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

Siguiendo la ley de los signos ¿qué signo obtenemos al multiplicar dos signos iguales?


•Suma?
•Menos?
•Positivo?
•Negativo?

Answers

Answer: Si se multiplica un número positivo por uno negativo, el resultado tiene signo negativo. Si se multiplican dos números con signos iguales, el resultado tiene signo positivo

Step-by-step explanation:

Can's box of chocolates is a rectangular prism. The dimensions are 10 inches by 5 inches by 8 inchesEach chocolate in the box is 2 inches by 2 inches by 2 inches. How many chocolates are in Cam's box

Answers

Answer:

I think 50 (not too sure)

Step-by-step explanation:

First find the volume of the Chocolate Box which is 400. (10 · 5 · 8)

Then find the volume of each chocolate which is 8. (2 ·2 ·2)

Then divide 400 by 8 to see how many chocolates can fit.

400 ÷ 8 = 50

And that's how I got the answer! Hope that helped! <3

Heeelp Asap please

Has to be turned in at 7

Answers

Answer:

I think its 1/2 of the pizza

Step-by-step explanation:

Plz correct me if im wrong

Answer:

its 1/6

Step-by-step explanation:

1/4 of the pizza is left

joe eats 2/3 of the 1/4 which equals 2/12 or 1/6

PLEASE HELP QUICKLY! 30 POINTS AND WILL MARK BRAINLIEST.

Write a recursive formula for the sequence.
6, 17, 28, 39, 50, ...

A. f(1)-6; f(n)=f(n-1)+11
B: f(1)=6; f(n)=6*f(n-1)+11
C. f(1)=6; f(n)=f(n-1)+6
D. f(1)=6; f(n)=11*f(n-1)

Answers

Answer:

C. f(1)=6; f(n)=f(n-1)+6

Step-by-step explanation:

whats is 183x194??????????

Answers

183 x 194 = 35,502

you could use a calculator or put it into the overlap form

Answer:

35502

Step-by-step explanation:

The product will be 35502, 183x100+183x90+183x4=18300+16500+732=35502. Hope it helps!

2 2/6 + 3 2/6?? help pls im dumb ​

Answers

Answer:

5 4/6

Step-by-step explanation:

You have to add the whole numbers then add the numerators of the fraction since the denominators are the same.

If f(x) = 2x - 3, find f(-2).

Answers

Answer:

0.5

Step-by-step explanation:

-2 = 2x - 3

1 = 2x

0.5 = x

Answer:

f(x) = -7

Step-by-step explanation:

f(x) = 2x - 3 turs into

f(x) = 2 x -2 - 3

f(x) = -4 - 3

f(x) = -7

Select the equation that most accurately depicts the word problem.

Mary Lou has 2 more nickels than pennies, and she has 30 coins all together. Use x for the number of pennies.

a. x + 2 = 30
b. x + (x + 2) = 30
c. 2(x + 2) = 30
d. 2x + 30 = 5

Answers

Answer:

B. x + (x+2) = 30

Step-by-step explanation:

If x equals pennies, then one part of the statement should include an addition of 2, along with the additions of the value of pennies; and it should all equal 30.

Answer:

B. x + (x + 2) = 30

Step-by-step explanation:

x = number of pennies

y = number of nickels

x + y = 30

y = 30 - x

She has two more nickels then pennies, therefore:

y = x + 2

30 - x = x  + 2

30 = x + x + 2

x + (x + 2) = 30

Help pls I need help

Answers

Answer:

3 3/7

Step-by-step explanation:

8/1 divided by 2 1/3 = 8/1 x 3/7

8/1 x 3/7 = 24/7

24/7 = 3 3/7

Noah walks to school from home by going 7 blocks north, to a post office, and then 24 blocks east. Noah's home, point H, is at (0,0); the post office, point P, is at (0,7); and the school, point S, is at (24,7). If Noah then walks home using the direct path, what would be the total distance Noah traveled to school and back home?

Answers

Answer:

25

Step-by-step explanation:

The total distance Noah traveled to school and back home will be Noah's displacement. Displacement of Noah can be gotten using Pythagoras theorem.

d² = y²+x²

Direction through north (along y-axis)

Direction through east (along x-axis)

Given

y = 7units

x = 24units

Substitute

d² = 24²+7²

d² = 576+49

d² = 625

d = √625

d = 25 units

Hence the total distance Noah traveled to school and back home is 25blocks from post office

Please do all and I’ll mark brainliest!! I’ve added extra points and I really need help ASAP!! Don’t worry about the 3D shape one

Answers

Answer:

Answers in step step-by-step explanation.

Step-by-step explanation:

1. 7

2. 0.3

3. 3

4. x = 50 degree

5. 15 (Sorry I accidentally made the answer to five the answer to six, 15 is the right answer)

6.  10.408125

7. 240

8. -29

9. I think 1/4 but double-check.

10. $5.4

ask me a question. any question. ill probably answer it. unless I'm lazy.

Answers

Answer:

What is your fav artist music wise

Step-by-step explanation:

A man starts out on a trip driving his car at a constant rate of 48 mph. A man riding a motorcycle starts out on the same route 1.5 hours later, traveling at a constant rate of 64 mph. How long will the car have been traveling when the motorcycle catches up?

Answers

Answer:

6 hours

Step-by-step explanation:

Pls help question is in the pic. Please give a right answer thx :D

Answers

Answer:

61.2

Step-by-step explanation:

Her friend comes to the rescue and brings 15 more cups of chocolate chips! How many more muffins will they be able to make with the additional chocolate chips?

Answers

Answer:

Not enough context.

Step-by-step explanation:

Please give us the full question. How many chocolate chips in a muffin?

Mrs. Wright sold t-shirts for $12.00, which was a 30% markup from what she paid for each. How much did Mrs. Wright pay for each t-shirt originally? (remember to round to the nearest hundredth so it looks like money

Answers

Answer:

She originally paid $3.60

Step-by-step explanation:

She originally paid for them $3.60 before the markup of 30%.

We can use this equation [tex]12 x 0.3 = 3.60[/tex] to confirm our answer. We also add a zero at the end because we are using units of money.

answer the questions lots of points

Answers

Answer:

Radius is half of diameter; the distance around a circle.

Step-by-step explanation:

Answer:

Radius is half of diameter  the distance around a circle

-x + 7 <10
Solving inequalities

Answers

Answer:

x>-3

Step-by-step explanation:

−x+7<10

Step 1: Subtract 7 from both sides.

−x+7−7<10−7

−x<3

Step 2: Divide both sides by -1.

−x−1<3-1

x>−3

PLEASE HELP!! Please show me work also!

Answers

There isn’t a picture, what’s the question?

Can anyone help me with thiss? I need the solution ASAP! [tex](n − m)2 for m = −3 and n = 7[/tex]

Answers

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

Actually Welcome to the Concept of the Algebric Operation,

here, m=-3 and n=7

, after substituting we get as,

(7-(-3))*2

=> (7+3)*2

=>10*2

=>20

hence, final answer is 20


Use the number line to complete the task.

Move numbers to the lines to create two absolute value expressions that represent the distance between the two points on the number line,
Expression A: -10 -
Expression B:| -10 + (_
-6
-4
4
6

Answers

Answer:

Expression A: |-10 - (-4)|

Expresion B: |-10+4|

Step-by-step explanation:

The distance (which you can get by counting on the numberline) is 6. This mean that the value derived wiithin the absolute value must be either 6 or -6. Answers of 4 and negative 4 get you this answer.

Work out the value of (2x10^4)+(7x10^3) in standard form

Answers

Answer:

27000x

Step-by-step explanation:

Answer:

27000

Step-by-step explanation:

(2 * 10^4) + ( 7 * 10^3)

rewrite in standard form

20000 + 7000

solve

= 27000

If the perimeter of a
square is 60 feet, what is
the area of the square?

Answers

Answer:

225 ft I believe  

Step-by-step explanation:

Answer:

225

Step-by-step explanation:

Well, the formula for perimeter is simply 2 times length + 2 times width. In the case of our square, this would simply be 2x+2x (since length = width), or 4x . Therefore, if given an area, all you'd do is take the square root (to get from x2 to x , and then multiply by 4 to find perimeter.

Given the functions f(x) = x^2 + 6x - 1, g(x) = -x^2 + 2, and h(x) = 2x^2 - 4x + 3, rank them from least to greatest based on their axis of symmetry.

f(x), g(x), h(x)
h(x), g(x), f(x)
g(x), h(x), f(x)
h(x), f(x), g(x)

Answers

Answer:

At least to greatest you've got  -3, 0,  1   so f(x),  g(x),  h(x). Answer a

Step-by-step explanation:

ik this is because i am in level 11 grade math

Answer:

h(x), g(x), f(x)

Step-by-step explanation:

I got that value because the axis of symmetry of GX and hx I've got them all the same, one and one the issue comes to the GX where ist has a negative value in front of the X I think when you put a negative value inside a bracket then you Square it you'll get a positive value in the end but since it has a negative value outside then it will be a negative value that is why I considered GX to be smaller than HX but even if I consider GX smaller it's not going to be smaller than FX that is why I got GX and then FX.

Hence, HX then GX then FX

What is the decimal equivalent of 23/9
A. 25
B. 0.39
C. 2.39
D. 2.55

Answers

2.55

To find a decimal you need to divide y and x (y/x)  

What I did was I divided 23/9 and got 2.55555555556. And 2.55 is closest to 2.55555555556.

5. A car travels at a speed of 72 miles per hour. Write a direct variation equation for the distance, y, the car will travel in x hours. How far will the car travels in 4.5 hours?​

Answers

Answer:

 y  = 72x

324miles

Step-by-step explanation:

Given parameters:

      Speed of the car = 72miles/hr

       distance  = y

        time  = xhrs

Unknown:

Write a direct variation equation for the distance=  ?

Distance covered in 4.5hrs =?

Solution:

A. Write a direct variation equation for the distance;

    A direct variation is a linear equation.

   It often takes the form y = kx

   

For this problem;

      Distance  = speed x time

input the parameters;

      y  = 72x

The direct variation equation is  y  = 72x

B. Distance traveled in 4.5hrs

   y  = 72x

  x is the time taken;

  So;

        y  = 72 x 4.5  = 324miles

Select all polynomials that have (x + 2) as a factor.
Choose all answers that apply:
A A(x) = x^3– 3x^2 – 10x
B B(x)= x^3+ 5x^2 + 4x
C C(x)= x^3 – 2x^2 – 13x – 10
D D(x) = x^3– 6x² + 11x- 6

Answers

Answer:

A. (x) = x^3– 3x^2 – 10xx) / (x - 5) x (x + 2) YES

B. (x)= x^3+ 5x^2 + 4x / x (x + 1) (x + 4) NO

C. (x)= x^3 – 2x^2 – 13x – 10 x / (x - 5) (x + 1) (x + 2) Yes

D. (x) = x^3– 6x² + 11x- 6 / x = (x - 3) (x - 2) (x - 1) NO

Step-by-step explanation:

The solution is:;

A. (x) = x^3– 3x^2 – 10xx) / (x - 5) x (x + 2)

C. (x)= x^3 – 2x^2 – 13x – 10 x / (x - 5) (x + 1) (x + 2),

are the polynomials that have (x + 2) as a factor.

What are Polynomials?

Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.

3x+2x-5, for example, is a polynomial.

EXPLANATION

We want to find which of the given polynomials has (x + 2) as a factor.

To do this, we have to equate (x + 2) to 0 and solve for x:

(x + 2) = 0

x = -2

Now, substitute that into each of the polynomials. If (x + 2) is a factor of a polynomial, the polynomial will become 0 after the substitution is made.

A. (x) = x^3– 3x^2 – 10xx) / (x - 5) x (x + 2) YES

B. (x)= x^3+ 5x^2 + 4x / x (x + 1) (x + 4) NO

C. (x)= x^3 – 2x^2 – 13x – 10 x / (x - 5) (x + 1) (x + 2) Yes

D. (x) = x^3– 6x² + 11x- 6 / x = (x - 3) (x - 2) (x - 1) NO

Hence, The solution is:;

A. (x) = x^3– 3x^2 – 10xx) / (x - 5) x (x + 2)

C. (x)= x^3 – 2x^2 – 13x – 10 x / (x - 5) (x + 1) (x + 2),

are the polynomials that have (x + 2) as a factor.

Know more about Polynomials here:

brainly.com/question/2833285

#SPJ2

HELP!!!
This is a geometry question!
Please give reasoning with your answer!
I can and will mark a "real" answer brainliest!

Answers

Since lmnp is on the y side, of you add 6+3 it gives you 9

Answer:

see below

Step-by-step explanation:

shape LNMP is :

translated as 0,-7flip of mirrored along y-axisreflected imaged is ABCD as given

Pens cost $0.20 each. Pencils cost $0.15 each. Write an algebraic expression that represents the total cost of buying p pens and n pencils. (Will give brainliest if correct)

Answers

Answer:

y=0.20p + 0.15n

Step-by-step explanation:

I believe this is correct I am 90% positive that it is right.

The algebraic expression will be C = 0.20 p + 0.15 n

It is given that a pen cost $0.20 and a pencil cost $0.15.

We have to give expression for total cost of p pens and n pencils.

What will be the value if 2 times of x is added to x ?

The value will be 3x.

Cost of 1 pen = $0.20

Cost of p pens will be ;

= 0.20 p

Cost of 1 pencil = $0.15

Cost of n pencils = 0.15 n

If total cost is represented by C then ;

C =  0.20 p + 0.15 n

Thus , the algebraic expression will be C = 0.20 p + 0.15 n

To learn more about algebraic expressions click here ;

https://brainly.com/question/2164351

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List the least common factor for 120
and 200

Answers

Answer: Lcm = 600

Step-by-step explanation: Find the prime factorization of 120

120 = 2 × 2 × 2 × 3 × 5

Find the prime factorization of 200

200 = 2 × 2 × 2 × 5 × 5

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

LCM = 2 × 2 × 2 × 3 × 5 × 5

LCM = 600

Answer:

600

Step-by-step explanation:

120= 2*2*2*3*5________eq1

200=2*2*2*5*5_________eq2

we get common factor from 1 and 2

2*2*2*5*3*5 = 600

so the least common factor is 600

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