A rectangle has a width of x centimetres and a perimeter of 8x centimetres. A square has
sides of length one fourth the length of the rectangle.
a) Determine the length of the rectangle.
b) Determine the perimeter of the square.
c) Determine how many centimetres greater the rectangle's perimeter is than the square's
perimeter if x = 4.
d) Determine how many square centimetres greater the rectangle's area is than the square's
area if x = 4.

Answers

Answer 1

Answer:

Part A) The length of rectangle is [tex]3x[/tex] [tex]cm[/tex]

Part B) The perimeter of the square is [tex]3x[/tex] [tex]cm[/tex]

Part C) [tex]20[/tex] [tex]cm[/tex]

Part D) [tex]39[/tex] [tex]cm^2[/tex]

Step-by-step explanation:

Part A) Find the length of the rectangle

we know that

The perimeter of rectangle is equal to

[tex]P=2(L+W)[/tex]

we have

[tex]P=8x[/tex] [tex]cm[/tex]

[tex]W=x[/tex] [tex]cm[/tex]

substitute and solve for L

[tex]8x=2(L+x)[/tex]

[tex]4x=(L+x)[/tex]

[tex]L=4x-x=3x[/tex] [tex]cm[/tex]

Part B) Find the perimeter of the square

we know that

The perimeter of a square is

[tex]P=4b[/tex]

we have that

[tex]b=(1/4)L[/tex]

substitute the value of L

[tex]b=(1/4)3x=(3/4)x[/tex] [tex]cm[/tex]

Find the perimeter of the square

[tex]P=4(3/4)x=3x[/tex] [tex]cm[/tex]

Part C) Find how many cm greater the rectangle's perimeter than the square's perimeter if x=4

Find the value of rectangle's perimeter

[tex]P=8x[/tex] [tex]cm[/tex] ------> [tex]P=8(4)=32[/tex] [tex]cm[/tex]

Find the value of square's perimeter

[tex]P=3x[/tex] [tex]cm[/tex] ------> [tex]P=3(4)=12[/tex] [tex]cm[/tex]

Find the difference

[tex]32[/tex] [tex]cm[/tex] [tex]-12[/tex] [tex]cm[/tex] [tex]=20[/tex] [tex]cm[/tex]

Part D) Find how many square cm greater the rectangle's area is than the square's area if x=4

Find the value of rectangle's area

[tex]A=(3x)(x)=3x^2[/tex] [tex]cm^2[/tex] ------> [tex]A=3(4^2)=48[/tex] [tex]cm^2[/tex]

Find the value of square's area

[tex]A=((3/4)x)^2[/tex] [tex]cm^2[/tex] ------> [tex]A=((3/4)(4))^2 = 9[/tex] [tex]cm^2[/tex]

Find the difference

[tex]48[/tex] [tex]cm^2[/tex] [tex]-9[/tex] [tex]cm^2[/tex] [tex]=39[/tex] [tex]cm^2[/tex]

Related Questions

What formula can we use to find the surface area of a rectangular prism? ​

Answers

Answer:

○ [tex]\displaystyle SA = 2lw + 2lh + 2wh[/tex]

Explanation:

A rectangle has four right angles, including two pairs of congruent edges, only containing two dimensions – height and length. Therefore, going three-dimensional, a rectangular prism has three dimensions – width, height, length. With this information, you should know what the answer is.

I am joyous to assist you at any time.

Which real-world scenario involves a right triangle?

Answers

Answer:

There are a few different scenarios

Step-by-step explanation:

Bathroom Tiles,Kitchen flooringTriangle Backsplash ( tile behind your sink in kitchenDrywall work if you need right edges, you will need a right triangleFinally any sort of contracting and Deck work

FROM- THE GENIUS ANSWERER

which is more likely to have a mass close to 3 kilograms small feather a five year old cat or a grown elephant or a peach. dont delete this question dbs at brainly (dbs = drag on balls)

Answers

Answer:

5 year old cat

Step-by-step explanation:

because a kg is about a pineapple

what is the answer 2⅓+⅚​

Answers

Answer:

3 1/6

Step-by-step explanation:

2+1/3+5/6

(1/3=2/6)

so 3/6+5/6 =  7/6

Segment AB has point A located at (6, 5). If the distance from A to B is 5 units, which of the following could be used to calculate the coordinates for point B? 5 = square root of the quantity of x minus 6 all squared plus y minus 5 all squared 5 = square root of the quantity of x minus 5 all squared plus y minus 6 all squared 5 = square root of the quantity of x plus 6 all squared plus y plus 5 all squared 5 = square root of the quantity of x plus 5 all squared plus y plus 6 all squared

Answers

The distance of segment AB is the number of units on the segment

The equation that can be used to determine the coordinates of point B is [tex]5 = \sqrt{(x -6)^2 + (y - 5)^2}[/tex]

How to determine the equation?

The given parameters are:

A = (6,5)AB = 5 units

The distance AB is calculated using:

[tex]AB = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2}[/tex]

This gives

[tex]5 = \sqrt{(x -6)^2 + (y - 5)^2}[/tex]

Hence, the equation that can be used to determine the coordinates of point B is [tex]5 = \sqrt{(x -6)^2 + (y - 5)^2}[/tex]

Read more about distance equations at:

https://brainly.com/question/7243416

Answer:

√(x-6)² + (y-5)²

Step-by-step explanation:

The Distance Formula is √(x2 - x1)² + (y2 - y1)²

If you plug in the known values, you get √(x - 6)² + (y - 5)²

This is our answer.


Car A uses regular gasoline at $1.21 a gallon and gets 19 miles per gallon (mpg) in town. Assume that
you drive 100 miles a week, or 400 miles a month. What is your gas bill each month?

Answers

Answer:

Step-by-step explanation:

Remark

If you drive 400 miles a month, and you get 19 miles per gallon, then you will need

gallons = miles / miles per gallon

Givens

m = 400

mpg = 19

Cost per gallon = 1.21

Solution

gallons = 400 / 19 = 21.05

You need to buy 21.05 gallons

1 gallon costs 1.21

21.05 gallons cost x            Cross multiply

x = 1.21 * 21.05

Answer: x = 25.47              Cost for 1 month's fuel.

simplify 8+6x6/11 +7×2.

Answers

Answer:

Step-by-step explanation:

Answer:

[tex]\frac{44}{25}[/tex]

Step-by-step explanation:

1) Simplify 6 × 6 to 36.

[tex]\frac{8+36}{11+7*2}[/tex]

2) Simplify 8 + 36 to 44.

[tex]\frac{44}{11+7*2}[/tex]

3) Simplify 7 × 2 to 14.

[tex]\frac{44}{11+14}[/tex]

4)  Simplify 11 + 14  to 25.

[tex]\frac{44}{25}[/tex]

ANSWER THE FOLLOWING:​

Answers

Answer:

1. (a) 1/12

(b)35/36

(c) 31/36

2. Blue - 1/3

Red- 4/15

Leila had 160 dollars to begin with. She just spent k dollars. Using k, write an expression for the number of dollars she has left.

Answers

Answer:

160 - k dollars

Step-by-step explanation:

Hello!

If Leila has 160 dollars and spends the amount k, then you are therefore subtracting k from 160. This is because you are using the value of k from 160.

So the expression would be 160 - k dollars

Which choice is the solution to the inequality below?
8x < 24
O A. x< 24
O B. x> 24
C. x>3
O D. x<3

Answers

Answer:

D

Step-by-step explanation:

8x < 24

divide both sides by the coefficient of x

8x/8 < 24/8

x < 3

Sketch advertising firm charges $150 to design a full-color flyer and 12 cents per flyer to print the flyer. Rose's Sweet Shop spent $192 on the flyers for the grand opening. How many Flyers did she buy?​

Answers

Answer:

210

Step-by-step explanation:

First, we keep $150 on the back of our minds(or our paper).

Second, we would assume that Rose's would've designed the flyer at $150, making us determine how much flyers they bought for the remaining $42.

($192 - $150 = $42)

Now that we know all of this, we can begin.

12 x 5 is 60, so 60 cents makes 1 dollar.

So for every dollar, they can make 5 flyers.

If we do 5 x 42, we'll get the answer of 210, which is the amount of flyers she bought!

2/3 of the pizza was left over from last night. Then, Marcy ate another 2/9 of it. Which of the following statements is true?

A.Very little of the pizza is left.
B.About half of the pizza is left.
C.Most of the pizza is left.​

Answers

Answer:

B.About half of the pizza is left.

Step-by-step explanation:

When we solve:

2/3 of the pizza was left over from last night. Then, Marcy ate another 2/9 of it.

We get 4/9.

-15 divided by -1 2/3

Answers

Answer:

9

Step-by-step explanation:

15 / 5/3 = 15 x 3/5=9

Because a negative numebr divided by a negative number is always positive.

Answer:

9

Step-by-step explanation:

3. The math exam scores for a class are shown below.
a
Make a data display. What percent of the scores are 90
and greater?
24, 68, 83, 75, 81, 99, 98, 80, 85, 70, 89, 92, 77, 96,
180, 64, 88, 96, 76, 88

Answers

Answer:

30 percent of the scores are 90 and greater

what is this number? 1,010,020,030,040,050,060,070,080,090,010,020,030,040,050,060,070,080,090,010,020,030,040,050,060,070,080,090,010,020,030,040,050 WILL MARK BRAINLIEST

Answers

Answer:

that isn't a number

Step-by-step explanation:

6 Jenny is y2 years old and her daughter Allyson is y years old, If Jenny lives to the age of 13y,
Allyson will be y years old. How old is Allyson now? (Note: the difference in ages must
remain constant.)

Answers

Answer:

Allison is 7 years now, Jenny is 49 yeas now. Check.  13y = 13*7 = 91 will happen in 91-49 = 42 years. Jenny will be 7 + 42 = 49 years old at that time.

Step-by-step explanation:

If the area of the following parallelogram is 30 square centimeters, what is the length of the base?



25 cm
5 cm
6 cm
150 cm

Answers

Answer: 6 cm

Step-by-step explanation:

The formula for the area of a parallelogram is

hb=a

Where

b is the base

h is the height (5 for this)

and a is the area (30 for this)

Let's sub these values into our equation

[tex]5b=30[/tex]

Divide both sides by 5 to isolate b

[tex]5b=30\\\frac{5b}{5} =\frac{30}{5} \\b=6[/tex]

The base is 6cm long.

Answer:

Base = 6 cm

Step-by-step explanation:

Given:

[tex]\text{Area of parallelogram} \text{ = 30 cm}^{2}[/tex]

[tex]\text{Height of parallelogram = 5 cm}[/tex]

Formula:

[tex]\text{Area of parallelogram} = \text{Base} \times \text{Height}[/tex]

Substitute the height and the area of the parallelogram:

[tex]:\implies 30 \ \text{cm}^{2} = \text{Base} \times 5[/tex]

Divide both sides by 5:

[tex]:\implies \dfrac{30}{5} = \dfrac{\text{Base} \times 5}{5}[/tex]

Simplify both sides:

[tex]:\implies 6 \ \text{cm} = \text{Base}[/tex]

Which graph of f(x) satisfies the conditions Limit of f (x) as x approaches 2 minus = –4 and Limit of f (x) as x approaches 2 plus = 0? HURRY WILL GIVE BRAINLIEST FOR CORRECT ANSWER!!

Answers

The graph of f(x) that satisfies the condition of f(x)'s left sided limit at 2 being -4 and right sided limit at x = 2 being 0 is given by the first graph.

What is one-sided limit for function of single variable?

In rough terminologies, the limit from one side is when we only use one side of the function with respect to the considered point of interest (in input) to predict the value of the function at that point.

For this case, we need to find the graph of the function f(x) from the considered 4  graphs for which:

[tex]\lim_{x\rightarrow 2^{-}}f(x) = -4\\\\\lim_{x\rightarrow 2^{+}}f(x) = 0\\[/tex]

For the first graph, for the point x=2, on left from the point x = 2 lies a ray. If thats the function, we can hope that the function will continue having the same line to the right too, so the prediction for value of function on x = 2 is the value that line gives for y.

That is -4.

Thus, prediction of function from left of x = 2 is -4, or

[tex]\lim_{x\rightarrow 2^{-}}f(x) = -4[/tex]

Similar to that, from the right of the point 2, there is some yellow curve. That predicts that the function's value at point x = 2 should be 0 (the yellow curve seems like touching the x-axis where y = 0 at the point x=2.

Thus, we have:

[tex]\lim_{x\rightarrow 2^{+}}f(x) = 0\\[/tex]

So graph first is correctly pertaining such function f(x).

Second graph when refered, we see that if we predict value at x =2 from left, the yellow curve in the left will make us predict that the function would be 0, so: [tex]\lim_{x\rightarrow 2^{-}}f(x) = 0[/tex]

Thus, its wrong graph.

Third graph when refered, we see that if we predict value at x =2 from left, the green line in the left will make us predict that the function would be -2 at x = 2 (see the green point in the third graph), so: [tex]\lim_{x\rightarrow 2^{-}}f(x) = -2[/tex]

Thus, its wrong graph.

Similarly, for the fourth graph, we see that if we predict value at x =2 from left, the yellow curve in the left will make us predict that the function would be 0, so: [tex]\lim_{x\rightarrow 2^{-}}f(x) = 0[/tex]

Thus, its wrong graph.

Thus, the graph of f(x) that satisfies the condition of f(x)'s left sided limit at 2 being -4 and right sided limit at x = 2 being 0 is given by the first graph.

Learn more about one-sided limits here:

https://brainly.com/question/23625942

#SPJ1

Answer:answer a

Step-by-step explanation: got right on edge 2023

Which statement is true?
∞Σn=1 0.2(-3)^n-1 converges because r< 1.
∞Σn=1 0.2(-3)^n-1 diverges because |r| <1.
∞Σn=1 0.2(-3)^n-1 diverges because |r| > 1.
∞Σn=1 0.2(-3)^n-1 converges because r> 1.​

Answers

The mode of the ratio of the sequence should be greater than one for the divergence. Then the correct option is C.

What are sequence and series?

A series is a sum of sequence terms. That is, it is a list of numbers with adding operations between them.

We know that the condition of the converges of the series will be given as

[tex]\rm \Sigma ^{\infty}_{n=1} \ 0.2(-3)^{n-1}\ \ diverges \ because \ |r| > 1.[/tex]

The mode of the ratio of the sequence should be greater than one for the divergence.

More about the series link is given below.

https://brainly.com/question/10813422

#SPJ1

Answer: It’s C

Step-by-step explanation:

Which expression is equivalent to 2(5z+3)?

Answers

Answer:

D

Step-by-step explanation:

That expression equals :

10z+6

So, now we need to find one of the expressions that ALSO gives us 10z+6

D

This is because:

2*3z=6z

2*2z=4z

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

6z+4z=10z, so we got that one so far.

NEXT

2*3=6.

We got the 6 too!

it is d

0.7 is equivalent to what fraction

Answers

Answer:

7/10

Step-by-step explanation:

Fractional form of 0.7 is 7/10.

1
N
3
5
6
B
10
56:0
What is the range of the function on the graph?
5
14
O all real numbers
O all real numbers less than or equal to -1
all real numbers less than or equal to 3
© all real numbers less than or equal to 0
-5-4-3-2-14
1 2 3 4 5 X
I
-2
-3
-4
-5

Answers

Answer:

pack you

pa brainliwa po

[tex] \tt(6x4−2x3 +7x2 −x) + ( 7x4+ 2x3−5x + 7)[/tex]

[tex] \\ [/tex]

With Solution!!​​

Answers

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

Let's solve ~

[tex]\qquad \tt \dashrightarrow \:\tt(6x {}^{4} −2x {}^{3} +7x {}^{2} −x) + ( 7x {}^{4} + 2x {}^{3} −5x + 7)[/tex]

[tex]\qquad \tt \dashrightarrow \:\tt6x {}^{4} −2x {}^{3} +7x {}^{2} −x + 7x {}^{4} + 2x {}^{3} −5x + 7[/tex]

Now, move all like terms aside :

[tex]\qquad \tt \dashrightarrow \:6 {x}^{4} + 7 {}x^{4} - 2 {x}^{3} + 2 {x}^{3} + 7 {x}^{2} - x - 5x + 7[/tex]

Add the like terms ~

[tex]\qquad \tt \dashrightarrow \:13 {}x^{4} + 7 {x}^{2} + 6x + 7[/tex]

Answer:

13(x)⁴ + 7(x)²-6(x) + 7

Explanation:

[tex]\hookrightarrow \sf (6x^4 -2x^3+7x^2-x)+(7x^4+2x^3-5x+7)[/tex]

remove the parenthesis

[tex]\sf \hookrightarrow 6x^4-2x^3+7x^2-x+7x^4+2x^3-5x+7[/tex]

group the variables

[tex]\hookrightarrow \sf 6x^4+7x^4-2x^3+2x^3+7x^2-x-5x+7[/tex]

add similar terms

[tex]\sf \hookrightarrow 13x^4+7x^2-x-5x+7[/tex]

simplify

[tex]\hookrightarrow \sf 13x^4+7x^2-6x+7[/tex]

please show your work, tysm :D

~giving brainliest!~

Answers

Answer:

1/16th

Step-by-step explanation:

You can write this problem as a function of time.

Let x be the amount of acetaminophen that you start off with.

Let n be the amount of 2.5 hour intervals that have passed

x*0.5^n

The reason this function works is because with each 2.5 hour interval, you multiply the total product by another 1/2.

Plugging in 4(because 4 2.5 hour intervals in 10 hours), you get:

x*0.5^4,

which is x/16.

This shows that 1/16th of the acetaminophen is left in the body after 10 hours.

382.85 rounded to three significant figures

Answers

Answer:

382.85

Sig Figs

   5

   382.85

Decimals

   2

   382.85

Scientific Notation

   3.8285 × 10^2

E-Notation

   3.8285e+2

Words

   three hundred eighty-two point eight five

Step-by-step explanation:

How many times larger is 8 x 10^9 than 4 x 10^3

Answers

Answer:

600

Step-by-step explanation:

10x9 =90

10x3=30

8x90=720

4x30=120

720-120= 600

5-6y^2=113 solve by square roots ​

Answers

Answer:

[tex]y=\frac{\sqrt{113}-5 }{-6}[/tex]

Step-by-step explanation:

[tex](5-6y)^2=113[/tex]

[tex]\sqrt{(5-6y)^2} =\sqrt{113}[/tex]

[tex]5-6y=\sqrt{113}[/tex]

[tex]-6y=\sqrt{113} -5[/tex]

[tex]y=\frac{\sqrt{113}-5 }{-6}[/tex]

I hope this helps!

Find the value of X.

Answers

Answer: 23

Step-by-step explanation:

Hi can someone help me pls

Answers

Answer:

f(x) = 45x + 5

Step-by-step explanation:

The parking fee for a minibus at an event is $5 entering the parking lot. There is an extra charge of $45 per passenger.

The formula that simulates the parking fee for this sentence is

f(x) = 45x + 5

This is because 45x represents the charge per passenger and we are using addition because the $5 minibus parking fee; to enter the parking lot - increases the total cost of the parking fee.

Pick one A,b,c,d,e will give brainlest

Answers

Answer:

E    (simalr to the other one you posted)

Step-by-step explanation:

Denominator cannot equal 0   so domain (x values) cannot include 2

  range: all numbers, buthere is no way to make a 0

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