21. You place a mat around a 25 in by 21 inch painting as shown. The mat
is twice as wide at the left and right of the painting as it is at the top an
bottom of the painting. The area of the mat is 714 square iinches (note:
the area of the border). How wide is the mat at the left and right of the
painting? At the top and bottom of the painting? (P.264 #66)
Answers
Using a quadratic equation according to the area of the rectangular mat, it is found that:
At the top and bottom of the painting, the width is 0.654 inches.At the left and right of the painting, the width is of 1.308 inches.The area of a rectangle of length l and width w is given by:
[tex]A = lw[/tex]
In this problem:
The length of the figure is of [tex]l = 25 + 4x[/tex].The width of the figure is of [tex]w = 21 + 2x[/tex].Area of 714 square inches, thus:[tex]lw = 714[/tex]
[tex](25 + 4x)(21 + 2x) = 714[/tex]
[tex]8x^2 + 134x + 525 = 714[/tex]
[tex]8x^2 + 134x - 189 = 0[/tex]
Which is a quadratic equation with [tex]a = 8, b = 134, c = -189[/tex].
The, to find the widths of the mat, we have to first find the value of x, solving the quadratic equation.
[tex]\Delta = 134^2 - 4(8)(-189) = 24004 [/tex]
[tex]x_{1} = \frac{-134 + \sqrt{24004}}{2(8)} = 0.654[/tex]
[tex]x_{2} = \frac{-134 - \sqrt{24004}}{2(8)} = -9.03[/tex]
We are interest in the positive value of x, so x = 0.654.
At the top and bottom of the painting, the width is of 0.654 inches.[tex]2(0.654) = 1.308[/tex]
At the left and right of the painting, the width is of 1.308 inches.A similar problem is given at https://brainly.com/question/14099239
Related Questions
Person 2 worked for 200 minutes and checked 1,325 comments every 5 minutes
Answers
Answer: 33.125
Step-by-step explanation:
So you would do 200 divdied by 5 which is 40 then you would do 1,325 divided by 40 which is the anwser 33.125. If you did it another way let me know.
HELP!! ASAP
A graphic designer makes a sketch for an image that will appear on a poster. The width of the sketch is 14 in. She figures that it should be enlarged to 220% to make the final image. How wide will the final image be?
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Answer:
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Step-by-step explanation:
what is 5.6 less than 25.3
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Answer:
19.7
Step-by-step explanation:
6. a + 6 < -2; a = -8
I
0. yes
P. no
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Answer:
yes
Step-by-step explanation:
Which of the following expressions is equivalent to 24/8 ·6/3 · 3?
-7 · 6/3 · 3
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-28/24/9
-7 ·6/9
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Answer:
I think second one is the ans
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Answers
Answer:
(3×1)+(4/10) & two and fifty-one hundredths
Step-by-step explanation:
In order to write a decimal in expanded form you need to create a equation that equals the decimal you are trying to expand, and for writing decimal in word form you need to remember the names of place values.
1. 3.4
[tex]3.4=(3\times`1)+(\frac{4}{10} )[/tex]
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two and fifty-one hundredths
Hope this helps.
If f(1) = 160 and
f(n)=1/2f(n-1) what is f(5)?
Answers
Answer:
10
Step-by-step explanation:
[tex]f(n) = \frac{160}{ {2}^{(n - 1)} } [/tex]
Answer:
This is 10
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A phone company offers two monthly plans. Plan A costs $10 plus an additional $0.12 for each minute of calls. Plan B costs $15 plus an additional $0.10 for
each minute of calls.
For what amount of calling do the two plans cost the
Same?
Answers
Answer:
250 minutes
Step-by-step explanation:
10 + 0.12x = 15 + 0.10x
0.02x + 10 = 15
0.02x = 5
x = 250
Your welcome!
Kayden Kohl
8th Grade Student
Write a three digit number that gives same answer when rounded to the nearest ten and to the nearest hundred .explain
Answers
Answer:
Numbers can be rounded to the nearest ten, the nearest hundred, the nearest thousand, the nearest million, and so on. All the numbers to the right of the place you are rounding to become zeros. Rounded numbers are easier to remember and easier to use.
An election is over and a new student body president has been elected. The new president received 3 votes for every vote received by his opponent. The new president received 2193 votes. How many votes did his opponent receive?
Answers
can someone plz help me with this
Answers
Answer:
option D .....11
Option c 36
A 4-quart jug of juice costs $4.48. What is the price per cup?
Answers
Answer:
28 cents.
Step-by-step explanation:
There are 4 cups in 1 quart. So, 4 quarts is 16 cups.
If 4 quarts costs $4.48, to find the price per cup, you need to divide $4.48 by 16.
4.48 ÷ 16 = 0.28
This means each cup is 28 cents.
I hope this helps! :)
Step-by-step explanation:
you devide 4.48by 16 and your answer is 0.28
NEED HELP FOR REAL 69 points!!!!!!!!!!!!!! ASAP
The physicist from the last problem lets the particle fall another 100 times, and finds that the average travel time is now 16 sec. Remember that when running the simulation many times it took 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. What does she conclude and why?
Answers
What is the fourth term of an arithmetic sequence whose first term is 23 and whose seventh term is 5?
A) 78
B) 32
C) 14
(Explain your work)
Answers
We have that the fourth term of an arithmetic sequence is
a_4=14
Option C
From the question we are told
What is the fourth term of an arithmetic sequence whose first term is 23 and whose seventh term is 5?
A) 78
B) 32
C) 14
(Explain your work)
Generally the equation for the arithmetic sequence is mathematically given as
[tex]a_4=a_1+(n-1)d[/tex]
Therefore
For seventh term
[tex]5=23+(6)d\\\\d=5-23/(6)\\\\d=-3[/tex]
Therefore
For Fourth term
[tex]a_4=23+(3*(-3))[/tex]
a_4=14
For more information on this visit
https://brainly.com/question/23366835
AAA help I need to do this for schoosleldkdk
Answers
Answer:
[tex] \frac{1}{8} [/tex]
Step-by-step explanation:
The total amount of cards is 8, and the stack have 4 even numbers, so the probability is
4/8 Simplify it and
1/2
Now, there are just 6 cars bigger than 6, so:
2/8. Simplify it
1/4
Now you have to multiply the two values:
1/2×1/4 = 1/8
If 5 pieces of steel bar each 6 1/2" long are welded together, how long will the new
bar be?
Answers
6.5 x 5= 32.5
17 - (-25) =
I need help
Answers
Negatives cancel each other
=17+25
Answer is 42
Answer:
42
Step-by-step explanation:
rewrite by changing subtraction sign to addition and the following number to opposite
- always involves two sign changes
have a good day
what does n equal in 4n − 2n = 4
Answers
Answer:
Step-by-step explanation:
4 = 2
Martina runs 3 miles in 25 minutes. At the same rate, how many miles would she run in 20 minutes?
Answers
Answer:
2 and a half mile
Step-by-step explanation:
As she runs three miles in 25 minutes so she can run 2 and a half miles in 20 minutes because she needs five minutes to complete the third mile
this helps!
Alyssa purchased 3 pounds of peanuts for $8.25. Write an equation that shows the relationship between the cost and the number of pounds purchased
Answers
Answer:$8.25 ÷ 3= x or 3·x =8.25
Step-by-step explanation:
3*x=8.25
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Answers
Answer:
I can't really see it so i don't know I'm sorry
Answer:
15
Step-by-step explanation:
find the value of a square + b square when a+b = 6 a_b = 4
Answers
Answer:
a+b=6
a-b =4
______subtract
(a-a)+(b-(-b))=6-4
0+2b = 2
b= 1
put the value of b at any equation
a+1 =6
then a=6-1=5
a square+b square= 25+1= 26
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It takes Shonda of an hour to dry one load of laundry in her dryer. How many hours will it take her to dry 4 loads of laundry?
A. 1/5
B. 1 3/5
C. 3 1/5
D. 4/5
Answers
No of hours
[tex]\\ \sf\longmapsto 4(1)[/tex]
[tex]\\ \sf\longmapsto 4 hours[/tex]
None of the above
Martha Stewart has developed a new perfume. She decides to test its side effects by spraying the perfume in 31 randomly chosen houses. She records the level of antigens that create an allergic response. If the antigen level is high enough, the person will go into anaphylactic shock. The mean of her sample is a lot bigger than the median, but Martha hopes that a 90% confidence interval will contain zero. Her confidence interval is (0.116, 1.884). Disappointed, she offers you $144 to find an acceptable, realistic way to change the confidence interval to contain zero. What could you say to earn the money
Answers
The acceptable and realistic ways to to change the confidence interval to contain zero are;
Martha should decrease x-bar by providing medicine to treat shock to the perfume users.Decrease sample size than 30Increase the confidence level, till the interval contains zeroReasons:
The confidence interval is given by the following formula;
[tex]CI=\bar{x}\pm t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex]
When the mean, [tex]\overline x[/tex], is positive and large, both values, [tex]\bar{x}+ t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex], and [tex]\bar{x} -t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex], will be positive.
Therefore, Martha has to either intervene to reduce the mean also known as x-bar
Increasing the confidence level will increase the allowable error such that [tex]\bar{x} < t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex], and the interval will contain zero
Therefore;
Martha should decrease x-bar, [tex]\overline x[/tex], by providing medicine to treat shock to the perfume usersUse a much smaller sample size, n, such that [tex]t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}} > \bar{x}[/tex]Increase the confidence level to 95% or 99%, thereby increasing the error boundLearn more here:
https://brainly.com/question/13034570
No links just answer
Simplify
Answers
Answer:
first option _32\21 is the answer
Step-by-step explanation:
the answer will
-32/21
I'm indian just came in Canada
indians are very intelligent in maths
Mr. Cruz bought 9 3/5 kg of meat. He used 2 3/5 kg for adobo, 4 3/5 kg for menudo and the rest for afritada. How many kilograms of meat did he use for afritada?
Answers
Answer:
Loading,please wait...
Step-by-step explanation:
9% out of 432 kids want to be lawyers. How many kids did not want to be lawyers?
Answers
Answer:
393.12 kids. This is technically impossible, as you can't have 0.12 of a kid, so I will round down to 393 kids.
Step-by-step explanation:
9% = 0.09
x = amount of kids who want to be lawyers
y = amount of kids who do not want to be lawyers
x = 0.09(432)
x = 38.88
y = 432 - 38.88
y = 393.12
Click this if you are a savage
Answers
Answer:
i am
Step-by-step explanation:
pro!
uhfy1gujhqfvwtfu
2x - 7= -11
What’s the answer?!?!?
Answers
Answer:
×=9
Step-by-step explanation:
2× - 7=11
2× - 7+7=11+7
3 Select the correct answer from each drop-down menu. The boundary of a park is shaped like a circle. The park has a rectangular playground in the center and 2 square flower beds, one on each side of the playground. The length of the playground island its width is w. The length of each side of the flower beds is a Which two equivalent expressions represent the total fencing material required to surround the playground and flower beds. Assume that the playground and beds do not overlap The total fending material required to fence the playground and both flower beds is
Answers
Answer:
Get the perimeter of the each shape and add it all up to get the total fencing material required. 2 square flower beds = 2 x 4a = 8a 1 rectangular play ground = 2l + 2w total fencing material = 8a + 2l + 2w
Answer:
2l + 2w + 8a
Step-by-step explanation: