Yumiko has a rectangular-shaped patio. She wants to double the area of the patio by increasing the length and the width by the same amount.
The length is 14 and the width is 10.

a. Write a function, in factored form, to calculate the number of feet Yumiko would need to add to the length and width.

b. What are the dimensions of the patio, rounded to the nearest hundredth feet?

I am not very good with completing the square and would like to understand it better. Any help would be very appreciated!

Answers

Answer 1

Answer:

For a rectangle of length L and width W, the area is:

A = L*W

In this case, we start with:

L = 14ft

W = 10ft

Then the initial area is:

A = 14ft*10ft = 140ft^2

a) Now she wants to increase the same amount in each measure, then the new measures will be:

L = 14ft + x

W = 10ft + x

Now we want this new area to be twice the one that we got before, then the equation will be:

(14ft + x)*(10ft + x) = 2*140ft^2 = 280ft^2.

b) Let's solve the equation:

(14ft + x)*(10ft + x) = 280ft^2

First lets distribute the multiplication:

140ft + x*10ft + 14ft*x + x^2 = 280ft

Now let's group terms with the same power of x.

x^2 + (10ft + 14ft)*x + 140ft - 280ft = 0.

x^2 + 24ft*x  - 140ft = 0.

Now we need to solve this quadratic equation, here we must use the Bhaskara equation for quadratic equations, and we will get two solutions for x.

[tex]x = \frac{-24ft +- \sqrt{(24ft)^2 - 4*140ft*1} }{2*1} = \frac{-24ft +- 33.7ft}{2}[/tex]

Then the two solutions are:

x = (-24ft - 33.7ft)/2 = -28.9 ft

This solution is negative, so it does not make sense and we can discard it.

x = (-24ft + 33.7ft)/2 = 4.85ft

This is positive, so we can use this.

Now we can find the new length and width:

L =  14ft + 4.85ft = 18.85ft

W = 10ft + 4.85ft = 14.85ft


Related Questions

Please help me out with this! *It's just an extra practice assignment :)​

Answers

Answer:

t and r are parallels

t and p are perpendicular

Step-by-step explanation:

r and t have the same coordinates 4,1 but one has a negative 4 and 1

t and p have a dot on the same spot

Which set contains the value below?

50


A.irrational B.Natural C. rational D.Integers

Answers

Answer:

A or d

Step-by-step explanation:a or d

A or d

The set of natural numbers, rational numbers and integers contain 50. Therefore, options B, C and D are the correct answer.

We need to find which set contains the value 50.

What are real numbers?

Real numbers include rational numbers like positive and negative integers, fractions, and irrational numbers.

Irrational numbers: Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers.

Here, 50 is not an irrational number.

Rational numbers: A rational number is any number that can be written as a fraction, where both the numerator (the top number) and the denominator (the bottom number) are integers, and the denominator is not equal to zero.

Here, 50=50/1 is a rational number.

Natural numbers: Natural numbers are the numbers that start from 1 and end at infinity.

So, 50 is a natural number.

Integers: An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

So, 50 is an integer.

The set of natural numbers, rational numbers and integers contain 50. Therefore, options B, C and D are the correct answer.

To learn more about the real numbers visit:

https://brainly.com/question/9876116.

#SPJ2

Identify the number of terms in this polynomial.
5k^5+7k-2

Answers

Answer:

cuatro terminos

Describe or show how to find the following product using both an algorithm and a diagram:

3 x 3/4

Answers

Answer:

Explanation:

PART 1. Using an algorithm:

First expression:

Step 1: Multiply numerators and denominators.

Second expression:

Step 1: Multiply numerators and denominators.

Third expression:

Step 1: Convert mixed fraction into improper fraction:

Step 2: Replace the improper form into the expression

Step 2: Multiply numerators and denominators.

PART 2. Using diagram:

The diagram is shown below. Basically the steps we follow are the same as if it were using algorithms.

Step-by-step explanation:

Answer:

hhahaahhahahaahhaahaha yalll so dum hahahahahahahhahaahah

Step-by-step explanation:

this is easy. hahahahahahahhaahahhaahahahhaahhaahahahaha

Anyone please answer only have 3 min

Answers

Answer:

A

Step-by-step explanation:

Answer:a

Step-by-step explanation:

HEY CAN ANYONE PLS ANSWER DIS MATH QUESTION!!!

Answers

Answer:

85% of 19 = 16.15

Step-by-step explanation:

19 times 0.85 will give you the answer! (16.15)

Bob owed S225 on his store credit card. Ile made a payment of S75. Ilow much does Bob owe on his credit card? 0 -150 O 150 O 300 -300



Help me pleasee !​

Answers

The answer is -300 because he owes -225 and then when he spends they subtract the amount he spent so the equation would be -225-75= the answer of -300

Find the value of X
(5x+4)°+(8x-71)°

Answers

Answer:

x = -4/5

Step-by-step explanation:

Solve for x:

(5 x + 4) (8 x - 71) = 0

Split into two equations:

5 x + 4 = 0 or 8 x - 71 = 0

Subtract 4 from both sides:

5 x = -4 or 8 x - 71 = 0

Divide both sides by 5:

x = -4/5 or 8 x - 71 = 0

Add 71 to both sides:

x = -4/5 or 8 x = 71

Divide both sides by 8:

Answer:  x = -4/5 or x = 71/8

What is the range of the function
graphed below?
(3,3)

Answers

" y ≥ 3 " might be the answer?

4y+2x+30 if x=2and y=5​

Answers

54 because if you substitute x and y then add them together you will get 54

Answer:

54

Step-by-step explanation:

First let's replace the values x and y.

4y + 2x + 30 will become (4 * 5) + (2 * 2) + 30

Then we do order of operations.

(4 * 5) is 20..

20 + (2 * 2) + 30

Then we do (2 * 2) which is just four.

20 + 4 + 30

Lastly we add it all up.

24 + 30 = 54

I hope this helps, I hope it's not wrong, but I don't think it is.

please help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

10

Step-by-step explanation:

Which function is a quadratic function?

A) p(x) = 2x (x^2 + 6) + 1
B) m(x) = -4 (x + 3) -2
C) t(x) = -8x^2 (x^2 - 6) + 1
D) h(x) = 3x (x - 2) - 4

Answers

Answer:

D

Step-by-step explanation:

3x (x-2) - 4

3x²-6x-4

I hope it's helpful

Car a travels 15 miles while car b travels 26 miles what is the ratio of car a to car b

Answers

Answer: 15:26

Step-by-step explanation:

Given: Car a travels 15 miles while car b travels 26 miles.

Now, the ratio of the distance traveled by car a to car b is given by :-

[tex]\dfrac{\text{15 miles}}{\text{26 miles}}=\dfrac{15}{26}[/tex] , which is the fraction in the simplest as highest common factor of 15 and 26 =1.

So, the the ratio of the distance traveled by car a to car b = 15:26

Hence, the ratio of car a to car b = 15:26

PLEASE HELP, GIVING BRAINLIEST!!!

These triangles are congruent by _____.

A. SAS
B. AAS
C. SSS
D. ASA
E. None of these

Answers

None of these


E

Hope this helps

Lines Project Journal
need help for number 3​

Answers

Answer:

Remember that a line segment is the portion of a straight line that directly connects two given points. Unlike a line, it does not extend off to infinity in both directions. To find the length, we just use the distance formula between the two points provided.

Example:

Find the distance between (-2,8) and (-7,-5). Said another way, find the length of the line segment between points (-2,8) and (-7,-5).

First, find the distance between the x-coordinates. To do this, subtract one number from the other and then take its absolute value.

We have: |-2-(-7)| = |5| = 5.

Then repeat with the y-coordinates.

We have: |8-(-5)| = |13| = 13.

NOTE: It does NOT matter which way you subtract the numbers because the absolute value of the answer would be the same anyway.

Finally, to compete the length (or distance), square BOTH values, add them, and take the square root. Here's the first part:

[tex]5^{2}[/tex]  +  [tex]13^{2}[/tex]  = 25  +  169  =  194

Taking the square root of 194 and rounding to TWO decimal places, we get a distance of 13.93:

[tex]\sqrt(194)[/tex]  =  13.93

By the way, what you are actually doing is using the Pythagorean Theorem on an imaginary right triangle with the line joining the two lines being the hypotenuse.

The general formula for distance between two points is the following:  [tex]\sqrt{x^2+y^{2}[/tex]  , where x and y are the change in x and y between the two points.

-13 = r/9 + 8

r =


r equals what

Answers

-5=r/9

-45=r

Step-by-step explanation:

you're just trying to get the r alone. so you have to subtract the 8 and multiply the nine. you're just reversing the problem.

Figure out what x and y are. Please explain well!

Answers

Answer:

(2y+50)+(7x-248)=180    (solve for x and y)    supplementary angles add up to 180 and these two angles are supplementary complements

(5y-17) + (x+44) = 180   (solve for x and y)

Step-by-step explanation:

What is a point.? endless flat surface,line that cross, an exact location a, straight path

Answers

Answer:

an exact location should be the right answer

Please help with this and explain your answer and how you got it.

Answers

Answer:

V=48

Step-by-step explanation:

V=whl

V=2*3*8

V=48

Hope this helps! :) Plz mark as brainliest

if 2025 students are arranged in equal number of rows and columns find the number of students in each rows​

Answers

Answer:

45

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

.....

....,..,.....


If ab = 5 and a² + b² = 25, then (a + b)² =​

Answers

Answer:

100

Step-by-step explanation:

because 5+5=10

the 10^2=10*10=100

Answer:
35
Explanation:
Recall that (a+b)^2=a^2+2ab+b^2.
We can rearrange it in a way that would make it easier to solve our problem:
(a^2+b^2)+2ab
Now, we just plug in 25 for a^2+b^2, and plug in 5 for ab:
25+2*5
=25+10
=35

solve the question please

Answers

Can’t see anything sorryyyyyy

what is the common difference between successive terms in the sequence​

Answers

9,2.5,-4,-10.5,-17

Let's find the difference between two consecutive terms

2.5 - 9 = -6.5

-4 - 2.5 = -6.5

-10.5 - (-4) = -6.5

-17 -(-10.5) = -6.5

We can see that the common difference is -6.5

-6.5 is the common difference between successive terms in the sequence 9,2.5,-4,-10.5,-17

the common difference is negative because we subtract 6.5 to get the next term.

Answer:

The common difference between 9, 2.5, –4, –10.5, –17, ...

Is –6.5

Step-by-step explanation:

Because,

2.5 - 9 = -6.5

-4 - 2.5 = -6.5

-10.5 - (-4) = -6.5

-17 -(-10.5) = -6.5

We can see that the common difference is -6.5

-6.5 is the common difference between successive terms in the sequence 9,2.5,-4,-10.5,-17

the common difference is negative because we subtract 6.5 to get the next term.

simba travel agency arranged trips for climbing mount kilimanjaro. for each trip, they charge an initial fee of 100$ in addition to a constant fee for each veriticle meter climbed. for instance, the total fee for climbing to the shira volcanic cone, which is 3000 meters above the base of the mountain is 400$. let y represent the total fee in dollars of a trip where they climbed x vertical meters.

Answers

Yesterday was a great

I have to do the “got it”!!! Please help

Answers

Answer:

Substitute

Step-by-step explanation:

Answer:

JKM = 36

Step-by-step explanation:

JKL = 72

KM bisects JKL - cuts into two equal parts

72 / 2 = 36

JKM = 36

Please let me know if I'm wrong!

whats love, in words dont give as random answer

Answers

To me...I think love is sacrifice,honesty,loyalty and selflessness. Lol that might be really cheesy but that’s just me! Heh! :3

Answer:

Love is something you have to take care of figuratively.

Love is life, but love is sometimes not the thing to have sometimes

Love could be great, Love could be bad.

Step-by-step explanation:

does anybody know how to solve this equation 5+3∣10−4x∣=20

Answers

x = 5/4   or   x = 15/4

Step-by-step explanation:

Which equation represents the graph shown?
A. y+7=-3(x-4)
B. y+1=-3(x+2)
C. y-4=3(x+7)
D. y-2=3(x-1)​

Answers

Answer: A

Graph cut the horizontal and vertical axis at 2 points A(0;5) and B(1.66666;0)

you calc x=0 in the answer and have y

you can choose A or B. Next, you calc y=0 into A,B. If x=1.6666666, your answer is A

Sorry about my bad english

What is the slope of the line shown?

Answers

Answer:
Slope = rise/run = 3/2

Answer:

3

Step-by-step explanation:

Subtract the two points on the graph, i did (2,-6) and (4,0), you then get 6/2, simplify that and you get 3

Find the area of this quadrilateral.

Answers

I think the area is 24
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