the rectangle shown has a perimeter of 56 cm and the given area. it's length is 8 more than three times it's width. write and solve a system of equations to find the dimensions of the rectangle.​

The Rectangle Shown Has A Perimeter Of 56 Cm And The Given Area. It's Length Is 8 More Than Three Times

Answers

Answer 1

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve ~

Assume width of rectangle be " x ", length = 3×width + 8 = 3x + 8 ~

Now, Perimeter of rectangle is :

[tex]\qquad \sf  \dashrightarrow \:2(l + w) = 56[/tex]

[tex]\qquad \sf  \dashrightarrow \:2(3x + 8 + x) = 56[/tex]

[tex]\qquad \sf  \dashrightarrow \:2(4x + 8) = 56[/tex]

[tex]\qquad \sf  \dashrightarrow \:4x + 8 = 56 \div 2[/tex]

[tex]\qquad \sf  \dashrightarrow \:4x + 8 = 28[/tex]

[tex]\qquad \sf  \dashrightarrow \:4x = 28 - 8[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 20\div 4[/tex]

[tex]\qquad \sf  \dashrightarrow \:x =5 \: cm[/tex]

Hence, width = x = 5 cm

[tex]\qquad \sf  \dashrightarrow \:l = 3w + 8[/tex]

[tex]\qquad \sf  \dashrightarrow \:l = 3(5)+ 8[/tex]

[tex]\qquad \sf  \dashrightarrow \:l = 15+ 8[/tex]

[tex]\qquad \sf  \dashrightarrow \:l =23 \:cm[/tex]

And, length = 26 cm


Related Questions

how many 1/4 foot cubes would fill the inside of a rectangular prism

Answers

Answer: 192 cubes.

Step-by-step explanation:  Each cube with side lengths of 1/4 have a volume of (1/4)3 which means each cube’s volume is 0.015625 cubic units. To find how many cubes are needed to fill the prism, divide 3 cubic units by 0.015625 cubic units. Your answer will be 192 cubes.

Describe these points with a double inequality

Answers

Answer:

-3 < x ≤ 13

Step-by-step explanation:

the filled circle is the less/greater than or equal to sign and the open circle is a less/greater than sign.

Which fraction is closer to 0 than to 1 ? Choose all that apply .
A. 5/8
B. 2/6
C. 1/4
D. 4/6
E. 3/8

Answers

B, C, and E are closer to 0 than to 1.

Pam has ridden her new bike 7.2 miles. Dale has ridden his new bike 12.5 times as far as Pam.
How far has Dale ridden his bike? Enter your answer in the box.

Answers

Answer:

He has ridden 90 miles

Step-by-step explanation:

7.2 X 12.5 = 90

Find the area of the figure.

Answers

Answer: 300 ft^2

Step-by-step explanation:

First, find the area of the rectangle on the bottom:

Area of a rectangle = length * width = 18 * 12 = 216

Now, find the area of the trapezoid:

Area of a trapezoid = (base 1 + base 2) / 2 * height → (10 + 18) / 2 * 6 = 84

Add these together: 216 + 84 = 300 ft^2 :)

18. Find the surface area of the prism.​

Answers

Step-by-step explanation:

the total surface area is the sum of the individual areas on the surface.

we have

2 triangles (top and bottom)

1 front rectangle

2 rectangles in the back

the area of a triangle is

baseline × height / 2

1.7 × 0.5 / 2 = 0.425 in²

both triangles together : 2×0.425 = 0.85 in²

the area of a rectangle is

length × width

so, the front is

1.7 × 1.5 = 2.55 in²

one back rectangle is

1 × 1.5 = 1.5 in²

both back areas are 2×1.5 = 3 in²

so, the total surface area is

0.85 + 2.55 + 3 = 6.4 in²

Find the solution of the system of equations shown on the graph

Answers

The solution of the system of the equations shown is where the equations intersect

   --> (-7, 1)

Hope that helps!

Answer:

(-7, 1),

Step-by-step explanation:

The solution is the coordinates of the point of intersection.

At this point x = -7 and y = 1.

What is the measure of an angle at the centre whose radius is equal to arc length?​

Answers

Answer:

radian

Step-by-step explanation:

A radian is a unit of angle that is equal to the angle created at the center of a circle whose arc is equal in length to the radius.

Hope it helps!!!Brainliest pls!!!

The measure of an angle at the center is 1 radian.

What is an angle measure?

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

Radius is equal to arc length.

To find the measure of the angle at the center:

We have the formula,

Angle in radian = arc length / radius

Let a be the arc length,

then a be the radius.

Substituting the values,

Angle in radian = a/a

Angle in radian = 1 radian

Therefore, 1 is the measure of an angle at the center.

To learn more about the angle measure;

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A triangle has an angle that measures 90°. The other two angles are in a ratio of 2:7. What are the measures of those two angles?

Answers

Answer:

70° and 20°

let the other 2 angles be 7x and 2x

90+7x+2x=180

9x=180-90

x=90/9

x=10

7x=7x10

70

2x=2×10

2p

can someone please help me

Answers

Answer:

1 - 50

5 - 90

10 - 140

50 - 540

Step-by-step explanation:

The rate of change is 10/1, while the Y-intercept is 40. The equation would be Y=10x+40

if the graph of f(x)=x^2 is shifted 4 units to the left, then what would be the equation of the new graph?​

Answers

Answer:

Step-by-step explanation:

Be careful. You can be confused by shifting left or right because the result is the opposite of what you might think.

f(x) = x^2

f(x + 4) = (x + 4)^2

To show you this in graphical form, see below.

Red: f(x) = x^2

Blue: f(x) = (x+4)^2 Notice that the blue graph is the the LEFT of the red graph

Which graph matches the equation y+5 = (x + 4)?

Please hurry

Answers

Answer:

Sorry i don’t know the answer

Step-by-step explanation

I don’t know

∠A and ∠B are corresponding angles, the measure of \angle ∠A is 110

Answers

Answer:

Step-by-step explanation:

if the measure of <A is 110°

Then the measure of <B is also 110°

Need help math.............

Answers

Answer:

P=39

Step-by-step explanation:

8X6=48 there's already 9 so

48-9=39

so p=39

To train for a marathon, Lily plans on running 4 miles per day for the first week and then increasing that daily distance by 1 mile each of the following weeks.

Which of these equations represent the problem.

Answers

The equation which represent the problem is given by an = 4 + 1.00(n - 1)

How to write equation?

Number if miles Lily run per day first week = 4 miles

Additional miles per day each week = 1 mile

let

n = total miles

The equation:

an = 4 + 1.00(n - 1)

When n = week 2

an = 4 + 1(n - 1)

= 4 + 1(2 - 1)

= 4 + 1(1)

= 4 + 1

= 5 miles

Learn more about equation:

https://brainly.com/question/2972832

Question 2
For three months after the training program, the sales director collected the sales data for the 200 sales representatives from
the Midwest and Northeast regions. The director then broke down the number of sales orders for the representatives
according to whether they received training or not. This data is shown in the table.
Three Months' Sales Orders
Training
No Training
Midwest
234
196
Northeast
252
178
Question
Use the data shown in the table to complete each statement.
Select the correct answer from each drop-down menu.
For the Midwest region, the average number of sales orders per representative for the group that had training is
more than the average number of sales per representative for the group that had no training,
For the Northeast region, the average number of sales orders per representative for the group that had training is
more than the average number of sales per representative for the group that had no training
The data from the sales director's study indicates that the one-month training program
sales

Answers

Answer:

see below for the whole unit activity

Step-by-step explanation:

I forgot to do homework and its due tomorrow
Solve:
-2 3/4 ÷ (-2.5)

Answers

Answer:

It is 1.1

Step-by-step explanation:

-hope this helps.

PLEASE HELPP QUICK!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

See below.

Step-by-step explanation:

Vertical angles can be found by adding the two degrees, and if they equal 180, they are vertical.

94 and 86

119 and 61

-hope it helps

in the four graphs below, determine what transformation was used to transform ABC to A’B’C’. then, for each one, write the correct description of the transformation along with the algebraic notation

Answers

Answer:

the first one seems like a 90 degree rotation counter clockwise and a reflection across the y=1 line (or is it x=1 line id-k) and the second is an 180 degree rotation.

Please help me this question

Answers

This is the answer. If this helps you please give brainliest.

Answer:  8

Work Shown:

[tex]\frac{2^x \times 3^y}{2^4 \times 3^2} = 6\\\\\frac{2^x \times 3^y}{2^4 \times 3^2} = 2\times3\\\\\frac{2^x \times 3^y}{2^4 \times 3^2} = 2^1\times3^1\\\\2^x \times 3^y = (2^4 \times 3^2)(2^1\times 3^1)\\\\2^x \times 3^y = (2^4\times2^1) (3^2\times 3^1)\\\\2^x \times 3^y = 2^{4+1} \times 3^{2+1}\\\\2^x \times 3^y = 2^{5} \times 3^{3}\\\\[/tex]

The 2^x matches with 2^5, showing that x = 5.

3^y matches with 3^3 to get y = 3

Therefore, x+y = 5+3 = 8

Reflect the shape A in the line y=5
What are the coordinates of the vertices of the image?

Answers

Answer:

(4,5) (4,8)(4,6)

Step-by-step explanation:

So now you're reflecting over the horizontal line that passes through the point (0,5)

:))

Step-by-step explanation:

(4,5),(4,6),(4,8)

the answer is this!

can anyone help me with this problem? Please it would be great.

Find the missing side of the triangle.

Answers

Answer:

[tex]\displaystyle 45 = x[/tex]

Step-by-step explanation:

Use the Pythagorean Theorem to define the hypotenuse:

[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ 36^2 + 27^2 = x^2 \hookrightarrow 1296 + 729 = x^2 \hookrightarrow \sqrt{2025} = \sqrt{x^2} \\ \\ \boxed{45 = x}[/tex]

I am joyous to assist you at any time.

NEED ANSWERS QUICKLY! CORRECT ANSWER GETS BRAINLIEST
When dividing fractions that are represented in the same terms, their quotient is simply the quotient of their numerators. Write an equation that demonstrates this.

Answers

Answer/Step-by-step explanation:

Quotient is simply the ratio of the first numerator to the second numerator:

Let's [tex]\frac{x_1}{y}\;and\;\frac{x_2}{y}[/tex] are two fractions in same terms.

Thus, [tex]\frac{x_1}{y}\div\frac{x_2}{y}[/tex] {Divided by a fraction is equal to multiplied by its reciprocal}

=[tex]\frac{x_1}{y}\times\frac{y}{x_2}[/tex]

Quotient is simply the quotient of their numerators.

Example could be:

[tex]\frac{2}{7}\div\frac{3}{7}[/tex]

[tex]\frac{2}{7}\times\frac{7}3}[/tex]

[tex]\frac{2}{3}[/tex]

2 is first numerator and 3 is the second numerator.

~lenvy~

the gravitational potential energy of an object is given by the formula p= mfg. which equation is correctly solved for the height, h?

a. h= p + mg
b. h= p-mg
c. h= p/(mg)
d. h=pmg

Answers

Step-by-step explanation:

c. h= p/(mg)

HOPE it helps

576 = 96 × 6
Which statement does the equation represent?

A. 96 is 6 more than 576
B. 576 is 96 more than 6
C. 96 is 6 times as many as 576
D. 576 is 96 times as many as 6.

Answers

Answer:

D

Step-by-step explanation

A.96=6+576

B.576=96+6

C. 96=6×576

D. 576=96×6

Please help me on all of these problems i am confused how they correlate

Answers

Answer:

Step-by-step explanation:

a) Area is multiplied by the square of the scale factor, so it is (3.1)^2 = 9.61 times larger.

b) Same logic, (1/6)^2 = 1/36

c) correct

d) 3

Please help answer this and give explanations. 20+ Points

Answers

Answer:

7 pairs of shoes

Step-by-step explanation:

So your equation is P(x) = -6x² + 60x - 126. This is a parabolic function, and it looks like we can factor it.

First, let's factor out -6 from the equation to simplify it. If we divide each part of the equation by -6, that leaves us with -6(x² - 10x + 21).

Now, we can factor the equation further by finding two numbers that add up to -10 and multiply to get 21. We know that both have to be negative numbers since they add up to a negative number and multiply to a positive one. The numbers you get are -3 and -7, making the equation P(x) = -6(x-3)(x-7).

x = 3 or 7. To maximize profit, you should sell 7 pairs of shoes.

Hope this helps! :)

Evaluate the expression 2bc for b = 1.5 and c = 5.

Answers

Answer:

15

Step-by-step explanation:

To answer this, simply input your values into the equation:

Since b is given as 1.5, and c is given as 5, you put it into the calculation 2bc

so, you would do 2x1.5x5

which is equal to 15

Answer: 15

Step-by-step explanation: Multiply it. You have 2bc, b=1.5, c=5 plug those values into 2bc. You should get 2(1.5)(5) and that'll be 15.

Dalvin's family took a road trip to Mount Rushmore. Dalvin fell asleep 44% of the way through the trip. If Dalvin fell asleep after they had traveled 176 miles, what was the total length of the trip?

Answers

Based on the given conditions, formulate:
176÷44%

Convert decimal to fraction:
176/44/100

Reduce the fraction:
176/11/25

Divide a fraction by multiplying its reciprocal:
176×25/11

Reduce the expression to the lowest term:
16×25

Calculate the product or quotient:
400

get the result:
400

Answer: 400m

Ignore this I deleted my answer cause I missread the question...

Leah invests money in an account paying simple interest. She invests $180 and no money is added or removed from the investment. After one year, she has $192.60. What is the simple percent interest per year?

Answers

The final statement is: The rate of interest is 7% and simple interest is $12.60

What Is Simple Interest?

Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.

Given here: Principal =$180 And amount after one year=$192.60

Therefore simple interest= 192.60-180

                                          =12.60

∴12.60=180×r×1/100

 r=7%

Hence, The rate of interest is 7% and simple interest is $12.60

Learn more about simple interest here:

https://brainly.com/question/25845758

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