The width of the mat around the photo is 3 inches
The combined area of the of the photo and math = 224 square inches
The combined area is represented as:
(2w +8)(2w + 10) = 224
Expand the equation using the distributive rule
[tex]4w^2+20w+16w+80=224\\\\4w^2+36w+80-224=0\\\\4w^2+36w-144=0[/tex]
Divide through by 4
[tex]w^2+9w-36=0[/tex]
Factorize the resulting quadratic equation to solve for w
[tex]w^2-3w+12w-36=0\\\\w(w-3)+12(w-3)=0\\\\(w-3)(w+12)=0[/tex]
w - 3 = 0
w = 3
w + 12 = 0
w = -12
The width of the mat around the photo is 3 inches
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The width of the mat around the photo is 3 inches
Combined area:
2w +8)(2w + 10) = 224
where,
w = width of the mat around the photo
(2w +8)(2w + 10) = 224
open parenthesis
4w² + 20w + 16w + 80 = 224
4w² + 36w + 80 - 224 = 0
4w² + 36w - 144 = 0
divide through by 4
w² + 9w - 36 = 0
solve quadratic equation using factorization method
w² + 12w - 3w - 36 = 0
w(w + 12) - 3(w + 12) = 0
(w + 12) (w - 3) = 0
w + 12 = 0 or w - 3 = 0
w = -12 or w = 3
The width of the mat around the photo cannot be a negative value.
Therefore, the width of the mat around the photo is 3 inches
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I need help solving this problem
Please hurry!! This assignment is almost due thank you!!
Answer:
x = 33
Step-by-step explanation:
(x-17)°+(5x-1)°=180°
6x-18 = 180
6x = 198
x = 33
need this soon please
Answer: pretty sure -7
Step-by-step explanation:
Answer:
-7
Step-by-step explanation:
(-80) - (-10) is -79
-70 / (+10) = -7
Oceanside Bike Rental Shop charges 13 dollars plus 8 dollars an hour for renting a bike. Tim paid 45 dollars to rent a bike. How many hours did he pay to have the bike checked out?
Step-by-step explanation:
Shop charges =13
Many left for renting bike = 45-13 =$32
If renting for 1hr cost $8
then renting for X Hrs will cost $32
1/X =8/32 cross multiplying
8X= 32
X= 32÷8= 4hrs
How can you solve multistep equations that represent real world
scenarios?
Please help me!! I don't understand
No linksssss
Answer:
thanks haahhahahaha
Step-by-step explanation:
Emily reads a story book. o the first day, she reads 1/9 of the whole book, and on the second day, she reads 24 pages. The ratio of the number of pages read to the remaining pages in the two days is 1:4. How many pages are there in this book
Answer:
Step-by-step explanation:
Let P be the number of pages
First day reads P/9 pages
Second day reads 24 pages
two days reading is P/5 (1 page read for every 4 pages left)
P/9 + 24 = P/5
P + 24(9) = 9P/5
5P + 24(9)(5) = 9P
1080 = 4P
P = 270 pages
There are 270 pages in this book.
Given that,
Emily reads a storybook the first day,
She reads 1/9 of the whole book, and on the second day, she reads 24 pages.
The ratio of the number of pages read to the remaining pages in the two days is 1:4.
We have to find
How many pages are there in this book?
According to the question,
Let, P is the number of pages,
The first day Emily reads p/9 pages of the whole book,
And the second day she read 24 pages.
The ratio of the number of pages read to the remaining pages in the two days = 1;4 = p/5.
Therefore,
The number of pages reads first day + the number of pages read the second day = The ratio of the number of pages read to the remaining pages in the two days
[tex]\rm \dfrac{p}{9} + 24 = \dfrac{p}{5}\\\\ \dfrac{p}{5} - \dfrac{p}{9} = 24\\\\\dfrac{p \times 9 - p\times 5}{45} = 24\\\\ \dfrac{9p-5p}{45} = 24\\\\\dfrac{4p}{45} = 24\\\\4p = 24\times 45\\\\4p = 1080\\\\p = \dfrac{1080}{4}\\\\p = 270 \ pages[/tex]
Hence, there are 270 pages in this book.
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The angle of depression from a window 10 m above the ground to a coin on the ground is 15°. Find the distance of the coin from the base of the building. Show your reasoning for each step.
Solve this plz question plz
We have: [tex](-\frac{15}{18})[/tex] ÷ [tex](-\frac{20}{24})[/tex] = [tex]\frac{-15}{18} .\frac{-24}{20} = \frac{(-3)(5).(-4)(6)}{(3)(6).(4)(5)} = 1[/tex]
ANSWER: 1
ok done. Thank to me :>
Answer:
1
Step-by-step explanation:
[tex]( - \frac{15}{18} ) \div ( - \frac{20}{24} ) \\ now \: you \: have \: fraction \: divided \: by \: fraction \: then \: do \: reciprocal \: \\ ( - \frac{15}{18} ) \times ( - \frac{24}{20} ) \\ = 1[/tex]
order the expression from least to greatest
Answer:
So it would be 4, 11, 20
Step-by-step explanation:
[tex]11^1 = 11[/tex]
[tex]2^2 * 5 = 20[/tex]
[tex]8^2-60 =4[/tex]
One hundred voters were asked whether they supported a bill that had
The question is cut off.
⦁ Simplify: –3|–2| + 4|–5|
show work
Answer:
-3|-2|+4|-5|=14Step-by-step explanation:
3| -2 =6
4| -5| =20
= -6+20
Simplify -
14
Thank You! I hope I could make your day just a little bit better!
There are two types of packages that are available for hotel stay
- you can use the hotel unlimited for $500 a month
- Or you can spend $50 a day per visit.
Enter an equation that can be used to find the number of visits per month needed for the two packages to cost the same amount
Answer:
for one month 500$
for daily visit 50$
500$=50$*x days
x days=500$/50$
x days = 10 days
10 days of daily visits costs 500$ equal to one month
what is 12 3/4 divided by 3
Answer:
4.25 as decimal and 4 1/4 as a fraction
Step-by-step explanation:
what is the value of x that makes the equation 8 x -4 equal 96 true
Answer:
x= 12.5 or 25/2
Step-by-step explanation:
8x - 4 (+4) = 96 (+4)
8x (/8) = 100 (/8)
x= 12.5 or 25/2
PLEASE HELP!!!! Identify the mistake and use the correct answer to the problem!!!
Answer:
1 [tex]\frac{3}{8}[/tex]
Step-by-step explanation:
the denominators must be the same so, since 4 goes evenly into 24 we can create an equivalent fraction from 3/4 to 18/24 (multiply numerator and denominator by 6)
now you can add:
[tex]\frac{15}{24}[/tex] + [tex]\frac{18}{24}[/tex] = [tex]\frac{(15+18)}{24}[/tex] = [tex]\frac{33}{24}[/tex]
since the numerator is larger than the denominator this is called an improper fraction and can be changed into a mixed number by dividing 24 into 33
24 goes into 33 one time with a remainder of 9
so 33/24 = 1 [tex]\frac{9}{24}[/tex] wherein 9 and 24 can each have a 3 factored out to make it fully simplified
9÷3 = 3
24÷3 = 8
final answer is 1 [tex]\frac{3}{8}[/tex]
Answer:
11/8 is the correct answer
Step-by-step explanation:
15/24 + 3/4
Reduce the fraction 15/24 to lowest terms by extracting and canceling out 3.
=5/8 +3/4
Least common multiple of 8 and 4 is 8. Convert 5/8 and 3/4 to fractions with denominator 8.
= 5/8 + 6/8
since 5/8 and 6/8 have the same denominator, add them by adding their numerators.
= 5 + 6/8
Add 5 and 6 to get 11.
=11/8
here is why 9/14 is wrong
A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below.
81 71 202 113 269 248 242
Find the median number of newspapers sold.
CE
O A. 242 newspapers
OB 175 newspapers
OC. 113 newspapers
OD. 202 newspapers
OD Step-by-step explanation:
The median of the of the number of newspapers sold by shopkeeper is 202 .
Given,
A store manager kept track of the number of newspapers sold each week over a seven-week period.
81 71 202 113 269 248 242.
Now,
The median of the dataset is the middle value of the dataset, which means that 50 % of the values are below the mean and 50% of the values are above the mean.
Rearrange the dataset in ascending order as
71, 81, 113, 202, 242, 248, 269.
Thus the median will be the 4th value.
Hence the median will be 202.
Thus the correct option will be 202 Newspapers.
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What is the length of LN in the right triangle below?
Answer:
D 280
Step-by-step explanation:
Pythagoras theorem
Answer:
a
Step-by-step explanation:
LN=√19^2 - 9^2
=√361 - 81
=√280
If the sum of six consecutive even integers is 438, what is the smallest of the six integers?
Given ω=[tex]\frac{3-2i}{5-6i}[/tex] , find ω in the a+bi form.
Answer:
Solution is given in the photo
The radius of the circle shown below is 8 centimeters. What is the
approximate length of XY?
115
A. 50.3 cm
B. 16.1 cm
C. 8.0 cm
D. 64.2 cm
A square is a quadrilateral with four equal sides and four 90 degree angles. Is quadrilateral ABCD a square?
Answer: yes
Step-by-step explanation:
Can someone help me with these 2 geometry questions?? Will mark brainiest :)
Answer:
Thats to hard Do it your self
please need help with this Calculus question
simplify [tex]y^{-3}[/tex]
Solve the equation square root of x-2+5 = 7 for the variable. Show each step of your solution process
Answer:
x=4
Step-by-step explanation:
x+3=7
subtract 3 from both sides
simplify
George is building a rabbit run in his backyard he makes the length 2/7km and the width 1/5km draw a sketch of his rabbit run and then find the area
Here !
I hope this helps you a little ,
One advantage of a variable interest rate over a fixed interest rate is that a
variable rate:
A. is often lower initially
B. offers borrowers more flexible terms.
c. can be used for large purchases.
D. increases when the market rate increases
The term variable implies that the rate is bound to change over time, in this context variable interest rate may double as an Advantage and also as a disadvantage.
D. increases when the market rate increases
Variable interest rate is advantageous because as the market rate increases, the rate at which the customer will receive his/her interest will increase too
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Answer: a
Step-by-step explanation:
shirt original price is $100 and is now 50% off what is the discount price now
Answer:
$50.00 is the discount price
Find the slope
(3,5) and (6,9)
Answer:
4/3 or 1 1/3
Step-by-step explanation:
To find slope, we subtract the y-values (9 - 5), then divide the difference we find from that by the difference of the x-values (6 - 3). So, let's go ahead and do that now. First, what's 9 - 5? Well, the answer is 4. Next, we have to divide this value by 6 - 3, which is equivalent to 3. Then, we divide the two numbers - what is 4 ÷ 3? Well, we can represent this as 4/3, or 1 1/3. Hopefully that's helpful - if you have any questions on that, let me know! :)
Answer:
Slope is 4/3
Step-by-step explanation:
Slope or gradient can be found by using several formulas. For this situation, we can use rate of changes between two points also known as rise over run or changes in y over change so in x.
The formula of slope between two points can be expressed as several equations, expressions, etc such as:
[tex]\displaystyle \large{m=\frac{dy}{dx}=\frac{y_2-y_1}{x_2-x_1} =\frac{\Delta y}{\Delta x}[/tex] where m is a variable representing the slope.
Since we are given two points, we are going to use the y2-y1 over x2-x1 formula.
Let (3,5) be (x1,y1,) and (6,9) be (x2,y2) thus the slope is [tex]\displaystyle \large{m=\frac{y_2-y_1}{x_2-x_1} =\frac{9-5}{6-3} =\frac{4}{3}[/tex]
Therefore the slope of two points is 4/3.
__________________
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