Answer:
[tex]Area = 129.5m^2[/tex]
[tex]Perimeter = 48m[/tex]
Step-by-step explanation:
Given
See attachment
Required
Determine the area and the perimeter of the garden
Calculating Area
First, we calculate the [tex]area\ of\ the\ rectangle[/tex]
[tex]A_1 = L * B[/tex]
Where:
[tex]L = 20-(3.5 +3.5)[/tex]
[tex]B = 7[/tex]
So:
[tex]A_1 = (20 - (3.5 + 3.5)) * 7[/tex]
[tex]A_1 = (20 - 7) * 7[/tex]
[tex]A_1 = 13 * 7[/tex]
[tex]A_1 = 91[/tex]
Next, we calculate the area of the two semi-circles.
Two semi-circles = One Circle
So:
[tex]A_2 = \pi r^2[/tex]
Where
[tex]r = \frac{7}{2}[/tex]
[tex]A_2 = \frac{22}{7} * (\frac{7}{2})^2[/tex]
[tex]A_2 = \frac{22}{7} * \frac{49}{4}[/tex]
[tex]A_2 = \frac{22}{1} * \frac{7}{4}[/tex]
[tex]A_2 = \frac{22*7}{4}[/tex]
[tex]A_2 = \frac{154}{4}[/tex]
[tex]A_2 = 38.5[/tex]
Area of the garden is
[tex]Area = A_1 + A_2[/tex]
[tex]Area = 91 + 38.5[/tex]
[tex]Area = 129.5m^2[/tex]
Calculating Perimeter
First, we calculate the perimeter of the rectangle
But in this case, we only consider the length because the widths have been covered by the semicircles
[tex]P_1 = 2 * L[/tex]
Where:
[tex]L = 20-(3.5 +3.5)[/tex]
So:
[tex]P_1 =2 * (20-(3.5 +3.5))[/tex]
[tex]P_1 =2 * (20-7)[/tex]
[tex]P_1 =2 * 13[/tex]
[tex]P_1 =26[/tex]
Next, we calculate the perimeter of the two semi-circles.
Two semi-circles = One Circle
So:
[tex]P_2 = 2\pi r[/tex]
Where
[tex]r = \frac{7}{2}[/tex]
[tex]P_2 = 2 * \frac{22}{7} * \frac{7}{2}[/tex]
[tex]P_2 = \frac{2 * 22 * 7}{7 * 2}[/tex]
[tex]P_2 = \frac{308}{14}[/tex]
[tex]P_2 = 22[/tex]
Perimeter of the garden is
[tex]Perimeter = P_1 + P_2[/tex]
[tex]Perimeter = 26 + 22[/tex]
[tex]Perimeter = 48m[/tex]
Planet X is 1/2 of a light-year away from Earth. Planet Y is 3/10 of a light-year away from Earth. How much farther away is Planet X?
Answer:
1/2= 5/10
5/10 - 3/10 = 2/10 or 1/5
so planet X is 1/5 of a light-year closer
Step-by-step explanation:
Answer:
5/10
Step-by-step explanation:
Simplified
100 points!!
Nicole has 425 candy bars to sell for a fundraiser. Let C be the number of candy bars. Let P be the amount made from selling the candy bars. Suppose that P = 2C - 300 gives P as a function of C.
Identify the correct description and appropriate set of values for the domain of the function.
Group of answer choices
the number of candy bars; open curly brackets 0 comma 1 comma 2 comma 3 comma horizontal ellipsis comma 425 close curly brackets
the number of candy bars; the set of all real numbers from 0 to 300
the amount made from selling the candy bars; the set of all real numbers from 0 to 300
the amount made from selling the candy bars; open curly brackets 0 comma 1 comma 2 comma 3 comma horizontal ellipsis comma 425 close curly brackets
Answer:
its c
Step-by-step explanation:
i just too quiz and it siad this
Answer:
c
Step-by-step explanation:
took the quiz and got 100% on it
Dan is driving from his hometown to California to Colorado for a ski vacation. The equation defines the distance he is from home h hours after noon. What are the meanings of the values in the equation?
y=70h+100
a. Dan is 100 miles from home at noon and is traveling at 70 miles per hour.
b. Dan is 70 miles from home at noon and is traveling at 100 miles per hour.
c. Dan leaves at 1:00 and is traveling at 70 miles per hour.
d. Dan leaves at noon and is traveling at 100 miles per hour.
Answer:
a. Dan is 100 miles from home at noon and is travelling at 70 miles per hour.
Step-by-step explanation:
Given
[tex]y = 70h + 100[/tex]
Required
Interpret
An equation has the form
[tex]y = mx + b[/tex]
Where
[tex]m = rate[/tex]
[tex]b = y\ intercept[/tex]
By comparison with [tex]y = 70h + 100[/tex]
[tex]m = 70[/tex]
i.e. He travels at 70 miles per hour
And
[tex]b = 100[/tex]
This represents the initial distance as at when he started travelling (12 noon)
i.e. At noon, he is 100 miles away from home
Answer:
A is the right answer.
Step-by-step explanation:
Can someone answer this for me ill give brainliest asap
F is inversely proportional to d 2 . When F = 8 , d = 6 Work out d (positive value rounded to 2 DP) when F = 7
Answer:
d ≈ 6.41
Step-by-step explanation:
Given that F is inversely proportional to d² then the equation relating them is
F = [tex]\frac{k}{d^2}[/tex] ← k is the constant of proportion
To find k use the condition when F = 8, d = 6 , then
8 = [tex]\frac{k}{6^2}[/tex] = [tex]\frac{k}{36}[/tex] ( multiply both sides by 36 )
288 = k
F = [tex]\frac{288}{d^2}[/tex] ← equation of proportion
When F = 7 , then
7 = [tex]\frac{288}{d^2}[/tex] ( multiply both sides by d² )
d² × 7 = 288 ( divide both sides by 7 )
d² = [tex]\frac{288}{7}[/tex] ( take the square root of both sides )
d = ± [tex]\sqrt{\frac{288}{7} }[/tex] ≈ ± 6.41
The positive value of d is 6.41 ( to 2 dec. places )
Answer:
when F = 7, d = 6.41
Step-by-step explanation:
We know that when 'y' varies inversely with 'x', we get the equation
y ∝ 1/x
y = k/x
where 'k' is called the constant of proportionality
Given that F is inversely proportional to d.
F ∝ 1/d
F = k /d²
When F = 8, d = 6, we need to find k
k = Fd²
k = 8×(6)²=288
Now, we need to find d when F = 7
so substitute k = 288, F = 7 in the equation
F = k /d²
d² = k/F
d² = 288/7
[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]
[tex]d=\sqrt{\frac{288}{7}},\:d=-\sqrt{\frac{288}{7}}[/tex]
but, we need to take the positive value of d, so
[tex]d=\sqrt{\frac{288}{7}}[/tex]
[tex]d=6.41[/tex]
Therefore,
when F = 7, d = 6.41
The local car dealership has noticed a 3:1
ratio for people purchasing SUV's to those
purchasing trucks. If they have room for
128 trucks and SUV's on their lot, how
many trucks should they have available to
sell?
Answer:
32 trucks.
Step-by-step explanation:
3:1
Every time 3 SUV's are sold, one truck is sold. This would also mean that [tex]\frac{3}{4}[/tex] of both trucks and SUV's sold are SUV's. If we divide 128 into fourths, then you get 32. One fourth of 128 is 32. So, they should have 32 trucks (and 96 SUV's)
Please help!! I included a pic of the problem to make it easier.
Find the quotient (z/w)
z = 6(cos(pi/3) + isin(pi/3), w = 3(cos(pi/6) + isin(pi/6)
[A]2(cos(pi/6)+isin(pi/6)
[B]2(cos(pi/90)+isin(pi/90)
[C]18(cos(pi/2)+isin(pi/2)
[D] None of these
Answer: i think it is D
we have:
[tex]\frac{z}{w}= \frac{6(cos\frac{\pi }{3}+i.sin\frac{\pi }{3} ) }{3(cos\frac{\pi }{6}+i.sin\frac{\pi }{6}) }\\\\\\<=>\frac{z}{w}=\frac{2(\frac{1}{2}+i.\frac{\sqrt{3} }{2}) }{\frac{\sqrt{3} }{2}+i.\frac{1}{2} }\\\\<=>\frac{z}{w}= \frac{2+2\sqrt{3}.i }{\sqrt{3}+i }[/tex]
Step-by-step explanation:
If the perimeter of the triangle is 40 cm, find the area of the triangle.
The area of the triangle is, ? cm2.
Answer:
102 cm²Step-by-step explanation:
Perimeter is:
P = 40 cmand P = 2x - 4 + 5x - 13 + x + 9 = 8x - 8Comparing the value:
8x - 8 = 40 8x = 48x = 8 cmAre formula:
A = 1/2ahReplacing values:
A = 1/2(x + 9)(2x - 4)A = 1/2(8 + 9)(2*8 - 4) = 1/2*17*12 = 102 cm²Answer:
60cm²
Step-by-step explanation:
To find :-
The Area of the triangle .We know that Perimeter is the sum of sides of a triangle. Here the perimeter is 40cm .
→ 2x - 4 +5x - 13 + x + 9 = 40cm .
→ 8x - 8 = 40cm
→ 8x = 40+8 cm
→ 8x = 48 cm
→ x = 6cm .
We know that the area of the triangle is half the product of base and height .
Base = x + 9 = 15cm Height = 2x -4 = 8cm .→ A = 1/2 × b × h
→ A = 1/2 × 8cm × 15cm
→ A = 60cm²
Pleaseee I need help
Answer:
32
Step-by-step explanation:
2x-16 + 4x+4 =180
6x=180+12
6x=192
x=32
I hope this helps, have a good day
what is the b in equation y=2x+12
Answer:
b = 12
Step-by-step explanation:
y = mx + b
b = 12
Answer:
the b is 12
Step-by-step explanation: y=mx+b
HELP ME 50 POINTS RN
Answer:
A
Step-by-step explanation:
Because it can only lift 2,200 pounds and that means it can lift 2,200 - 0 Pounds
2 (x - 3) + x(x + 1)
Answer:
[tex]x^{2}[/tex] + 3 - 6
Step-by-step explanation:
Answer:
x2+3x-6
Step-by-step explanation:
The points (10, 8) and (19, 17) fall on a particular line. What is its equation in slope-intercept
form?
Answer:
Step-by-step explanation:
First, find the slope using the two given points and the slope equation.
[tex]m=\frac{y2-y1}{x2-x1}=\frac{17-8}{19-10}=\frac{9}{9}=1[/tex]
We can enter [tex]m[/tex] into our slope-intercept form now.
[tex]y=mx+b\\y=1x+b\\y=x+b[/tex]
Now, plug in one of the given points to solve for b.
[tex]8=10+b\\b=-2[/tex]
So our final form is:
[tex]y=x-2[/tex]
Hope this helps!
The equation of the line passing through the points (10, 8) and (19, 17) is y = x - 2.
What is the general equation of a straight line?The general equation or the slope - intercept form of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is a line such that points (10, 8) and (19, 17) lie on this line.
The given coordinates are (10, 8) and (19, 17).
First, we will find the slope of the line as follows -
m = (17 - 8)/(19 - 10)
m = 9/9
m = 1
So, the equation of the line will be -
y = x + c
Now, we will find the y - intercept. As the line pass through the point
(10, 8), we can write -
8 = 10 + c
c = 8 - 10
c = -2
So, the equation of the line will be y = x - 2.
Therefore, the equation of the line passing through the points (10, 8) and (19, 17) is y = x - 2.
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HELP PLEASE AWARDING BRAINLIEST IF CORRECT
Answer:
y=1/4x+9
Step-by-step explanation:
x-4y=-36
add 4y to both sides to find x
x=4y−36
To find y=
add -x to both sides
−4y=−x−36
divide both sides by -4
y=mx+b
y=1/4x+9
Hakim Ellison wants to buy a 4 door sport utility vehicle 4 wheel drive hybrid. There is an 8% sales tax on the purchase price of the SUV in his state. If he pays the full sticker price for the SUV, how much is the total?
Answer: $60401.16
Step-by-step explanation:
From the attached image, the total price for the vehicle = $55,927.
If he were to pay the full sticker price for the SUV, the total would sum up to
= $55,927 + 8% sales tax
= $55,927 + 8/100( $55,927)
= $55,927 + 0.08($55,927)
= $55,927 + $4474.16
= $60401.16
The total would sum up to $60401.16
Which of the following expressions is in simplified form?
9 j - 3 - j
4 w - 5
1 1/2 n + 2.9 n
-2 + 1.4 m + 0.5
Answer:
The answer is 4w-5 its in its simplest form
Demons answer this for me.
Answer:
Step-by-step explanation:
if you have negative numbers of x (this means negative meters) then the equation transform them into negative yards.
then replace y by 40yd in the equation like
40 = 1.09x
x = 40/1.09 = 36.7 meters
so in a 40yd race, there are 36.7 meters.
if the slope is -2/5 and the y-intercept is 5/2 the slope-intercept form is y=5/2x-2/5 true or false
Answer:
is false
explanation
just trust me
20z-8 please helpppp
Answer: 4(5z−2)
Step-by-step explanation: Brainliest pls
−2, −1, 4 , find all numbers listed that are solution of the equation. (Careful, there might be more than one that work!) If you find several solutions, separate them with a comma. If none of the given numbers work, just enter DNE for 'does not exist'.
k3−k2+k−4=−2k2+k−4
Answer:
k3-k2+k-4=−2k2+k−4 that is the answer
Find the equation of the line that is perpendicular to y = –3x + 1 and passes though the point (6, 3).
A) y =
1
3
x + 1
B) y = –
1
3
x + 1
C) y = 3x – 5
D) y = –3x – 5
Answer:
A. y=1/3x+1
Step-by-step explanation:
When finding a line that is perpendicular to another line, all you have to do is find the "opposite reciprocal" of the slope. In this case that means writing the slope as the fraction -3/1, and then flipping the fraction over (1/-3) and taking away the negative sign which gets you 1/3 for the slope of your new line. Now, all you have of your new equation is the slope. You need to take your new equation (y=1/3x+b) and plug in the x and y coordinates to that equation, and then solve for the last variable which is b. That solving process goes as follows:
3=1/3*6+b
3=2+b
1=b
now you can replace the b with 1 in your equation to get your final answer of y=1/3x+1
A bricklayer can build a wall of a certain size in 5 hours. Another bricklayer can do the same job in 4 hours. If the bricklayers work together, how long would it take to do the job?
a. 9h
b. 2(2/9)h
c. 20h
d. 4(1/2)h
Answer:
b
Step-by-step explanation:
It will take [tex]\frac{20}{9}[/tex] hours as per linear equation to complete the wall.
What is a linear equation?A linear equation is an equation where the variable of the equation has the highest power of degree one.
Given, the 1st bricklayer build a complete wall of certain size in 5 hours.
Therefore, that bricklayer build [tex]\frac{1}{5}[/tex]th of the complete wall in 1 hour.
Similarly, the 2nd bricklayer build a complete wall of certain size in 4 hours.
Therefore, that bricklayer build [tex]\frac{1}{4}[/tex]th of the complete wall in 1 hour.
If they work together, in 1 hour they build a total of ([tex]\frac{1}{5}[/tex]+[tex]\frac{1}{4}[/tex])th = [tex]\frac{9}{20}[/tex] of the complete wall.
Hence, they will complete the wall in (1÷[tex]\frac{9}{20}[/tex]) hours = [tex]\frac{20}{9}[/tex] hours.
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A= 12.8m
B=13.9m
C=12m
D= 7m
Answer:
C: 12m
Step-by-step explanation:
We can solve this by using the Pythagorean Theorem [tex]a^{2} + b^{2} = c^{2}[/tex]
For this triangle
a= x b= 5 c= 13
We now have the equation
[tex]x^{2} + 5^{2} =13^{2}[/tex]
If we simplify this we get
[tex]x^{2} + 25 = 169[/tex]
Next, we subtract 25 from both sides
[tex]x^{2} = 144[/tex]
Finally, if we take the square root of both sides of the equation, we find that
x= 12
Giving brainless! Don’t answer if you don’t know I’ll flag you.
Answer:
The sales tax is $0.40
Step-by-step explanation:
10 x 0.04 = 0.4
0.04 is 40% when multiplying
What is the answer to 0.5x(y - z) in distributive Property?
what is. the value of x in the equation 2.5(6x-4)=10+4(1.5+0.5x)?
Answer:
x=2
Step-by-step explanation:
We first distribute this. So we have 15x-10 = 10 + 6 +2x.
Then we move the variable to one side and have 13x= 10+10+6
Simplify to get 13x = 26.
x=2
nya wants to buy a sweater that had an original price of 55. the sweater is now discounted 20% and the sales tax rate is 5.5%. how much will nya pay for the swearter
Answer:
Step-by-step explanation:
55 - 20% = 44
5.5% of 44 = 2.42
2.42 + 44 = 46.42
hope this helps. :]
Consider the rates 4/5 miles in 8 minutes and 4 minutes to travel 2/5 mile
Answer:
960
Step-by-step explanation:
I'm not sure exactly what's the question, but here's what I found. Lets first put it in our own words.
Consider the speed 4/5 miles in 12 minutes to travel 2/8.
8 + 4 = 12, so you can replace that with 12 minutes.
Now, you can absolutely guess your question.
Time = 12 minutes.
Distance = x (Let x be distance)
Speed = 4/5.
Now, you find distance.
Distance Formula: You can use the equivalent formula d = st which means distance equals rate times time.
So 4/5 × 12, is 9.6.
In fraction, if you have 1 numbers after the decimal point, multiply both numerator and denominator by 10. So 9.6 = (9.6 × 10) × 10 = 960.
Here is a pattern I found
2/5 divided by 4 is 1/10
4/5 divided by 8 is 1/10
If , we consider the given rates , we find that both rates are equivalent.
Two rates are given which are 4/5 miles in 8 minutes and 2/5 miles in 4 minutes.
We have to find out what they actually indicate.
What is the unitary method?
The unitary method is a method in which we find the value of a unit and then the value of the required number of units.
As per the question ;
Two rates are given which are ; 4/5 miles in 8 minutes and 2/5 miles in 4 minutes.
Let's find out what they are actually indicating.
So ;
If , distance travelled in 8 minutes = 4/5 miles
Then ;
In 1 minute , distance travelled will be ;
= [tex]\frac{4}{5*8}[/tex]
= [tex]\frac{4}{40}[/tex]
= 1 / 10 miles
and
If , distance travelled in 4 minutes = 2/5 miles
Then ;
In 1 minute , distance travelled will be ;
= [tex]\frac{2}{5*4}[/tex]
= [tex]\frac{2}{20}[/tex]
= 1 / 10 miles
So , we can conclude that both rates are equivalent.
Thus , if we , consider the given rates , we find that both rates are equivalent.
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Lauren and her sister are buying their mom a watch for her birthday. The original price of the watch is $50, but the store is having a 25% off sale on watches. The sales tax in Lauren’s state is 6%.
How much will Lauren and her sister pay for the watch including tax?
What percent of the original price do Lauren and her sister pay for the watch, after paying tax?
Step-by-step explanation:
75×50/100= 37.5$
37.5×6/100=225/100=2.25$
37.5+2.25= 39.75$
Please help me please!
Answer:
(2) 19
Step-by-step explanation:
[tex]2(3^x)+1[/tex][tex]2(3^2)+1[/tex][tex]2(9)+1[/tex][tex]18+1[/tex][tex]19[/tex]