The length of a rectangle is four times its width.
If the perimeter of the rectangle is 60 ft , find its area.

The dimensions of the rectangular garden are 20 feet and 29 feet respectively.

It is vital to note that the formula for the area of a rectangle is expressed as;

Area = lw

Where;

From the information given, we have that;

Area =  580ft²

Length = 9 + width

L = 9 + w

Substitute the values into the formula, we have;

580 = (9 +w)(w)

expand the bracket

580 = 9w + w²

Make into quadratic equation

w² + 9w - 580 = 0

Factorize the equation

w² + 29w - 20w - 580 = 0

Factor the common terms

w( w + 29) - 20(w + 29) = 0

Then,

w + 29 = 0

w = -29

and w - 20 = 20 feet

We have the expression of length as l = 9 + w

Length, l = 9 + 20

Length, l = 29 feet

Thus, the values are 20 feet and 29 feet

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Answer:

Step-by-step explanation:

Mapping diagram (D) is not a function.

So, an option which is not a function:

Therefore, mapping diagram (D) is not a function.

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Answer:

a. 4.67 dollars per hour

b. 0.43 minutes per page

Explanation:

Part a.

To know the cost per hour of bike use, we need to divide the total cost by the number of hours, so:

So, the cost is 4.67 dollars per hour

Part b.

In the same way, the number of minutes per page can be calculated as the division of the number of minutes by the number of pages, so:

So, it takes 0.43 minutes per page.

Answer: (0,3)

Step-by-step explanation:

The y-intercept for f(x)=x would be (0,0). Therefore, if we translate it up by three to get g(x), then the y coordinate would go up by 3, resulting in (0,3).

If Nolan is dividing 2 by 11 and he continues the process, the the result will be repeating quotient 0.181818...

Here Nolan is dividing 2 by 11.

Division is one of  the basic arithmetic operation. Division is operation of splitting a specific number into equal parts

The quotient is the result from dividing a number from another number.

Divide the given terms and the result will be

2/11 = 0.1818...

The result will be a repeating quotient . Here the pattern is repeating endlessly

Hence, if Nolan is dividing 2 by 11 and he continues the process, the the result will be repeating quotient 0.181818...

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Step-by-step explanation:

5 people went on the Carowinds trip.

The width of the rectangle DOGS is 119cm

To solve this, since is a ratio problem, we know that the two ratios must add to the total. This is, for a ratio of 5:7, 5 + 7 = 12 is the total "divisions" for the ratio.

This means that if 12 of 12 parts add to the perimeter (408cm):

12/12 represents the perimeter 408cm.

The, we can divide the perimeter by 12 and get:

Since the width is 7/12 of the perimeter:

But, we are taking the perimeter of a rectangle, which is twice the width plus twice the length, thus we need to divide this number by 2:

And we get the final answer of 119cm

Answer: 3 17/20 is bigger than 3 13/28

Step-by-step explanation:

2 ways:

1) Turn the fractions into decimal form.

13/28 = 0.464

0.464 + 3 = 3.464

17/20 = 0.85

0.85 + 3 = 3.85

2) Check which one is bigger

3.85 is bigger than 3.464 because the tenth place is bigger than the second number.

Second way:

1) Remove the 3s.

Both equations have three, so you could remove both sides three

3 13/28  ?  3 17/20

13/28 ? 17/20

2) Multiply both bottom expressions by itself.

(The numbers that its multiplying equals to 1. When multiplying a number by 1, it stays the same.)

13/28 * 20/20 = 260/560

17/20 * 28/28 = 476/560

3) Compare the fractions

260/560  ?  476/560

260/560  <  476/560

The number in the fraction is bigger

Answer:

No, 3 ¹³/₂₈ is smaller than 3 ¹⁷/₂₀.

Step-by-step explanation:

Convert both mixed numbers into improper fractions:

[tex]\implies 3 \frac{13}{28}=\dfrac{3 \times 28+13}{28}=\dfrac{97}{28}[/tex]

[tex]\implies 3 \frac{17}{20}=\dfrac{3 \times 20+17}{20}=\dfrac{77}{20}[/tex]

The lowest common multiple of 28 and 20 is 140.

Therefore, multiply the numerator and denominator of each improper fraction by the same number to make both denominators 140:

[tex]\implies \dfrac{97 \times 5}{28 \times 5}=\dfrac{485}{140}[/tex]

[tex]\implies \dfrac{77 \times 7}{20 \times 7}=\dfrac{539}{140}[/tex]

Therefore, as 539 > 485:

[tex]\implies \dfrac{539}{140} > \dfrac{485}{140}[/tex]

[tex]\implies \dfrac{77}{20} > \dfrac{97}{28}[/tex]

[tex]\implies 3 \frac{17}{20} > 3 \frac{13}{28}[/tex]

Therefore, 3 ¹³/₂₈ is smaller than 3 ¹⁷/₂₀.

Using Cramer's rule, the solution to the system of equations is given as follows:

x = -10, y = 9.

A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the problem.

There are multiple ways to solve a system of equations, and one of them is Cramer's Rule, in which we use the determinants of matrices to find the solutions.

In the context of this problem, the system is:

The matrix for the system is:

[tex]M = \left[\begin{array}{cc}1&2\\-3&-2\end{array}\right][/tex]

Hence it's determinant is:

|M| = 1(-2) - (-3)(2) = -2 + 6 = 4.

The matrix for x is given by:

[tex]M_x = \left[\begin{array}{cc}8&2\\12&-2\end{array}\right][/tex]

Hence it's determinant is:

|Mx| = 8(-2) - 2(12) = -16 - 24 = -40.

The matrix for y is given by:

[tex]M_y = \left[\begin{array}{cc}1&8\\-3&12\end{array}\right][/tex]

Hence it's determinant is:

|My| =  12 - (-3)(8) = 12 + 24 = 36.

Then the solutions are given as follows:

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If the temperature is 13 degrees at midnight, then the temperature will be 6 degrees at 3:00 AM.

Temperature at midnight = 13 °

Temperature drop per hour = 2 °

We need to find the temperature at 3:00 AM

Number of hours till then = 3 hours.

Temperature drop will be calculated by using multiplication.

Temperature drop = 2 × 3 = 6°

Temperature ate 3:00 AM = 12 - 6 = 6°

Therefore, we get that, if the temperature is 13 degrees at midnight, then the temperature will be 6 degrees at 3:00 AM.

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All the identifiers that are included when identifying significant digits are-

Each of the digits of a number starting with the digit farthest to a left that is not zero as well as ending with the digit farthest to a right that is neither zero or is a zero but is considered exact.

For the given options.

Except option 1 every option is correct.

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Given the fraction below

To simplify the above fraction, we will divide both the numerato

The answer to the given function is [tex]B(a)= a/6-9[/tex].

A trapezoid, also referred to as a trapezium, is an open, flat object with 4 straight sides and 1 set of parallel sides. A trapezium's bases are its parallel sides, while its legs are its non-parallel sides.

Given :

[tex]A(b)= 12( b+9)/2[/tex]

where, A(b) is the trapezoid's area

and b is the other base value

On solving the above equation further we get ;

[tex]A= 6(b+9)[/tex]

[tex]A/6= b+9[/tex]

this implies we get;

b= [tex]A/6-9[/tex]

Now convert this into function notation we get

[tex]B(a)= a/6-9[/tex]

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Answer:   The graph is below

======================================================

Explanation:

If x = 0, then,

g(x) = -x+1

g(0) = -0+1

g(0) = 0+1

g(0) = 1

Therefore, x = 0 leads to y = 1. The point (0,1) is on the g(x) line.

Now try x = 1

g(x) = -x+1

g(1) = -1+1

g(1) = 0

The point (1,0) is also on the g(x) line.

Draw a line through the points (0,1) and (1,0)

Then erase the portion that is to the left of x = -4

This is because g(x) is only graphed when x > -4; i.e. we're only graphing stuff to the right of x = -4.

We'll have an open hole when x = -4 since we aren't including it as part of the graph.

See below.

The simplified form for (3x² + 2y² - 5x + y) + (2x² - 2xy - 2y² -5x + 3y) is (5x² + 0y² - 10x + 4y - 2xy).

At least one squared term must be present because a quadratic is a second-degree polynomial equation. It is also known as quadratic equations. The answers to the issue are the values of the x that satisfy the quadratic equation. These solutions are called the roots or zeros of the quadratic equations. The solutions to the given equation are any polynomial's roots. A polynomial equation with a maximum degree of two is known as a quadratic equation, or simply quadratics.

The equation can be made simpler by adding up all of the coefficients for the specified correspondent term through constructive addition or subtraction of terms, as suggested in the question.

Given, the equation is (3x² + 2y² - 5x + y) + (2x² - 2xy - 2y² -5x + 3y)
Removing brackets and the adding we get,
3x² + 2x² + 2y² - 2y² + (- 5x) + (- 5x) + y + 3y + (- 2xy) = (5x² + 0y² - 10x + 4y - 2xy)

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Explanation

Lets first find the slope:

Now let's use the point-slope formula:

Answer

Let's look at car A first.

As already solved, just after it is purchased its value decreases 20%.

Purchased at $30000, its value inmediatly decreases to $24000 ($30000 -

0.2*$30000 = $24000).

We know the yearly depreciation for car A os $2000.

Then, at the end of the first year, its value will decrease from $24000 to $24000 - $2000 = $22000.

Every year its value decreases $2000. Followint the same logic, at the end of the second year its value will decrease from $22000 to $22000 - $2000 = $20000 and so on. Now, we can build the table:

End of first year: $24000 - $2000 = $22000

End of second year: $22000 - $2000 = $20000

End of third year: $20000 - $2000 = $18000

End of fourth year: $18000 - $2000 = $16000

End of fifth year: $16000 - $2000 = $14000

Answer:

c. 250 miles

Step-by-step explanation:

[tex]d=(50)(5)=250[/tex]

If An industrial scale is guaranteed by the manufacturer to have a percent error of no more than 1%. Its  possible reading on the scale if you put 500 kilograms of iron ore on it is :495, 505.

Percent error = 1%

Kilogram of iron ore = 500 kilograms

First step is to find the 1% of 500 kilograms

= .01 × 500 kilograms

= 5

Second step is to find the possible reading

Possible reading :

500 - 5

=495

500 + 5

= 505

Therefore we can conclude that  based on the above analysis the possible reading can be between 495 and 505.

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Ms. Lantz would need to finish in 50.28 minutes to be eligible for the Houston Marathon.

The relationship between a score and the mean over a set of scores is simply quantified by a Z-Score, which is a measurable statistic.

A Z-score can explain to a trader why a value is unusual or average for a given set of data.

A Z-score below 1.8 suggests that a company is on the verge of bankruptcy, while a score closer to 3 shows that the company is doing well financially.

Solution:

The z-score is calculated using the formula: 

z = (x - μ)/σ

μ = Sample's average

σ = Sample's standard deviation

The values are as follows:

μ equals 57 minutes.

σ = 8 minutes

Probability equals 20%, or 0.20.

Determine the z-score for 0.20 using the negative z-table.

Z score is -0.84.

To find x, enter the values into the z formula.

z = (x - μ)/σ

-0.84 = (x - 57)/8

Simplifying;

x = -6.72 + 57

x = 50.28 minutes

Thus, Ms. Lantz would need to complete the Rocket Run 5k in 50.28 minutes in order to be eligible for the Houston Marathon.

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In the picture there is a cylinder with height 5 inches and diameter 4 inches. The surface area of cylinder is 87.62.

Given that,

In the picture there is a cylinder with height 5 inches and diameter 4 inches.

The surface area of a cylinder is the area that is enclosed by the flat bases and the curving surface of the cylinder. The cylinder's total surface area includes the area of the curving surface as well as the areas of the two circle-shaped bases of the cylinder.

The surface area of cylinder is 2πr²+2πrh

r is radius which is diameter/2

r=4/2=2

h is 5

Surface area of cylinder= 2πr²+2πrh

=2π×2²+2π×2×5

=8π+20π

=28π

=28×3.14

=87.92

Therefore, the surface area of cylinder is 87.62.

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Answer:

The percentage change is 15%

Step-by-step explanation:

Can I have brainliest?

Answer:

1/6 chance

Step-by-step explanation:

Using the formula for the area of a circle calculate the area for both deals.

for the 18-inch pizza

for the two 12-inch pizza

So we need to solve the following equation for x:

We can apply a square root to both sides but it is important to remember the following property. For any given number a we have:

Which means that:

So for our case we have:

Then the solutions are 7 and -7.

Answer:

Step-by-step explanation:

[tex]2\frac{5}{8} =\frac{2 \times 8+5}{8} =\frac{21}{8} \\2\frac{1}{4} =\frac{2 \times 4+1}{4} =\frac{9}{4} \\2\frac{5}{8} / 2\frac{1}{4} \\=\frac{21}{8} /\frac{9}{4} \\=\frac{21}{8} \times \frac{4}{9} \\=\frac{7}{6} \\=1\frac{1}{6}[/tex]

6/18=×/36

solve for x

x=(6/18)36

x=6(36/18)

x=6(2)

x=12

The number of different committees that can be formed is 34,650.

First, we know that there are 11 teachers and the committee needs to have two teachers, so let's find the number of combinations here.

Remember that if we have a set of N elements and we need to select K of these, the number of different selections is given by:

[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]

In this case we would have N = 11 and K = 2, so we get:

[tex]C(11, 2) = \frac{11!}{(11 - 2)!*2!} = \frac{11*10}{2} = 11*5 = 55[/tex]

There are 55 combinations.

For the students we do the same thing, here we have 36 students and we need to select two, so:

[tex]C(36, 2) = \frac{36!}{(36 - 2)!*2!} = \frac{36*35}{2} = 630[/tex]

So we have 55 combinations for the teachers and 630 for the students, then the total number of different committees is:

C = 630*55 = 34,650

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The range of the equation of the function given as y = x^2 + 4x + 7 is y >= 3

The equation of the function is given as

y = x^2 + 4x + 7

Differentiate the function with respect to x

So, we have

y' = 2x + 4

Set the differentiated function to 0

So, we have

2x + 4 = 0

This gives

2x = -4

Divide by 2

x = -2

Substitute x = -2 in the equation y = x^2 + 4x + 7

So, we have

y = (-2)^2 - 4 x 2 + 7

Evaluate

y = 3

The leading coefficient is positive

This means that the vertex is a minimum

So, we have the range to be

y >= 3

Hence, the range is y >= 3

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