2. A high school wants to double the size of its parking lot by expanding the existing lot as
shown below. By what distance should the lot be expanded?
x ft
kin
75ft
old parking lot
165ft
school
300 Ft
75 ft xft
Answers
The parking lot is located along the front and one side of the school
building.
The distance x with which the lot should be expanded is 60 feet.Reasons:
The given dimensions in the compound are;
Length of the school and the old parking lot = 300 + 75
Width of the school and the old parking lot = 165 + 75
Length of the school, the old and new parking lot = 300 + 75 + x
Width of the school and the old and new parking lot = 165 + 75 + x
Area of the new parking lot the school wants = Double the old parking lot
In terms of areas, we have;
New compound - School = 2 × (old compound - school)
Which gives;
(300 + 75 + x) × (165 + 75 + x) - 300 × 165 = 2 × ((300 + 75) × (165 + 75) - 300 × 165)
2 × (375 × 240 - 49,500) = (375 + x) × (240 + x) - 49,500
Simplifying gives;
81,000 = x² + 615·x + 40,500
x² + 615·x + 40,500 - 81,000 = 0
x² + 615·x - 40,500 = 0
Factorizing with a graphing calculator gives;
(x - 60)·(x + 675) = 0
Therefore;
x = 60 or x = -675
Given that x is a natural number, we have, the correct value is; x = 60;
The distance with which the lot should be expanded, x = 60 feet.
Learn more about writing equations here:
https://brainly.com/question/20475360
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Related Questions
If Jenny can read 7 books in 8 days, exactly how many days would it take her to read 20 books?
Answers
Answer:
23 daysStep-by-step explanation:
Given,
No. of days taken by Jenny to read 7 books
= 8
So,
No. of days taken by her to read 1 book
[tex] = \frac{8}{7} [/tex]
Therefore,
No. of days taken by her to read 20 books
[tex] = \frac{8}{7} × 20 [/tex]
[On Simplification][tex] = \frac{160}{7} [/tex]
[On dividing]= 22.85.....
[On approximating]= 23 days (approx. )
Hence,
Jenny will take 23 days to read 20 books (Ans)
If Jenny can read 7 books in 8 days, exactly how many days would it take her to read 20 books?
Answer:-22.85714 or 23 days
Explanation:-[tex]GIVEN,[/tex]
Number of books Jenny can read in 8 days = 7
[tex]NOW,[/tex]
Number of days taken by Jenny to read 1 book = [tex] \frac{8}{7} [/tex]
Number of days taken by her to read 20 books =
→ [tex]20 \times \frac{8}{7} [/tex]
→ [tex] \frac{160}{7} [/tex]
→ 22.85714 or 23 days
Write the slope-intercept form of the equation with the given point and slope. Through (2,5) and m=1/2
Answers
Answer:
y=1/2x+4
Step-by-step explanation:
y-y1=m(x-x1)
y-5=1/2(x-2)
y=1/2x-2/2+5
y=1/2x-1+5
y=1/2x+4
Note that the slope-intercept form is y=mx+b where m=slope and b=y-intercept.
If you're satisfied with the answer, then please mark me as Brainliest. Thank you.
Can someone please help me with this question
Answers
m11=54°
m8=117°
m7=63°
Step-by-step explanation:
a) m2=m12 (corresponding angles)
m12=126°
180=m12+m11 (supplementary angles equal 180)
180=126+m11
m11=54°
b) m14=m8. (corresponding angles)
m8=117°
C) m7=180-m8 (supplementary angles equal 180)
m7=180-117
m7=63°
The population of a city, y, in thousands of people, measured x years after 1800 can be modeled by the regression equation
y = 187.6/1 + 29.4e^-0.03x
Which statement best interprets a value in the equation?
The city population in 1800 was 187,600 people.
The city population grows by 29,400 people per year.
The limiting value of the city population is 29,400 people.
The limiting value of the city population is 187,600 people.
Answers
Answer:
D. The limiting value of the city population is 187,600 people.
Step-by-step explanation:
I'm honestly not sure, but it's based on the 187.6 on top of the equation. Correct on Edge 2021
Name three equal ratios from the graph
Answers
250:10
125:5
100:4
Step-by-step explanation:
ratio of y to x
What is another way to write the calculation add 16 and 25, and then multiply by 47?
Answers
Answer:
(16+25)×47
Step-by-step explanation:
..........
(16+25)x47 , theree you go
It takes violet 3/5 hour to paint a chair. How much of the chair will be finished after 1/3 hour? Plz answer this plzzzzz!!
Answers
which multiplication can be used to explain the solution to 15 divided by one over 3
Answers
Answer:
3x5=15
5x3=15
Step-by-step explanation:
Solve for x when 4x+16/12=x-4
Answers
Answer:
In short, Your Answer would be either 1 or 7
Step-by-step explanation:
|4x + 12| = 16
As it is in modulus function, it could be either +ve or -ve
4x+12 = 16 OR 4x - 12 = 16
4x = 16-12 OR 4x = 16 + 12
4x = 4 OR 4x = 28
x = 4/4 OR x = 28/4
Write a multiplication equation that corresponds to each division equation.
10 divided by 5 =
4.5 divided by 3 =
3 ½ divided by 4
Answers
Answer:
1. 10/1×1/5
2.5/1×1/3
3.1/2×1/4
Step-by-step explanation:
to turn it into a multiplication problem, turn the second fraction into its reciprocal (flip the numerator and denominator )
If ABC is right-angled at B , AB = 3 cm. , BC = 4 cm. , then the length of the median from B is
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my Christmas present to you
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Answer:
THX santa
Step-by-step explanation:
An item is regularly priced at $70. It is on sale for 20% off the regular price. How much (in dollars) is discounted from the regular price?
Amount discounted:?
Answers
Answer:
$14 discount$56 discounted priceStep-by-step explanation:
The amount of the discount is ...
20% of $70 = 0.20·$70 = $14 . . . discount
The discounted amount is ...
$70 -14 = $56 . . . discounted price
you are going to wash a large glass window in a shape of a trapezoid. The lenghts of the bases of the window are 10 feet and 14 feet. the height is 8 feet. you can wash 6 square feet of the window in 1 minute. how long will it take you to wash the entire window
Answers
Answer:
16 minutes
Step-by-step explanation:
First we are going to want to find the area of the window. We then divide that by the amount of area you can wash per minute ( 6 square feet )
So first lets find the area.
We are told that the window is in a shape of a trapezoid.
The area of a trapezoid can be calculated using the formula A = [tex]\frac{a+b}{2} h[/tex]
Where a and b are the base lengths and h is the height
We are told that the length of the bases are 10 ft and 14ft so a and b = 10 and 14. We are also told that the window has a height of 8 so h = 8 .
We then plug these numbers into the formula to find the area
Recall formula: [tex]A=\frac{a+b}{2} h[/tex]
a = 10 , b = 14 and h = 8
plug in these values into formula
[tex]A=\frac{10+14}{2} 8[/tex]
add 10 and 14 to get 24
[tex]A=\frac{24}{2} 8[/tex]
simplify fraction : 24 / 2 = 12
[tex]A=(12)(8)[/tex]
multiply 12 and 8 to get 96.
A = 96 square feet.
To find how long it would take to wash the window we divide the total area of the window by the amount of area that can be washed per minute
Total area of window = 96
Area that can be washed per minute = 6
Time it would take to wash the whole window = 96 / 6 = 16 minutes
Graph: y = 3 * x + 5
Answers
Answer:
2
Step-by-step explanation:
take the 3 put on the side
convert 3 3/4 into a improper fraction
Answers
Answer:
3 3/4 = 15/4
Step-by-step explanation:
To turn a mixed number into an improper fraction, multiply the whole number with the denominator of the proper fraction. Add the numerator of the proper fraction to this product to obtain the numerator of the improper fraction.
Hoped this helped.
Someone plz help ToT
Answers
The scale factor is 1.5 because:
9 x 1.5 = 13.5
5 x 1.5 = 7.5
A truck is 2000 kg and has a cargo load of 1000 kg. Its speed is 50 km/h. The momentum for the truck and cargo is
Answers
Answer:
The momentum for the truck and cargo is 150000 kg·km/h
Step-by-step explanation:
p = mv
p = (2000 kg + 1000 kg)(50 km/h)
p = (3000 kg)(50 km/h)
p = 150000 kg·km/h
Leon has to drive 36 miles to work. If he can average a speed of 48 miles per hour, about how long does it take him to get to work each day? (Hint: Use the formula d = rt.)
1. a quarter of an hour
2. three-fourths of an hour
3. half an hour
4. more than an hour
Answers
Answer:
i think the answer is 45 mins sorry if im wrong
Read aloude The price of a cell phone was reduced from $450 to $225. By what percentage was the price of the cell phone reduced?
Answers
Answer:
50% 250x2=450
Step-by-step explanation:
Answer:
50%
Step-by-step explanation:
$225 x 2 = 450
this means the cell phones price was reduced by 50%
glad to help ;)
2) If it is 12° outside and the temperature is going to -7° drop 19º. What will the new temperature be?
Answers
Answer:
69 degrees
Step-by-step explanation:
yeah
HOPE I MADE YOU SMILE!!
Answers
Answer:
ok points
Step-by-step explanation:
Answer:
Thank You so much.....You made me smile lol :Dwhat is -150 + -12 =?
Answers
Answer:
-162
Step-by-step explanation:
Answer:
your answer is -162
Step-by-step explanation:
if you owe someone 150 dollars and then you owe them another 12 dollars you'll owe them a total of 162 dollars. Your losing 162 dollars which is -162 form the amount that you have
Foundations in Algebra: Probability Assignment
1. Andrew claims:
A spinner has 4 sections -
red, yellow, green, and blue.
The probability of getting the
red section is 0.25.
Is he correct? Explain your answer fully:
I
Answers
Answer:
yes a 1/4 probability is 0.25
How is the key event in this paragraph illustrated?
Answers
Question 6 of 12
✓ 49
A. 8
O O
B. 14
C. 7
SUBMIT
Answers
Answer:
C. 7
Step-by-step explanation:
7 · 7 = 49
I hope this helps!
Is it a expression 3x - 7
Answers
Answer:
It’s an expression.
Step-by-step explanation:
An expression is technically an equation but without the answer.
Answer:
yes
Step-by-step explanation:
The difference between an equation and an expression is that an equation as an equals sign. An equation shows that 2 expressions are equal to each other.
Expression:
[tex]3x-7[/tex]
Equation:
[tex]3x-7=5y[/tex]
Question 34, the answer is C. I just need the working. Tysm
Answers
Answer:
C
Step-by-step explanation:
∠ ABC = 90° ( angle in a semicircle )
Using the cosine ratio in right triangle ABC and the exact value
cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
cos30° = [tex]\frac{adjacent }{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{10}{AC}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
AC × [tex]\sqrt{3}[/tex] = 20 ( divide both sides by [tex]\sqrt{3}[/tex] )
AC = [tex]\frac{20}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] ( rationalising denominator )
AC = [tex]\frac{20\sqrt{3} }{3}[/tex]
radius AO = [tex]\frac{1}{2}[/tex] AC = [tex]\frac{1}{2}[/tex] × [tex]\frac{20\sqrt{3} }{3}[/tex] = [tex]\frac{10\sqrt{3} }{3}[/tex] → C
In a hypothetical economy, current inflation-adjusted economic output is rising and is expected to continue rising in the coming months. This economy is currently in the___
peak stage of the business cycle
trough stage of the business cycle
contraction stage of the business cycle
expansion stage of the business cycle
Answers
The economic output is rising and is expected to continue rising in the coming months, the economy is currently in the expansion stage of the business cycle.
The business cycle consists of the following stages which changes with time;
Expansion stage: continuous rise in economic output.Peak stage: maximum economic output.Contraction (recession) stage: a continuous decline in economic output.Trough stage: the point of lowest economic output.Thus, when the economic output is rising and is expected to continue rising in the coming months, the economy is currently in the expansion stage of the business cycle.
Learn more about business cycle here: https://brainly.com/question/904465
Factorise
3-x^2
Someone answer this question please
Answers
Answer:
No factors.
3 - x^2 is prime.
Step-by-step explanation: