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3 years ago

The area of a rectangle is 135 square feet. The width is 6 feet less than the length. Find the dimensions of the rectangle

Mathematics

1 answer:

drek231 [11]3 years ago

7 0

The length is 15 inches and width is 9 inches

Step-by-step explanation:

Let

l be the length

and

w be the width

w = l-6

The area of rectangle is 135 ft^2

The formula for area is:

$Area=l*w\\135=l*(l-6)\\135=l^2-6l\\l^2-6l-135=0\\l^2+9l-15l-135=0\\l(l+9)-15(l+9)=0\\(l+9)(l-15)=0\\l+9 = 0 => l=-9\\l-15 = 0 => l=15\\$

As the length cannot be negative, so we will use the value of length 15

If length 15,

w=l-6

w=15-6

w=9

So,

The length is 15 inches and width is 9 inches

Keywords: Area of rectangle, Quadratic equation

Learn more about quadratic equation at:

#LearnwithBrainly

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2. Create an estimated probability distribution for the time teens spend texting.

Furkat [3]

Answer:

Hours 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Frequency* 0.2 0.09 0.25 0.18 0.11 0.07 0.05 0.02 0.01 0.02 0.01

Problem Statement:

The table shows the number of hours, to the nearest half hour per day, that teens spend texting according to a random sample of 870 teenagers aged 13–18 in a large urban city.

Hours 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Frequency 170 82 220 153 92 58 40 15 12 18 10

Step-By-Step Explanation:

As we need the estimated probability distribution for teens spending time texting, we will be needing the total sample size.

As given in the problem statement,

Total Sample Size = 870

To calculate estimated probability distribution, we will convert the frequency sample into estimated probability distribution, for that:

Estimated Probability Distribution (Frequency*)= $\frac{Frequency.Sample.Size.of.that.hour}{Total.Sample.Size}$

For Example:

Estimated probability distribution that teens spend 0 hours texting= $\frac{170}{870} =0.20$

Similarly

Estimated probability distribution that teens spend 0.5 hours= $\frac{82}{870} =0.09$

Using the same formula we get:

Hours 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Frequency* 0.2 0.09 0.25 0.18 0.11 0.07 0.05 0.02 0.01 0.02 0.01

(Note: Frequency* is the estimated probability distribution)

4 0

3 years ago

Read 2 more answers

Two car rental companies charge an initial rental fee plus a fee per day. The table shows the total costs of renting a car for x

Fynjy0 [20]

Answer:

a) Which rental company charges less per day?

Payless rental company

b) How many days must you rent a car for the total costs to be the same?

3 days.

Step-by-step explanation:

We have car rental companies

Discount car rentals and Pay less car rentals.

x = number of days

y = Total cost.

a) Let's assume the starting day of renting a car is 2 days

We need to determine the Equation for discount rentals.

For Discount car rentals

2 days = $185

4 days = $265

6 days = $345

8 days = $425

The difference between 2 days = $265 - $185 = $80

If the difference between 2 days = $80

Difference between 1 day = $80/2

= $40

If you rent a car for 1 day,

185 - 40 =$145

Hence, the Equation for payment for Discount rentals =

y = 40x + 105

b) For Pay less car rentals

This equation was given: y = 55x + 60.

y = Total cost, x = number of days

a) 1 day

y = 55(1) + 60

y = $115

b) 2 days

y = 55(2) + 60

y = 110 + 60

y = $170

c) 3 days

y = 55(3) + 60

= 165 + 60

= $225

d)For 4 days

y = 55x + 60.

y = 55 × 4 + 60

y = 220 + 60

y = $280

e) For 5 days

y = 55x + 60.

y = 55 × 5 + 60

y = 275 + 60

y = $335

f) For 6 days

y = 55x + 60.

y = 55 × 6 + 60

y = 330 + 60

y = $380

g) For 7 days

y = 55x + 60.

y = 55 × 7 + 60

y = 385 + 60

y = $445

h) For 8 days

y = 55x + 60.

y = 55 × 8 + 60

y = 440 + 60

y = $500

a) Which rental company charges less per day?

The total coast for renting a car as determined in the above calculation

For 1 day in Discount car rentals = $145

For 1 day in Payless car rentals = $115

From the above calculation, it is Payless rental company

b) How many days must you rent a car for the total costs to be the same?

We equate both equations to each other

y = 40x + 105 = y = 55x + 60.

40x + 105 = 55x + 60

105 - 60 = 55x - 40x

45 = 15x

x = 45/15

x = 3 days.

Therefore, after 3 days, the total cost of renting a car from Discount car rentals or Payless car rentals is the same.

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3 years ago

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madreJ [45]

Answer: 5
So the triangle KNL is an equilateral triangle meaning all angles are the same. If all angles are the same, all the lengths are the same.
If KL is 4, then NL is 4.
Since NL is 4, the opposite side LM is 4 because it is an isosceles triangle.
X - 1 = 4
X = 5

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ivolga24 [154]

it is at least 180 degrees

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Helppppp! What do the factors in (-7x + 60)(x + 4) represent ??

geniusboy [140]

Answer:

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