The length of a rectangle is 6 m longer than its width. If the perimeter of the rectangle is 64 m find its length and width in meters

The functions g(0) = 20, g(−2.5) = 0, g(4) = 0, g(0.75) = 21.125, g(20) = -720 as a result of the mapping with the function g(x) = −2x² + 3x + 20

A function is a mapping whose codomain is the set of real numbers. It can also be defined as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

From the function g given as g(x) = −2x² + 3x + 20, by careful mapping we have the following;

put 0 for values of x

g(0) = -2(0)² + 3(0) + 20

g(0) = 20.

put -25 for values of x

g(-25) = -2(-25)² + 3(-25) + 20

g(-25) = -12.5 - 7.5 + 20

g(-25) = 0

put 4 for values of x

g(4) = -2(4)² + 3(4) + 20

g(4) = -32 + 12 + 20

g(4) = 0

put 0.75 for values of x

g(0.75) = -2(0.75)² + 3(0.75) + 20

g(0.75) = -1.25 + 2.25 + 20

g(0.75) = 21.125

put 20 for values of x

g(20) = -2(20)² + 3(20) + 20

g(20) = -800 + 60 + 20

g(20) = -720

Therefore, by proper mapping of the function g(x) = −2x² + 3x + 20, we derived g(0) = 20, g(−2.5) = 0, g(4) = 0, g(0.75) = 21.125, and g(20) = -720.

Know more about functions here: https://brainly.com/question/24431768

#SPJ1

Answer:

g(0) = 20

g(-2.5) = 0

g(4) = 0

g(0.75) = 21.125

g(20) = -720

Step-by-step explanation:

Hello!

We can evaluate each value by plugging the value inside the parenthesis into x in the equation [tex]-2x^2 + 3x + 20[/tex].

The values are, in order, 20, 0, 0, 21.125, and -720.

Answer:

----------------------------

The solutions to the financial ratio requirements based on the supplied facts are:

A. Current ratio is 1.125.

B. Acid test is 1.

C. Average days' collection is 26.7 days.

D. Asset turnover is 1.4x.

E. Profit margin on sales is 14.63%.

Financial ratios are ratios that show the relative magnitude of one financial account to another.

Financial ratios are used to compare or represent an entity's financial performance or position in relative terms.

Current Ratio = Current Assets ÷ Current Liabilities

= $18,000 ÷ $16,000

= 1.125

Acid Test Ratio = (Current Assets - Inventory) ÷ Current Liabilities

= ($18,000 - 2,000) ÷ $16,000

= $16,000 ÷ $16,000

= 1

Average Days' Collection = Accounts Receivable ÷ Net Sales x 365 days

= $3,000 ÷ $41,000 x 365

= 26.7 days

Asset Turnover = Net Sales ÷ Total Assets

= $41,000 ÷ $29,000

= 1.4x

Profit Margin on Sales = Net Income ÷ Net Sales x 100

= $6,000 ÷ $41,000 x 100

= 14.63%

Current Assets = $18,000

Accounts Receivable = $3,000

Current Liabilities = $16,000

Inventory = $2,000

Net Sales = $41,000

Total Assets = $29,000

Net Income = $6,000

Learn more about financial ratios at https://brainly.com/question/9091091

#SPJ1

The number of square inches of the wrapping paper left over is 380 square inches

From the question, we have the following parameters that can be used in our computation:

Box:

Dimension = 8 inches by 9 inches by 10 inches

Rectangular-shaped wrapping paper

Dimension = 2 feet by 3 feet.

The surface area of the box is

Box = 2(lw + lh + wh)

So, we have

Box = 2 * (8 * 9 + 8 * 10 + 9 * 10)

Evaluate

Box = 484 square inches

The surface area of the wrapping paper is

Wrapper = lw

So, we have

Wrapper = 2 * 3

Evaluate

Wrapper = 6 square feet

Convert to square inches

Wrapper = 864 square inches

The amount of square inches left is

Amount left = Wrapper - Box

Amount left = 864 square inches - 484 square inches

This  gives

Amount left = 380 square inches

Hence, the amount left is 380 square inches

Read more about surface areas at

https://brainly.com/question/76387

#SPJ1

Answer:

the probability of rolling a 6 is 1/6

Step-by-step explanation:

because there are six possible outcomes and it is a fair die, each outcome must be equally as likely, therefore there is a 1/6 chance of rolling any number.

Answer:

i can help but first what the questions and where are the options?

Step-by-step explanation:

Stock used to sell for $105.81 ten years ago.

[tex]CAGR = ((\frac{EV}{BV} )^{\frac{1}{n}}-1)*100[/tex]

Here, CAGR = Compounded Annual Growth Rate = -2.3%

               EV = Ending Value = x

               BV = Beginning Value = $83.80

                  n = No. of years = 10

Putting the values in the equation,

[tex]-2.3 = ((\frac{83.80}{x} )^{\frac{1}{10}}-1)*100[/tex]

[tex]\frac{-2.3}{100} = ((\frac{83.80}{x} )^{\frac{1}{10}}-1)[/tex]

[tex]\frac{-2.3}{100}+1 = (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]

[tex]\frac{100-2.3}{100}= (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]

[tex]\frac{97.7}{100}= (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]

[tex]0.977 = (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]

[tex](0.9777)^{10} = \frac{83.80}{x}[/tex]

[tex]\frac{83.80}{x}=0.792[/tex]

[tex]x = \frac{83.80}{0.792}[/tex]

x = 105.81

Hence, the beginning value is $105.81.

To learn more about sell here:

https://brainly.com/question/5530185

#SPJ1

Answer:

below

Step-by-step explanation:

0.1

0.15

0.175

0.00125

1.13

2.02125

D after three rotations: 3 × 36° = 108°

F after five rotations: 5 × 36° = 180°

H after seven rotations: 7 × 36° = 252°

I after eight  rotations: 8 × 36° = 288°

Given,

In the question:

ABCDEFGHIJ is a regular decagon. It rotates clockwise about its center to form the polygon A'B'C'D'E'F G'HIJ.

To find the each angle of rotation to the point A' coincides with after that rotation.

Now, According to the question:

let's know about Decagon:

A decagon is a ten-sided polygon or 10-gon. The total sum of the interior angles of a simple decagon is 1440°. A self-intersecting regular decagon is known as a decagram.

Every regular polygon with n sides can be divided into n  congruent triangles. The angle with vertex the center of the polygon will measure

360 : n degrees.  We are given a regular decagon, therefore:

n = 10

α = 360 : n = 36°

We consider that, if the decagon is not rotated, A' coincides with A and the rotation is towards the next letter of the alphabet. This means that after one rotation of 36° A' will coincide with B, after two rotations A' will coincide with C and so on.

A' will coincide with D after three rotations: 3 × 36° = 108°

A' will coincide with F after five rotations: 5 × 36° = 180°

A' will coincide with H after seven rotations: 7 × 36° = 252°

A' will coincide with I after eight  rotations: 8 × 36° = 288°

Learn more about Angle Rotation at:

https://brainly.com/question/14380185

#SPJ1

Answer:

9 days (round up)

Step-by-step explanation:

70 ÷ 8 = 8.75

           ≈ 9 (round up)

The solution to the mathematical expression -(1/4x1/4x1/4x1/4) in exponent form is [tex]\mathbf{-4^{-4}}[/tex]

Number multiplication is a basic and common operation. However, the product of multiplication can be stated differently at times, whether to reduce the equation or to explain the mathematics required. Many numbers can be expressed exponentially.

The concept of exponential form is a method of expressing a number that has been multiplied by itself several times. The fundamental formula is [tex]\mathbf{y=b^x}[/tex]

Exponential expressions are simply a shorthand way of writing powers. The exponent specifies how many times the base has been utilized as a factor.

From the information given

:= -(1/4*1/4*1/4*1/4)[tex]

=-(4^{-1}\times4^{-1}\times4^{-1}\times4^{-1})[/tex][tex]=-(4^{(-1+(-1)+(-1)+(-1))})[/tex][tex]=-(4^{(-1-1-1-1)})[/tex][tex]=-(4^{(-4)})[/tex][tex]\mathbf{=-4^{-4}}[/tex]

Learn more about exponent on:

https://brainly.com/question/13669161

#SPJ1

Answer:

9 quarters and 26 dimes

Step-by-step explanation:

your welcome :)

Answer:

[tex]y_1=\boxed{-3}[/tex]

[tex]y_2=\boxed{-8}[/tex]

[tex]y_3=\boxed{-16}[/tex]

[tex]y_4=\boxed{-28.5}[/tex]

Step-by-step explanation:

Given:

Use Euler’s method with h = 0.5 to find approximate values for the solution of the initial value problem:

[tex]y'=y-2x, \;\;y(3)=0[/tex]

at x = 3.5, 4, 4.5, 5.

Therefore:

[tex]f(x,y)=y-2x, \quad x_0=3 \;\;\text{and}\; \;y_0=0[/tex]

Euler's Method

[tex]\boxed{y_{n+1}=y_n+hf(x_n,y_n)}[/tex]

[tex]\begin{aligned}\implies y_1&=y_0+hf(x_0,y_0)\\&=0+(0.5)f(3,0)\\&=0+0.5[0-2(3)]\\&=0+0.5(-6)\\&=-3\end{aligned}[/tex]

[tex]\begin{aligned}\implies y_2&=y_1+hf(x_1,y_1)\\&=-3+(0.5)f(3.5,-3)\\&=-3+0.5[-3-2(3.5)]\\&=-3+0.5(-10)\\&=-3-5\\&=-8\end{aligned}[/tex]

[tex]\begin{aligned}\implies y_3&=y_2+hf(x_2,y_2)\\&=-8+(0.5)f(4,-8)\\&=-8+0.5[-8-2(4)]\\&=-8+0.5(-16)\\&=-8-8\\&=-16\end{aligned}[/tex]

[tex]\begin{aligned}\implies y_4&=y_3+hf(x_3,y_3)\\&=-16+(0.5)f(4.5,-16)\\&=-16+0.5[-16-2(4.5)]\\&=-16+0.5(-25)\\&=-16-12.5\\&=-28.5\end{aligned}[/tex]

[tex]\begin{array}{|c|c|c|}\cline{1-3} \text{Step}\;(n) & x_n&y_n\\\cline{1-3} 0&3&0\\\cline{1-3} 1&3.5&-3\\\cline{1-3} 2&4&-8\\\cline{1-3} 3&4.5&-16\\\cline{1-3} 4&5&-28.5\\\cline{1-3} \end{array}[/tex]

After 9 months each car will have the same number of miles on it.

What is a linear equation?

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Here,

Let miles per month be x.

then, by a linear equation, we get

4298 + x(426) = 6129 + x(223)

203x = 1831

x = 9 months

Hence, after 9 months each car will have the same number of miles on it.

To learn more about linear equations from the given link

https://brainly.com/question/26310043

#SPJ13

Answer:

$66

Explanation:

Sam earns a 5.5% commission on everything he sells. He sells a television for $1200. What is 5.5% of $1200?

Convert 5.5% to decimal form: 0.055. Now, multiply 1200 by 0.055.

Sam will earn $66 because 5.5% of 1200 is 66.

The value of the test statistic when the engineer has designed a valve is -2.83.

From the information, the following can be deduced:

Sample mean = 5.8

Population mean = 6.0

Population standard deviation = 1

Significance level = 0.02

(Sample mean - Population mean) /(Standard Deviation / ✓200)

= (5.8 - 6.0) / (1 / ✓200)

= -0.2 ✓200

= -2.83

The value is -2.83.

It's important to note that the test statistic is the z value. This will be:

=

Learn more about test statistic on:

brainly.com/question/15110538

#SPJ1

Explanation:

Technically you could isolate any variable you wanted, from either equation. However, convention is to pick the variable in which isolating it is easiest, and most efficient.

The key thing to look for is if there's a coefficient of 1. This is found in the second equation for the y term. Think of -4x+y = -13 as -4x+1y = -13. Due to the coefficient of 1, when solving for y we won't involve messy fractions.

If you were to solve for y, then you'd get y = 4x-13, which is then plugged in (aka substituted) into the first equation. That allows you to solve for x. Once you know x, you can determine y.

A. Yes, the data justifies a function because there is no repeating x values.

B. The relation f(x) = 2x + 13 has a greater value at x = 7

C. The value of x when f(x) = 75 is; 31

A) The general formula for equation of a line in slope intercept form is;

y = mx + b

where;

m is slope

b is y-intercept

Slope is;

m = (y₂ - y₁)/(x₂ - x₁)

m = (5 - 2)/(6 - 5)

m = 3

Let us test the first coordinate;

2 = 3(5) + b

2 = 15 + b

2 - 15 = b

-13 = b

so the equation is : y = 3x - 13

B) When x = 7, we have;

y = 3(7) - 13

y = 21 - 13

y = 8

Let us now test for when  f(x) = 2x + 13 to get;

f(x) = 2x + 13, when x = 7

f(7) = 2(7) + 13

f(7) = 14 + 13

f(7) = 27

the function has a greater value for f(x) = 2x + 13

C. f(x) = 2x + 13

when f(x) = 75

Thus;

75 = 2x + 13

75 - 13 = 2x

62 = 2x

62/2 = x

31 = x

Read more about Function Table at; https://brainly.com/question/3632175

#SPJ1

Answer:

6x=24-12y

x=24-12y/6

x=4-12y

The amount that is outstanding when Brett tallies up the transactions in his check.is $9.19.

From the information, Brett tallies up the transactions in his check register and comes up with a total balance of $248.53, but his bank statement says that his balance is $257.72.

The amount that is outstanding will be the difference between the amount given. This will be:

= Bank statement - Total balance

= $257.72 - $248.53

= $9.19

This is the outstanding amount.

Learn more about bank on:

brainly.com/question/25642105

#SPJ1

The number of pounds of 29% alloy and 51% alloy required to make the third alloy containing 50% aluminum is 45.82 pounds and 2.18 pounds respectively.

Let

x + y = 48

29x + 51y = 50*48

x + y = 48

29x + 51y = 2400

Solve simultaneously

From (1)

x = 48 - y

Substitute into (2)

29x + 51y = 2400

29(48 - y) + 51y = 2400

1392 - 29y + 51y = 2400

- 29y + 51y = 2400 - 1392

22y = 1008

y = 1008/22

y = 45.82 pounds

Substitute y = 45.82 pounds into (1)

x + y = 48

x + 45.82 = 48

x = 48 - 45.82

x = 2.18 pounds

So therefore, the number of pounds of 29% alloy and 51% alloy is 45.82 pounds and 2.18 pounds respectively.

Read more on simultaneous equation:

https://brainly.com/question/16863577

#SPJ1

The width of the rectangle is given as w = p/2 - l which is derived from perimeter of rectangle

The perimeter of a rectangle is the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides.

In this question, we simply need to make the width (w) the subject of formula.

The equation given is

p = 2w + 2l

p = 2w + 2l

p = 2(w + l)

p / 2 = w + l

w = p/2 - l

learn more on perimeter of rectangle here;

https://brainly.com/question/19819849

#SPJ1

The slope of given line is 43

The slope of the line is the rate of change of y with respect to xSlope of a line gives the steepness of line.

The formula of finding the slope of line with two given points is as follows,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Thewith[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]TheThe[tex]Hdb\pi[/tex]TheThelinem=y2-yy2-y1/xw-xq
x2-x1
x2-x1
x2-x1

It can be seen from the given image thatthat the line moves 3unit in x direct and 4unit in y direction.So the slope will be
be m=43

Hence,the slope of the give line is 43

To learn more about slope of line visit the be

brainly.com/question/3493733

#SPJ1

N × (-5/6) ≥ -1/2 is the inequality for the statement

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

Given the statement: negative one half is a minimum of the product of a number and negative five sixths.

This statement can also be written as the product of a number and negative five sixths is greater than or equal to negative one half

Let N represent the number. Thus, the inequality of the statement is:

N × (-5/6) ≥ -1/2    

Note: The symbol ≥ is pronounced as greater than or equal to

Therefore, the inequality for the statement is N × (-5/6) ≥ -1/2

Learn more about inequality on:

https://brainly.com/question/25275758

#SPJ1

There are '5n' computers set up if they each set up the same number of computers.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Ching and his 4 brothers set up computers at their family company.

Now,

Let the number of computers for each person = n

The total number of persons = 5

So, We can formulate;

⇒ The number of computers set up if they each set up the same number of computers = 5n

Thus, There are '5n' computers set up if they each set up the same number of computers.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

Answer:

Step-by-step explanation:

A=60

B=75

C=45

D=60

E=75

F=45

G=90

The equation for the value of x will be 11/C.

According to the question,

We have the following equation:

Cx — 4 = 7

Now, we can easily find the value of x from this equation by following the given steps.

We will first add 4 on both sides of the equation:

Cx = 7+4

Adding the two numbers on the right hand side:

Cx = 11

Dividing by C on both sides of the equation:

x = 11/C

(More to know: we can now find the value of x if the value of C is given.)

Hence, the equation for the value of x will be 11/C.

To know more about equation here

https://brainly.com/question/3162971

#SPJ1

Answer: mode  50  Mean x¯¯¯ 158.33333333333

Median x˜ 167.5

Step-by-step explanation: hope this helps

Range 250

Minimum 50

Maximum 300

Count n 12

Sum 1900