Answer:
314 square feet
Step-by-step explanation:
we know that
The area that will be covered by the spray of the quarter-circle sprinkler head, is equal to the area of a quarter circle with radius of 20 feet
so
The area of a quarter circle is
[tex]A=\frac{1}{4}\pi r^{2}[/tex]
we have
[tex]r=20\ ft[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]A=\frac{1}{4}(3.14)(20)^{2}=314\ ft^2[/tex]
The area covered by the quarter-circle sprinkler head to the nearest square foot is 314 square feet.
To find the area covered by the quarter-circle sprinkler head, we need to calculate the area of a quarter circle with a radius of 20 feet. The formula for the area of a circle is [tex]\( A = \pi r^2 \), where \( r \)[/tex] is the radius. Since we are dealing with a quarter circle, we will take [tex]\( \frac{1}{4} \)[/tex] of the full circle's area.
Given that the radius [tex]\( r \)[/tex] is 20 feet, the area of the full circle would be:
[tex]\[ A_{\text{full circle}} = \pi \times (20 \text{ feet})^2 \] \[ A_{\text{full circle}} = \pi \times 400 \text{ square feet} \] \[ A_{\text{full circle}} = 400\pi \text{ square feet} \][/tex]
Now, to find the area of the quarter circle, we divide the full circle's area by 4:
[tex]\[ A_{\text{quarter circle}} = \frac{1}{4} \times 400\pi \text{ square feet} \] \[ A_{\text{quarter circle}} = 100\pi \text{ square feet} \][/tex]
Using the value of [tex]\( \pi \)[/tex] as approximately 3.14159, we get:
[tex]\[ A_{\text{quarter circle}} \approx 100 \times 3.14159 \text{ square feet} \] \[ A_{\text{quarter circle}} \approx 314.159 \text{ square feet} \][/tex]
Rounding to the nearest square foot, the area covered by the quarter-circle sprinkler head is 314 square feet.
What is the parallel line to y=-4x-5 and passes the point (-2,6)
Answer:
y = - 4x - 2 is the required equation of the line.
Step-by-step explanation:
Equation of two parallel lines differ only by a constant.
If the equation of a line is [tex]$ ax + by + l = 0 $[/tex] then the equation of the line parallel to it is given by [tex]$ ax + by + k = 0 $[/tex].
Note that only the constants differ in both the equations.
The given equation is: y = - 4x - 2
This is equivalent to 4x + y + 2 = 0.
Therefore, the equation of the line parallel to the given line will be:
4x + y + k = 0.
We are also given the point which passes through the line. We can substitute it to determine the value of 'k'.
Substituting (- 2, 6), we get:
4(-2) + 6 + k = 0
⇒ - 8 + 6 + k = 0
⇒ k = 2
Hence, the equation of the required line is: y = - 4x - 2
5 to the power of 3 simplified by 2.5 to the power of 2
Answer:
2500
Step-by-step explanation:
5^3 is 125/2.5 is 50 and 50^2 is 2500
Answer:
20
Step-by-step explanation:
5x5x5= 125
2.5x2.5=6.25
125÷6.25= 20
Solving for t?
[tex]6t - 2 = 5t[/tex]
[tex]8t + 6 = 7t + 6[/tex]
Answer:
Step-by-step explanation:
6t-2=5t
8t+6=7t+6
Walt received a package that is 2 1/3 inches long, 6 ¾ inches high, and 8 ½ inches wide. What is the surface area of the package?
plz help
The surface area of prism is 185.815 square inches
Solution:
Given that,
[tex]Length = 2\frac{1}{3}\ inches = \frac{3 \times 2 + 1}{3} = \frac{7}{3}\ inches = 2.33\ inches[/tex]
[tex]Width = 8\frac{1}{2}\ inches = \frac{17}{2}\ inches = 8.5\ inches[/tex]
[tex]Height = 6\frac{3}{4}\ inches = \frac{27}{4}\ inches = 6.75\ inches[/tex]
The surface area of package is given as:
[tex]A=2(wl+hl+hw)[/tex]
Where,
"l" is the length
"w" is the width
"h" is the height
Substituting the values we get,
[tex]A = 2((8.5 \times 2.33) + (6.75 \times 2.33) + (6.75 \times 8.5))\\\\Simplify\ the\ above\ equation\\\\A = 2(19.805+15.7275+57.375)\\\\A = 2 \times 92.9075\\\\A = 185.815[/tex]
Thus the surface area of prism is 185.815 square inches
Answer:
The surface area of the prism is 185.815 square inches.
Hope this helps!
Five times the sum of -2 and a number is 91 more than the sum of the opposite of the number and 1
Answer:
n or the number = 5
Step-by-step explanation:
5 * (-2 + n) = 91 + (-n + 1)
-10 + 5n = 19 - n + 1
6n = 20 + 10
6n/6 = 30/6
n = 5
Answer:
The number is 51.
Step-by-step explanation:
Let the number be x and the opposite of a number is -x.
5(-2+x) = 91 + (-x + 1)
-10 + x = 91-x+1
-10 + 2x = 92
2x = 102
x = 51
A circular mirror is surrounded by a square metal frame. The radius of the mirror is 3x. The side length of the metal frame is 15x. What is the area of the metal frame?
The area of the metal frame surrounding a circular mirror can be calculated by figuring the expression 225x² - 9πx², which represents the area of the square minus the area of the circle.
Explanation:The subject of this question is based in mathematics, specifically the area of geometry. The area of the metal frame surrounding the mirror can be found by calculating the difference between the area of the square frame and the area of the circular mirror.
The area of the square frame is given by the formula A = s² where 's' is the length of a side of the square. In this case, each side of the square is 15x so the area of the square frame would be (15x)² = 225x².
The area of the circular mirror is given by the formula A = πr² where 'r' is the radius of the circle. For this mirror, the radius is 3x, so the area of the mirror would be π*(3x)² = 9πx².
So, the area of the metal frame is the difference between the area of the square and the area of the circle. Thus, the area of the frame = 225x² - 9πx².
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Final answer:
To find the area of the metal frame, calculate the area of the square then subtract the area of the circle. The area of the frame is the difference between the square's area, (15x)², and the circle's area, π(3x)².
Explanation:
The question asks for the area of the metal frame surrounding a circular mirror with the mirror's radius being 3x and the frame's side length being 15x.
To find the area of the frame, first calculate the area of the square and then subtract the area of the circle (mirror). The area of the square is given by the formula A = side², so:
Area of the square (Frame + Mirror): A = (15x)²Next, calculate the area of the circle using the formula A = πr²:
Area of the circle (Mirror): A = π(3x)²Finally, subtract the mirror's area from the frame's area to find the area of the metal frame alone:
Area of the metal frame: Aframe = (15x)² - π(3x)²The sum of two numbers is a hundred one number is at least 16 more than the other number. What are the numbers? Please help
Answer:
42 and 58
Step-by-step explanation:
Let the two numbers be represented by A And B
A + B = 100
A = B + 16
Substitute B + 16 in place of A in equation 1
We have,
B + 16 + B = 100
It can also be written as
B + B + 16 = 100
2B + 16 = 100
Subtract 16 from both sides
2B + 16 - 16 = 100 - 16
2B = 84
Divide both sides by 2
2B/2 = 84/2
B = 42
Now substitute 42 for B in any of the equations to get A.
Using equation 1
A + B = 100
A + 42 = 100
Subtract 42 from both sides
A + 42 - 42 = 100 - 42
A = 58
Therefore the two numbers are 42 and 58
What is the place value of the underlined number 4,382
Answer: Unit =2
tens=8
hundred= 3
thousand= 4
Step-by-step explanation:
PLLLEEEAAASSSEEE HELP FAST!!
What is the expression in radical form?
(5x^4y^3)^2/9
Answer:
the 3rd one i believe.
not sure.
hope this helps!
Which is not a characteristic of the linear parent function?
O
A. It goes through the origin.
O
B. The range is positive real numbers (y> 0).
O
C. The domain is all real numbers.
O
D. It has a slope of 1.
The characteristic of the linear parent function that is not true is that the range is positive real numbers (y > 0).
Explanation:The correct answer is B. The characteristic of the linear parent function that is not true is that the range is positive real numbers (y > 0).
A linear parent function is represented by the equation y = x and passes through the origin (0,0). Its domain is all real numbers (-∞, ∞) and its range is also all real numbers (-∞, ∞).
A linear function with a slope of 1 is represented by the equation y = x and is a straight line that passes through every point on the graph that has the same x and y value.
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Option B 'The range is positive real numbers (y>0)' is not a characteristic of the linear parent function. The function y=x, known as the linear parent function, has its range as all real numbers, not just positive.
Explanation:The characteristic of the linear parent function, which is not accurate, is: 'The range is positive real numbers (y>0)'.
The linear parent function is y = x, which indeed meets the criteria of the remaining options. It goes through the origin (0,0), its domain covers all real numbers, as x can be any real number, and it has a slope of 1 throughout. However, its range is not only positive real numbers (y>0). The range of the linear parent function actually includes all real numbers because y (the output) can take any real value, both positive and negative, not just positive.
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Megan says she needs a piece of rope that is 15/6 feet long how can megan rename the fraction as a mixed number?
Answer:
2 3/6
Step-by-step explanation:
When reducing the fraction you see how many times the denominator of 6 can fit into to numerator of 15. It is 2 with 3 left over. So you write 2 3/6
Answer:
2 1/2
Step By Step:
15 divided by 6: 2 R3
2 3/6
GCF is 3
Divide both sides by 3, and get 2 1/2
If the ratio of a circle's sector to its total area is 3/11, what is the measure of
its sector's arc?
Answer:
6πr/11.
Step-by-step explanation:
The length of the arc = rC where C is the central angle of the sector in radians and r = the radius.
C = (3/11) * 2π
= 6π/11 radians.
So the measure of the arc = 6πr/11.
What is 45% of 36 ft?
Please show work that I can write down on a piece of paper, last time my teacher yelled at me because I didn't have any work down. :(
Answer:
16.2
Step-by-step explanation:
45% = 0.45 (as a decimal)
36 × 0.45 = 16.2
Solve for the variable 8x+7=-9
Answer:
x=-2
Step-by-step explanation:
first u subtract 7 on both sides resulting on 8x=-16. Then to isolate x u divide by 8 on both sides.
Answer:
Step-by-step explanation:
I've already solved this problem.
A bank is offering you an introductory credit card promotion. Your interest for the first year is 8%. But, at the beginning
of the 2nd year your interest rate will go up to 23%. If you have an $1,800 balance on your card throughout both years, what will be the
difference in the monthly interest owed during year 1 and year 2?
O a) $10.80
Ob) $15.66
O c) $22.50
O d) $34.50
Answer:
c) $22.50
Explanation:
1. Calculate the monthly interest owed during year 1
Interest for first year: 8%The monthly rate is the yearly rate divided by 12: 8% / 12 = 0.08/12The monthly interest owed is the monthly rate times the balance: (0.08/12)×$1,800 = $12.002. Calculate the monthly interest owed during year 2
Interest for second year: 23%The montly rate is the yearly rate divided by 12: 23% / 12 = 0.23/12The monthly interest owed is the monthly rate times the balance: (0.23/12)×$1,800 = $34.50
3. Calculate the difference
Difference in the monthly interest owed during year 1 and year 2 = $34.50 - $12.00 = $22.50Hence, the answer is the option c) $22.50
Y = 3x + 2
-4x + 2y = 8
Answer: x=2 and y=8
Step-by-step explanation:see attachment
factors of 48 that add to equal 26
tan 116° =
A) tan 64°
B) -tan 64
C) tan 26
D) -tan 26
Answer:
B)
Step-by-step explanation:
All three trigonometric functions are positive in Quadrant I
Sine only is positive in Quadrant II
Tangent only is positive in Quadrant III
Cosine only is positive in Quadrant IV
Now
tan 116° tan 116° means that the angle 116° lies in the second quadrant.
sin is positive while cos and tan are negative in the second quadrant
tan 116° = -tan(180°-116)
= -tan(64°)
Today is 4 jan and day is monday.what day will be on 23 jan. With step by step
Answer:
Saturday
Step-by-step explanation:
Each day of the week is repeated after 7 days
So, after 19 days it would be Saturday
Given that the surface of the area cube is given by the formula SA equals 6S2 what is the value of essay if S equals 1/2 cm
Answer:
[tex]SA=1.5\ cm^2[/tex]
Step-by-step explanation:
we know that
The surface area of a cube is equal to
[tex]SA=6s^2[/tex]
where
s is the length side of a cube
we have
[tex]s=\frac{1}{2}\ cm[/tex]
substitute
[tex]SA=6(\frac{1}{2})^2[/tex]
[tex]SA=(\frac{6}{4})=1.5\ cm^2[/tex]
helppppppppppppppppppppppppppppppppppppppp
i have 10 apples i give away 4 how many do i have now
Answer:
You have 6 apples left.
Step-by-step explanation:
You have 10 apple and give away 4.
10 - 4 = 6 apples
You have 6 apples left.
Australia is approximately 3,000,000 square
miles in area. Sand dunes cover 40% of the land.
How much of Australia is
covered by sand dunes?
Answer:
1,200,000 square miles
Step-by-step explanation:
Given data:
Total land = 3 000 000
40% is covered by sand dunes
Land covered by sand dunes is 40% of the total area therefore
Land covered by sand dunes=(40/100) * 3000000
Land covered by sand dunes= 0.4 * 3000000
Land covered by sand dunes= 1 200 000
Final answer:
Approximately 1,200,000 square miles of Australia are covered by sand dunes, which is 40% of Australia's total area of about 3,000,000 square miles.
Explanation:
The student has asked how much of Australia is covered by sand dunes given that Australia's area is approximately 3,000,000 square miles and sand dunes cover 40% of the land.
To calculate the area covered by sand dunes, we apply the percentage to Australia's total area:
Convert the percentage into decimal form: 40% = 0.40.
Multiply the total area of Australia by the decimal: 3,000,000 square miles × 0.40.
The result gives us the area covered by sand dunes: 1,200,000 square miles.
Therefore, sand dunes cover about 1,200,000 square miles of Australia.
A container holds sugar shape of a cylinder that radius of the containers 3 inches in the height of the container is 10.5 inches which measurement is closest to the volume of the container cubic inches
Answer:94.5pie
Step-by-step explanation:
Final answer:
To calculate the volume of a cylindrical sugar container with a radius of 3 inches and a height of 10.5 inches, use the formula V = πr²h, which yields approximately 296.78 cubic inches.
Explanation:
The question asks for the volume of the container that has the shape of a cylinder. The given dimensions are a radius of 3 inches and a height of 10.5 inches. To find the volume of a cylinder, we use the formula:
V = πr²h
Where V is the volume, π (pi) is a constant approximately equal to 3.14159, r is the radius, and h is the height of the cylinder.
We calculate the volume as follows:
V = π × (3 inches)² × 10.5 inches
V = π × 9 in² × 10.5 in
V = π × 94.5 in³
V ≈ 296.78 in³
Thus, the volume of the cylinder is approximately 296.78 cubic inches
* 14 * x=2 * 28 . What x equal ?
Answer:
answer is 4
Step-by-step explanation:
look at picture
Answer:
x = 1
Step-by-step explanation:
14 x 2x = 28
2 x 1 = 2
14 x 2(1) = 28
14 x 2 = 28
(m3 - 6m2 - 16m + 63) divided by (m - 7)
Therefore( [tex]m^3 -6m^2-16m +63[/tex] )÷ (m-7) [tex]= (m^2 +m-9)[/tex]
Step-by-step explanation:
[tex]m^3 -6m^2-16m +63[/tex]
[tex]=m^3 -7m^2[/tex][tex]+m^2 -7m[/tex][tex]-9m+63[/tex]
[tex]= m^2(m-7)[/tex][tex]+m(m-7)[/tex][tex]-9(m-7)[/tex]
[tex]= (m-7 ) (m^2 +m-9)[/tex]
Therefore( [tex]m^3 -6m^2-16m +63[/tex] )÷ (m-7) [tex]= (m^2 +m-9)[/tex]
What is the product?
(2x-1)(x+4)
2x²-4
0
2x²+4
0
2x² + 7x-4
2x² – 7x-4
Answer:
C) 2x^2+7x-4
Step-by-step explanation:
(2x-1)(x+4)=2x^2-x+8x-4=2x^2+7x-4
describe the error in using the percent equation to answer the equation.
30 is 60% of what number is?
solve the proportional equation 3/r = 5/r+3
Answer:
r=9/2 or 4.5
Step-by-step explanation:
First of all our goal is to get R by itself
by cross multiplying we get,
(r+3)*3=5r
by distributive property we get
3r+9=5r
substracting 3r from both sides we get
9=2r
by dividing by 2 in both sides we get
r=9/2 or 4.5
45 percent of a group of people have blue eyes. How many people are in the group if 180 people have blue eyes
Answer:
81
Step-by-step explanation: