The area of a rectangular wall of a barn is 270 square feet. It’s length is 12 feet longer than twice it’s width. Find the length and width of the wall of the barn.

Answers

Answer 1

Answer: 258

Step-by-step explanation: 270-12=w

Answer 2

The width of the wall is 9 feet and length is 30 feet.

What is perimeter of a rectangle ?

The perimeter of a rectangle is the sum of all the sides.

According to the given question the area of a rectangular wall of a barn is 270 square feet. It’s length is 12 feet longer than twice it’s width.

Assuming the width of the rectangular wall to be x feet.

∴ From the given data length is 2x + 12 feet.

We know area of a rectangle is product of it's length and width.

So, { x × ( 2x + 12 ) } = 270.

2x² + 12x = 270.

2x² + 12x - 270 = 0

x² + 6x - 135 = 0

x² + 15x - 9x - 135 = 0

x(x + 15) - 9(x + 15) = 0

( x + 15 ) = 0 OR ( x+ 9 ) = 0

∴ x = -15 OR x = 9.          ( we know length can note be negative )

So, Width of the rectangle is 9 feet and length is 30 feet.

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Related Questions

If 3 out of 24 students made an "A" what percent of students
made an "A"?

Answers

3 / 24 = 12.5% - hope this helps

i have 4 questions

1. Suppose point T is between points R and V on a line. If RT = 63 units and RV = 131 units, then what is TV? 131 194 68 80

2.Given point P is between M and N. If MN = 26, MP = x + 4, and PN = 2x + 1, what is the value of x? x = 3 x = 7 x = 12.5 x = 22

3.Given M is the midpoint of HJ, HM = 4x - 12, and MJ = 3x + 9. What is the value of x?

4.If D is the midpoint of CE, DE = 2x + 4, and CE = 6x + 2, then what is CD?

Answers

Answer:

1.   [tex]TV = 68[/tex]

2.  [tex]x = 7[/tex]

3.   [tex]x = 21[/tex]

4.    [tex]CD = 8[/tex]

Step-by-step explanation:

Solving (1):

Given

[tex]RT = 63[/tex]

[tex]RV = 131[/tex]

Required

Determine TV

To solve TV, we make use of the following formula;

[tex]RV = RT + TV[/tex]

Substitute values for RT and RV

[tex]131 = 63 + TV[/tex]

Make TV the subject of formula

[tex]TV = 131 - 63[/tex]

[tex]TV = 68[/tex]

Solving (2):

Given

[tex]MN = 26[/tex]

[tex]MP = x + 4[/tex]

[tex]PN = 2x + 1[/tex]

Required

FInd x

To solve x, we make use of the following formula;

[tex]MN = MP + PN[/tex]

Substitute values for MP, MN and NP

[tex]26 =x + 4 + 2x + 1[/tex]

Collect Like Terms

[tex]2x + x = 26 - 4 -1[/tex]

[tex]3x = 21[/tex]

Divide both sides by 3

[tex]x = 7[/tex]

Solving (3):

Given

[tex]HM = 4x - 12[/tex]

[tex]MJ = 3x + 9[/tex]

Required

Find x

Since M is the midpoint;

[tex]HM = MJ[/tex]

This gives

[tex]4x - 12 = 3x + 9[/tex]

Collect Like Terms

[tex]4x - 3x = 12 + 9[/tex]

[tex]x = 21[/tex]

Solving (4):

Given

[tex]CE = 6x + 2[/tex]

[tex]DE = 2x + 4[/tex]

Required

FInd CD

Since D is the midpoint;

[tex]CD= DE[/tex]

and

[tex]CE = CD + DE[/tex]

Substitute CD for DE

[tex]CE = DE + DE[/tex]

[tex]CE = 2DE[/tex]

Substitute values for CE and DE

[tex]6x + 2 = 2(2x + 4)[/tex]

Open Bracket

[tex]6x + 2 = 4x + 8[/tex]

Collect Like Terms

[tex]6x - 4x = 8 - 2[/tex]

[tex]2x = 6[/tex]

Divide both sides by 2

[tex]x = 3[/tex]

Recall that;

[tex]CD= DE[/tex]

So;

[tex]CD = 2x + 4[/tex]

Substitute 2 for x

[tex]CD = 2 * 2 + 4[/tex]

[tex]CD = 4 + 4[/tex]

[tex]CD = 8[/tex]

look at the attachment

Answers

Answer:

x=-6

For PA:  78-29=49

For AQ:  48+3=51

Step-by-step explanation:

The line is from left to right PAQ

It says PQ is 100 which is the whole line

PA +AQ is PQ so that means:

-13x-29-8x+3=100

-21x-26=100

-21x=126

x=-6

Plug in the x values to PA and AQ

For PA:  78-29=49

For AQ:  48+3=51

An ad for an above-ground pool states that it is 25 m2. From the ad, you can tell that the pool is a circle. If you swim from one point at the edge of the pool to another, along a straight line, what is the longest distance d you can swim? Express your answer in three significant figures.

Answers

Answer:

d ≈ 5.64 m

Step-by-step explanation:

We are told that the pool is circular and that the area is 25 m².

Now, the longest chord that connects two points in a circle is the diameter.

Thus, the longest distance d will be the diameter

Area of circle is given by the formula;

A = πr²

Thus;

25 = πr²

r² = 25/π

r = √(25/π)

r = 5/√π

Diameter is twice the radius. Thus;

d = 2 × 5/√π

d = 10/√π

d ≈ 5.64 m

PLEASE HELP ME I WILL MARK AS BRAINLIEST

A map has a scale of
5 in. = 10 mi. If you measured the distance between two cities to
be 17 in. on the map, how many miles would it actually be?
If necessary, round your answer to the nearest tenth.

Answers

If you turn it into a ratio where x=miles; 5/10=17/x
X=34 miles

If presented with the following equation, what is the next step in the equation solving sequence? x + 3x = -50 - 23+5 ​

Answers

Answer:

Add the similar elements

[tex]x+3x=4x\\-50-23+5=-68\\\\4x=-68[/tex]

Step-by-step explanation: Further steps

Divide both sides by 4

[tex]\frac{4x}{4}=\frac{-68}{4}[/tex]

Simplify

[tex]x=-17[/tex]

Answer:

combine like

Step-by-step explanation:

Before the election, you want to determine the number of possible president/vice-president combinations for the sorority you belong to. if both positions are chosen from nine people, how many combinations are possible​

Answers

Answer:

The possible number of combination to select two positions from 9 people is 72.

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times the measure of the first angle. The third angle is 16 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.

Answers

Step-by-step explanation:

z=y+16

y=y

:.z+y=5x where z=y+16

2y+16=5x

x=(2y+16)/5

.:z+y+x=180

y+16+y+(2y+16)/5=180

12y+80+16=900

y=67

z=16+67=83

x=30

Alan can do 2/3 part of his work and sam can do 3/4 part of her work .Who can do more work​

Answers

Answer:

Sam can do more work.

Step-by-step explanation:

2/3 equals out to just over half of his work done. 0.66666667.

3/4 equals out to almost all of her work done. 0.75.

*hope this helps*

Answer:

Sam can do more work:)

Step-by-step explanation:

Help i dont understand Pls Help :( Given h(x)=4x-4h(x)=4x−4, solve for xx when h(x)=0h(x)=0.

Answers

Answer:

x=1

Step-by-step explanation:

So when it's h(5)= whatever equation you all the x in the equation to 5 and solve. When it says h(x)=0, it's asking you to find x for the equation to equal 0.

It's easy! all you have to do is set the equation to 0

so 4x-4=0

add 4 from both sides

4x = 4

divide

x=1


What is the quotient of 75,120 ÷ 16?

Answers

Answer:

4695

Step-by-step explanation:

Answer:

4,695

use long divison

Find the function rule
X Y
0 -5
10 15
20 35
y=___

Answers

Answer:

y=2x-5

Step-by-step explanation:

y is double x minus 5

NarStor, a computer disk drive manufacturer, claims that the median time until failure for their hard drives is more than 14,400 hours. You work for a consumer group that has decided to examine this claim. Technicians ran 16 NarStor hard drives continuously for almost three years. Recently the last drive failed. The times to failure (in hours) are given in the following table. Give the test statistic.330 620 1870 2410 4620 6396 7822 81028309 12882 14419 16092 18384 20916 23812 25814

Answers

Answer:

The test statistics is  [tex]t  =  -1.727[/tex]

Step-by-step explanation:

From the question we are told that

The data given is  

   330 620 1870 2410 4620 6396 7822 81028309 12882 14419 16092 18384 20916 23812 25814

 The population mean is  [tex]\mu  =  14400[/tex]

    The  sample  size is  n =  16

  The  null hypothesis is  [tex]\mu \le  14400[/tex]

    The  alternative hypothesis is  [tex]H_a  :  \mu > 14400[/tex]

The sample mean is mathematically evaluated as

  [tex]\= x  =  \frac{\sum x_i}{n}[/tex]

So

   [tex]\= x  =  \frac{330+ 620+ 1870 +2410+ 4620+ 6396+ 7822+ 8102+8309+ 12882+ 14419+ 16092+ 18384 +20916+ 23812+ 25814 }{16}[/tex]

=>  [tex]\= x = 10799.9[/tex]

The  standard deviation is mathematically represented as

      [tex]\sigma =\sqrt{\frac{ \sum (x_i - \=x)^2}{n}} [/tex]

So

[tex]\sigma =\sqrt{\frac{(330- 10799.9)^2 + (620- 10799.9)^2+ (1870- 10799.9)^2 +(2410- 10799.9)^2 + (4620- 10799.9)^2 +(6396- 10799.9)^2 +(7822- 10799.9)^2 }{16}}  \ ..[/tex]

   [tex]..\sqrt{ \frac{(8102 - 10799.9)^2 +(8309 - 10799.9)^2 + (12882 - 10799.9)^2 + (14419 - 10799.9)^2 + (16092 - 10799.9)^2 + (18384 - 10799.9)^2 +(20916 - 10799.9)^2  }{16}} \ ...[/tex]

  [tex]\ ... \sqrt{\frac{(23812 - 10799.9)^2 +(25814 - 10799.9)^2 }{16}}[/tex]

=>  [tex]\sigma  =  8340[/tex]

  Generally the test statistic is mathematically represented as

  [tex]t =  \frac{10799.9- 14400}{ \frac{8340}{\sqrt{16} } }[/tex]

[tex]t  =  -1.727[/tex]

From the z-table  the p-value is  

     [tex]p-value  = P(Z > t) =  P(Z >  -1.727) =  0.95792[/tex]

 From the values obtained we see that

        [tex]p-value  >  \alpha[/tex]  so we fail to reject the null hypothesis

Which implies that the claim of the NarStor is wrong

What is the algebraic rule for a translation that moves the points right 4 units and down 3 units?

Answers

Answer: (x,y) —> (x+4, y-3)

it could also be T 4, -3 (x,y)

Step-by-step explanation:

If you move something right 4, x+4. Moving something down 3 is y-3.

the general form is always (x,y) —> (x + (whatever)), y + (whatever))

Or T whatever, whatever (x,y)

The first (whatever) is applied to x, second is for y.

hopes this helps

the difference of a number and 6 is the same as 5 times the sum of the number and 2

Answers

Answer:

n - 6 = 5 * ( n + 2 ) ; n = -4

Step-by-step explanation:

For this problem, we will use the words to create an equation.  The left hand side of the equation will be the difference of a number and 6 and the right hand side of the equation will be 5 times the sum of the number and 2.  Hence, we can build the equation:

n - 6 = 5 * ( n + 2 )

If we wanted, we can solve the equation for the number, n.

n - 6 = 5 * ( n + 2 )

n - 6 = 5 * n + 5 * 2

n - 6 = 5n + 10

-16 = 4n

-4 = n

Thus, we have found the missing number to be negative four.

Cheers.

Find the least common multiple of 20, 4, and 5

Answers

Answer:

LCM = 20

Step-by-step explanation:

You need to make everything into 20. Luckily, 4X5 is 20 and vise versa.

Give two ways to write the algebraic expression:
10s

Answers

Answer:

10 * s, 10(s), s(10), s * 10.

Step-by-step explanation:

Hope this helps

Adsila and Carlos volunteer to fill gift boxes for soldiers serving overseas.
Both work at a constant rate. They work together for 6 hours and fill 126 boxes,
Adsila fills 9 boxes every hour. How many boxes does Carlos fill every hour?

Answers

Answer:

12 boxes an hour

Step-by-step explanation:

If Adsila made 9 boxes an hour for 6 hours,she made 54 boxes (9*6=54). Take how many she made away from the total (126-54=72). If Carlos made 72 boxes in 6 hours, divide 72 by 6 to get 12 (72/6=12). Carlos made 12 boxes an hour.

what is 9 as a percent of 90​

Answers

Answer:

8.1

Step-by-step explanation:

the answer the problem is 8.1

Answer:

10%

Step-by-step explanation:

convert fraction (ratio) 9/90 Answer : 10%

Jeson formed two-digit numbers using the following rules. (i) The digit in the tens place is an EVEN number. (ii) The two-digit number is divisible by 5. How many numbers did Jeson form? a) 5 b) 8 c )16 d) 18

Answers

Answer:

b) 8.

Step-by-step explanation:

The tens digit must be 2, 4, 6 or 8.

The units digit must be 0 or 5 ( as the 2 digit number must be divisible by 5).

So they are:

20, 25, 40, 45, 60, 65 , 80 and 85.

Answer:The tens digit must be 2, 4, 6 or 8.

The units digit must be 0 or 5 ( as the 2 digit number must be divisible by 5).

So they are:

20, 25, 40, 45, 60, 65 , 80 and 85.

Step-by-step explanation:

An image point after 180 rotation is Z'( 3,7) what are the coordinates of the pre-image point

Answers

Answer:

(-3 , -7)

Step-by-step explanation:

Which angles are adjacent to each other?

Answers

The answer is HAI and EAD

Adjacent angles are when two angles have a common side and a common vertex and don’t overlap :)

Step-by-step explanation

dab and aeb

they are adjacent

You just found 13,406,190 pennies! How many dollars did you actually find? If each penny weighs 4 grams, how much did all that loot weigh in lbs?

Answers

Answer: 134,061.9 dollars and 118,222.45 lb

You have a balance of $213 in a savings account you withdraw $68 one day and $128 the next day without making any deposit what is the new balance

Answers

Answer:

17. . . . . . . . . . . . . . . "" " . . .

Answer:

$213

- $68

______

 $145

- $128

______

  $17

Step-by-step explanation:

If you start with $213 and withdraw $68 it would be $145 and then withdraw $128 you would only have $17 dollars left in your savings.

explain all steps in detall. Incluide your final answer.. 9²+3•(9-5)²/4=

Answers

Answer: 93

Step-by-step explanation:

To solve this problem, we need to use the order of operations, or PEMDAS.

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

For multiply/divide and add/subtract, you don't necessarily go in that specific order. You go from left to right, depending on what comes first. For example, if division comes before multiply, you would divide first, then multiply. Same goes for add/subtract.

9²+3×(9-5)²/4                          [solve parenthesis]

9²+3×(4)²/4                              [solve exponent]

81+3×16/4                                [solve multiply or divide, whichever comes first]

81+12                                        [solve add or subtract, whichever comes first]

93

Now, we know that 93 is our final answer.

Solve for x: −2(x + 3) = −2x − 6

Answers

Answer:

All real numbers

Step-by-step explanation:

Solution set of -2(x +3) = -2x -6 is all x ∈R (real numbers).

What is equation?

" Equation is defined as when two algebraic expression which are related with the sign of equality."

According to the question,

Given,

-2(x + 3) = -2x - 6

Open the brackets of the equation we get,

-2(x) + (-2)(3) = -2x - 6

⇒ -2x - 6 = -2x - 6

Add 6 on both the sides of the equation we get,

-2x = -2x

Divide by -2 of the equation both sides

x = x                                 _____(1)

Add (-x) both the sides we get,

0 = 0                                 _____(2)

From (1) and (2) we conclude ,

Solution is true for all  the real values of x.

Hence, solution set of -2(x +3) = -2x -6 is all x ∈R (real numbers).

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Alan sells electronics, earning a base wage of $320 for one week, and a commission equal to 5% of his sales. he needs to earn at least $600 each week to cover his expenses. set up and solve an inequality to determine what Alans sales can be in order to ensure his expenses are covered.

Answers

Answer:

320 +0.05s ≥ 600sales ≥ $5600

Step-by-step explanation:

For sales of 's', Alan's earnings will be ...

  320 +0.05s

He wants that to be at least 600, so the inequality is ...

  320 +0.05s ≥ 600

__

Its solution is found by subtracting 320 and dividing by 0.05.

  0.05s ≥ 280

  s ≥ 5600

Alan's weekly sales must be at least $5600 for his earnings to cover his expenses.

Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years, the United States has lost more than half its wetlands. Environmental Almanac gives the percentage of wetlands lost in each state in the last 200 years. For the lower 48 states, the percentage loss of wetlands per state is as follows:
46 37 36 42 81 20 73 59 35 50
87 52 24 27 38 56 39 74 56 31
27 91 46 9 54 52 30 33 28 35
35 23 90 72 85 42 59 50 49
48 38 60 46 87 50 89 49 67
The percentages are concentrated from 20% to 60% The percentages are concentrated from 60% to 90%
There is a gap showing that none of the lower 48 states has lost from 60% to 69% of its wetlands.
These data are strongly skewed left.
These data are fairly symmetric, perhaps slightly skewed right.
There is a gap showing that none of the lower 48 states has lost from 10% to 19% of its wetlands.
There are no gaps in the data.

Answers

Question Completion:

How are the percentages distributed? Is the distribution skewed? Are there any gaps? (Select all that apply.)

Answer:

1. The percentages are concentrated from 20% to 60%.

2. These data are strongly skewed left.

3. There are no gaps in the data.

Step-by-step explanation:

1. Data

Percentage loss of wetlands per state

46 37 36 42 81 20 73 59 35 50

87 52 24 27 38 56 39 74 56 31

27 91 46 9 54 52 30 33 28 35

35 23 90 72 85 42 59 50 49

48 38 60 46 87 50 89 49 67

2. Re-arrangement of

Percentage loss of wetlands per state (in ascending order)

9    20  23  24  27  27   28  30

31   33  35  35  35  36   37  38  

38  39  42  42  46  46   46 48

49  49   50  50  50  52   52 54

56 56   59  59  60  67   72  73  

74  81  85  87   87   89  90  91  

Find the midpoint of the line segment with the given endpoints. 1) (-4, -9), (-6, -6)

Answers

Answer:

The answer is

[tex]( - 5 \: , \: - \frac{15}{2} )[/tex]

Step-by-step explanation:

The midpoint M of two endpoints of a given line segment can be found by using the formula

[tex]M = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )[/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-4, -9), (-6, -6)

The midpoint is

[tex]M = ( \frac{ - 4 - 6}{2} , \: \frac{ - 9 - 6}{2} ) \\ = ( - \frac{10}{2} , - \frac{15}{2} )[/tex]

We have the final answer as

[tex]( - 5 \: , \: - \frac{15}{2} )[/tex]

Hope this helps you

Values of k for which the quadratic equation 2x - kx + k 0 has equal roots is
a)0only
b)4
c)8 only
d)0,8​

Answers

Answer:

The answer is D.

Step-by-step explanation:

We have to apply Discriminant Law. When a quadratic equation, ax² + bx + c = 0 has equal roots so the discriminant will be 0. Then, you have to substitute the values into the formula :

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

[tex]let \: D = 0 ,a = 2,b = k,c = k[/tex]

[tex]0 = {k}^{2} - 4(2)(k)[/tex]

[tex] {k}^{2} - 8k = 0[/tex]

[tex]k(k - 8) = 0[/tex]

[tex]k = 0[/tex]

[tex]k - 8 = 0[/tex]

[tex]k = 8[/tex]

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