City officials are putting a garden around a memorial site as shown below.
Part A Determine the area of the memorial site in terms of x.
Write your answer as a trinomial and include units. Show or explain your work.
Part B The outside edges of the garden form a rectangle whose length and
width are proportional to the sides of the memorial site, increased
by a scale factor of 3. Determine the lengths of the outside edges of
the garden. Write your answer in simplest form.
Part C Determine the area of the garden in terms of x. Write your answer in
simplest form. Show or explain your work
Answers
Answer:
I only remember how to do part A, so sorry for using up an answer.
Step-by-step explanation:
Part A:
[tex](3x+5)(4x+7)\\ 12x^2+21x+20x+35\\ 12x^2+41x+35 ft^2[/tex]
(I also don't know if this is the form you need it in, but I hope I could help a little.)
The area of the memorial site is 12x² + 41x + 35 square units, the lengths of the outside edges of the garden are 12x + 21 units and 9x + 15 units and 108x²+369x+315 is the area of the garden in terms of x.
What is Area of Rectangle?The area of Rectangle is length times of width.
(a) The area of the memorial site is given by multiplying the length and width:
Area = (4x + 7)(3x + 5)
Expanding this expression using the distributive property, we get:
Area = 12x²+ 41x + 35
Therefore, the area of the memorial site is 12x² + 41x + 35 square units.
(b) The length and width of the garden are proportional to the length and width of the memorial site, increased by a scale factor of 3.
Length of garden = 3(4x + 7) = 12x + 21
Width of garden = 3(3x + 5) = 9x + 15
Therefore, the lengths of the outside edges of the garden are 12x + 21 units and 9x + 15 units.
(c) The area of the garden is given by multiplying the length and width:
Area of garden = (12x + 21)(9x + 15)
=108x²+180x+189x+315
=108x²+369x+315
Hence, the area of the memorial site is 12x² + 41x + 35 square units, the lengths of the outside edges of the garden are 12x + 21 units and 9x + 15 units and 108x²+369x+315 is the area of the garden in terms of x.
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Related Questions
Which plot correctly displays the data set with maximum of 48, a minimum of 27, a median of 36, an upper quartile of 45, and a lower quartile of 32?
Answers
Options :
A box-and-whisker plot. The number line goes from 25 to 50. The whiskers range from 27 to 48, and the box ranges from 32 to 45. A line divides the box at 36.
A box-and-whisker plot. The number line goes from 25 to 50. The whiskers range from 27 to 46, and the box ranges from 32 to 45. A line divides the box at 36.
A box-and-whisker plot. The number line goes from 25 to 50. The whiskers range from 27 to 48, and the box ranges from 31 to 39. A line divides the box at 36.
A box-and-whisker plot. The number line goes from 25 to 50. The whiskers range from 27 to 46, and the box ranges from 31 to 39. A line divides the box at 36.
Answer:
A box-and-whisker plot. The number line goes from 25 to 50. The whiskers range from 27 to 48, and the box ranges from 32 to 45. A line divides the box at 36.
Step-by-step explanation:
Given the five number summary which are all displayed on a box and whisker plot :
Maximum = 48
Minimum = 27
Median = 36
Upper Quartile = 45
Lower quartile = 32
Maximum and minimum values are displayed by the whiskers :
Starting point of whisker = minimum value
End point of whisker = maximum value
The quartiles are displayed by the box :
Starting point of the box = lower quartile
End point of the box = upper quartile
Line in between the box = Median
Neal purchases a digital camera for his
family to use on their vacatlart. The model he
purchases is on sale for $129. The sales tax
rate for his city iş 7.5%.
How much sales tax does Neal pay on the
digital camera?
Answers
Answer:
101.91
Step-by-step explanation:
Which fraction is equivalent to the fraction below?
18/24
Answers
Answer:
6/8 , 12/16 , 48/64
Step-by-step explanation:
In ΔNOP, the measure of ∠P=90°, the measure of ∠N=27°, and PN = 50 feet. Find the length of NO to the nearest tenth of a foot.
Answers
Answer:56.1
Step-by-step explanation:
Clicked see solution
Simplify the following question:
Answers
At a car dealership yesterday, the ratio of trucks sold to cars sold was 5.6. If the dealership sold 30 cars, how many trucks were sold?
Answers
Answer:
25
Step-by-step explanation:
ratio 5:6
[tex]\frac{5}{6} = \frac{x}{30}[/tex]
6x = 5(30)
6x = 150
x = 25
4
NEVAEH Last Saved: 11:16 AM
A vase in the shape of a cylinder has a radius of 4.3 centimeters and a volume of 1330.2 cubic centimeters, as
shown in the diagram.
What is the height of the vase in centimeters? Round your answer to the nearest tenth.
Answers
Answer:
h = 22.91 cm
Step-by-step explanation:
Given that,
The volume of a vase, A = 1330.2 cm³
Radius of the vase, r = 4.3 cm
We need to find the height of the vase. The formula for the volume of a cylinder is given by :
[tex]V=\pi r^2 h\\\\h=\dfrac{V}{\pi r^2}\\\\h=\dfrac{1330.2 }{3.14\times (4.3)^2}\\\\h=22.91\ cm[/tex]
or
h = 23 cm
So, the height of the vase is equal to 23 cm.
Remove the brackets using the distributive law for the following: 5(4x - 3y) - 4(4x - 3y)
Answers
Answer:
4x - 3yStep-by-step explanation:
5(4x - 3y) - 4(4x - 3y)
= 5 × 4x - 5 × 3y - 4 × 4x + 4 × 3y
= 20x - 15y - 16x + 12y
= 20x - 16x - 15y + 12y
= 4x - 3y (Ans)
Javier estimates the square root of 18 in the following way:
√18=2√9=2*3=6
A: Explain why her reasoning is incorrect.
B: Without using a calculator, the square root of 18 will be between what two values (remember to look for perfect squares/perfect square roots)? Show your reasoning. You do not need to find the decimal equivalent of the root.
Answers
Step-by-step explanation:
√18 = √(2x9) = 3√2. so they pulled the 2 out of the square root incorrectly.
4x4 = 16
5x5 = 25
so √18 is between 4 and 5. closer to 4
Simplify the expression.
1/2r – 2r + 6 – 3
Answers
Answer:
-3(r-2)/2
Step-by-step explanation:
r/ 2 − 2 r + 6 − 3
r /2 − 2 r⋅ 2/ 2+ 6 − 3
r/ 2 + − 2r ⋅ 2/ 2 + 6 − 3
r − 2 r ⋅ 2 /2 + 6 ⋅ 2/ 2 + − 3 ⋅ 2/ 2
r − 2 r ⋅2 + 6⋅ 2 − 3 ⋅ 2 /2
r − 4 r + 12 − 6 /2
−3 ( r − 2 ) /2
Hope that helps! Plz, mark brainiest! :D
Have a great day!
which set of side lengths will form a right triangle 8,15,17
7,24,26
6,8,11
10,24,25
Answers
1) 8^2+15^2=17^2
289=289 Yes
2) 7^2+24^2=26^2
625 ≠ 676 No
3) 6^2+8^2=11^2
100 ≠ 121 No
4) 10^2+24^2=25^2
676 ≠ 625 No
Therefor, 8,15,17 is your answer
14.5 divided bye 9 please
Answers
Answer:
1.61111111
Step-by-step explanation:
calculator
Answer:
1.6111111111.... or 1 11/18
Step-by-step explanation:
Well you just divide
14.5/9
Maly is going to throw a fair coin 70 times. Write down an estimate for the number of times the coin will land on head
Answers
Answer:
there are 2 sides for a coin
so divide 70/2 = 35
estimate for heads - 35
Step-by-step explanation:
HELP FAST!! IF RIGHT YOU WILL GET BRAINLIST! AND 5 STARS ⭐️
Solve for x.
x - 2(2 - 3/2x)= 2(4-x) + 10
A) -11/3
B) -3/11
C) 11/3
D) 3/11
Answers
Answer: The answer is C 11/3
Isolate the variable by dividing each sides by a factors that don't contain the variable.
ANSWER THIS PLEASE ASAP
Candice and Chris run a relay race at recess. Candice runs 3/3 of a lap
around the track. Chris runs 1/3 of a lap around the track. How much farther does Candice run than Chris?
Answers
Step-by-step explanation:
we know that
To find out how much further Candice runs than Chris, subtract the distance Chris runs from the distance Candice runs
so
The image of the point (2, -3) under a translation is (-1, 1). Find the coordinates of the image of the point (5, 6) under the same translation.
Answers
Answer:
the anser is b great job
Step-by-step explanation:
Find the area of the parallelogram
Answers
Answer:
18 x 16 = 288
Step-by-step explanation:
Formula of a parallelogram:
BH
(B x height) Your base times your height.
A recipe calls for 3 cups of sugar and 9 cups of water. How many cups of water should
be used with 2 cups of sugar?
3 cups
B
8 cups
4 cups
D
6 cups
ANZWER QUICK PlZZ
Answers
Answer:
Step-by-step explanation:
3/9 = 2/w
Cross multiply.
3w = 18
w = 6 cups
-7y-4 = 4y×(8-6)-64 answer fast
Answers
Answer: y=4
Step-by-step explanation:
-7y-4=8y-64
-7y-4+4=8y-64+4
-7y=8y-60
-7y-8y=8y-60-8y
-15y= -60
[tex]\frac{-15y}{-15}[/tex] =[tex]\frac{-60}{-15}[/tex]
y=4
Lashonda's penny bank is
7/10 full. After she removes 240 pennies, it is 1/2 full. How many pennies can Lashonda's bank hold?
Answers
In 2016, the number of Internet users in the Middle East was about 1×108, and in Australia, it was about 3×107. Approximately how many times larger was the number of Internet users in the Middle East than in Australia in 2016?
0.03 times
0.3 times
3 times
30 times
Answers
how much is a a $479.00 purchase with 7.5% sales tax
Answers
Answer:
$514.93
Step-by-step explanation:
Before Tax Price: $479.00
Sale Tax: 7.50% or $35.93
After Tax Price: $514.93
Could someone please give the answer to this question.?
Answers
Answer:
25
Step-by-step explanation:
v^2 - 10v + __ : what number when added to itself gives you -10 ? -5
what's -5 x -5 ? 25
(v-5)^2 is a perfect square
Suppose the population of a town is 17,400 and is growing 2% each year.
Predict the population after 9 years.
Answers
Answer: 20,532
Step-by-step explanation:
17,400(.02)=348
348(9)=3132
17,400+3132=20,532
Answer:
Step-by-step explanation:
This is an exponential growth function of the form:
[tex]y=ab^x[/tex] where a is the initial population and b is the growth rate. This could also be written as
[tex]y=a(1+r)^x[/tex] which is a bit more accurate. We'll use that one. r is the percent growth: 2% for us.
Filling in the formula:
[tex]y=17400(1+.02)^x[/tex] and then simplifying:
[tex]y=17400(1.02)^x[/tex]
That's the model for this population. Filling in any number of years for x will give you the population y. Our time is 9 years:
[tex]y=17400(1.02)^9[/tex]
Take care of the exponents first, giving us:
[tex]y=17400(1.195092569)[/tex] and then multiply to get
y = 20,794.6 or 20,794 people (since you can't have 6/10 of a person)
Two observers are standing on shore ½ mile apart at points A and B and measure the angle to a sailboat at a point C at the same time. Angle A is 63° and angle B is 56°. Find the distance from each observer to the sailboat. Round to the nearest hundredth of a mile.
Answers
Answer:
Step-by-step explanation:
The length 0.51 miles and 0.47 miles are the distances from each observer to the sailboat.
What is the Sine Rule?The Law of Sines (also called the Sine Rule) is defined as it relates all three sides of a triangle with an angle of a triangle.
Triangle is a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry.
As per the given question, the given data as:
A = 63
B = 56
C = 61 (because these angles should add up to 180)
c = 1/2
We know that the Sine Rule,
sin 63 / a = sin 61 / .5
a = 0.51 miles
sin 56 / b = sin 61 / .5
b = 0.47 miles
Therefore, the length 0.51 miles and 0.47 miles are the distances from each observer to the sailboat.
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A swimming pool manager is making a schedule for his lifeguards next Monday. The pool policy states that there must be 2 lifeguards on duty for a pool attendance of up to 20, 3 lifeguards on duty for an attendance of 21-50, 4 lifeguards on duty for an attendance of 51-75, and 5 lifeguards on duty for an attendance of 76-100. Based on last Monday's pool attendance shown in the graph, how many lifeguards should be scheduled at 2:00?
A. 4 lifeguards
B. 5 lifeguards
C. 3 lifeguards
D. 2 lifeguards
Answers
Answer: A.4
Step-by-step explanation:
Here is some more
Find the value of x: 3x−7=8x+23
Answers
Answer: x=6
Step-by-step explanation:
Answer:
x = -6
Step-by-step explanation:
Subtract 3x from both sides to get -7=5x+23.
Subtract 23 from both sides to get -30=5x.
Divide 5 from both sides.
x = -6.
Help please thank you:) QUICKLY!!!!!!!!!
Answers
Answer:
y = -8
Step-by-step explanation:
2x2 - 12
4 - 12 = -8
hope this helps
Which one would it be
Answers
Answer:
A or [tex]\frac{\sqrt{6} }{2}[/tex]
Step-by-step explanation:
*note- this method only works because the denominator values are being multiplied, if they were being added then there are extra steps to keep in mind but for now this is simple*
Start by dividing the root 12 in the numerator by the root 2 in the denominator
[tex]\frac{\sqrt{12} }{\sqrt{2} }=\sqrt{6}[/tex]
Then we simply substitute back in the 2 (from the denominator) that we ignored for a second to get our answer
[tex]\frac{\sqrt{6} }{2}[/tex]
*note- if you are allowed to use a calculator then you could also plug in your values to check each answer option but since this question isn't too complicated there should be no need to do so unless you forget how to solve it algebraically*
For her science fair project, Emily
conducted an experiment to investigate
the effects of watering on tomato plants.
She varied the amount of water given to
the plants and measured each plant's
height after two weeks. Emily
hypothesized that the more water she
added, the taller her tomato plants would
be.
1. Was Emily's hypothesis correct? Explain
your answer.
2. According to Emily's data, what is the
optimal weekly amount of water for
tomato plant growth? Explain your answer.
Answers
Answer:1 yes it is correct because the more water you give a plant the helter it is
2 about 2 times a day
Step-by-step explanation: