A rectangle can be defined as a 4 sided geometric figure. One side of a rectangle is longer than the other sides. A rectangle can also be referred to as a quadrilateral.
The dimensions of the background are given as Width: 8 feet and the Length: 18 feet
The formula for the area of a rectangle is Length x Width.
The question says:
The owners want the length to be 10 feet more than its width. Hence:
L = W + 10
The area of the fenced backyard = 144 square feet.
Hence,
(W + 10) x W = 144
W² + 10W = 144
Rewriting the equation
W² + 10W - 144 = 0
We factorize the algebraic expression above
W² - 8W + 18W - 144 = 0
W(W - 8) + 18(W - 8) = 0
(W - 8) (W + 18) = 0
W - 8 = 0, W = 8
W + 18 = 0, W = -18
Since the width cannot be a negative value, the width of the backyard is 8 feet
Solving for the Length,
L = W + 10
L = 8 + 10
L = 18 feet
The length of the backyard is 18 feet.
Therefore, the dimensions of the backyard are Width: 8 feet and Length: 18 feet.
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A clothing business finds there is a linear relationship between the number of shirts, n ,it can sell and the price, p , it can charge per shirt. In particular, historical data shows that 1000 shirts can be sold at a price of $66, while 10000 shirts can be sold at a price of $48. Give a linear equation in the form p
Answer: p = [tex]\frac{-n}{500} +68[/tex]
Step-by-step explanation:
Let n represent the number of shirts and p represent the price, the there is a linear relationship between n and p, then the model equation is given as:
p = mn + b, where
m = slope and b is the intercept
From the question, when n = 1000, p = $66
And, when n = 10,000 , p = $48
The formula for finding slope is given as:
m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
[tex]y_{1} = 66[/tex]
[tex]y_{2} = 48[/tex]
[tex]x_{1} = 1000[/tex]
[tex]x_{2} = 10000[/tex]
substituting the values,
m = [tex]\frac{48-66}{10000-1000}[/tex]
m = [tex]\frac{-18}{9000}[/tex]
m = [tex]\frac{-2}{1000}[/tex]
m = [tex]\frac{-1}{500}[/tex]
The linear equation thus becomes
p = [tex]\frac{-n}{500}+b[/tex]
To find the value of b, substitute p = 66 and n =1000 into the equation
That is,
66 = [tex]\frac{-1000}{500}+b[/tex]
66 = -2 + b
68 = b
Therefore b = 68
The linear equation is therefore
p = [tex]\frac{-n}{500} +68[/tex]
1/5 divided by 2/3 help meee loll
Answer:
3/10 or 0.3
Hope this helps
the awnser is 0.3 .......................
The ratio of men to women working for a company is 4 to 5. If there are 110 women working for the company, what is the total number of employees?
Answer:
198
Step-by-step explanation:
?/4 110/5
cross-multiply 4*110
440
divide 440/5
88 men
add total employees
110 women + 88 men = 198
20.7 rounded off to the nearest tens place
Answer:
20
Step-by-step explanation:
help me with this please
Answer: 65
Step-by-step explanation:
Item 1
What is the slope of the line on the graph?
WORTH 20 POINTS
Enter your answer in the box.
Answer:
-2
Step-by-step explanation:
Hope it helps
george is building a fence at a consent rate of 1/3 section of fence every 1/2 hour at the rate. what fraction represents the section iof fence george can build per hour
Find the upper quartile for the data. {9, 6, 13, 8, 8, 10, 9.5, 8, 7.5, 8.5}
A. 9
B. 9.5
C. 10
D. 8.5
Answer:
the answer is 9.5 (B)
Step-by-step explanation:
Classify the quotient as positive, negative, or zero - 25 ÷ - 5
Answer:
-25÷-5= 5 The quotent is positive.
Step-by-step explanation:
positive+positive=positive
negative+negative= positive
positive+negative=negative
negative+positive=negative
Which statement correctly compares the shapes of the distributions?
Team A's scores
58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100
Team B's scores
58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 998 100
O A. Team A's scores are symmetric, and team B's are negativ
skewed.
O B. Team A's scores are symmetric, and team B's are positively
skewed.
O C. Team A's scores are negatively skewed, and team B's are
symmetric.
D. Team A's scores are positively skewed, and team B's are
The statement that compares the distribution shapes is (C) Team A's scores are negatively skewed, and team B's are symmetric.
How to interpret the distribution shapes?From the complete question (see attachment for box plots), we have the following highlights:
Team A scores has more points at the left. This represents a negative skewTeam B scores has more points at the center. This represents a symmetric skewnessHence, the statement that compares the distribution shapes is (C) Team A's scores are negatively skewed, and team B's are symmetric.
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Find the EQUATION of the line through (-10,-12) and (-15,3). Use the form y=mx+b.
At town has a population of 17000 and grows at 4% every year. What will be the population after 12 years, to the nearest whole number?
Answer:
25,160
Step-by-step explanation:
17,000 x 0.04 = 680
Town gains 680 people every year.
After 12 years, town will have 25,160 people.
This could also be wrong because it may be 4%+ the added people from the previous number. However, I think it is 25,160.
Calculate the surface area of the three-dimensional objects below.
Solve For x for the remaining problems. You MUST show your work.
Answer:
x = 6
Step-by-step explanation:
All angles of a triangle equal 180
180 - 70 - 60 = 50
8x+2 = 50
x = 6
Answer:
x = 6
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 given angles and equate to 180
70 + 60 + 8x + 2 = 180 , collect like terms
132 + 8x = 180 ( subtract 132 from both sides )
8x = 48 ( divide both sides by 8 )
x = 6
3over 7 = blank over 35
Let blank be x
[tex]\\ \sf\longmapsto \dfrac{3}{7}=\dfrac{x}{35}[/tex]
[tex]\\ \sf\longmapsto 7x=35(3)=105[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{105}{7}[/tex]
[tex]\\ \sf\longmapsto x=15[/tex]
May I please receive help?
Please???
Answer:
m1 is 25 and m2 is 50
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
x+2x=75
Write a unit rate for each situation . 20$ saved in 4 weeks
Answer:
so the answer is 5
Step-by-step explanation:
20/4=5
I WILL GIVE YOU BRAINYIST IF YOU ANSWER THIS FOR ME
Answer:
A
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Can someone help me with number 8 :(
Answer:
a1=5
d=9-5=4
a20=5+19×4=81
pls help ASAPPPP11!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
It's between 0 and 1
Step-by-step explanation:
1/64 = 0.015625
Is 12 × –1 positive or negative? positive negative Submit
Answer:
it's a negative number. the answer would be
Step-by-step explanation:
-12
The perimeter of a triangle is 65 cm. The
lengths of the sides are x cm, x+8 cm, and
X+ 12 cm.
What is the length, in cm, of the longest side of
the triangle?
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The longest side measures :
[tex]27\: \: cm[/tex][tex] \large \boxed{ \mathfrak{Explanation}}[/tex]
Perimeter of a triangle is equal to sum of measures of its all three sides, that is :
[tex]x + x + 8 + x + 12[/tex]and according to the question, the perimeter of the triangle is = 65 cm
so, let's equate both the expressions to find value of x :
[tex]x + x + 8 + x + 12 = 65[/tex][tex]3x + 20 = 65[/tex][tex]3x = 65 - 20[/tex][tex]3x = 45[/tex][tex]x = 45 \div 3[/tex][tex]x = 15[/tex]The longest side of the Triangle is :
[tex]x + 12[/tex][tex]15 + 12[/tex][tex]27 \: \: cm[/tex]27cm
Step-by-step explanation:
(xcm) + (x+8cm) + ( x+ 12cm) = 65cm
Open Bracket
xcm + x+8cm + x+12cm = 65cm
3x+ 20cm = 65cm
Collect like terms
3x = 65cm - 20cm
3x = 45cm
Divide both sides by 3
3x/3 = 45cm/3
x = 15cm
The longest side of the triangle =( x+12cm)
= (15+12)cm= 27cm
hi pls help me thanksss
pls provide me with workings thankss :)
Step-by-step explanation:
(i)
Using cos(a - b) = cos a cos b + sin a sin b
[tex]\frac{4}{5}[/tex] = cos a cos b + [tex]\frac{1}{5}[/tex]
cos a cos b = [tex]\frac{4}{5} -\frac{1}{5} = \frac{3}{5}[/tex]
(ii)
Using cos(a + b) = cos a cos b - sin a sin b
cos(a + b) = [tex]\frac{3}{5}-\frac{1}{5}=\frac{2}{5}[/tex]
(iii)
Using cot a = [tex]\frac{cos a}{sin a}[/tex]
[tex]=(\frac{cos A}{sin A} )(\frac{cos B}{sin B} )[/tex]
[tex]=\frac{cos A cos B}{sin A sin B}[/tex]
[tex]=\frac{\frac{3}{5} }{\frac{1}{5} }[/tex] [tex]=\frac{3}{5}[/tex] × [tex]5[/tex]
= 3
please give me a brainliest answer
To find out how fast a tree grows, you can measure its trunk. A giant red oak's diameter was 248 inches in 1965. The tree's diameter had grown to 251 inches in 2005. Find the average rate of change in the diameter of the tree per year.
CLEAR CHECK
1313 inches per year
-0.075 inch per year
0.075 inch per year
3 inches per year
I think it's 0.075 inch per year
Answer:
Your answer is C. or 0.075 inches per year.
Step-by-step explanation:
251-248 = 3 ( To figure out how much it grew )
2005 -1965 = 40 ( To figure out how long it took )
3/40 = 0.075
8z + 6 = 7z + 4
I need help with it please show the steps
Can someone plsss help me with the 2 one
Answer: [tex]\sqrt{73}[/tex] for number 7
Step-by-step explanation:
a²+b²=c²
3²+8²=c²
9+64=c²
[tex]\sqrt{73}=\sqrt{c^2}\\\sqrt{73}=c[/tex]
plz help answer the following questions
PLEASE HELP!!
(04.03)
Given the function g(x) = 5(2)^x, compare the average rate of change from x = 1 to x = 2 and from x = 3 to x = 4.
How many times greater is the average rate of change from x=3 to x=4 than from x=1 to x=2?
О 4 times
O 5 times
O 2 times
O The average rate of change of Section B is not greater than the average rate of change of Section A.
Answer: Choice A. 4 times
========================================================
Explanation:
We'll be using this formula
[tex]m = \frac{f(b)-f(a)}{b-a}[/tex]
to compute the average rate of change (AROC) from x = a to x = b. Note how this is effectively the slope formula because y = f(x).
To start things off, we'll compute the AROC from x = 1 to x = 2.
[tex]m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(2)-g(1)}{2-1}\\\\m = \frac{5(2)^2-5(2)^1}{2-1}\\\\m = \frac{10}{1}\\\\m = 10\\\\[/tex]
Do the same for the AROC from x = 3 to x = 4.
[tex]m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(4)-g(3)}{4-3}\\\\m = \frac{5(2)^4-5(2)^3}{4-3}\\\\m = \frac{40}{1}\\\\m = 40\\\\[/tex]
The jump from m = 10 to m = 40 is "times 4", which is why choice A is the final answer.
A 144-inch board is cut into two pieces. One piece is five times the length of the other. Find the length of the shorter piece.
The shorter piece is inches long.
Answer:
shorter piece is 28.8 inches
Step-by-step explanation:
Answer28.8
Step-by-step explanation:
28.8 x 5 = 144
Someone help me I will mark you as brain
Answer:
- 1
Step-by-step explanation:
-3 (-3) -10
9 - 10 = -1