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3 years ago

A rectangle has a length that is 9 feet less than four times its width. Its area is 90 square feet

Mathematics

1 answer:

kramer3 years ago

5 0

Answer:

The length of rectangle is $15\ ft$

The width of rectangle is $6\ ft$

Step-by-step explanation:

Let

x-----> the length of rectangle

y----> the width of rectangle

we know that

The area of rectangle is equal to

$A=xy$

$A=90\ ft^{2}$

$90=xy$ -----> equation A

$x=4y-9$ -----> equation B

substitute equation B in equation A and solve for y

$90=(4y-9)y$

$4y^{2}-9y-90=0$

using a graphing calculator

The solution is

$y=6\ ft$

Find the value of x

$x=4y-9$ -----> $x=4(6)-9=15\ ft$

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At the movie theater child admission is 6000 and $.30 an adult mission is $9.60 on Wednesday 172 tickets were sold for a total s

jasenka [17]

Answer:

The number of child tickets sold was 75 and the number of adult tickets sold was 97

Step-by-step explanation:

The correct question is

At the movie theater child admission is $6.30 an adult admission is $9.60 on Wednesday 172 tickets were sold for a total sales of $1403.70 How many child tickets and adult tickets were sold that day?

Let

x ----> number of child tickets sold

y ----> number of adult tickets sold

we know that

$x+y=172$ ----> equation A

$6.30x+9.60y=1,403.70$ -----> equation B

Solve the system by graphing

Remember that the solution of the system is the intersection point both lines

Using a graphing tool

The intersection point is (75,97)

see the attached figure

therefore

The number of child tickets sold was 75 and the number of adult tickets sold was 97

8 0

3 years ago

The sum of 2 times a number and 8 is 7

My name is Ann [436]

Answer:

The number is -1/2

Step-by-step explanation:

Let x be the number

2x+8 = 7

Subtract 8 from each side

2x+8-8 = 7-8

2x = -1

Divide each side by 2

2x/2 =-1/2

x = -1/2

The number is -1/2

8 0

3 years ago

Read 2 more answers

Suppose that a jewelry store tracked the amount of emeralds they sold each week to more accurately estimate how many emeralds to

RUDIKE [14]

Answer:

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And for this case the 95% confidence interval is given by (2.13; 2.37)

We have a point of estimate for the sample mean with this formula:

$\bar X = \frac{Upper+ Lower}{2}= \frac{3.37+2.13}{2}= 2.75$

And for the margin of error we have the following estimation:

$ME= \frac{Upper -Lower}{2}= \frac{3.37-2.13}{2}= 0.62$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And for this case the 95% confidence interval is given by (2.13; 2.37)

We have a point of estimate for the sample mean with this formula:

$\bar X = \frac{Upper+ Lower}{2}= \frac{3.37+2.13}{2}= 2.75$

And for the margin of error we have the following estimation:

$ME= \frac{Upper -Lower}{2}= \frac{3.37-2.13}{2}= 0.62$

5 0

3 years ago

A bag contains yellow marbles in red marbles 65 in total. The number of yellow marbles is five more than four times the number o

antoniya [11.8K]

Answer: there would be 52 yellow marbles

Step-by-step explanation:

Ok we know that there is 65 marbles in total? Right? So then we’d take 65 and think, what could we divide this by and start guessing and estimating numbers. (I guessed 5, one because it’s divisible by 65, two there is 5 times more yellow marbles than red marbles.) So 5 divided by 65 is 13. But, in order to find the amount of yellow marbles, we need to subtract the whole number by the amount of red marbles. (So 65-13 =?) if you subtract that you get 52 yellow marbles. :)

7 0

2 years ago

51^7 -51^6 by 25 __*25

BartSMP [9]

Answer:

Step-by-step:

51⁷-51⁶ = 51⁶(51-1) = 51⁶(50)

50 is divisible by 25, so 51⁷-51⁶ is divisible by 25.

7 0

3 years ago

Read 2 more answers