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
Serga [27]
3 years ago
5

A rectangular piece of plywood has a diagonal that measures three times the width. The length of the plywood is three feet more

than the width. What is the length of the plywood’s diagonal?
Mathematics
1 answer:
Karolina [17]3 years ago
3 0

Answer:

The length of diagonal is 4.922 feet.

Step-by-step explanation:

Let the width be = w

Let the diagonal be = d

Let the length be = l

Given is that the diagonal measures three times the width, this gives: d=3w

Also given is the length of the plywood is three feet more than the width. This is : l=x+3

Now, in terms of x we get:

Width = x

Length = (x+3)

Length of Diagonal = 3x

Now applying Pythagorean Theorem

a^{2}+b^{2}=c^{2}

x^{2}+(x+3)^{2}=(3x)^{2}

x^{2}+x^{2}+6x+9=9x^{2}

Solving this we get,

-7x^{2}+6x+9=0

We will use quadratic formula to solve this and get the answer,

x = 3/7 +/- (12√2) / -14

x = 1.64075 or x = -0.783612(neglect this negative value)

So, x = 1.64075 feet

Now length of diagonal is 3x = 3*1.64075 = 4.922 feet

So, length of diagonal is 4.922 feet.

You might be interested in
Which of the following statements best describes the graph of −5x + 2y = 1?
Nina [5.8K]

First, we determine that the given equation in this item is a linear equation. Thus, it should be a straight line. With this, we are left with the third and fourth choice. Then, we substitute the given data points to the equation and see if the points satisfy the given.

Choice 3:

<span>            (1,3)   :    (-5)(1) + (2)(3) = 1   TRUE</span>

<span>            (3,8)   :    (-5)(3) + 2(8) = 1      TRUE</span>

<span>            (-3,-7) :    (-5)(-3) + (2)(-7) = 1 TRUE</span>

 

Choice 4:

<span>            (4,-3)  :  (-5)(4) + (2)(-3) ≠ 1     FALSE</span>

<span>            (-1,2)   : (-5)(-1) + (2)(2) ≠ 1     FALSE</span>

<span>            (-4,5)   : (-5)(-4) + (2)(5) ≠ 1    FALSE</span>

 

<span>Thus, the answer is the third choice.</span>

5 0
3 years ago
Read 2 more answers
State the property or properties illustrated by the statement.<br><br> 5.<br> 23 + = 23
Ksju [112]

Answer:

23 + 0

Step-by-step explanation:

calculator

3 0
3 years ago
What are the solutions of the system? {y=2x+6y=x2+5x+6 ​(−3, 0)​ and (−2, 0) (0, −3) and (6, 0) (−3, 0) and (0, 6) ​(0, 6)​ and
SSSSS [86.1K]
<span>(−3, 0) and (0, 6)

Each of these work in both equations</span>
3 0
3 years ago
Read 2 more answers
For a fair coin, suppose you toss the coin 100 times.
Natasha_Volkova [10]

Using the normal distribution, it is found that there is a 0.0005 = 0.05% probability of getting more than 66 heads.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

Z = \frac{X - \mu}{\sigma}

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
  • The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with \mu = np, \sigma = \sqrt{np(1-p)}.

For the binomial distribution, the parameters are given as follows:

n = 100, p = 0.5.

Hence the mean and the standard deviation of the approximation are given as follows:

  • \mu = np = 100(0.5) = 50.
  • \sigma = \sqrt{np(1-p)} = \sqrt{100(0.5)(0.5)} = 5

Using continuity correction, the probability of getting more than 66 heads is P(X > 66 + 0.5) = P(X > 66.5), which is <u>one subtracted by the p-value of Z when X = 66.5</u>.

Z = \frac{X - \mu}{\sigma}

Z = \frac{66.5 - 50}{5}

Z = 3.3

Z = 3.3 has a p-value of 0.9995.

1 - 0.9995 = 0.0005.

0.0005 = 0.05%

More can be learned about the normal distribution at brainly.com/question/4079902

#SPJ1

6 0
2 years ago
A regular octagon with one side 6 In.
Gwar [14]
The perimeter is 48 inches if that's what you need to know...
5 0
3 years ago
Read 2 more answers
Other questions:
  • What is n+ -741 = -542 and the explaination? Thanks!
    6·2 answers
  • Find the difference. 7 7/8 - 3 1/4 ?
    11·2 answers
  • Can someone help me out ASAP and possible step by step
    11·1 answer
  • A recipe calls for 2 1/2 cups of flour to make 2 dozen cookies. how many cups of flour would be required to bake 15 dozen cookie
    8·1 answer
  • True or False
    14·1 answer
  • What does it mean to solve an equation?
    12·1 answer
  • A rancher wishes to enclose a rectangular pasture with 320 feet of fencing. the fencing will be used on three sides of the pastu
    12·1 answer
  • Zoom bomb this let's go get on at 12:45
    12·2 answers
  • Please help due tomorrow!
    6·1 answer
  • PLEASE HELP, i have no clue what to do and it has to be quick please :)
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!