Mathematics Middle School

The length of a rectangle is twice the width. If the perimeter of the rectangle is 60 units, find the area of the garden.

Answers

Answer 1

Set the following: Length = L Width = W

The length is twice the width: L = 2*W or: W = L/2

Perimeter: P = 60ft = 2*L + 2*W

Substituting L for W in the perimeter equation gives:

P = 60ft = 2*L + 2*(L/2) = 2*L + L = 3L

L = 60ft/3 = 20ft W=L/2=20ft/2=10ft

Verify result: Perimeter= P = 60ft = 2L + 2W = 2*20ft +2*10ft = 40ft+20ft = 60ft

The area of the rectangular is: Area = A = Length*Width = L*W = 20ft*10ft = 200 (ft)^2

Hopefully This Helps!!

Answer 2

Final answer:

To find the area of a rectangle when the perimeter is given, determine the dimensions using the relationship between length and width and then calculate the area. In this case, the area of the garden is 200 square units.

Explanation:

The length of a rectangle is twice the width. If the perimeter of the rectangle is 60 units, find the area of the garden.

Let the width of the rectangle be x. Therefore, the length is 2x.

The perimeter of a rectangle is given by 2(length + width), which in this case is 2(2x + x) = 60 units.

Solving for x, we get x = 10. Therefore, the width is 10 units and the length is 20 units. The area of the garden is length x width = 20 x 10 = 200 square units.

Related Questions

Given the two expressions shown below:
A. square root of 3 + square root of 2
B. square root of 3 + square root of 6

Which statement best describes the two expressions?

A. both rational
B. both irrational
C. A is rational and B is irrational
D. A is irrational and B is rational

Plz help Thanks for Everything Guys

Answers

C. A is rational and B is irrational

-2+3n>-14
A -16/3
B -3
C -20/3
D none of the above

Answers

the answer is B (-3).
-2+3n>-14
+2 +2
3n>-12
n>-4

Write using algebra.

A bucket holds c liters of water, but a jar holds 8 liters less. How many times as much water can the bucket hold as the jar?

Answers

The ratio representing how many times as much water the bucket can hold as the jar is [tex]\frac{c}{c-8}[/tex], where c is the capacity of the bucket in liters.

If a bucket holds c liters of water and a jar holds 8 liters less than the bucket, then the jar holds c - 8 liters of water. To find how many times as much water the bucket can hold as the jar, we divide the bucket's capacity by the jar's capacity. This gives us the ratio of the bucket's capacity to the jar's capacity, which is [tex]\frac{c}{c-8}[/tex].

10. Solve the equation for f. Show all of your work.
4f-5=7h+g

Answers

4f-5=7h+g
add 5
4f= 7h + g + 5
divide by 4 to get f by its self
f = 1/4g + 7/4h + 5/4

Find an equation of the line that has a y-intercept of -2 and is perpendicular to the graph of 3x+6y=2

Answers

To do that u need to solve the equation for y
First move the 3x over to get

6y= -3x + 2

Now solve for y by divided by 6

Y= -3/6x + 2/6

A line perpendicular to this equation would have a slope that is the opposite reciprocal, so flip the -3/6 and change the sign

This gives u 6/3 which simplifies to two

The new equation of the line would be y= 2x - 2

Use exponents to write the number 64 three different ways

Answers

8^2
4^3
(the ^ means the number after is the exponent)

8 ^ 2

4^ 3

2^6

those are your three ways hope that helps

Which number is not in scientific notation? 11 ⋅ 1021 5.7 ⋅ 109 3.1 ⋅ 10−12 1.67 ⋅ 10−5

Answers

11 * 10^21 is not in scientific notation.

Scientific notation requires that the digits part is greater than zero and less than 10 (it cannot be 10).

So, to put that number in scientific notation 11 must be converted to 1.1*10 and 11 * 10^21 is 1.1 * 10 * 10^21 = 1.1 * 10^22.

Note tha 11 * 10^21 is the same that 1.1 * 10^22 but the last is in scientific notation while the former is not.

All the other numbers have the digit part in the range [1,10), so they are in scientific notation.

Answer:

11 * 10^21

Step-by-step explanation:

I took the test

Susan is buying supplies for a party. If spoons only come in bags of 8 and forks only come in bags of 6, what is the least number of spoons and the least number of forks she can buy so that she has the same number of each? asap and tell my how you got the answer please

Answers

it would be 4 packs of spoons and 3 packs of forks. This is because if you multiply 6 times 4 you get 24 and 8 times 3 you will get 24 and then that would be even. If this needs to be further explained please ask me

Answer:

3 bags of spoon and 4 bags of fork.

Step-by-step explanation:

If Susan will buy 3 bags of spoon then, the total spoon is 3 × 8 = 24 spoons

and, If he will buy 4 bags of fork then, the total fork is 4 × 6 = 24 forks.

Thus, for getting equal numbers of spoon and fork he has to buy a minimum of 3 bags of spoon and 4 bags of fork.

1 __ 6/3 Is less than greater than or =

Answers

Well, 6 / 3 is a solid 2.

So, 1 is less than 6/3
or
1 < 6/3

Hope this helped! ☺♥

1 __ 6/3
1 < 2 (cause 6/3 = 2)

answer
less than

Gabriela works at a nearby electronics store. She makes a commission of 14%14, percent on everything she sells. If she sells a camera for $589.00dollar sign, 589, point, 00, how much money does Gabriela make in commission?

Answers

Good question I don’t know maybe ask you’re professor

Karla is given the equation 10x + 15 = 20 to solve. She says the solution is 1/2

Which reason justifies her solution?

A) Karla says that to solve the equation you first add 15 and then multiply by 10.

B) Karla says that to solve the equation you first multiply by 10 and then add 15.

C) Karla says that to solve the equation you first subtract 15 and then divide by 10.

D) Karla says that to solve the equation you first divide by 10 and then subtract 15.

Answers

the answer is c because you need to isolate the x

The answer is C.

you do the inverse of positive 15, which is negative 15. so put it on both side .

10x +15 =20
-15 =-15

to equal

10x =5

then divide 10 on both side

10x = 5
----- -----
10 10

x = 5/10 or 1/2

The saving-borrowing-investing cycle generally begins with consumer borrowing to fund their purchases and for seed capital. They then use this capital to invest in their future, which then allows them to bring in more money. They then are able to use income to pay off their loans and to save.

Answers

The statements above are TRUE.
The saving borrowing investing cycle is used by people to achieve financial stability. They cycle is initiated when an individual borrow a sum of money to invest in a business. As time goes on the business begins to yield profits. Part of the profits will be used to repay the borrowed loan. After the repayment, the profits can then be reinvested into the business to generate more profits.

Please answer, , I need this by 10:00, thank you!

Answers

(2, 7) abd (5, 1)

Let m = slope

m = (1 - 7)/(5 - 2)

m = (-6)/(3)

m = -2

Use the slope and one of the points to plug into the point-slope formula.

I will use the point (5, 1).

y - 1 = -2(x - 5)

y - 1 = -2x + 10

The equation is

y = -2x + 11

you have 33 marbles. Besides 1 group of 33 marbles, is it possible to divide the marbles into groups with the same number of marbles with no marbles left over

Answers

Yes you could have three groups of 11 with no marbles left over.

Yes hi could have 11 groups with 3

Find the value of x so that the function has the given value.

h(x)=−7x ; h(x)=63

Answers

Us x=-9

you get this by dividing 63/-7

The value of x for which the function h(x) = - 7x is h(x) = 63 is - 9.

What is a function?

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, h(x) = -7x and h(x) = 63.

∴ We can equate these two functions as h(x) = h(x) which is,

- 7x = 63.

- x = 63/7.

- x = 9.

x = - 9.

learn more about functions here :

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You start out driving from your house to an old friend’s house in a different town, which is 280 miles away. After an hour and a half, you have gone 105 miles.

a) Assuming your speed is constant, find a linear function , which gives the distance from your house (in miles) as a function of time (in hours).

b) Find and interpret D(1).

c) Solve D(t)=280

d) Solve D(t)^3>=140 and interpret the result.

e) Considering the context of this function, what is the domain?

f) What is the range?

Answers

Part A:

Given that after an hour and a half, you have gone 105 miles and that your speed is constant, this means that the slope which represents the speed with which you are driving is given by

[tex] \frac{105}{1.5} =70 \ miles \ per \ hour[/tex]

At 0 hours, he has travelled 0 miles.

The equation of a straight line is given by y = mx + c, where m represent the slope and c is the y-intercept (the value of y when x is 0).

Therefore, a linear function , which gives the distance from the house (in miles) as a function of time (in hours) is given by D = 70t.

Part B:

D(1) is the value of D when t = 1.

D(1) = 70(1) = 70

This means that the distance traveled after 1 hour is 70 miles.

Part C:

D(t) = 280 means the time it takes you to travel 280 miles.

70t = 280

t = 280 / 70 = 4

t = 4.

Part D:

[tex]D(t)^3 \geq 140 \\ \\ \Rightarrow 70t^3 \geq 140 \\ \\ \Rightarrow t^3 \geq \frac{140}{70} =2 \\ \\ \Rightarrow t \geq \sqrt[3]{2} [/tex]

Part E:

The domain is a set of the possible values of the independent variable, from the context of the function, the independent variable is the time it took him for the journey.

Therefore, the domain of the function is [0, 4].

Part F:

The range is the set of the possible values of y, y in the context of the question is the distance travelled at each particular time.

Therefore, the range of the function is [0, 280].

a) D(t)=70t. To find this, consider that we traveled 105 miles in the first 1.5 hours. Since the speed is constant, we simply divide the 105 miles by the 1.5 hours. 105/1.5=70, which tells us we are going 70 mph. To express this as a function, we write the speed of travel (70) times the number of hours (t). Thus D(t)=70t. b) D(1)=70. This means that we traveled 70 miles after one hour. To find this, plug in 1 hour for t and simplify: 70(1)=70. c) t=4. To solve this, set 280=70t and solve for t. 280/70=4. d) t=.0741784872. To solve, take the cube root of both sides. This gives us D(t)=5.192494102. This can be written 70t=5.192494102. Dividing both sides by 70 we get that t=0741784872. e) Domain is t-interval [0,4]. To find this, consider that the trip is 280 miles and we are traveling at 70 mph. Dividing 280 by 70, we see that we will make the trip in 4 hours. Thus our trip starts at t=0 and ends at t-4. f) Range is the D-interval [0,280]. To find this, consider that the domain is [0,4]. d(0)=0 and D(4)=280. Thus the range is [0,280].

If g( n ) = 3 n - 2, then what is the value of g(10)?

Answers

the correct answer is 28

Write the equations of three distinct lines that have the same y-intercept,-1.

Answers

Three possible answers are:
y = 2x-1
y = 5x-1
y = -3x-1

All of them have the same y intercept of -1. The slopes are the only thing that differ.

Any linear equation can be written in the form y = mx+b where
m = slope
b = y intercept

What is the measure of the angle 20x + 5= 24x - 1

Answers

4x=4
x=4/4=1
All the best

20x +5 = 24x -1

add 1 to each side

20x+6 = 24x

subtract 20x from each side

6 = 4x

divide both sides by 4

x = 6/4 = 1.5

measure of angle: 20(1.5) +5 = 30+5 = 35 degrees

24(1.5) - 1 = 36-1 = 35 degrees

What is 9.27 with a repiton bar over the 27 simplified to as a fraction?

Answers

That will be 3/11.

According to your question. It is incorrect. You meant repetitive.

https://socratic.org/questions/how-do-you-convert-0-27-27-repeating-to-a-fraction

This will prove my answer correct.

The answer to your problem is 3/11

please help ❗️❗️❗️❗️❗️❗️

Answers

Pool A is filling up slower than Pool B because the slope of the graph for Pool A is less than that of the graph for Pool B.

The slope of the graph tells you the unit rate in gallons per minute. (gallons/minute)

_____
Side Note: Pool A starts with more water in the pool, so even though it is filling more slowly, it may be filled first.

Find the total cost to the nearest cent $1,500 computer; 7% tax?

Answers

it is 1605

tax is 105

add tht to your original

the answer is 1395 all you need to do is subtract 1500 and 7% and that = 1395

Explain the steps when solving 3(N+5)>= 3n+8. Please explain how to solve.

Answers

1. distribute .
3(N+5)
3n +15
2. Switch variables to make one .
3n-3n = n
NEW EQUATION ::
5= n+8
3. bring numebers to make one .
8-5=3
n=3

In triangle ABC, the measure of angle A is , the measure of angle B is , and the measure of angle C is . What is the combined measure of the three angles?

Answers

Final answer:

The combined measure of the three angles in triangle ABC is angle A + angle B + angle C degrees.

Explanation:

The combined measure of the three angles in triangle ABC can be found by summing the measures of angle A, angle B, and angle C.

So, the combined measure of the three angles is angle A + angle B + angle C = angle A + angle B + angle C degrees.

For example, if angle A = 40 degrees, angle B = 60 degrees, and angle C = 80 degrees, then the combined measure of the three angles would be:

40 + 60 + 80 = 180 degrees.

Learn more about Angles in a triangle

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solve the equation for y

5 ( y + 1 ) = 30

y = ??

Answers

Hi again :)

5(y + 1) = 30
Once again, use the distributive property
(5)(y) + (5)(1) = 30
5y + 5 = 30
Add -5 to both sides
5y + 5 - 5 = 30 - 5
5y = 25
Divide both sides by 5
5y/5 = 25/5
y = 5

Best of luck!

The answer for the following problem is 5

Write 10x10x10x10x10x10 as an exponent

Answers

it would be10 to the 6th power

The required answer for 10x10x10x10x10x10 as an exponent is 10⁷.

What is an exponent?

An exponent is a number or letter written above and to the right of a mathematical expression called the base.

Now the given expression is,
10 x 10 x 10 x 10 x 10 x 10

Using the property,

a^a . a^b = a^(a+b)

Thus,

10 x 10 x 10 x 10 x 10 x 10 = 10^(1+1+1+1+1+1)

⇒ 10 x 10 x 10 x 10 x 10 x 10 = 10^7

or, 10 x 10 x 10 x 10 x 10 x 10 = 10⁷

Thus, the required answer for 10 x 10 x 10 x 10 x 10 x 10 as an exponent is 10⁷.

To learn more about exponent:

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Haji rows his canoe 10 mph in still water. He noticed one day that he could row 4 miles upstream in the same amount of time he could row 6 miles downstream. What was the approximate speed of the current that day?

Answers

so you see that he was rowing up stream and could go 4 miles an hour, but down stream, with the push of the current gave him an extra boost of 2 miles an hour

Answer:

2.0 mph

Step-by-step explanation:

roberto needs to convert the equation 3x + y = -5 into slope-intercept form. why is able to add or subtract the variable term from either side of the equation?

Answers

3x + y = -5

-3x + 3x + y = -3x - 5

y = -3x - 5

A student answers
90%
of the questions on a math exam correctly. If
sheshe
answers
27
questions correctly, how many questions are on the exam?

Answers

So, we have the percentage she gets which is, 90% and the number of questions she answers correctly, which is 27

To find the number of questions in the exam, make an equation
(90% = [tex] \frac{90}{100} [/tex] = 0.9)
[tex] \frac{90}{100} [/tex] = [tex] \frac{27}{x} [/tex]
cross multiply and equate them
90x = 27 x 100
90x = 2700
divide by 90 on either sides to isolate x in order to find the answer
[tex] \frac{90x}{90} = \frac{2700}{90} [/tex]
90 and 90 cancels out
x = 30
So your final answer will be, there were 30 questions in the exam paper.

Final answer:

To find the total number of questions on the exam, set up a proportion 27 / x = 90% / 100%. Solve for x to find that there are 30 questions on the exam.

Explanation:

To find the total number of questions on the exam, we can set up a proportion. Let's represent the total number of questions on the exam as x.

The proportion would be:

Correctly Answered Questions / Total Questions = Percentage Correct

Substituting the given values:

27 / x = 90% / 100%

Cross multiplying:

27 * 100% = x * 90%

27 = 0.9x

Dividing both sides by 0.9:

x = 27 / 0.9

x = 30

Therefore, there are 30 questions on the exam.

A family budgets 1/2 of its income for housing and 1/3 for food. What fraction of their budget do these expenses cover?

Answers

1/2 of the income goes for housing.
1/3 of the income goes for foor.

The sum of these fractions are their expenses.
Note that
[tex] \frac{1}{2} = \frac{3}{6}, \, and \, \frac{1}{3}= \frac{2}{6} [/tex]

Therefore the fraction of the budget is
[tex] \frac{1}{2}+ \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} [/tex]

Answer: 5/6

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