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konstantin123 [22]
3 years ago
5

The width of a rectangle is 3ft less than the length. The perimeter is 62ft. Find the length and width of the rectangle.

Mathematics
1 answer:
Assoli18 [71]3 years ago
8 0
I believe the length of the rectangle is 17 ft and the width is 14
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MATH HELP!!! 100PTS!!!
Lostsunrise [7]

Answer:

x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}

Step-by-step explanation:

<u>Given functions</u>:

  p(x)=2x-4

  r(x)=\dfrac{6x-1}{9x+1}

Solve for p(x) = r(x):

\begin{aligned}p(x) & = r(x)\\\implies 2x-4 & = \dfrac{6x-1}{9x+1}\\(2x-4)(9x+1)&=6x-1\\18x^2+2x-36x-4&=6x-1\\18x^2-40x-3&=0\end{aligned}

As the found quadratic equation cannot be factored, use the Quadratic Formula to solve for x:

<u>Quadratic Formula</u>

x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0

Therefore:

a=18, \quad b=-40, \quad c=-3

Substitute the values of a, b and c into the <u>quadratic formula</u> and solve for x:

\begin{aligned}\implies x & =\dfrac{-(-40) \pm \sqrt{(-40)^2-4(18)(-3)} }{2(18)}\\\\& =\dfrac{40 \pm \sqrt{1816}}{36}\\\\& =\dfrac{40 \pm \sqrt{4 \cdot 454}}{36}\\\\& =\dfrac{40 \pm \sqrt{4}\sqrt{454}}{36}\\\\& =\dfrac{40 \pm2\sqrt{454}}{36}\\\\& =\dfrac{20 \pm\sqrt{454}}{18}\end{aligned}

Therefore, the solutions are:

x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}

Learn more about quadratic equations here:

brainly.com/question/27750885

brainly.com/question/27739892

6 0
1 year ago
Anita is a door-to-door saleswoman for a company selling bedcovers. The company pays her a fixed salary of Rs W every month and
lorasvet [3.4K]

Given:

Anita's fixed salary = Rs. W

Bonus = Rs. Z for every bedcover sold by her.

To find:

Her total earnings if she sold 46 bedcovers.

Solution:

We have,

Bonus if she sold 1 bedcover = Rs. Z

Bonus if she sold 46 bedcover = Rs. Z × 46

We know that,

Total earnings = Fixed salary + Bonus

                        = W+Z\times 46

Therefore, the correct option is (b).

3 0
3 years ago
A rectangle with an area of 8 ft² is dilated by a factor of 4. What is the area of the dilated rectangle?
prohojiy [21]

Answer:

Option 4) 128\ ft^{2}

Step-by-step explanation:

we know that

If two figures are similar then the ratio of its areas is equal to the scale factor squared

Let

z------> the scale factor

x-----> the area of the dilated rectangle

y----> the area of the original rectangle

so

z^{2}=\frac{x}{y}

we have

z=4

y=8\ ft^{2}

substitute and solve for x

4^{2}=\frac{x}{8}

x=16(8)=128\ ft^{2}

4 0
3 years ago
Read 2 more answers
What is the equation of the trend line? <br><br> K = __ J + __
alexandr402 [8]

Answer:

-2 and 24

Step-by-step explanation:

the trend line is linear,

let the unknowns be A and B

hence the equation becomes

K = AJ + B

from the graph we can see the following:

when J = 0, K = 24 (substitute this into the equation)

K = AJ + B

24 = A(0) + B

24 =  B  (Answer)

Also notice that when K = 0, J = 12

together with our previous finding that B = 24, the equation becomes:

K = AJ + B

0 = A(12) + 24

12A = -24

A = -24 / 12

A = -2  (answer)

6 0
3 years ago
A research group is curious about their city’s participation in flu shot clinics. They suspect that there is a difference betwee
Kipish [7]

Answer:

t=\frac{(162-156)-0}{\sqrt{\frac{41^2}{22}+\frac{36^2}{20}}}}=0.505  

p_v =2*P(t_{40}>0.505)=0.61633  

Comparing the p value with the significance level \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, then the difference between the two groups is NOT significantly different.  

Step-by-step explanation:

Data given and notation

\bar X_{1}=162 represent the mean for sample of clinic attendees

\bar X_{2}=156 represent the mean for the sister city  

s_{1}=41 represent the sample standard deviation for 1  

s_{2}=36 represent the sample standard deviation for 2  

n_{1}=22 sample size for the group 2  

n_{2}=20 sample size for the group 2  

\alpha=0.05 Significance level provided

t would represent the statistic (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the difference in the population means, the system of hypothesis would be:  

Null hypothesis:\mu_{1}-\mu_{2}=0  

Alternative hypothesis:\mu_{1} - \mu_{2}\neq 0  

We don't have the population standard deviation's, so for this case is better apply a t test to compare means, and the statistic is given by:  

t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}} (1)  

And the degrees of freedom are given by df=n_1 +n_2 -2=22+20-2=40  

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.  

With the info given we can replace in formula (1) like this:  

t=\frac{(162-156)-0}{\sqrt{\frac{41^2}{22}+\frac{36^2}{20}}}}=0.505  

P value  

Since is a bilateral test the p value would be:  

p_v =2*P(t_{40}>0.505)=0.61633  

Comparing the p value with the significance level \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, then the difference between the two groups is NOT significantly different.  

3 0
3 years ago
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