents the cost, y, and the number of bagels, x is D. y=1.25x

An 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.

It should be noted that 1 dozen = 12

The equation the represents the information will be:

y = (15/12) × x

y = 1.25 × x

y = 1.25x

where x = number of bagels

The equation is y = 1.2x.

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The value of the equation (2a^2 +a + 3) divided by (a - 1) is 2a + 3.

An 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.

In this case, the equation is illustrated as:

(2a² +a - 3) divided by (a - 1). This will be

(2a² +a - 3) / (a - 1)

It should be noted that (2a² +a + 3) will be:

(2a² +a + 3)

= 2a² - 2a + 3a - 3

= 2a(a - 1) + 3(a - 1)

= (2a + 3)(a - 1)

This will be:

= (2a + 3)(a - 1) / (a - 1)

= 2a + 3

The value is 2a + 3.

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Complete question

(2a^2 +a - 3) divided by (a - 1)

Answer:

It looke like the point given is (1,2) and the slope is 3

Point slope form: y - 2 = 3(x -1)

Slope Intercept form: y = [tex]\frac{-1}{3}[/tex]x + 1

Step-by-step explanation:

Point slope  As they name implies, you need a point and a slope.  The picture is a little hard to read, but it looks like the point plotted is (1,2)  The slope is the change in y over the change in x.  It looks like from that point to get back on the line only using horizontal and vertical moves, we would move up three and 1 to the right to get back on the line at point (2,5).

The point slope form of a line is:

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])    Plug in 2 for [tex]y_{1}[/tex] and 1 for [tex]x_{1}[/tex] amd 3 for m

y = 2 = 3( (x-1)

Slope intercept form:  As the names implies we need a slope and a yi-intercept.

The slope is [tex]\frac{-1}{3}[/tex].  Select a point on the line.  If you can only move veritacl and horizontal.  You  would move down 1 unit and three units to the right.  The y intercept is where the line crosses the y axis.  In this case 1

y = [tex]\frac{-1}{3} x + 1[/tex]

The estimates for the number of transistors per IC, using an exponential function, are given as follows:

The format of an exponential function is presented as follows:

[tex]y = ab^\frac{x}{n}[/tex]

In which the parameters of the function are listed as follows:

Moore's Law states that the number of transistors per IC doubles every two years, hence the values of parameters b and n both have values of two, hence:

b = 2, n = 2.

The number of transistors per IC in the reference year of 1972 was of 4000, hence the initial value is of:

a = 4000.

Then the exponential function is:

[tex]y = 4000(2)^{\frac{x}{2}}[/tex]

2012 is 2012 - 1972 = 40 years after 1972, hence the estimate is given as follows:

[tex]y = 4000(2)^{\frac{40}{2}} = 4,194,304,000[/tex]

2040 is 68 years after 1972, hence hence the estimate is given as follows:

[tex]y = 4000(2)^{\frac{68}{2}} = 6.87 \times 10^{13}[/tex]

The chart is given by the image at the end of the answer.

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The present value of an annuity is $736.01

We know that the formula for Present Value of Annuity:

PV = P * [1 - (1 + r)^(-n)]/r

where, PV = present value of an ordinary annuity

P = value of each payment

r = interest rate per period

n = number of periods

From given data:

P = $100, n = 10 and r = 0.06

So, the present value would be,

PV = 100 * [1 - (1 + 0.06)^(-10)]/0.06

PV = 100 * 7.3601

PV = $736.01

Therefore, the present value of an annuity is $736.01

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1) The scatter plot at the right most likely represents the number of siblings a person has and the person’s GPA.

2) The most reasonable estimate of the gallons of gas in a tank if it has been 3 days since filling up is; 17 gallons

1) Scatter plots are defined as the graphs that present the particular relationship between two variables in a data-set.

A scatter plot is also defined as a chart type that is usually used to observe and visually display the relationship between variables.

From the given scatter plot, we can say that the scatter plot at the right would most likely be used to represent the number of siblings a person has and the person’s GPA.

2) From the given scatter plot, we can see that the x-axis shows the number of days left since filling up while the y-axis represents the gallons of gas.

Now, we want to find out the most reasonable estimate of the gallons of gas in a tank if it has been 3 days since filling up. We will trace 3 on the x-axis and the corresponding value on the y-axis would be approximately 17 gallons.

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