Alice drew a rectangle with a perimeter of 30 cm and an area of 56 cm2. Which dimensions match Alice's rectangle?

Answers

Answer 1

Answer:

The dimensions that match Alice's rectangle are 7 cm and 8 cm.

Step-by-step explanation:

The perimeter of the rectangle is given by:

[tex] P = 2(a + b) = 30 cm [/tex]    (1)                              

Where a and b are the sides of the rectangle

Also, the area of the rectangle is:

[tex] A = a\times b = 56 cm^{2} [/tex]   (2)

By solving equation (1) for a, we have:

[tex] a = 15 cm - b [/tex]      (3)                      

Now, by entering equation (3) into (2) we can find one side of the rectangle:

[tex] 56 cm^{2} = (15 cm - b)\times b [/tex]          

[tex] b^{2} - 15b + 56 = 0 [/tex]                                                        

Solving the above quadratic equation we have:

b₁ = 7 cm  and b₂ = 8 cm                      

Now, the other side of the rectangle can be calculated with equation (3):

[tex] a = 15 cm - b_{1} = 15 - 7 cm = 8 cm [/tex]                          

or    

[tex] a = 15 cm - b_{2} = 15 - 8 cm = 7 cm [/tex]            

Taking the first solution (b₁) or the second (b₂), we find that the dimensions that match Alice's rectangle are 7 cm and 8 cm.          

Therefore, the dimensions that match Alice's rectangle are 7 cm and 8 cm.

                                               

I hope it helps you!                            


Related Questions

Chris rode his bike 4 miles west and then 3 miles south. What is the
shortest distance he can ride back to the point where he started?

Answers

Answer:

5 miles

Step-by-step explanation:

This is because if you draw a line going west and label it as 4 miles, then draw another line going south and label it 3 miles, you form a right angle, right? So, the fastest way to go back would be taking a diagonal-like route back to the beginning. Does this shape look familiar to you? Right! It's a right triangle. And do the numbers 3, 4, and 5 sound familiar to you? Yup, it's a Pythagorean triplet. If the legs of a right triangle are 3 and 4, the hypotenuse is 5. Why am I saying this? Because, in the drawing you just did, the 4 miles west and 3 miles south were the legs, and the diagonal path back to the beginning is the hypotenuse. Get it now?

Happy to help! :)


A TV costs £400. David pays a deposit of £150.
Express David's deposit as a percentage of the full price of the TV.
Give your answer to 1 decimal place.

Answers

Answer:

37.5

Step-by-step explanation:

150/400*100 is the percentage

Answer:

37.5

Step-by-step explanation:

150/400 is .375 * 100 = 37.5

use this formula N/B*100

number divided by base x 100

find the missing side each triangle.round your answers to the nearest tenth if necessary

Answers

Answer:

x = 6

Step-by-step explanation:

The triangle is a right triangle, as denoted by the red square at the bottom, we can use the Pythagorean Theorem to figure out the second side (since we are given the other side and the hypotenuse).

a² + b² = c²

(8)² + b² = (10)²

64 + b² = 100

b² = 100 - 64 = 36

b = ±[tex]\sqrt{36}[/tex]

b = ± 6

But we know that distance is always positive, so

b = 6

I have used b in place of x if you are confused about the variable usage.

I have a D in math. Please help me with this. I need to bring my grade up!! 15 pts!!

Answers

Answer:

20 meters thru 80

Step-by-step explanation:

0.8(5)^2=20

0.8(10)^2=80

Jill works on the weekends. Last saturday, she worked 5.75 hours. Sunday she worked 6.75 hours. she earn $7.50 per hours. How much did she earn last weak​

Answers

93.75 because 5.75x7.50=43.125 and 6.75x7.50=50.625 and 50.625+43.125=93.748 and round it to the near test hundredth because it’s money and that’s 93.75

100 Ponits give away to answer the question.


Which relationship describes angles 1 and 2?





adjacent angles


complementary angles


supplementary angles


vertical angles

Two parallel horizontal lines intersected by an angled line with one labeling the top left angle and two labeling the bottom right angle of the top line

Answers

Answer:

vertical angles

Step-by-step explanation:

Mike took a taxi from his home to the airport. The taxi driver charged an initial
fee of $6 plus $3 per mile. The total fare was $24, not including the tip. How many
miles did mike travel by taxi on this ride?
A. 2
B. 6
C. 8
D.10

Answers

Answer:

B. 6

Step-by-step explanation:

SInce the total amount paid by Mike was $24, you subtract the initial amount he paid ($6) which leaves you with $18. Since the taxi driver charges $3 per mile you divide $18 by $3 to get 6 so that means Mike travel 6 miles.

The answer would be ~6~ because 6+3*x= 24 which x=6

Hope this helps

Have a great day/night

Feel free to ask any questions

Colin & Brian share a lottery win of £2100 in the ratio 4 : 1.
Colin then shares his part between himself, his wife & their son in the ratio 2 : 5 : 3.
How much more does his wife get over their son?​

Answers

Answer:

2

Step-by-step explanation:

I think but am not sure sorry I can not help

???????????????????????????????

Answers

Answer:

i think its A

Step-by-step explanation:

you add all the numbers up together and dvide by how many numbers there are. thats what i did and got 6

I REALLY NEED HELP!!! PLEEEEEASE

A landscaper needs to fill a path measuring 2 feet by 8 feet with patio stones.
The patio stones are each 1 foot by 2 feet, so the landscaper calculates that she
will need 8 of them.
Before arranging the patio stones, the landscaper wants to look at all her options.
She can not cut or overlap the stones, and they all must fit inside the path area
without any gaps. Two possible arrangements of the stones are shown below.
How many different arrangements are there in total?

Answers

Answer:

I think its 4.

Step-by-step explanation:

decimal greater than 1% but less than 2%

Answers

Answer:

1.5%

Step-by-step explanation:

Answer:

1.5% of 100=1.5is your answer

help me plz bc i don't understand this and this is from 2 weeks ago and I have straight F's in school

Answers

bae what you failing

Answer:

y = -3x + 3

Step-by-step explanation:

So, basically I can't remember how to do this the long way but I used a calculator on Desmos (the graphing one to be specific). You should be able to find tutorials on how to use it and graph problems to find their answers but if not, you can just message me and I'll walk you through how to use it.

As for the form it asked for in the question, slope-intercept form is just:

y = mx + b

m is the slope, and b is the y-intercept (the place where the line crosses the y-axis)

-8x + 4 - 9 - 5x
help me ASAP

Answers

Answer:

-13x-5?

Step-by-step explanation:

simplify? if not this answer is wrong

In AWXY, W = 4.8 inches, x = 7.2 inches and y=9.3 inches. Find the measure of ZW
to the nearest degree.

Answers

Answer:

31

Step-by-step explanation:

trust me

Answer:

31

Step-by-step explanation:

W=30.584≈31

The perimeter of a triangle is 26 feet. The second side is twice as long as the first. the third side is 1 foot longer than the second side. What is the length of the 3 sides?

Answers

Answer:

5, 10 and 11 feet.

Step-by-step explanation:

Let length of first side be x feet then

second side  = 2x feet

third side = 2x + 1 feet.

So we have the equation:

x + 2x + 2x + 1 = 26

5x + 1 = 26

5x = 25

x = 5 feet.

So first side = = 5 feet, second = 10 and third = 11 feet.

Select the quadratic equation that has no real solutions. 25x-10x+4=0

Answers

Answer:

Step-by-step explanation:

Were there not several equations from which to choose?

The coefficients of 25x^2 - 10x + 4 are {25, -10, 4}.  The discriminant is thus b^2 - 4ac, or (-10)^2 - 4(25)(4), or 100 - 400, or -300.  Because the discriminant is negative, the quadratic has no real solutions.

The quadratic equation with no real solution is 25x²-10x+4 = 0

What is a quadratic equation?

The meaning of quadratic equation is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

Given that, which of the equations have no real solution,

Considering the quadratic equation 25x²-10x+4 = 0

D = [tex]\sqrt{b^{2} -4ac}[/tex]

We know, when √D > 0, real roots

√D = 0, equal roots

√D < 0, imaginary roots

[tex]\sqrt{b^{2} -4ac}[/tex] =

[tex]\sqrt{10^{2} -400} \\\sqrt{-300}[/tex]

Since, the discriminant is less than 0, therefore, its roots are imaginary.

Hence, The quadratic equation with no real solution is 25x²-10x+4 = 0

For more references on quadratic equation, click;

https://brainly.com/question/17177510

#SPJ2

The diameter of a circle has endpoints of (2, 5) and (-4, 13). What is the correct equation of this circle? Pls explain and I will mark brainliest!

Answers

Answer:

Option 4

Step-by-step explanation:

Midpoint of the diameter is the center.

Use midpoint formula to determine the coordinates:

x = (2 - 4)/2 = -1y = (5 + 13)/2 = 9

Find the radius using the midpoint and one of the endpoints and the distance formula:

r = [tex]\sqrt{(-1 - 2)^2 + (9 - 5)^2} = \sqrt{9+16} = \sqrt{25} = 5[/tex]

Use the equation of the circle:

(x - (-1))² + (y - 9)² = 5²(x + 1)² + (y - 9)² = 25

Correct choice is 4

-12x + 2 y = 8
-6x + y = -3

Answers

Answer:

PEMDAS

Step-by-step explanation:

USE PEMDAS

Algebra 1 need help (Solving exponents equations)

Answers

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the exponents and indices.

here, we should remember one thing that,

3 ^3 = 27 and 1/3^x = 3^-x

so we get as,

(3^-3)^4-x = (3^3)^2x-1

==> 3^-12+3x = 3^6x-3

since the base is same that is 3 , we equate their powers.

-12x+3=6x-3

==> 3+3 = 6x+12x

==> 6 = 18x

hence ===> x = 6/18 = 1/3

hence, x = 1/3

Linda's dog ate 6 cans of dog food this week. Each can contained 44.7 grams of protein. How much protein was this in all?

Answers

Answer:

268.2 grams

Step-by-step explanation:

44.7 times 6

please mark brainliest

A bottle of italian salad contains 0.7 grams of sugar. How many milligrams of sugar are in 6 bottles of italian salad dressing

Answers

Answer:

420mg

Step-by-step explanation:

0.7x6 = 0.42g which is 420mg

1g = 1000mg

2x(3 + 4x) - x +4-(x + 1)
Which expression is equivalent to the expression?
O 8x2 + 4.C + 3
O 8x2 + 4x + 5
O 822 +63 +3
O 8x2 +63 +5

Answers

The answer is 8x2 + 4.C + 3

how can I solve this?​

Answers

Answer:

40/30 or 4/3

Step-by-step explanation:

Tangent is opposite leg over adjacent.

The adjacent leg to A is 30 while the opposite is 40

40/30 simplified is 4/3.

Answer:

40/30 or 4/3 I think

Step-by-step explanation:

correct answer gets brainliest

Answers

Answer:

1.) 12³

Step-by-step explanation:

side = 12 ft

volume of cube = side³

----------------------------------follow me

Answer:

first option

Step-by-step explanation:

The volume (V) of a cube is calculated as

V = s³ ( s is the side length )

Here s = 12, then

V = 12³

5 and2/3 divide by 4?

Answers

Answer:

The answer is 1 5/12 or 17/12.

Step-by-step explanation:

First we turn 5 2/3 into a Improper fraction.

5 2/3 = 17/3

Next we change 4 to 1/4 then multiply 1/4 by 17/3.

17/3 * 1/4 = 17/12

17/12 = 1 5/12

Hope this helps! :)

Answer:

17/12

Step-by-step explanation:

5[tex]\frac{2}{3}[/tex] / 4 = [tex]\frac{17}{3}[/tex] / [tex]\frac{4}{1}[/tex] = [tex]\frac{17}{3}[/tex] * [tex]\frac{1}{4}[/tex] = 17/12

HELP MEEEEEEEEEEEEE PLEASEEEEEEEEEEEEEEEE

( 6 x 7- 22 ) + 7

And ik it's not 27

Answers

Answer:

The answer would be 13

Step-by-step explanation:

(6 x 7 - 22) - 7

(42 - 22) - 7

(20) - 7

13

james and elaine share a box of sweet in the ratio 2:3 what fraction of sweets does james receive and elaine receive​

Answers

Answer: james gets 2/5 of the candy while elaine gets 3/5

Step-by-step explanation:

2/5 + 3/5 = 5/5 = 1 box

The length of the rectangle is 6 feet. The width is three times the length. What is the total area of the rectangle?

Answers

i believe the answer would be 108

Answer:

should be A=108

Step-by-step explanation:

6 times 3 = 18

A=LxW

6x18=108

Melvin has $25 dollars to spend. He spent $10.81, including tax, to buy a new DVD. He needs to save $10.00 but he also wants to buy peanuts. Peanuts cost $0.38 per package including tax.
Write and solve an inequality that will determine the maximum number of packages of peanuts that Melvin can buy

Answers

Answer:

Melvin can buy 11 package Peanuts

Step-by-step explanation:

f(x)= (x+2)2
f(x)=a (x-h)2+k
find : vertex, domain,range,axis of symetery , up/down, min/max , graph

Answers

f(x) = (x + 2)²    ⇒   f(x) = (x - (-2))² + 0    ⇒   h = -2 ,   k = 0

vertex:   (-2, 0)

domain:    R  

range:   <0, ∞)

axis of symetery:  x = -2

up   {a=1>0}

min:  f(-2) = 0

graph:  {f(0)=4}

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