The width of a rectangle is 7x - 1 feet and the length is 2x + 10 feet. Find the perimeter of the rectangle.

Answer:

  7.5 in²

Step-by-step explanation:

You want the area of a triangle shown as having a base of 6 inches and a height of 2.5 inches.

The formula for the area of a triangle is ...

  A = 1/2bh

where b is the base length, and h is the height.

The figure shows the base of the triangle as 6 in, and the height as 2.5 in. This means the area is ...

  A = 1/2(6 in)(2.5 in) = 7.5 in²

__

Additional comment

The attachments show the triangle to be overs-specified. If the side dimensions are correct, the area is actually about 7.48 square inches. If the base and height are correct, at least one side length is slightly off.

The number of time it take  Katherine to drive from home back to college is: 3 hrs 21 min.

Going home:

Rate =  65.1 mph , distance  = x miles ; time = distance /rate = x/ 65.1 hrs

Going to college:

Rate = 70.7 mph ; distance  = x miles ; time = x/70.7 hrs

Equation:

x/70.7+ x/ 65.1=  11

70.7x + 65.1x = 7 × 65.1 × 70.7

Combine like terms

135.8x = 32,217.99

Divide both side by 135.8x

x = 32,217.99/ 135.8

x = 237.25 miles

Home back to college

=  237.25 /70.7

=3.35 hrs

= 3 hrs 21 min

Therefore it take Katherine 3 hrs 21 min.

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Answer:

Question 1 is G.

Question 2 is B

Question 3 is D

Question 4 is A.

Step-by-step explanation:

Answer: 125

Step-by-step explanation:

100% = 100

25% of 100 = 100/4 = 25

100 + 25% (25) = 125

The real width of the building is given by 47 meters.

Given that the actual length of the building is 62 meters.

In a scale drawing, the length of the building is 12.4 cm.

So, 12.4 cm = 62 meters

1 cm = 62/12.4 = 620/124 = 5 meters.

Also given that the width of building on scale drawing = 9.4 cm

Hence the real width of the building = 9.4 * 5 = 47 meters.

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Answer:

y=12x-7

Step-by-step explanation:

Slope intercept is  y=mx+b

                            y = slope+y-int

always start with variable y =

slope = 12

y=12

slope needs x

y=12x

y-int = -7 so just plug it in as is

y=12x-7

Out of all the given situations, all are fair gambles,

Any gamble is considered to be a fair gamble if the expectation of it is 0. Here, gamble means any situation which has a probabilistic uncertainty attached to it.

The expectation of any game is

E(X) = ∑xp(x)

In the first case

The probability to get a had or tails on flipping a coin is 1/2

Hence the expectation will be

E(X) = 0.5 X 10  +  0.5 X (-10)

= 5 - 5

= 0

Hence this is a fair gamble

In the next gamble, two coins are tosses

The probability to get 2 head is 1/4

The probability to get 2 tails is 1/4

The probability to get one head and one tail is 1/2

Hence,

E(X) = 0.25 X 10  +  0.25 X (-10)  +  0.5 X 0

= 2.5 - 2.5

= 0

Hence this too is a fair gamble

Here,it is given that

Probability              Gain

0.5                            $100

0.25                       - $200

0.25                           $0

Therefore,

E(X) = 0.5 X 100  +  0.25 X (-200)  +  0.25 X 0

= 50  - 50

= 0

Hence, all are fair gambles.

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Correct Question

which of the following is a fair gamble?

one coin toss: win $10 if heads, lose $10 if tails.

two coin tosses: win $10 if two heads, lose $10 if two tails, and no change of wealth otherwise.

a game in which you win $100 with a probability of 50%, lose $200 with a probability of 25%, and gain nothing with a probability of 25%.

all of the above are fair gambles.

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Answer: y = -4/5x - 5

Step-by-step explanation:

So you can view that fancy F with the parenthesis number inside of it as an input, just like X, and when -1 is the output, that means that y=-1, so your first set of numbers is (5,-1) now do the same with the second pair and you get (0,-5), we know that this is the Y intercept because X=0 in this pair.

-5 - (-1) = -4

0-5 = -5

slope = - 4/5

y intercept = -5

The equation of the graph is a straight line written in slope-intercept form as y = -33.3x + 450. When Misty travelled for 9 hours, he drove 150.3 miles.

The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept. It is the most common form of the equation of a straight line that is used in geometry. The equation of a straight line can be written in different forms such as point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a two-dimensional geometrical entity that extends on both its ends till infinity.

The equation of a straight line is a mathematical equation that gives the relation between the coordinate points lying on that straight line. It can be written in different forms and tells the slope, x-intercept, and y-intercept of the line. The most commonly used forms of the equation of straight line are y = mx + c and ax + by = c. Some other forms are point-slope form, slope-intercept form, general form, standard form, etc. Let us go through the formula for the equation of a straight line

13: The equation of graph in slope-intercept form

But for this case, we will represent our equation using point-slope formula which is y = mx + c

Let's find the slope of the line.

To do this, we will pick any two points and solve for the slope.

A = (0, 450), B = (6, 250)

The equation of slope of a line is given as

m = y₂ - y₁ / x₂ - x₁

m = 250 - 450 / 6 - 0

m = -200/6

m = -33.3

The y-intercept is the point which the line touches the y-axis or y-plane and in this case, the y-intercept is 450.

The equation of the line is y = -33.3x + 450

14: If he has been travelling for 9 hours, how many miles left ?

Using the equation y = -33.3x + 450; put x = 9

y = -33.3(9) + 450

y = 150.3 miles

Misty has 150.3 miles left.

15: If there are 50 miles in the trip left, how many hours has Misty travelled.

Using the equation y = -33.3x + 450

50 = -33.3x + 450

-400 = -33.3x

x = 12 hours

Misty has approximately travelled 12 hours.

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Answer: 3.6

Step-by-step explanation: Annual means yearly, therefore 43.2 divided by 12 is 3.6. So 3.6 inches monthly.

If the average annual stock return is 11. 3%, the average holds a portfolio of $8600 worth 30 years.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.

It is given that, the average annual stock return is 11. 3% and you begin your investment portfolio with $2,000,

Suppose the amount he earns in one year is x,

x=  11. 3%. of $2,000

x=220

The portfolio be worth 30 years if the average holds are,

=220 × 30

=$ 6600

The net cost is the sum of the return and the initial investment,

=$ 6600 + $ 2000

=$8600

Thus, if the average annual stock return is 11. 3%, the average holds a portfolio of $8600 worth 30 years.

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Answer:

  7

Step-by-step explanation:

You want the integer length of the shortest third side that will form a triangle with sides 12 and 18.

The triangle inequality requires the sum of any two sides exceed the measure of the third side. If x is the short side, we want ...

  x +12 > 18

  x > 6 . . . . . . subtract 12

The smallest integer greater than 6 is 7.

The third side must be at least 7 units long.

__

Additional comment

Some authors write the triangle inequality as a+b≥c. If you use that version, then the shortest side can be 6 units. The resulting "triangle" will have zero area, and will look like a line segment 18 units long.

The total change in temperature is 58°F.

It should be noted that temperature simply means the degree of hotness and coldness in a body.

In this situation, the temperature in a town increased 18°F in 4 hours and the temperature decreased 40°F in the next 6 hours.

The change in temperature will be:

= Old temperature - New temperature

= 18°F - (-40°F)

= 18°F + 40°F

= 58°F

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The measure of the non-felex DOB in degrees is 140°.

It is important to note that the value of the angles at a point is 360°.

Therefore, it should be noted that also vertically opposite angles are equal.

Therefore, the angles will be:

3.5y + 3.5y + y + y = 360°

9y = 360°

Divide

y = 360° / 9

y = 40°

Therefore, DOB will be:

= 3.5y.

= 3.5 × 40

= 140°

DOB is 140°.

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The value of the fraction 2 2/3 + 2 1/4 is 4 11/12.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the addition of the fraction will be:

= 2 2/3 + 2 1/4

= 2 8/12 + 2 3/12

= 4 11/12

The value is 4 11/12.

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The graph g(x)=log(-3x + 9)+4 is the outcome of a transformation on the function, f (x) = log (x), which can be visualized as a reflection across the y-axis. Then you contract by a factor of 3 horizontally, 3 to the right, and 4 to the up.

The connection between an independent variable and a dependent variable is established by a mathematical expression, rule, or law (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given function:

Parent function: f(x) = log(x)

Transformation function: g(x) = log(-3x + 9) + 4

Step 1 -  Shift 3 unit right, to achieve the function

y = log (x - 3) (x - 3)

Step 2 - Reduce the graph by thrice by multiplying x by three:

y = log 3(x - 3) (x - 3)

Step 3 -  The formula y = log 3(x - 3) to line -3 = x is to be reflected to obtain: y = -3 (x - 3)

Step 4 - The function y = log 1 - 3(x - 3) should be translated by four units to reach

Therefore, the function can be transformed by reflection and translation.

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The amount Heidi earned in commission is $30 and the amount store made from her sale is $720.

We will solve the given problem using percentages.

We are given the following;

A salesperson at a jewelry store eams 4% commission each week.

Last week, Heidi sold $750 worth of jewelry.

We need to find the amount Heidi earned in commission and the amount store made from her sale.

Let us find the amount Heidi earned in commission;

$750 * 4% = 750 * 4 / 100 = 7.5 * 4 = 30

So, Heidi earned $30 from the commission.

Let us find the amount store made from her sale;

The amount store earns

= The total amount of sales - commission of Heidi

= $750 - $30

= $720

So, the store earns $720.

Thus, the amount Heidi earned in commission is $30 and the amount store made from her sale is $720.

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Answer: A number which is divided by 5, with the result as 50 less than if the number had been divided by 6 would be; -1500

How to solve Algebra Word Problems?

Let the number be x. We are asked that it is divided by 5, and the result is 50 less than if the number had been divided by 6;

(x/6) - (x/5) = 50

Multiply by 30 to get;

5x - 6x = 1500

-x = 1500

x = -1500

Let the older turtle be represented x and the younger one be y.

Todays age,

Older turtle = 11y years

Younger turtle = y years

Also the equation form as;

11y + 24 = 7(y + 24)

11y + 24 = 7y + 168

11y - 7y = 168 - 24

4y = 144

y = 144/4

y = 36

Thus;

Age of older turtle today = 396 years

Age of younger turtle today = 36 years

Therefore,

3(36 + t) = 396 + t

108 + 3t = 396 + t

2t = 292

t = 292/2

t = 146 years

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Step-by-step explanation:

The statement which best reflects the solutions of the equation; as given in the task content is; x = 3 is a valid solution and x = 2 is an extraneous solution.

It follows from the task content that the statement which represents the solution of the given equation be determined.

Since the given equation can be written algebraically as follows;

x/(x - 1) - 1/(x - 2) = (2x - 5) / (x² - 3x + 2)

By observation; (x - 1) (x - 2) = x² - 3x + 2.

Therefore, by multiplying through the equation by; x² - 3x + 2; we have;

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

x² - 2x - x + 1 = 2x - 5

x² - 5x + 6 = 0.

Hence, the equation above can be solved quadratically so that we have;

(x - 3) (x - 2) = 0.

Therefore, the solution to the given equation is; x = -3 Or x = 2.

However, the solution x = 2 renders the equation undefined, hence, it is not a valid solution but an extraneous solution.

Therefore, the statement which reflects the solutions to the given equation is; x = 3.

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Really hope this helps you!

Answer:

THE ANSWER IS x= 33/20

hope it help

with the steps:

1) Multiply all terms by the same value to eliminate fraction denominators

2) Cancel multiplied terms that are in the denominator

3) Multiply the numbers

1) 4x//3==11/5 then 15 ✖️ 4x/3= 15 ✖️ 11/5

2) 5 ✖️ 4= 3 ✖️ 11

3) 5 ✖️ 4x=3 ✖️ 11

          20x=3 ✖️ 11

solution : x= 33/20

Answer:

x = [tex]\frac{33}{20}[/tex]

Step-by-step explanation:

[tex]\frac{4x}{3}[/tex] = [tex]\frac{11}{5}[/tex]  cross multiply and solve

20x = 33 divide both sides by 20

x = [tex]\frac{33}{20}[/tex]

The Correct option is D .

System of linear equations,gives us the result that given system has unique solution such that 13x= 6 or x = 6/13 and y = -40/13 .

If a, b, and c are real numbers, the graph of the equation ax + by = c

is a straight line (unless both a and b are zero), so such an equation is called a linear equation in variables x and y. There are three possible types of solutions to a set of linear equations.

given system of equations is

2x - y = 4 --(1)

and 5x + 4y = -10 ---(2)

comparing the above equations with linear system , a1 x + b1 y = c1 and a2 x + b2y = c2

we get, a1 = 2 , a2= 5 , b1 = -1 , b2= 4 , c1= 4 ,

c2= -10

Now, the ratio are

a1/a2 = 2/5 ; b1/b2 = -1/4 ; c1/c2= -4/10 = 2/5

=> a1/a2 not equal to b1/ b2

therefore the given system of equations has unique solution.

Now , we find the soltion of given system using Elimination method,

multipling equation (1) by 4 to making same cofficient of y in both equations of system we get

8x - 4y = 16 --(3) and 5x +4y = -10

adding equation (2) from (3) we get,

8x -4y + 5x + 4y = 16 -10 => 13x = 6 => x = 6/13

putting this value of x in (1)

2×6/13 - y = 4 => y = 12/13-4 = -40/13

Hence , unique solution for given system of equations is x= 6/13 , y = -40/13.

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Complete Question:

Alfred tried to solve the system of equations shown below..

2x - y = 4 and 5x + 4y = -10

He concluded that the system has an infinite number of solutions. Which is the BEST evaluation of Alfred's conclusion?

He is correct. Both equations describe lines that have infinitely many solutions.

He is correct. If the first equation is multiplied by 4 and subtracted from the second equation, the result is -3x +8y = -14 , which means the system has an infinite number of solutions.

He is incorrect. For any positive value of , the corresponding value of is negative, which means the system has no solution.

He is incorrect. If the first equation is multiplied by 4 and added to the second equation, the result is 13x = 6 , which leads to exactly one solution.

Answer:u dont

Step-by-step explanation:

Answer:

There is no solution because after solving the absolute value, the number will be multiplied by -4 which would be getting positive 9 impossible.

The line graphed with the y-intercept 3 and slope -4/3 is shown in the graph added in the attachments.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

m=(y₂-y₁) / (x₂-x₁)

It is given that,  the line is having the y-intercept 3 and slope -4/3.

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

The equation with the y-intercept 3 and slope -4/3 is,

y=mx+c

y= -4/3x+3

3y= -4x+9

Thus, the line graph with the y-intercept 3 and slope -4/3 is shown in the graph added in the attachments.

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Answer:

360

Step-by-step explanation:

it has four right angles 90×4 =360

The percentage of airline passengers covered by this fee is 85.99%.

If the distribution is normal, use the Z-score formula. For a set of means and standard deviations, the measure's z-score X is given by z-score measures how many standard deviations a measure is from its mean. After finding the Z-score, look at the Z-score table to find the p-value associated with that Z-score. This p-value is the probability that the value of the measure is

less than X, the percentile of X Subtracting 1 from the p-value gives the probability that the value of the measure is greater from X means 46 pounds with a standard deviation of 3.7 pounds.

This is the p-value of Z for X = 50 minus 1 as a

ratio. So the p-value of is 0.8599or 0.8599× 100 = 85.99%

So, 85.99% of the airline passengers pay this fee.

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