Mathematics College

A rectangle is drawn so that the width is 3 feet shorter than the length. The area of the rectangle is 70 square feet. Find the length of the rectangle.

Answers

Answer 1

Answer:

The length of the rectangle (l) = 10 cm

The width of the rectangle (w) = 7 cm

Step-by-step explanation:

Step(i):-

Let 'x' be the length of the rectangle

Given that the width is 3 feet shorter than the length

The width of the rectangle = x -3

Area of the rectangle = length × width

Step(ii):-

Area of the rectangle = length × width

                                  = x ( x-3)

Given that the area of the rectangle = 70 square feet

                       x ( x-3) = 70

              ⇒   x² - 3x - 70 =0

              ⇒  x² - 10 x + 7 x - 70 =0

             ⇒  x (x -10) +7( x-10) =0

            ⇒ ( x+7) ( x-10) = 0

           ⇒  x =-7 and x=10

Final answer:-

we choose x=10

The length of the rectangle (l) = 10 cm

The width of the rectangle (w) = 7 cm

Related Questions

Scottie is testing to see if people who go to a lot of movies do better than average on the Verbal SAT (which has a mean of 500 and a standard deviation of 100 and is normally distributed). She has a sample of six people. What kind of hypothesis testing do we use

Answers

Answer:

The kind of hypothesis testing we can use is z-test for means

Step-by-step explanation:

Given that;

sample mean x" = 500

standard deviation σ = 100

sample size n = 6

What kind of hypothesis testing do we use?

There are two cases where z-test can be use;

first, when we know the population standard deviation or variance

and secondly, when the population size is more than 30.

So from the question, the population standard deviation was given, which is 100.

Since we know the S.D, it meets the first condition.

Therefore, The kind of hypothesis testing we can use is z-test for means

If the data below were represented by a comparative bar chart, the bar
representing which of these would be the tallest?
A. Left-handed girls
B. Right-handed boys
C. Right-handed girls
D. Left-handed boys

Answers

Answer:

b right handed boys

Step-by-step explanation:

Write fractions in order 5/8 2/3 3/8

Answers

Answer:

3/8, 5/8, 2/3

3/8 5/8 2/3 that’s is them in smallest to greatest

Simplify using Synthetic Division

Answers

Step 1
Write down the first coefficient without changes:
−3223−10−3
−3
2
3 −10 −3
2

Step 2
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
−3223(−3)⋅2=−63+(−6)=−3−10−3
−
3
2
3
−10 −3
(
−
3
)
⋅
2
=
−
6
2
3
+
(
−
6
)
=
−
3

Step 3
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
−3223−6−3−10(−3)⋅(−3)=9(−10)+9=−1−3
−
3
2 3
−
10
−3 −6
(
−
3
)
⋅
(
−
3
)
=
9
2
−
3
(
−
10
)
+
9
=
−
1

Step 4
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
−3223−6−3−109−1−3(−3)⋅(−1)=3(−3)+3=0
−
3
2 3 −10
−
3
−6 9
(
−
3
)
⋅
(
−
1
)
=
3
2 −3
−
1
(
−
3
)
+
3
=
0

We have completed the table and have obtained the following resulting coefficients: 2,−3,−1,0
2
,
−
3
,
−
1
,
0
.
All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.
Thus, the quotient is 2x2−3x−1
2
x
2
−
3
x
−
1
, and the remainder is 0
0
.
Therefore, 2x3+3x2−10x−3x+3=2x2−3x−1+0x+3=2x2−3x−1
2
x
3
+
3
x
2
−
10
x
−
3
x
+
3
=
2
x
2
−
3
x
−
1
+
0
x
+
3
=
2
x
2
−
3
x
−
1
Answer: 2x3+3x2−10x−3x+3=2x2−3x−1+0x+3=2x2−3x−1

Max walks 10 meters in 4 seconds what is his walking rate in meters per second

Answers

Answer:

2.5 m/s

Step-by-step explanation:

10/4 gets the answer. it is just distance over time

Answer: 2.5 m/s

Step-by-step explanation:

Mr. Santor cuts 1/2 of a piece of construction paper. He uses 1/6 of the piece to make a flower. What fraction of the sheet of paper does he use to make the flower?

Answers

Answer:

1/12

Step-by-step explanation:

1/2 multiplied by 1/6 equals 1/12

I need help
are all intergers a closed or open whoel number when subtracting or adding them together

Answers

Answer:

Integers are always closed under subtraction, addition and multiplication, not division though. Hope this helped! :D

Step-by-step explanation:

Question need help very hard pls

Answers

Well I think the scale is number 7 because

apriquide Rd
.) Travis is planning to ride at a constant speed during an upcoming bike trip. He wants to know
how many miles he will ride after different numbers of hours.
c) Plot two points that show how far Travis
will ride after 3 hours and after 4 hours.

Answers

Answer:

3 times 30 miles and 4 times 40 miles

Step-by-step explanation:

Travis will ride at a distance of 30 miles after 3 hours and at a distance of 40 miles after 4 hours.

What is Speed?

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Given that,

Travis is planning to ride at a constant speed during an upcoming bike trip.

This implies that the slope of the graph will be a constant.

So the graph will be a straight line.

We have two points on the graph (1, 10) and (2, 20).

The starting point will be (0, 0).

Slope = (20 - 10) / (2 - 1) = 10

So the equation of the line is y = 10x.

When x = 3 hours, y = 30 miles

When x = 4 hours, y = 40 miles

Hence the points has to be marked at (3, 30) and (4, 40).

Learn more about Speed and Slope here :

https://brainly.com/question/13281781

#SPJ2

The complete question with the graph is given below.

True or false, A triangle with side lengths of 9 cm, 19 cm, and 17 cm is a right triangle.

Answers

Answer:

False

Step-by-step explanation:

A right triangle has all side lengths the same

Answer: give me brainliest now

Step-by-step explanation:

PLZ HELP VERY EASY BRAINLIEST
Identify a pair of mutually exclusive events and a pair of independent events.

Answers

You can’t run backwards and forwards at the same time (mutually exclusive event). Rolling a dice and landing on 3 then landing on tails during a coin toss (independent events)

Please help me I’m not good with graphs

Answers

Answer:

I'm pretty sure it's 2 and 3

2 and 3

Good luck:)

Discussion Prompt: A fair coin is tossed twice and the number of heads is recorded. Jose says the P(1 head) = 1/2, while Jeff students says P(1 head) = 1/3. Explain in detail why Jose is correct.

Answers

Let H represent heads and T represent tails.

Writing HH means we get two heads and HT means we get heads first, then tails second, and so on.

We have these four possible outcomes when flipping two coins

HHHTTHTT

Of those four outcomes, two of them have exactly one head show up (HT and TH). The probability of getting exactly one head is 2/4 = 1/2, so this is why Jose is correct.

9. Put these numbers in greatest to least order: 2/3, 60%, 0.06, 3/4

Answers

Step-by-step explanation:

0.0660%2/33/4

hope it's right :)

Factor the common expression: 2x + 4 =

Answers

Answer:

2(x+2)

Step-by-step explanation:

Hope it helps you

help! algebra question

Answers

I think it’s y=10x+45 because the line starts at 45 and it’s increasing by 10. If i’m right can you mark me brainliest?

Explain whether the following statement is true or false. The function notation f-1(x) means 1/f(x)

Answers

Answer:

True

Step-by-step explanation:

f-1(x) otherwise known as the inverse of f(x) is the mathematical equivalent as 1/f(x).

Being inverse simply means that it "reverses" the operation that was applied to it with the original function .

For example: suppose f(x) = x+1, then if x = 1, f(1) = 1+1 =2

Now if we do f-1(x) or 1/f(x), then 1/f(1) = 1/1 +1 = 1/2

So, 2/1 is in fact the inverse of 1/2.

Hence, f-1(x) is the same as 1/f(x)

solve for x -2x + 2 = x -13

Answers

Answer:

x = 5

Step-by-step explanation:

Add 2x to both sides: 2 = 3x - 13

Add 13 to each side: 15 = 3x

Divide both sides by 3: 5 = x

Isolate with the variable by dividing each side by factors that don't contain the variable. So, x= 15

Determine which choice best shows the distributive property of multiplication.

Question 2 options:

1 × 6 = 6


6 × 9 = 9 × 6


6 × (9 + 8) = (6 × 9) + (6 × 8)


6 × (9 × 8) = (6 × 9) × 8

Answers

Answer:

c) 6× (9+8) = (6 × 9) + (6× 8)

Step-by-step explanation:

Distributive property of multiplication

The distributive property of multiplication

a(b+c) = a b + a c

(a+b)c = ac + bc

6× (9+8)  = (6× 9) + (6×8)

Evaluation 6ab when a = 1/2 and b = 7

Answers

Answer:

21

Step-by-step explanation:

6x1/2x7

6 x 1/2=3, 3 x 7=21

I hope this helps and have a nice day!

Please help don’t understand

Answers

Answer:

first you choose one of the varibles to solve for so im going to start with s you would add them up and subtract them that way there on the other side of the = sighs so you equation would be 8+2d+3=-7s then you add the 8 and the 3 and you would get 11+2d=-7s i dont know what you do after this i think this is the answer.

Answer:

the other guy is right trust him

Write an algebraic expression. The product of two numbers is 94, and one of the numbers is n. What is the other number?

Answers

Answer:

Let say the another number y

N×Y=94

Y=94/N

So the algebric expression is 94/N



A superball rebounds half the height it drops. A student drops the superball from the top of a building, 176 feet above the ground. How far
above the ground is the ball when it has traveled a distance of 500 feet?

Answers

Answer:

62.48 ft.

Step-by-step explanation:

Initial height: 50 ft.

First rebound: 10 ft.

Second rebound: 2 ft.

Third rebound: 0.4 ft.

Fourth rebound: 0.08 ft.

If we approximate the fourth rebound to zero, we'll have:

50 + 10 + 2 + 0.4 + 0.08 = 62.48 ft.

Recall the Spice Girls Emporium example. A list of useful information is given below. n = 36 The sample mean income is $41,100 The population standard deviation is estimated to be $4,500 What if we wanted to change our level of confidence to be 99%? What would our new margin of error be? Your answer should be given as an integer.

Answers

Answer: Margin of error = 1932

Step-by-step explanation: Margin of Error is the amount of variation a survey's results have. In other words, it is understood as the measure of variation one can see if the same survey was taken multiple times.

Margin of error is calculated as [tex]z\frac{\sigma}{\sqrt{n}}[/tex]

z is z-score related to the percentage of confidence, in this z = 2.576

σ is population standard deviation

n is how many individuals are there in the sample or population

With a new level of confidence of 99%:

ME = [tex]2.576.\frac{4500}{\sqrt{36}}[/tex]

ME = 2.576(750)

ME = 1932

The new margin of error would be 1932.

10. Find the rate of change in the table below.
Show all work.
х
18
20
22
24
y
4.5
5
5.5
6

Answers

Answer:

it's times 4 every time

Step-by-step explanation:

4.5 times 4 is 18 etc

What is the Percentage of 23000

Answers

Answer:

2300000%

Step-by-step explanation:

0.01 = 1%

1 = 100%

23000 X 100 = 2300000%

Hope It Helps

Find the vertex of the parabola defined by the following equation. 3x^2-12x+11

Answers

Answer:

y= 3(x-2)^2-1

Step-by-step explanation:

The Picture has the answers and the question.

Answers

Answer:

B

Step-by-step explanation:

PLEASE HELP I NEED HELP WITH AN ALGEBRA 2 QUESTION ILL GIVE BRAINLEST

Answers

Answer:

the zeros of the function are those that result, when plugged into the equation, in zero; the zeros are -3, 1, and 1/2

Step-by-step explanation:

all possible factors:

±3/2,  ±1/2,  ±3,  ±1

2x³ + 3x² - 8x + 3

let '2' = p and let '3' = q

factors of 'p' are 1 and 2

let '3' = q

factors of 'q' are 1 and 3

possible factors are q/p

PLEASE HELP ILL GIVE BRAINLIEST AND FOLLOW using y=mx+b form

Answers

Answer:

y=1+5

Step-by-step explanation:

b is the y intercept and 1 is the slope gradient

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