The length of a rectangle is four meters less than twice it's width. If the area of the rectangle is 96 square meters what is the width?

Answers

Answer 1

Answer: (I'm sorry if this is not the right answer)

The width = 8 meters

Step-by-step explanation:

The length: a (m)

The width: b (m)

We cannot have a negative length and a negative width: a>b>0

Eq. I: a=2b-4

Eq. II: ab=96

Substitute the value of a from Eq. I into Eq. II: (2b-4).b=96

Solve for b:

(2b-4).b=96

2[tex]b^{2}[/tex]-4b-96=0

[tex]b^{2}[/tex]-2b-48=0

[tex]b^{2}[/tex]+6b-8b-48=0

b.(b+6)-8.(b+6)=0

(b+6).(b-8)=0

b=8; b=-6

As mentioned above, b>0. Therefore, b=8

Conclusion: if the area of the rectangle is 96 square meters then its width is 8 meters.

Answer 2

The width of the given rectangle is 8 units.

What is a rectangle?

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

Perimeter of rectangle = 2( length + width).

Let's say the length of the rectangle is L and the width is W

Given that,

The length of a rectangle is four meters less than twice its width.

So,

L = 2W - 4

And,

Area = 96 square meter

LW = 96

Now by substituting

2W² - 4W = 96

W² - 2W - 48 = 0

W² -8W + 6W - 48 = 0

W(W - 8) + 6(W - 8) = 0

(W + 6)(W - 8) = 0

W = 8, -6 since distance cannot be negative so it will be 6 meters.

Hence "The width of the given rectangle is 8 units".

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Related Questions

Angie and Kenny play online video games. Angie buys 1 software and of game play. Kenny 2 buys software and 6 months of game play. Each software package costs ​$50. If their total cost is ​$295​, what is the cost of one month of game​ play?

Answers

Answer:$12

Step-by-step explanation:

Answer:

months of game play (m) =$11

Step-by-step explanation:

1) 6,875 28
In the problem above,
(estimate: 6,875 28 as 6,000 + 30 = 200).
After the first digit is placed in the hundreds place in the quotient and students have
divided, multiplied, subtracted, and compared, the student should bring down the 7.
Now, estimate 1270 28 and perform a second division (repeat).
1,270 28 is estimated as 1,200 + 30 = 40.
Students then divide, multiply, subtract, and compare the remainder to the divisor,
making sure it is smaller.
Finally, perform 115 -28, by estimating, dividing, multiplying, subtracting, and
comparing
After writing the remainder in the quotient, the division is complete.
What is the Quotient? Answer:

Answers

Answer:

?

Step-by-step explanation:

Radianes a grados 5 pi sobre 3

Answers

Answer:

5pi/3x180grados/piradianes

900/3=300 grados

Step-by-step explanation:

The shaded set of numbers shown on the x-axis can be expressed in interval notation as _____

Answers

Answer:  [1, 4)

This is basically saying [tex]1 \le x < 4[/tex]

The square bracket says "include this endpoint" while the curved parenthesis means "exclude this endpoint". We can tell what is included/excluded based on how the endpoint is drawn.

Open circle = exclude endpoint

Closed/filled in circle = include endpoint

Your teacher has also drawn a square bracket at the left endpoint, and a curved parenthesis at the right endpoint. This style of drawing the endpoints helps set up [1, 4). Though sometimes you might see the use of open/closed circles instead for the endpoints. I'm referring to the number line portion.

We want to express the shaded set of numbers on the x-axis with interval notation.

The interval notation is:

[1, 4)

Let's start by analyzing the graph.

We have two ends, one at x = 1, with a colored dot, which means that that value belongs to the set.

We have the other end at x = 4, with a white dot, which means that the value does not belong to the set.

Then the interval notation is:

[1, 4)

Where [] are used for colored dots.

() are used for white dots.

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a town has a population of 450000 people.if 60% of the population are under 25 years of age how many people in the town are 25 years old and over?​

Answers

Answer:

180000

Step-by-step explanation:

100%-60%=40% - 40% of the population are above 25 years old40/100=0.4450000*0.4=180000 - There are 180000 people in the town ages 25 and up.

What is 10x-2(x+6)=52 ?

Answers

Answer:x=8

Step-by-step explanation:Reorder the terms:

10x + -2(6 + x) = 52

10x + (6 * -2 + x * -2) = 52

10x + (-12 + -2x) = 52

Reorder the terms:

-12 + 10x + -2x = 52

Combine like terms: 10x + -2x = 8x

-12 + 8x = 52

Solving

-12 + 8x = 52

Solving for variable 'x'.

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

Add '12' to each side of the equation.

-12 + 12 + 8x = 52 + 12

Combine like terms: -12 + 12 = 0

0 + 8x = 52 + 12

8x = 52 + 12

Combine like terms: 52 + 12 = 64

8x = 64

Divide each side by '8'.

x = 8

Simplifying

x = 8

Answer:

x=5

Step-by-step explanation:

The temperature in Fahrenheit, x, is converted into the temperature in Celsius with the formula [tex]c(x)=\frac{5}{9}(x-32)[/tex]. What transformations are used in transforming the parent graph y = x, to obtain the graph of [tex]c(x)=\frac{5}{9}(x-32)[/tex]
horizontal translation

vertical compression

reflection in the x-axis

vertical translation

reflection in the y-axis

Answers

The temperature in Fahrenheit, x, is converted into the temperature in Celsius with the formula . What transformations are used in transforming the parent graph y = x, to obtain the graph of blank. The answers would be:

horizontal translationvertical compression

To obtain the graph of c(x) = (5/9){ x - 32 } we need as horizontal transformation. The correct option is A.

What is a function?

A function is defined as the expression that set up the relationship between the dependent variable and independent variable. A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Given function of temperature is c(x) = (5/9){ x - 32}. The two graphs are plotted on the x-y plane. It is observed that y = x is transformed to the horizontal direction.

The graph of the two functions y = x and c(x) = (5/9){ x - 32 } is attached with the answer below.

Therefore, to obtain the graph of c(x) = (5/9){ x - 32 } we need as horizontal transformation. The correct option is A.

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Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
y = 4x - 2
y = x + 13
A. (1, 13)
B. (0, -2)
C. (5, 18)
D. (4,-2)

Answers

Answer:

c

Step-by-step explanation:

just plug each coordinates

5=x

18=y

if its tru for both then thats the answer

Answer:

5,8

Step-by-step explanation:

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

y=x+13----(ii)

Equating equation i and ii we get,

[tex]4x - 2 = x + 13[/tex]

[tex]4x - x = 13 + 2[/tex]

[tex]3x = 15[/tex]

[tex]x = 3[/tex]

[tex]substitutin \: the \: value \: of \: x \: in \: equation \: (i)[/tex]

[tex]y = 4x - 2[/tex]

[tex]y = 4 \times 5 - 2[/tex]

[tex]y = 20 - 2[/tex]

[tex]y = 18[/tex]

Marks this as a brainest answer ok.

The distance from the green point on the parabola to the parabola's focus is
11. What is the distance from the green point to the directrix?
Focus
11
Directrix
O A. 11
B. 9.5
C. 5.5

Answers

Answer:

11

Step-by-step explanation:

sawarasenaaa kimi wa-

Simplify the ratio 45 to 75

Answers

The GCF of 45 and 75 is 15.

So, divide both numbers by 15.

45/15 = 3

7515 = 5

Therefore, the simplified version of the ratio is 3 to 5

Best of Luck!

Write down an expression for the nth term of the following sequence 7,16,25,34,43

Answers

Answer:

So in this sequence, we are adding by 9 in each term

So our pattern is: 7 , 7 +9 , 7 + 2(9) , 7 + 3(9) .....

hence, we can write it as: 7 + [tex]9^{n-1}[/tex] where n is the number of the term you want

A train travels at a constant speed of 60.4 miles per hour for 101.5 minutes. What distance does the train cover?

Answers

Answer:

102.2 miles

Step-by-step explanation:

First, convert the minutes to hours:

101.5/60

= 1.69 hours

Multiply this by 60.4 to find how many miles it covered:

= 102.2 miles

Point B lies on segment AC . Find the length of segment BC if AB = 4 mm and AC = 4 cm.

Answers

Answer:

4cm - 4mm = 3.6 cm

So, B and C equals 3.6 cm

An oil tanker can be emptied by the main pump in 4 hours. An auxiliary pump can empty the tanker in 11 hours. If the main pump is started at 7 PM​, when should the auxiliary pump be started so that the tanker is emptied by 10 PM​?

Answers

Answer:

The pump should be added by 8PM

Step-by-step explanation:

An oil tanker can be emptied by the main pump in 4 hours.

An auxiliary pump can empty the tanker in 11 hours.

the main pump is started at 7 PM,and we have 10 PM - 7PM = 3 hours to empty the tank.

So we have to look for the combined rate of the both pumps .

Let's say the volume= x

Rate of first pump= x/4

Rate of second pump= x/11

The rate will be added together

Combined rate= x/11 + x/4

Combined rate= 15x/44

But they have three hours to complete their pump

15x/44 = 3

X=1.0227

The pump should be added by 8PM

rochelle needs to pick a frame that measures 7 6/11 inches on each side ?

Answers

no the frame will not fit

7 6/11 =7.545454

7.545454 is larger than 7.5

What fraction is greater than 3/8? 1/4 7/16 1/8 3/16

Answers

Answer:

7/16

Step-by-step explanation:

3/8 = 6/16

7/16 is greater than 6/16

Hope This Helps :)

Answer:

7/16

Step-by-step explanation:

Simplified 7/16 is 3.5/8, which is more than 3/8. The rest of the answers are less than 3/8.

which of these equations or inequalities below are true 4 - 5< -2

Answers

Answer:

4-5<-2 is false it should be 4-5>-2

Step-by-step explanation:

Answer:b

Step-by-step explanation:

Use the number line to find 1/4+-21/8

Answers

Answer:

[tex]-\frac{19}{8}[/tex]

Step-by-step explanation:

[tex]\frac{1}{4}-\frac{21}{8}=\frac{2}{8}-\frac{21}{8}=\frac{2-21}{8}=-\frac{19}{8}[/tex]

The required number line represents 2 whole intervals (16/8) and then 7 more parts (7/8) from 0, and ends up at the point marked 2 3/8.

What is Number Line?

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

To add fractions with different denominators, we need to find a common denominator. In this case, we can use 8 as the common denominator:

1/4 + -21/8

1/4 - 21/8

2/8 - 21/8

-19/8

-2 3/8

To represent 19/8 on a number line, we need to divide the interval between 0 and 3 into 8 equal parts, and then count 23 of these parts from 0.

The number line would look something like below as shown.

Thus, the required number line represents 2 whole intervals (16/8) and then 7 more parts (7/8) from 0, and ends up at the point marked 2 3/8.

Learn more about the number line here:

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Question 6 of 15, Step 1 of 1
Correct
Two trucks leave a warehouse at the same time. One travels due east at an average speed of 58 miles per hour, and the other travels due west at an average speed of
65 miles per hour. After how many hours will the two trucks be 369 miles apart?

Answers

Answer:

3 hours

Step-by-step explanation:

369 divided by (58+65)

Find the standard equation of a sphere that has diameter with the end points given below. (3,-2,4) (7,12,4)

Answers

Answer:

The standard equation of the sphere is [tex](x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53[/tex]

Step-by-step explanation:

From the question, the end point are (3,-2,4) and (7,12,4)

Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.

The midpoint can be calculated thus

Midpoint = [tex](\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})[/tex]

Let the first endpoint be represented as [tex](x_{1}, y_{1}, z_{1})[/tex] and the second endpoint be [tex](x_{2}, y_{2}, z_{2})[/tex].

Hence,

Midpoint = [tex](\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})[/tex]

Midpoint = [tex](\frac{3 + 7 }{2}, \frac{-2+12 }{2}, \frac{4 + 4 }{2})[/tex]

Midpoint = [tex](\frac{10 }{2}, \frac{10}{2}, \frac{8 }{2})\\[/tex]

Midpoint = [tex](5, 5, 4)[/tex]

This is the center of the sphere.

Now, we will determine the distance (diameter) of the sphere

The distance is given by

[tex]d = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} + (z_{2}- z_{1})^{2} }[/tex]

[tex]d = \sqrt{(7 - 3)^{2} +(12 - -2)^{2} + (4- 4)^{2}[/tex]

[tex]d = \sqrt{(4)^{2} +(14)^{2} + (0)^{2}[/tex]

[tex]d = \sqrt{16 +196 + 0[/tex]

[tex]d =\sqrt{212}[/tex]

[tex]d = 2\sqrt{53}[/tex]

This is the diameter

To find the radius, r

From [tex]Radius = \frac{Diameter}{2}[/tex]

[tex]Radius = \frac{2\sqrt{53} }{2}[/tex]

∴ [tex]Radius = \sqrt{53}[/tex]

r = [tex]\sqrt{53}[/tex]

Now, we can write the standard equation of the sphere since we know the center and the radius

Center of the sphere is [tex](5, 5, 4)[/tex]

Radius of the sphere is [tex]\sqrt{53}[/tex]

The equation of a sphere of radius r and center [tex](h,k,l)[/tex] is given by

[tex](x-h)^{2} + (y-k)^{2} + (z-l)^{2} = r^{2}[/tex]

Hence, the equation of the sphere of radius [tex]\sqrt{53}[/tex] and center [tex](5, 5, 4)[/tex] is

[tex](x-5)^{2} + (y-5)^{2} + (z-4)^{2} = \sqrt{(53} )^{2}[/tex]

[tex](x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53[/tex]

This is the standard equation of the sphere

show that n(n+1)(n+2) is divisible by 6
Solution
(​

Answers

Proof by induction

Base case:

n=1: 1*2*3=6 is obviously divisible by six.

Assumption: For every n>1 n(n+1)(n+2) is divisible by 6.

For n+1:

(n+1)(n+2)(n+3)=

(n(n+1)(n+2)+3(n+1)(n+2))

We have assumed that n(n+1)(n+2) is divisble by 6.

We now only need to prove that 3(n+1)(n+2) is divisible by 6.

If 3(n+1)(n+2) is divisible by 6, then (n+1)(n+2) must be divisible by 2.

The "cool" part about this proof.

Since n is a natural number greater than 1 we can say the following:

If n is an odd number, then n+1 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.

If n is an even number" then n+2 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.

Therefore by using the method of mathematical induction we proved that for every natural number n, n(n+1)(n+2) is divisible by 6. QED.

Help me find this asap

Answers

Answer:

DQ = [tex]\frac{5}{(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}-\sqrt{x+h})}[/tex]

Step-by-step explanation:

Given function is f(x) = [tex]\frac{5}{2-\sqrt{x}}[/tex]

f(x + h) = [tex]\frac{5}{2-\sqrt{x+h} }[/tex]

Therefore, indicated difference quotient will be,

DQ = [tex]\frac{f(x+h)-f(x)}{h}[/tex]

Now we substitute the values in the difference quotient,

DQ = [tex]\frac{\frac{5}{2-\sqrt{x+h} }-\frac{5}{2-\sqrt{x}}}{h}[/tex]

      = [tex]\frac{5(2-\sqrt{x})-5(2-\sqrt{x+h})}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]

      = [tex]\frac{10-5\sqrt{x}-10+5\sqrt{x+h}}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]

      = [tex]\frac{-5\sqrt{x}+5\sqrt{x+h}}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]

      = [tex]\frac{5(-\sqrt{x}+\sqrt{x+h})}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]

      = [tex]\frac{5(-\sqrt{x}+\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}{h(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]

      = [tex]\frac{5[(x+h)-x]}{h(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]

      = [tex]\frac{5h}{h(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]

      = [tex]\frac{5}{(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]

2.64 gallons = how many liters

Answers

Answer:

9.9924 liters

Step-by-step explanation:

there are 3.785 liters in one gallon

multiply 3.785 liters times 2.64

that comes out to 9.9924 liters

Blueberries cost 4.99 a pound. Diego paid 14.95 for his blueberries. How many pounds did he buy?

Answers

Answer:

The answer is 3.

Step-by-step explanation:

The equation would be: x = 14.95 divided by 4.99, rounded to the nearest one:

14.95 divided by 4.99 = 2.99599...

Normally, I would not round the number to the nearest digit in problems like these, but 2.99599 is quite close to 3, so this might be an exception.

Anyways, that's how I got my answer.

Hope this helped.

SOLVING EQUATIONS
1) Solve 3x - 5 = -26
SOLVING QUADRATIC EQUATIONS

Answers

Answer:

x = -7

Step-by-step explanation:

This isn't a quadratic.

Step 1: Write out equation

3x - 5 = -26

Step 2: Add 5 to both sides

3x = -21

Step 3: Divide both sides by 3

x = -7

Step-by-step explanation:

[tex]\sf \bf We \: have,[/tex]

[tex]\sf 3x - 5 = -26[/tex]

[tex]\sf : \implies \bf 3x - 5 \green{+5}= -26\green{+5}[/tex]

[tex]\sf : \implies \bf 3x =-21[/tex]

[tex]\sf : \implies \bf 3x× \green{\dfrac{1}{3}}=-21× \green{\dfrac{1}{3}}[/tex]

[tex]\sf : \implies \bf \underline{\boxed{\sf \bf x = -7}}[/tex]

100 POINTS I NEED HELP ASAP

If h(x) = |2x-4| , find (h-7)

Answers

Answer:

The answer is 18.

Step-by-step explanation:

You just need to plug in -7 to the equation 2x-4. You get -18, but absolute value is always positive, so its 18.

The answer is 18.

Sorry no explanation im soooo sorry

What is the first step to evaluate 28-64\div828−64÷828, minus, 64, divided by, 8?

Answers

Answer:

64 Divided by 8

Step-by-step explanation:

Solve the following inequality

-x<-7​

Answers

Answer:

The answer could be any number above -7.

So, it could be...

(-8)

(-9)

(-10)

etc.

Step-by-step explanation:

The bigger the negative number, the lower the value.

If you continue the pattern below so that you write all of the numbers in the pattern less than 500, how many even numbers will you write? 4, 9, 14, 19, 24, 29...

Answers

Answer:

I think it would be 50 even numbers

4.75 lbs what is the amount in grams​

Answers

Answer: 4.75 lbs is 2,154.56 grams
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