a square was altered so that one side is increased by 9 inches and the other side is decreased by 2 inches. the area of the resulting rectangle is 60 square inches. What was the are f the original square.

Answers

Answer 1

Answer:

36 square inches.

Step-by-step explanation:

Since the original figure was a square, all four side lengths are equivalent. The area for the square will be:

[tex]A=s^2[/tex]

Where s is the length of one side.

One side is increased by nine inches and the other side was decreased by two inches. The area of the resulting rectangle is 60 square inches.

So, one of the new sides is (s + 9).

And the other is (s - 2).

The area with these dimensions is 60. Thus:

[tex]60=(s-2)(s+9)[/tex]

Solve for s. Distribute:

[tex]60=s^2+7s-18[/tex]

Isolate the variables:

[tex]s^2+7s-78=0[/tex]

Factor:

[tex](s+13)(s-6)=0[/tex]

Zero Product Property:

[tex]s+13=0\text{ or } s-6=0[/tex]

Solve for each case:

[tex]s=-13\text{ or } s=6[/tex]

A side length cannot be negative. So, our only solution is:

[tex]s=6\text{ inches}[/tex]

Since each side of the square measures six inches, the area of the original square will be 36 square inches.


Related Questions

please find the median!!!

will give brainliest!!!

Answers

Answer:

8, 10, 15, 16, 17, 17, 22

16 is the median

Step-by-step explanation:

Answer:

median is 16

Step-by-step explanation:

John belongs to a boating club that rents sailboats for $60 for the first hour and $20 for each additional hour. After renting a boat one day, he owed the boating club a fee of $140.

Write and solve an equation to find how many hours he kept the boat.

Answers

Answer:

4 Hours

Step-by-step explanation:

The original boating fee is $60 then you add $20 per hour so 20 x 4 = 80

80+60=140 $140

Answer: 140=60+20x. He kept the boat for 4 hours

Step-by-step explanation:

x=hours

y=final cost and the final cost is $140

to find x you would use the equation: 140=60+20x

you would first subtract 60 from both sides and you would get:

80=20x

Now you would divide 20 from both sides

So x is 4

Please help I’ll give brainlieast

Answers

Can you add the information so we can solve the problem ? you only added the questions. Add the stuff above that.

The population of rabbits on an island is growing exponentially. In the year 1992, the population of rabbits was 8300, and by 2000 the population had grown to 21500. Predict the population of rabbits in the year 2009, to the nearest whole number.

Answers

Answer:

36350

Step-by-step explanation:

1992 : 8300

2000 : 21500

1992/2000 = 8300/21500

Each year, population grow around 1650 rabbits

In 2009: 21500+(1650*9) = 36350

Find p and q .......

Answers

Answer:

Q = 9

P = 5

Step-by-step explanation:

3y - 21 = 12x
Help please

Answers

Simply
3Y+-21=12X

Re-order the terms
-21+3Y=12X

(Solving for Y variable)

Move all terms containing y to the left, all other terms to the right.

Add 21 to each side of the equation
-21+21+3Y=21+12X

Combine like terms: -21+21=0
0+3Y=21+12X
3Y=21+12X

Divide each side by 3
Y=7+4X

Simplifying
Y=7+4x
I hope this helps!! :)

find x and y in
(i) 23x- 29y= 98 and 29x -23y =110
(ii) 99x +101y =499 and 101x +99y =501

Answers

Answer:

23 x-29y=98.......(1)

29 x-23y=110.......(2)

adding (1) and (2)we get

52 x-52y=208

52(x+y)=208

x-y=4...(3)[we get four by dividing 208 with 52]

subtract (2) from (1) we get

-6 x-6y=-12

x-y=2.....(4)

adding (3) and (4) we get

2x=6

therefore x=3

now from (4) we get

x-y=2 [we substitute xfor 3]

3-y=2

y=2-3

y=-1( that is the answer for your first question)

Step-by-step explanation:

99x+101y=499.....(1)

101x+99y=501.....(2)

add (1) and (2)

(99+101)x+(101+99)=(499+501)

200x+200y=1000

200(x+ y)=1000

x+y=5.....(3)

subtract (2)from(1) we get

2x-2y=2

2(x-y)=2

x+y=1.......(4)

x+y=5

x-y=1(add them together)

2x=6

x=3

substitute x equal to 3 in equation (3)

x+y=5

3+y=5

y=2

y equal to 2 and x equal to 3

hope is not too late

A 960-square-foot apartment in New York City costs $540,000. What is the price per square foot? $

Answers

Answer:

The price per square foot is $468.75

Step-by-step explanation:

You would take the price and divide it by the square footage.

540,000

-------------    =    468.75

  960

a class has 10 students how many choices for a president and a vice president are possible?

Answers

Answer:

for president there are 10, and in vice president there are 9

Identify the expression that has the largest value when a<-1

1-2a
a
a^2
a^3

Answers

Answer:

1-2a is the largest for   -1 > a > -2.41

a^2 is the largest for  -2.41 > a.

Step-by-step explanation:

We want to find the expression with the largest value.

Remember that the sign is important here, because:

1 is larger than -10

So we will look at the expressions that, when evaluated in a negative number, give a positive number.

The only two options in the case:

a < -1

are:

1-2a

and

a^2

So we have a linear equation and a quadratic equation.

We know that quadratic equations grow a lot faster than linear equations for all values larger than 1 (or minus one, because the sign does not matter).

if -1 < a < 1, a quadratic function grows really slow, but this is not the case.

So from now, we can guess that a^2 is larger.

But let's solve it graphically.

Let's define two functions:

f(a) = 1 - 2*a

g(a) = a^2

Now we can graph these two, and look at the region a < -1, and see which one is larger.

in the image, you can see that there is a small region from:

-1 > a > -2.41

Where the linear equation is larger, and for:

a < -2.41

The quadratic equation is larger.

write and equation to solve for x.
what is the value of x?

Answers

Well since both angles equal a right triangle (90 degrees) you would set up the equation 90=2x+3x+5

90=2x+3x+5
85=5x
17=x

and to find the angles, just plug in x which is 17

The system shown is
• Inconsistent
• equivalent
© consistent

Answers

the system shown is inconsistent!

Answer:

Consistent

Step-by-step explanation:

Box 1 measures 6 cmon width, 12 cm in length and 4 cm in height. The height is doubled to 8cm to produce a larger box, Box 2 Which phrase accurately describes the volume of Box 2 in relation to Box 1

Answers

Answer: put A

Step-by-step explanation:

Put A cause 1 can’t be measure so you have to add 4 .

Can someone tell me the answer, please?

Answers

I believe it is rose bouquets good luck!!

Answer:

Rose bouquets

Step-by-step explanation:

Please mark me branliest?!?!

and hb this any answer please

Answers

Answer:

Using the Pythagorean Theorem we can see that:

[tex]9^2+40^2=1681\\\sqrt{1681}=41[/tex]

Thus, x is 41.

Hi! I could really use some help :)

Answers

Answer:

A=330

Step-by-step explanation:

im not sure which is the length width height

but if length is 10

width is 3/5

height is 15

A=2(wl+hl+hw)=2·(0.6·10+15·10+15·0.6)=330

then the area would be 330

Which side lengths do not make a triangle ?
10, 15, 23
1, 2, 4
5, 6, 7
6, 8, 9

Answers

Answer:

1,2,4

Step-by-step explanation:

Okay so basically in a triangle, the sum of any two sides should be greater than the third remaining side. So if we had a triangle with sides A, B, and C, A+B>c, A+C>B, and B+C>A. If you look at 1,2, and 4, 1=2=3 which is less than 4. That is why that is not a triangle.

1/8 of 4 yards= ? feet not in decimal form​

Answers

9514 1404 393

Answer:

  3/2 feet

Step-by-step explanation:

4 yards = (4 yd)(3 ft/yd) = 12 ft

1/8 of that is ...

  (1/8)(12 ft) = (12/8) ft = 3/2 ft = 1 1/2 ft

please help i dont understand

Answers

Answer:

imma say 45m

Step-by-step explanation:

im not sure but tell me if im wrong so i can fix it. thanks

find the area of the figure​

Answers

The area of your problem is 432

Find the value of x.

Answers

Answer:

X = 9

okay If I'm wrong sry what's 9x3 it's 45 right ( me not using a caluctalter ) ( I didn't even spell that Right lol ) but anyways it's X=9

0
ZA=
Round your answer to the nearest hundredth.
B
3
4
6
с

Answers

Answer:

B?346C is the answer get noob
B 346c step by step

HELP PLEASE DUE IN 3 MINUTES

Answers

Answer:

The answer is 5 TRUST ME

Step-by-step explanation:

Answer:

5 is the median

Step-by-step explanation:

Median

Arrange your numbers in numerical order.

Count how many numbers you have.

If you have an odd number, divide by 2 and round up to get the position of the median number.

If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.

Decrease £120 by 12.5%

Answers

Answer:

£ 105.

Step-by-step explanation:

Since it is required to decrease £ 120 by 12.5%, to perform this subtraction the following mathematical operation must be performed:

100 - 12.5 = 87.5

100 = 120

87.5 = X

87.5 x 120/100 = X

10,500 / 100 = X

105 = X

Thus, decreasing £ 120 by 12.5% you get a total of £ 105.


Decrease £101 by 43%

Answers



101 - Percentage decrease =

101 - (43% × 101) =

101 - 43% × 101 =

(1 - 43%) × 101 =

(100% - 43%) × 101 =

57% × 101 =

57 ÷ 100 × 101 =

57 × 101 ÷ 100 =

5,757 ÷ 100 =

57.57

Answer:

Step-by-step explanation:

100-43=57%

57/100 x 101

0.57 x 101

£57.57

or

43/100 x 101

0.43 x 101

43.43

100-43.43

=£57.57

Help........Betty wants to bake the perfect cookie. She wants to determine the ideal temperature at which to bake the cookies. She has enough batter to make 60 cookies. She decides to randomly assign 15 cookies to be baked at 300°, 15 at 325°, 15 at 350°, and 15 at 375°. The baking time for each batch is 12 minutes. Which statement about the randomization for the completely randomized design is correct? Betty should place the first 15 balls of cookie dough that she scoops from the batter on a tray, and those will be baked at 300°. The next 15 will be placed onto a second tray to be baked at 325°. She should continue in this manner until all 60 cookies have been placed on trays. Betty should scoop a ball of cookie dough from the batter, and then roll a die. Numbers 1–4 would indicate at which temperature the cookies will be baked, and 5–6 would indicate that she should roll again. She should repeat this process until all 60 cookies have been allocated. Betty should prepare all 60 cookies. Each cookie will receive a number. The numbers will be written on slips of paper, put into a hat, and shuffled well. The first 15 numbers drawn will indicate the cookies to be baked at 300°, the next 15 will indicate the cookies to be baked at 325°, and so on until all 60 cookies are allocated. Betty should place the first cookie on a tray to be baked at 300°. The second cookie will go on a tray to be baked at 325°, the third will go on a tray to be baked at 350°, and the fourth will go on a tray to be baked at 375°. She will continue placing the cookies in this pattern until all 60 cookies are on trays to be baked.​

Answers

Answer: Betty should prepare all 60 cookies. Each cookie will receive a number. The numbers will be written on slips of paper, put into a hat, and shuffled well. The first 15 numbers drawn will indicate the cookies to be baked at 300°, the next 15 will indicate the cookies to be baked at 325°, and so on until all 60 cookies are allocated.

Step-by-step explanation: I just got it correct on Edge :)

The true option about the randomized design is (c) Betty should prepare all 60 cookies. Each cookie will receive a number. The numbers will be written on slips of paper, put into a hat, and shuffled well. The first 15 numbers drawn will indicate the cookies to be baked at 300°, the next 15 will indicate the cookies to be baked at 325°, and so on until all 60 cookies are allocated.

The given parameters are:

[tex]\mathbf{n = 60}[/tex]

[tex]\mathbf{Batches = 4}[/tex]

[tex]\mathbf{Cookies= 15}[/tex] ---- the number of cookies in each batch

[tex]\mathbf{Temperature= 300,325,350,375}[/tex]

To randomly assign the cookies to the given temperatures, all cookies have to be subjected to the same conditions (except the difference in the temperature).

This means that, she can bake all the cookies at once at different temperatures, while noting down the cookies with a given number.

Hence, the true option is (c)

Read more about randomization at:

https://brainly.com/question/20046524

please help! anybody know a math activity i could do for preschoolers? i have to make a sample as well but i just need an idea

Answers

hi :)
maybe finger print counting or Toss beanbags to learn place value.

help agin please number 8

Answers

Answer:

G

Step-by-step explanation:

5 + 7 > 9

12 > 9

5 + 9 > 7

14 > 7

7 + 9 > 5

16 > 5

Answer:

G as

5+7 more than 9

5+9 more than 7

7+9 more than 5

can you help me with this, please? ​

Answers

9514 1404 393

Answer:

  b, c, d -- (all but the first)

Step-by-step explanation:

The key take-away regarding what relation is or is not a function is the following: a function has no repeated x-values.

The x-values in the table are -3, -1, 0, 2, so any suggested ordered pair with one of those as an x-value cannot be added to the table. The only such pair in the list is the first one (-3, 4). It cannot be added. All of the remaining three pairs can be added and the relation will remain a function.

Plz help me with this question plz

Answers

Answer:

Quarters: 2 = 50 cents. 50cents

Dimes: 2 = 20 cents. 70cents

Nickels: 8 = 40 cents. $1.10

Hope this Helps!

:)

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