1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Kryger [21]
3 years ago
8

A rectangle has a length of 34 inches less than 5 times it’s width. If the area of the rectangle is 867 square inches, find the

length of the rectangle.
Mathematics
1 answer:
pshichka [43]3 years ago
5 0

Length of the rectangle is 51 inches

<u>Solution:</u>

Given that

Length of the rectangle in 34 miles less than 5 times its width

Area of rectangle = 867 square inches

Need to determine length of the rectangle.

Let assume width of the rectangle be represented by variable x.

So 5 times width of the rectangle =5x

34 inches less than 5 times width of the rectangle = 5x – 34

As Length of the rectangle in 34 miles less than 5 times its width

=> Length of the rectangle = 5x – 34

<em><u>The formula for rectangle is given as:</u></em>

\text { area of rectangle }=length \times width

As given that Area of rectangle = 867 square inches

\begin{array}{l}{=>867=(5 x-34) \times(x)} \\\\ {=>5 x^{2}-34 x-867=0}\end{array}

On solving quadratic equation by using quadratic formula

x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}

In our case a = 5, b = -34 and c = -867

On substituting value of a, b and c in quadratic formula we get

\begin{array}{l}{x=\frac{-(-34) \pm \sqrt{(-34)^{2}-4 \times 5 \times(-867)}}{2 \times 5}} \\\\ {=>x=\frac{34 \pm \sqrt{18496}}{10}=\frac{34+136}{10}} \\\\ {=>x=\frac{34+136}{10}=17 \text { or } x=\frac{34-136}{10}=-10.2}\end{array}

Since x represents width, it cannot be negative, so x = 17

Length of the rectangle = 5x – 34 = 5(17) – 34 = 51

Hence length of the rectangle is 51 inches

You might be interested in
A contractor purchases 4 dozen pairs of padded work gloves for ​$56.16. She incorrectly calculates the unit price as ​$14.04 per
8090 [49]

Answer:

The correct unit price is $1.17 per pair of gloves. The error is she used number of dozens so, firstly convert it to number of pairs of gloves then divide.

Step-by-step explanation:

It is given 4 dozen pairs of gloves for $56.16.

So, unit price = Divide the price by number of pairs of gloves.

And 1 dozen =12

So 4 dozen =4*12=48 pairs of gloves

So, to find unit rate divide 56.16  by 48.

Unit price =\frac{56.16}{48}= $1.17

So, the error is she didn't convert the dozen to units.

That made mistake in finding unit price.

6 0
3 years ago
5. Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately norma
Triss [41]

Answer:

percent (%) of ancient prehistoric thinner than 3 is 0.0013

Step-by-step explanation:

Given data

mean =  5.1 millimeters (mm)

standard deviation = 0.7 mm

to find out

percent (%) of ancient prehistoric thinner than 3

solution

we have given mean and SD

so Z will be = x -mean  / SD

Z = ( x - 5.1 ) / 0.7

so P( x < 3 ) = P ( (x - 5.1 ) / 0.7  <  ( 3 - 5.1 ) / 0.7 )

P( Z  = ( 3 - 5.1 ) / 1.5 )

P( Z  =  -3 ) = 0.0013

percent (%) of ancient prehistoric thinner than 3 is 0.0013

4 0
3 years ago
Ryan and Khalil each have their own savings. Together, they borrowed $72 from a friend to buy a gift for their coach. Each has t
Amanda [17]
I believe that your answer is A.
4 0
3 years ago
Read 2 more answers
Pls help me !! will mark brainliest... i just need you to solve for m&lt;1 and m&lt;7 !! thanks !!
frez [133]

Step-by-step explanation:

=( n-2)180

= ( 4 - 2 )180

= 360

So, 144 + 90 + m<2 +m<1 = 360

144 + 90 + 85 + m<1 = 360

319 + m<1 = 360

m<1 = 360 - 319

m<1 = 41

their is an unknown angle so let's call it x

let's find x first ( m<6=49)

x + m<6 = 180

x + 49 = 180

x = 180 - 49

x = 131

Now let's find m<7

m<7 + 38 + m<4 + x = 360

m<7 + 38 + 85 + 131 = 360

m<7 + 254 = 360

m<7 = 360 - 254

m< 7 = 106

8 0
3 years ago
N-78+_=37_N= WHAT IS N?
Lesechka [4]
115 is n that’s the answer
5 0
3 years ago
Other questions:
  • Sari has 3 times as many pencil erasers as Sam. Together, they have 28 erasers. How many erasers does Sari have?
    11·2 answers
  • the remains of an ancient ball court include a rectangular playing alley with a perimeter of about 64 M. the length of the alley
    12·1 answer
  • PLEASE HELP ASAP !! UPVOTING What is the direct linear variation equation for the relationship?
    12·1 answer
  • Rocky simplified an expression in three steps, as shown:
    14·2 answers
  • What is the simplified form of -24m^5 n^4/ 8m^-7 n^-2
    14·1 answer
  • What is the distance between the points (-3, 9) and (5, 1)? Round to the
    6·1 answer
  • A rectangle has a perimeter of 35.8 inches and a base of 12.6 inches. What is the height?
    5·2 answers
  • Help me plzzzzz I will give you branliest
    11·1 answer
  • A vet is preparing a diet for a group of dogs. Each serving should be no larger than 8
    10·1 answer
  • Solve the system using the linear combination method:<br> x + 5y= -3<br> 2x + 7y=3
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!