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
FinnZ [79.3K]
3 years ago
11

the length of a rectangle is 8cm more than the width and its area is 172cm2 .find the width of the rectabgle

Mathematics
1 answer:
nikdorinn [45]3 years ago
4 0
l-the\ length\\l+8-the\ width\\A=172\ cm^2\\\\A=lengtf\cdot width\\\\subtitute\\\\l(l+8)=172\\\\l^2+8l=172\ \ \ |subtract\ 172\ from\ both\ sides\\\\l^2+8l-172=0\\a=1;\ b=8;\ c=-172\\\\\Delta=b^2-4ac\\\\\Delta=8^2-4\cdot1\cdot(-172)=64+688=752 > 0\\\\l_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ l_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{752}=\sqrt{16\cdot47}=4\sqrt{47}\\\\l_1=\dfrac{-8-4\sqrt{47}}{2\cdot1}=-4-2\sqrt{47} < 0\\\\l_2=\dfrac{-8+4\sqrt{47}}{2\cdot1}=-4+2\sqrt{47} > 0\\\\The\ width:l+8=-4+2\sqrt{47}+8=4+2\sqrt{47}\\\\Answer:\boxed{length=(2\sqrt{47}-4)cm;\ width=(4+2\sqrt{47})cm}
length\approx9.71cm;\ width\approx17.71cm
You might be interested in
A group of retired admirals, generals, and other senior military leaders, recently published a report, "Too Fat to Fight". The r
weqwewe [10]

Answer:

z=\frac{0.694 -0.75}{\sqrt{\frac{0.75(1-0.75)}{180}}}=-1.735  

p_v =P(z  

If we compare the p value obtained and the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of americans between 17 to 24 that not qualify for the military is significantly less than 0.75 or 75% .  

Step-by-step explanation:

1) Data given and notation  

n=180 represent the random sample taken  

X=125 represent the number of americans between 17 to 24 that not qualify for the military

\hat p=\frac{125}{180}=0.694 estimated proportion of americans between 17 to 24 that not qualify for the military

p_o=0.75 is the value that we want to test  

\alpha=0.05 represent the significance level  

Confidence=95% or 0.95  

z would represent the statistic (variable of interest)  

p_v represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that less than 75% of Americans between the ages of 17 to 24 do not qualify for the military :  

Null hypothesis: p\geq 0.75  

Alternative hypothesis:p < 0.75  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.  

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.694 -0.75}{\sqrt{\frac{0.75(1-0.75)}{180}}}=-1.735  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.05. The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

p_v =P(z  

If we compare the p value obtained and the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of americans between 17 to 24 that not qualify for the military is significantly less than 0.75 or 75% .  

6 0
3 years ago
What is the solution of the equation below?<br> x² - 4= - 5
madam [21]

Answer:

Not possible to work out

Step-by-step explanation:

NO Explanation can be explained as this question cannot be solved

8 0
2 years ago
Please explain thank you
mixas84 [53]
Okjhgfdfghjjhgfdfghjhgfdfghjsdfghjkhgfdsfghjrhrthrthtj
6 0
2 years ago
Identify each sequence as arithmetic or geometric. Explain your answer, and write an explicit formula for the
NeX [460]

Answer:

Geometric Sequence

Step-by-step explanation:

In this case it is Geometric Sequence as it has a common ratio of 5

Formula for nth term: a(n) = ar∧n-1

so if we take the third term we will calculate as follows:

50 = 2(r)∧3-1

50÷2 = r∧2

√25= r

r=5

7 0
3 years ago
12k + 26 factor completely<br><br>pls help ​
Liula [17]

Answer:

2\left(6k+13\right)

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • There is a ​$40 fee to rent a chain​ saw, plus ​$9 per day. Let x represent the number of days the saw is rented and y represent
    14·1 answer
  • How many applications of integration by parts are required to evaluate integral (x^7)(e^x) dx?
    14·1 answer
  • I need help completing the two-column proof.
    8·2 answers
  • What is the volume of this cylinder?
    10·1 answer
  • Determine the measure of angle BZC.
    15·1 answer
  • HELP For each triangle, find x and the measure of each side.
    12·1 answer
  • There are 10 boys and 10 girls. What is the probability that 2 boys will be chosen
    11·2 answers
  • Please help! I'll mark your answer as brainiest if right &lt;3
    13·2 answers
  • Can i get the answer to this?
    10·1 answer
  • What is the equation in point slope form of the line that passes through the point ( 2 , -4 ) and has a slope of 4?
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!