The area of a bulletin board is 90 ft. The length is nine feet less than four times the width. Find the length and the width, in feet, of the bulletin board.
width
ft
length
ft
+

Answers

Answer 1
Area (A) = 90 ft
Width = x
Length = 4x - 9

A = L*W, so the equation is:
x(4x - 9) = 90

Solve:
4x^2 - 9x = 90
4x^2 - 9x - 90 = 0
(4x + 15)(x - 6) = 0
4x + 15 = 0
4x = - 15
x = -15/4
^^^ reject because distance can’t be negative
x - 6 = 0
x = 6 ft (width)

Length = 4x - 9
L = 4(6) - 9
L = 24 - 9
L = 15 ft

Check:
A = L*W
90 = 15 * 6
90 = 90

Answer: The length is 15 feet and the width is 6 feet.

Related Questions

Sonya buys a baseball jersey for her brother on sale for 20% off. If the price she paid was $6 lower than the regular price, what was the original price of the jersey?

Answers

Answer:

30

Step-by-step explanation:

6x5

The original price of the jersey is $ 30

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data ,

Let the original price of the jersey be = $ x

The percentage discount on the original price = 20 %

The difference between the original price and the discounted price = $ 6

So ,

By the percentage equation ,

Percentage discount on the original price = difference between the original price and the discounted price

And ,

( 20 / 100 ) of original price = $ 6

On simplifying the equation , we get

( 20/100 ) x = 6

( 1/5 ) x = 6

Multiply by 5 on both sides , we get

x = 5 x 6

x = $ 30

So , the original price of the jersey is $ 30 and the discounted price is $ 24

Hence , the original price of the jersey is $ 30

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solve for y, 10x-4y=24​

Answers

Answer:

y=-2.5x-6 is the answer

1
2
3
4
5
10
50
Which function has an inverse that is a function?
Ob(x) = x2 + 3
Od(x) = -9
Om(x) = -7x
O p(x) = 1x1
Which function has an inverse that is a function?

Answers

Step-by-step explanation:

an equation is a function, if it delivers for every possible input value x exactly one result value y.

b(x) = y = x² + 3

y - 3 = x²

x = sqrt(y -3)

our formally correct

y = sqrt(x - 3)

that is actually NOT a function, as a square root delivers for most x values 2 y values : a positive and a negative value.

d(x) = -9

that means for every possible value of x the result is -9.

reversing this means that the input value of -9 has infinitely many possible results

that is NOT a function.

m(x) = y = -7x

x = -y/7

or formally correct

y = -x/7

that is a normal function. every possible value of x leads to exactly one value of y.

p(x) = y = 1x¹ = x

y = x is its own inverse function.

and this is, of course, a function. every possible value of x leads to exactly one value of y.

Animal
Is a bird can fly



Pig
Penguin
Seagull
Tiger
Crow
Bat
Mosquito



Let event A = The animal is a bird
Let event B = The animal can fly.
Which outcomes are in A and B?
O A. {seagull, crow}
O B. {penguin, seagull, crow, bat, mosquito}
O c. {penguin, seagull, crow}

O D. (seagull, crow, bat, mosquito)
Need Helpp

Answers

Answer:

A. {seagull, crow}

Step-by-step explanation:

sorry im late but hopefully this helps anyone!

The option A is correct {seagull, crow}.

What is probability?

Chance is represented by probability. A part of math manages the event of an irregular occasion. The value is expressed as a number from 0 to 1. Likelihood has been acquainted in Math's with anticipate how likely occasions are to occur. The extent to which something is likely to occur is basically what probability means. The probability distribution is also based on this fundamental probability theory.

Given a table shows relation in  Animals  is a bird and can fly

where, Let event A = The animal is a bird

Let event B = The animal can fly.

to find the  outcomes are in A and B

According to the table, each of the two events provided by the problem describes a condition that must be verified. The first event specifies that it must be a bird, while the second event specifies that it must fly.

Accordingly, the creatures that have the two occasions confirmed in the table are he seagull and crow.

Hence the  {seagull, crow} are  outcomes are in A and B.

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HELP ME NOW!!! PLS I DONT KNOW THSE TPYE OF STUFF

Answers

Answer:

10 yd, because you subtract 15 to 5.

20pens cost #300 and 50pens cost #750
(a)is the cost of pens directly proportional to the number of pens?​

Answers

Answer:

669

Step-by-step explanation:

in the similarity transformation of abc to def, abc was dilated by a scale factor of [?], reflected across the [ ], and moved through the translation [ ].​

Answers

The complete similarity transformation is: triangle abc was dilated by a scale factor of [2], reflected across the [x-axis], and moved through the translation [0].​

How to complete the similarity statement?

From the figure, we have:

AB = 2 units

DE = 4 units

So, the scale factor (k) is:

k = DE/AB

k = 4/2

k = 2

So, the scale factor is 2

Also, both shapes are on either sides of the x-axis, and they are equidistant from the x-axis.

This means that the triangle is reflected across the x-axis with no translation.

Hence, the complete similarity transformation is:

abc was dilated by a scale factor of [2], reflected across the [x-axis], and moved through the translation [0].​

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8 in+ 34 in. Round to the correct precision

Answers

It 42 inc hope that helps:)

Answer:

3 feet 6 inches

Step-by-step explanation:

If we add those inches together, we get 42 inches. Turn that to feet (12 in in a foot) and we get 3.5 feet, or 3 feet and 6 inches.

¿A qué velocidad debe circular un auto de carreras para
recorrer 50km en un cuarto de hora?

Answers

Answer:

creo que la respuesta es 3,333.33 mph

Step-by-stepStep-by-step explanation:

2 5/14 divided by (2 5/8 times 1 3/4)

Answers

Answer:

1.947

Step-by-step explanation:

if you write down the equation you will get this answer and see it is not respecting meaning it does not go on it has a different pattern

Explain the steps you would take to find a quotation of 1/3÷4/3

Answers

Answer:

Answer btw is 1/4 ;)

Step-by-step explanation:

First step in dividing fractions is to flip the second fraction, aka find the inverse.

[tex]\frac{1}{3}/\frac{4}{3} \\\frac{1}{3}*\frac{3}{4}[/tex]

All you have to do from here is multiply.

[tex]\frac{3}{12}=\frac{1}{4}[/tex]

Boom.

please solve this question I give you brainliest answer

Answers

Answer:

6. 9^2+4x-1

7. 7x - 3 cm

8. -6x^2+3x-4

9. 4x+10y+4z

10 13x^2 - 2x

11. -5x^2 - 8x - 16

Step-by-step explanation:

6. (13x^2+x-3)-(4x2-3x-2) = 9x2+4x-1

7. x +4+2x+1+4x-8

= 7x-3 cm

8. (-8x^2 + 8x + 1) + (14x^2-11x+3)

10. (8x^2+x)-(-5x^2+3x)

11. (-x^2-6x+5) - (4x^2+2x+11)

Factor x⁴ + 3x² + 2 completely.

All factors in your answer should have integer coefficients.

Answers

Answer:

x = i, ~1.41i

Step-by-step explanation:

Assuming "integer coefficients" allows imaginary numbers:

(x^2 + 1)(x^2 + 2)

x^2 = -1 = i

x^2 = -2 = ~1.41i

f(x)=10x^2-5x-3, evaluate f(-3)

Answers

Answer:

f(-3)= 10(-3)^2 - 5(-3) - 3

       =90 + 15 -3

f(-3) = 102

Step-by-step explanation:

25,812-4.2d=31.311-5.5d

Answers

Answer:

d=−19831.299231

Step-by-step explanation:

find the value of a square + b square when a+b = 8 and ab = 10

Answers

As we know,

[tex] \boxed{ \boxed{(a + b) {}^{2} = {a}^{2} + {b}^{2} + 2ab}}[/tex]

now, let's plug the given values to find a² + b²

[tex](8) {}^{2} = {a}^{2} + {b}^{2} + (2 \times 10)[/tex]

[tex]64 = {a}^{2} + {b}^{2} + 20[/tex]

[tex] {a}^{2} + {b}^{2} = 64 - 20[/tex]

[tex]a {}^{2} + b {}^{2} = 44[/tex]

A farmer is enclosing a square area for his pigs as shown below. Use the formula A = s to the second power to find the area of the pig pen.

Answers

The area of the given figure that is mentioned is 64.

A square has congruent angles on each side. The square's area is thus equal to its square divided by its side length.

Let a represent the square's side length. The area of the square will be calculated as:

Area of the square = a² square units

The side provided is 8 ft

The area will be

= a²

= 8²

=64

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10 push-ups in 2 days= ?


Answers

Answer:20

Step-by-step explanation:

Cuz 10+10=20

PLS HURRY!!!!!
Identify the prime factorization for 75
A 25x3
B25x 3
C 52x3

Answers

Answer:

C 52x3

Step-by-step explanation:

Can you solve and give me explanation how to solve

Answers

9514 1404 393

Answer:

  3 < x < 6

Step-by-step explanation:

Use the perimeter formula to write an expression for the perimeter. Then put that in an inequality with the given limits. Solve for x.

  P = 2(L +W)

  P = 2((4x) +(2x +1)) = 2(6x +1) = 12x +2 . . . . . fill in the given values; simplify

The perimeter wants to be between 38 and 74 cm, so we have ...

  38 < 12x +2 < 74

  36 < 12x < 72 . . . . . subtract 2

  3 < x < 6 . . . . . . . . . divide by 6

_____

Additional comment

Solving a compound inequality is very much like solving a single inequality. You need to "undo" what is done to the variable. The rules of equality (ordering) still apply. If you were to multiply or divide by a negative number, the direction (sense) of the inequality symbols would reverse in the same way they do for a single inequality.

Here, our first step was to subtract 2 from all parts of the inequality:

  38 -2 < 12x +2 -2 < 74 -2   ⇒   36 < 12x < 72

The division by 12 worked the same way: all parts are divided by 12.

  36/12 < (12x)/12 < 72/12   ⇒   3 < x < 6

__

If it makes you more comfortable, you can treat the perimeter limits as two separate inequalities: 38 < 12x+2 and 12x+2 < 74. Both restrictions apply, so the solution set is the intersection of the solution sets of these separate inequalities.

The perimeter P of a triangle is equal to the sum of the lengths of sides a, b, and c.

Answers

The given statement "The perimeter P of a triangle is equal to the sum of the lengths of sides a, b, and c" is absolutely correct.

What is the perimeter?

Perimeter is the addition of an external measure of sides it will always positive.

A perimeter is a length and has a degree of the unit as one.

For example

Perimeter of square = side + side + side + side

The perimeter of the circle = πd where d is the dia of the circle.

Given a triangle with sides a,b and c

The perimeter of triangle is = a + b+ c

So,

The perimeter of the triangle is the sum of all sides.

Hence The given statement "The perimeter P of a triangle is equal to the sum of the lengths of sides a, b, and c" is absolutely correct.

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(w2x−3)÷10⋅z when w=−9, x = 2.7, and z=−2/5

Answers

w=-9x=2.7z=-2/5

[tex]\\ \sf\longmapsto \dfrac{w^2x-3}{10z}[/tex]

[tex]\\ \sf\longmapsto \dfrac{(-9)^2(2.7)-3}{10(-2/5)}[/tex]

[tex]\\ \sf\longmapsto \dfrac{81(2.7)-3}{-2(2)}[/tex]

[tex]\\ \sf\longmapsto \dfrac{218.7-3}{-4}[/tex]

[tex]\\ \sf\longmapsto \dfrac{215.7}{-4}[/tex]

Rounding up numerator

[tex]\\ \sf\longmapsto \dfrac{216}{-4}[/tex]

[tex]\\ \sf\longmapsto -44[/tex]

Step-by-step explanation:

(-9)^2(2.7)-3/10(-2/5

= 81(2.7)-3/-2(2)

= 218.7-3/-4

= 215.7/-4

= -44


Set A represents rational numbers. Set B represents integers. Which diagram shows the numbers placed in the correct sets?

Answers

Answer:

from the little i can see, they are all correct

PLEASE HELP ITS MATH THANK YOUUUU

Answers

Answer:

6 ft

Step-by-step explanation:

Multiply by 2 on each side: (8*2) = (3*2)

New ratio: 16 = 6

Final answer: 6ft

It would be 6ft.. he 8inches to represent 3 feet so if the closet was 16inches it would be 6 feet if that helped at all

Y varies directly with x. If y = 21, when x = 7, find y when x = 28.

Answers

This statement means
y

x
, which can also be written in the form
y
=
k
x
when it is directly proportionate and
y
=
k
x
when inversely proportionate, where
k
is a value we need to work out.
Since the equation is in the form
y
=
k
x
we know that...
21
=
K
×
7


k
=
21
7
=
3
.
So we can write this as the formula:
y
=
3
x
Therefore using the value of
x
=

1.66
y
=
3
x

y
=
3
×

1.66
=

4.98

Answer:

y = - 4.98

Step-by-step explanation: This statement means

y

x

, which can also be written in the form

y

=

k

x

when it is directly proportionate and

y

=

k

x

when inversely proportionate, where

k

is a value we need to work out. Since the equation is in the form

y

=

k

x

we know that...

21

=

K

×

7

k

=

21

7

=

3

.

So we can write this as the formula:

y

=

3

x

Therefore using the value of

x

=

1.66

y

=

3

x

y

=

3

×

1.66

=

4.98

Express 960% as a mixed number

Answers

Answer:

9 3/5

Step-by-step explanation:

When we see a percentage, we know that the base is 100. In other words, 960% is equal to 960/100

With this, its just a matter of transforming the improper fraction to a mixed number.

100 fits 9 times in 960 so there will be 9 wholes

the remaining 60/100 can be simplified to 3/5 through this process:

60/100 = 6/10 = 3/5

Answer:

9 3/5

Step-by-step explanation:

Step 1: Write down the percent divided by 100 like this:

960% = 960/100

Step 2: Multiply both top and bottom by 10 for every number after the decimal point:

As 960 is an integer, we don't have numbers after the decimal point. So, we just go to step 3.

Step 3: Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(960,100) = 20. So,

(960÷20)/(100÷20) = 48/5 when reduced to the simplest form.

As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 960/100 is also equal to 9 3/5 when expressed as a mixed number.

Help
Solve the inequality. Then, graph the solution set on a number line. (Show all your work)

Answers

that's what it's graph looks like.

Step-by-step explanation:

[tex] |2w + 8| \geqslant 15[/tex]

[tex] \implies \mathsf{2w + 8 \geqslant 15 \: }\\ \mathsf{or }\\ \mathsf{ \: 2w + 8 \leqslant - 15}[/tex]

(that's a property, if |x| >= a

=> x >= a or x <= -a)

[tex] \implies \mathsf{2w \geqslant 15 - 8\: }\\ \mathsf{or }\\ \mathsf{ \: 2w \leqslant - 15 - 8}[/tex]

[tex]\implies \mathsf{2w \geqslant 7\: }\\ \mathsf{or }\\ \mathsf{ \: 2w \leqslant -23}[/tex]

[tex]\implies \mathsf{w \geqslant \frac{7}{2} \: }\\ \mathsf{or }\\ \mathsf{ \: w \leqslant \frac{ - 23}{2} }[/tex]

Write the slope-intercept equation of the line with slope -3/4 passing through the point (-4,5). If necessary, answer using fractions, not decimals.

Answer: ​

Answers

Answer:

y = -3/4x + 2

Step-by-step explanation:

y = -3/4x + b

5 = -3/4(-4) + b

5 = 3 + b

2 = b

Pls help ASAP pls it’s reasoning with fractions

Answers

84 decimetres is the answer!

Y-(-3y) create an equivalent equation

Answers

9514 1404 393

Answer:

  4y

Step-by-step explanation:

There are an infinite number of equivalent expressions. One of them can be obtained by combining the terms

  y -(-3y) = y +3y = y(1 +3) = 4y

__

All of the expressions shown as equal are equivalent.

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