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The length of a rectangle is 5 less than twice the width. What values of the width will make the area less than 150 square feet? Define your variable(s). Write inequalities that could be used to solve this problem. Then solve the problem.

Answers

Answer 1

Answer: Anything between 0 and 10, excluding both endpoints.

In terms of symbols we can say 0 < w < 10 where w is the width.

===================================================

Explanation:

You could do this with two variables, but I think it's easier to instead use one variable only. This is because the length is dependent on what you pick for the width.

w = width

2w = twice the width

2w-5 = five less than twice the width = length

So,

width = wlength = 2w-5

which lead to

area = length*width

area = (2w-5)*w

area = 2w^2-5w

area < 150

2w^2 - 5w < 150

2w^2 - 5w - 150 < 0

To solve this inequality, we will solve the equation 2w^2-5w-150 = 0

Use the quadratic formula. Plug in a = 2, b = -5, c = -150

[tex]w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\w = \frac{-(-5)\pm\sqrt{(-5)^2-4(2)(-150)}}{2(2)}\\\\w = \frac{5\pm\sqrt{1225}}{4}\\\\w = \frac{5\pm35}{4}\\\\w = \frac{5+35}{4} \ \text{ or } \ w = \frac{5-35}{4}\\\\w = \frac{40}{4} \ \text{ or } \ w = \frac{-30}{4}\\\\w = 10 \ \text{ or } \ w = -7.5\\\\[/tex]

Ignore the negative solution as it makes no sense to have a negative width.

The only practical root is w = 10.

If w = 10 feet, then the area = 2w^2-5w results in 150 square feet.

----------------------

Based on that root, we need to try a sample value that is to the left of it.

Let's say we try w = 5.

2w^2 - 5w < 150

2*5^2 - 5*5 < 150

25 < 150 ... which is true

This shows that if 0 < w < 10, then 2w^2-5w < 150 is true.

Now try something to the right of 10. I'll pick w = 15

2w^2 - 5w < 150

2*15^2 - 5*15 < 150

375 < 150 ... which is false

It means w > 10 leads to 2w^2-5w < 150  being false.

Therefore w > 10 isn't allowed if we want 2w^2-5w < 150 to be true.


Related Questions

Solve please 9 to the second power =97 . Is the awnser a rational number ?

Answers

Answer:

yes becauss it can be expressed as a ratio

Step-by-step explanation:

What times 5 is 60, or what times 3 is 39?

Answers

Answer:

for the first it is 12 and for the other its 13

Step-by-step explanation:

Answer:

5*12=60

3*13=39

Step-by-step explanation:

can someone please help?

Answers

Answer:

please type the statements it gives u in a comment, we can't see it in the picture

a bank of 16 floodlights together 4000 watts of power. how much power is used by each bulb?

Answers

Answer:

250 watts

Step-by-step explanation:

If 16 floodlights together use 4000 watts of power, each floodlight uses 250 watts.

1. 16 floodlights use 4000 watts together

2. 4000÷16=250

3. 250 watts used by each floodlight

The answer might be incorrect, as power may not be straight forward to calculate with division, but hopefully the explanation helps!

In the figure below,
What is the value of x?

Answers

Answer: 16 degrees

Step-by-step explanation:

(3x + 18) = 66

Because vertically opposite angles are equal

66 - 18 = 48

48 divided by 3

=16

find the average speed of a man that travel in 120km in 5hrs

Answers

Answer: 24 km/hour

Step-by-step explanation: 120/5= 24

• Evaluate the expression
33 • (12 - 2) = 2.

Answers

Answer:

33 * (12-2) = 2 is not correct answer the real answer is 330

Step-by-step explanation:

(12-2) = 10

33 * 10 = 330

what is The greatest common factor of 42 and 96

Answers

Answer:

I think that the answer is 6

The greatest common factor of 42 and 96 is 6 so, option A is correct.

What is GCF?

The biggest positive number that divides each of the two or more non-zero integers is known as the greatest common divisor.

Given:

The two numbers are 42 and 96,

Factorize the numbers as shown below,

42 = 2 × 3 × 7

96 = 2 × 2 × 2 × 2 × 2 × 3

Calculate the GCF as shown below,

GCF = 2 × 3

GCF = 6

Thus, the GCF is 6.

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Which statements about the system are true? Check all that apply.


y= -13x - 4

3y-x= -7

a
Both lines have the same y–intercept.
b
The system consists of parallel lines.
c
The equations represent the same line.
d
The system has one solution.
e
Both lines have the same slope.

Answers

Answer: D

Step-by-step explanation:

To compare the two lines, we want to a=make sure that they are in the same form.

3y-x=-7           [add both sides by x]

3y=x-7            [divide both sides by 3]

y=1/3x-7

Now that the equations are in the same form, we can compare them.

In order for the equations to have the same y-intercept, the "b" must be the same. The y-intercept for the first equation is -4, while the y-intercept for the second equation is -7. Therefore, A is not the answer.

If the lines are parallel, they must have the same slope. Parallel lines NEVER touch or cross, hence the slope has to be the same. The slope for the first equation is -13, while the slope for the second equation is 1/3. Therefore, B is not the answer.

We know that E is not the answer because the paragraph above proved that the slope are not equal.

We also know that the equations do not represent the same line. If they are the same line, the equations would be identical.

We know that D is the correct answer. A system of linear equaitons can only have ONE solution. We set the equations equal to each other to find the solution. The intersection point is the solution.

Therefore, we know that D is the right answer.

Find the slope of the line that passes through (2, 6) and (-7, 8)

Answers

Answer:

-2/9

Step-by-step explanation:

The slope of the line passing through the given points is  [tex]\frac{2}{-9}[/tex]

What is slope?

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Given are two points (2, 6) and (-7, 8) from which a line passes. We need to find the slope of the line.

We know that, the slope of a line passing through points (x₁, y₁) and (x₂, y₂) = (y₂-y₁) / (x₂-x₁)

In the given points, y₂ = 8, y₁ = 6, x₂ = -7 and x₁ = 2

Therefore, the slope of line = 8-6 / -7-2 = [tex]\frac{2}{-9}[/tex]

Hence, the slope of the line passing through the given points is  [tex]\frac{2}{-9}[/tex]

Learn more about slope, click

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Find the distance between the points (0,-9) and(4,-6)

Answers

Answer:

d=5

Step-by-step explanation:

1. use the distance formula: d=[tex]\sqrt{(x_{2} - x_{2} )^{2} +(y_{2} -y_{1} )^{2}[/tex]

2. plug in the points: d=[tex]\sqrt{(0-4)^{2} +(-9+6)^{2}[/tex]

3. solve problem inside parentheses: d=[tex]\sqrt{(-4)^{2} +(-3)^{2}[/tex]

4. square -4 and -3: d=[tex]\sqrt{16+9[/tex]

5. add:d=[tex]\sqrt{25[/tex]

6. find square root: d=5

find the slope of Y=5/4x-7

Answers

the slope is 5/4

the equation is written in the form y= mx+b

m is the slope
b is the y-intercept

Answer:

Slope=5/4

Step-by-step explanation:

To figure this out you need to know the equation y=mx+b. (m being slope and b being the y intercept.

Here your m would be 5/4, so 5/4 is your slope.

Mr. Peters has 40 Bible students. Of the students, 3/4 of them are boys. How many are boys?

Answers

Answer:

Step-by-step explanation:

40·(3/4)= 10·3= 30 boys are Bible students.

Answer:

The answer would be 30 boys

Step-by-step explanation:

you would divise 40 by 4 which equals 10 and then 10x3=30 and then that would be the andwer to the problem of yours

50 points for this!!!!!

Answers

i think that they’re all true except for the last statement.
It’s the fourth answer down I believe


Part I: Evaluate f(0).
A. Identify the function that will be used when x = 0. (1 point)
B. Find the value of this function when x = 0.

Answers

Answer:

A. x^2    x ≤ 1

B. value=0 because (0)^2=0

It takes 8 minutes to cut a board twice. How long does it take to cut the board into 9 pieces

Answers

Answer:

36 minutes


Step-by-step explanation:

With the data given, we can calculate that if it takes 8 minutes to cut a board twice then, it takes four minutes to cut one board. We can then determine how long it takes the cut a board into 9 pieces by multiplying 9 x 4 to equal the amount that it takes for a board to be cut into 9 pieces which would be 36.

In conclusion, it would take 36 minutes to cut a board into 9 pieces.


Have a great rest of your day
#TheWizzer

How would A DEF be different if you transformed
A ABC by translating it 5 units down first and then reflect
ing it over the y-axis?
10
A
2
2
A
TC
6
8
10
6


Please helppp

Answers

Bro, we go to the same school, I'm reporting you to Mr. Fisher or whoever's homeroom you're in

(4,3)(-3,1) slope intercept

Answers

Answer:

y = 2/7x + 13/7 (slope intercept : y = mx + b)

Given two points (4, 3), and (-3, 1) You can start off with point slope because you are just given points.

Point slope: y - y1 = m(x - x1).

Point 1 : (4, 3) → (x1, y1). Point 2 : (-3, 1) → (x, y).

→ 1 - 3 = m(-3 - 4)

-2 = m ( -7 )

-2 = -7m

2/7 = m

m = 2/7.

Since you have the slope, all you need is one point.

y - 3 = 2/7 ( x - 4 )

y = 2/7 ( x - 4 ) + 3

y = 2/7x - 8/7 + 3

y = 2/7x - 8/7 + 21/7

y = 2/7x + 21/7 - 8/7

y = 2/7x + 13/7

*taydah*

______________

or if you don't like point slope, you can just find the slope between the two points, and then find the y intercept.

m = y2-y1/x2-x1

m = 3-1/4--3

m = 2/7

Then multiply the slope by the x of one of the coordinates, and subtract one of the y values from the coordinates from the slope multiplied by the x of the same coordinate.

let's use (-3, 1)

→ 1 - -3 ( 2/7 )

1 + 3 ( 2/7 )

1 + 6/7

13/7

*Here is the y intercept*.

Then just put this in the form y = mx + b and you are done!

y = mx + b → y = 2/7x + 13/7

The drama club is selling popcorn so they can earn enough money to travel to their next competition. The table below shows how much money the drama club earns for the amount of popcorn sold. Let p represent the number of bags of popcorn sold. Let t represent the total amount earned, in dollars. Number of Bags of Popcorn Sold p Total Amount Earned t 2 $3 4 $6 6 $9 8 $12 Enter an equation that represents the relationship between the number of bags of popcorn sold and the total amount of money earned.

please

Answers

Answer:

t=3/2p

Step-by-step explanation:

We can see the linear pattern between t and p as

p/t = 2/3=4/6=6/9 etc... So t/p=1/(2/3) =3/2 and therefore t=3/2p

(2,3)(4,6)(6,9)(8,12)

Slope

m=(6-3)/4-2m=3/2

Equation

y=3/2x

Or

t=3/2p

What is 4⁹+ 4⁷ =
I need help I can’t figure this out

Answers

Answer:

278528

Step-by-step explanation:

1st we need to get the 1st 2 values of exponets

4 to the power of 9 is 4x4 9 times and that's 262144,

4 to the power of 7 is 4x4 7 times and that's 16384

16,384 + 262,144 is 278528

Answer: 278,528

Step-by-step explanation:

4⁹+ 4⁷ =

(4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4) + (4 x 4  x 4 x 4 x 4 x 4 x 4)

262,144 + 16,384= 278,528

Which decimal number is NOT between the two decimal numbers on the
number line?
0.65
0.70
A
0.659
B
0.67
0.648

Answers

Answer:

0.648 I believe, i apoligize if its wrong, hope it goes well!

Obtain two numbers such their HCF is 20 and their LCM is 300....... BY STEPS!!!! .. ​ ​

Answers

Answer:

60 ; 100

Step-by-step explanation:

Hi there !

HCF = 20 = 4×5 = 2²×5

LCM = 300 = 3×100 = 3×4×25 = 2²×3×5²

LCM/HCF = 2²×3×5²/2²×5 = 3×5

a = 3×hcf = 3×20 = 60

b = 5×lcm = 5×20 = 100

Good luck !

The length and width of a rectangle are in the ratio 3:4. The perimeter of the rectangle is 84 cm. Find the length and width of the rectangle.

Answers

Length of rectangle = 84 cm.

Ratio of length to width = 4:3.

Therefore, width of the rectangle = 3x84/4 = 63 cm.
282 viewsView 1 upvote

1



1


1 comment from
Steve Triglianos
Profile photo for Sonal Kumar
Sonal Kumar
, lives in Noida, Uttar Pradesh, India
Answered Aug 13, 2018

The length of the rectangle is 18 cm, and the width is 24 cm as per the concept of perimeter.

Let the length of the rectangle be 3x and the width be 4x, where x is a common factor.

The perimeter of a rectangle is given by the formula:

Perimeter = 2 × (Length + Width)

Given that the perimeter is 84 cm, we can write the equation as:

84 = 2 × (3x + 4x)

Now, let's solve for x:

84 = 2 × 7x

42 = 7x

x = 42 / 7

x = 6

Now that we have the value of x, we can find the length and width of the rectangle:

Length = 3x = 3 × 6

           = 18 cm

Width = 4x = 4 × 6

          = 24 cm

Therefore, the length of the rectangle is 18 cm, and the width is 24 cm. The length and width are in the ratio 3:4, and the perimeter of the rectangle is indeed 84 cm.

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100 points!!! (Look at the photo) don’t send links or I’ll report it.

Answers

Answer:

The mean of this weeks temp

The mean of last weeks temp

The range of this weeks temp

Step-by-step explanation:

:)

Answer:

1. The mean of this week's temp

2. The mean of last week's temp

3. The range of this week's temp

Step-by-step explanation:

that is what i think

Please help me solve this, I will give you brainliest

Answers

2008 payan walang yan ha kaya mo yan

100 − (x + 2)
100 − (x − 2)
Please compare which is greater?

Answers

Answer:

100-(x+2)

Step-by-step explanation:

Answer:

100 − (x - 2)

Step-by-step explanation:

100-(x+2)

100+(-x-2)

-100x-200

100-(x-2)

100+(-x+2)

-100x+200

GIVING BRAINLST MATHHH

Answers

Answer:

276.32, 401.92, 1256

Step-by-step explanation:

Volume is equal to the height times the surface of the base. The base is a circle, so its 3.14*(radius)^2. just plug in the values and round to the nearest hundred.

Which of the following functions will represent $500 placed
into a mutual fund yielding 10% per year for 4 years.

• A = 500(.10)^4
• A = 500(1.1)^4
• A = 500(4)(.10)
• A = 500(1.04)^10

Answers

Answer:

the answer is the first one

Step-by-step explanation:

The  functions will represent $500 placed into a mutual fund yielding 10% per year for 4 years is  A = 500(1.1)^4

what is Compound Interest?

In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one. You will then be left with the principal amount of the loan plus compound interest.

given:

P= $500

First, convert R as a percent to r as a decimal

r = R/100

r = 10/100

r = 0.1 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 500.00[tex](1 + 0.1/1)(1)^4[/tex]

A = 500.00[tex](1.1)^4[/tex]

A = $732.05

Hence, the functions will represent $500 placed into a mutual fund yielding 10% per year for 4 years is  A = 500(1.1)^4

Learn more about Compound Interest here:

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Consinulas is good at 2k

Answers

Answer:

1

Step-by-step explanation:

Use the SOH-CAH-TOA method.

We are given an angle (37°).

We know a side that is opposite of the angle.And we are trying to find the hypotenuse.

So we use SOH

[tex] \sin(x) = \frac{o}{h} [/tex]

[tex] \sin(37) = \frac{0.6}{h} [/tex]

Isolate h

[tex]h = \frac{0.6}{ \sin(37) } [/tex]

Which gives us 1.

So the answer is 1.

A student has a 2% salt water solution and a 7% salt water solution. To best imitate salt water at a local beach, he needs 1 liter of a 3.5% salt water solution. He defines x as the amount of 2% solution and writes this equation:

0.2x + 0.7(x – 1) = 0.35(1)
He solves the equation and determines that x is about 1.17 liters. He interprets this as needing 1.17 liters of 2% solution to make 1 liter of 3.5% solution

Answers

The student clearly made a mistake, because he found that he needs to mix more solution that he wants to end up with. Mixing 1.17 L of one solution with more of some other solution will make more than 1 L of another solution.

The mistake is writing x - 1 instead of 1 - x.

Answer:

The answers:

It’s A & B

A.) The percent values were written incorrectly in the equation.

B.) The amount of 7% solution should be written as 1 – x, not x – 1.

Step-by-step explanation:

Tap the THANKS button

(If helpful)

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