Answer:
10 cmStep-by-step explanation:
The volume of cone formula:
V = 1/3πr²hSubstitute te given values into the formula and solve for r:
400π = 1/3πr²(12)100 = r²r = √100r = 10Answer:
10 cm
Step-by-step explanation:
Volume of a cone
[tex]\sf V= \dfrac{1}{3} \pi r^2 h[/tex]
where:
V = volumer = radiush = heightGiven information:
V = 400π cm³h = 12 cmTo find the length of the radius, substitute the given values into the formula and solve for r:
[tex]\begin{aligned}\sf V& = \sf \dfrac{1}{3} \pi r^2 h\\\\\implies \sf 400 \pi & = \sf \dfrac{1}{3} \pi r^2(12)\\\\ \sf 400 \pi & = \sf \dfrac{12}{3} \pi r^2\\\\ \sf 400 \pi & = \sf 4\pi r^2\\\\ \sf \dfrac{400 \pi}{4 \pi} & = \sf r^2\\\\ \sf r^2 & = \sf 100 \\\\ \sf \sqrt{r^2} & = \sf \sqrt{100}\\\\ \sf r & = \sf 10\end{aligned}[/tex]
Therefore, the length of the radius of the cone is 10 cm.
Learn more about cones here:
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y=|x-3|+|x+2|-|x-5| if x < -2
what does y equal
Answer:
y= |x-3|+ |x+2|-|x-5|; x<-2
y=-2
If K is the midpoint of segment JL, JK = 8x + 11 and KL = 14x - 1, find JK.
Answer:
27 units
Step-by-step explanation:
A midpoint divides a line segment into two congruent parts. K being the midpoint of segment JL means ...
JK = KL
8x +11 = 14x -1 . . . . . substitute given expressions
12 = 6x . . . . . . . . add 1 -8x
2 = x . . . . . . . . divide by 6
Then the length of JK is ...
8x +11 = 8(2) +11 = 27
JK is 27 units long.
_____
Additional comment
KL = JK = 27 units
JL = 2(27 units) = 54 units
A circular concrete patio has a circumference of about 53 yards. The patio has a diameter of d yards. Which expression best represents the value of pi?
The expression that best represents the value of pi is 53/d.
What is the expression that represents pi?Pi can be described as the ratio of the circumference of a circle to its diameter. The circumference of the patio is the distance round the patio. The formula that can be used to represent the circumference of the patio is πD
53 = πD
π = 53/d
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When Sally decided to run for class treasurer, she predicted how many votes she would get. After the election, Sally found out she had received 150 votes. She had predicted she would get 20% fewer votes than that. How many votes did Sally predict she would get?
Answer:
3000
because you need to dived it
HELP!! I’m in class I just need help with the fill in blanks segment help me please
Answer:
First Blank: “controlled” Second Blank: "a Different" Third Blank: "the same" Last Blank: "Height of the ramp"
Step-by-step explanation:
If x+2y=13 find the value of y when x is
Answer:
x is what????
Step-by-step explanation:
A school gym has an area of 4,641 square feet and a perimeter of 284 feet. What are the dimensions of the gym?
Answer:
dimensions are 51x91
Step-by-step explanation:
Assuming that the gym is rectangular in shape, then...
l*w=4641
and 2l+2w=284
We have two variables and two equations so to solve this we plug one equation into another.
Solve for one variable:
l*w=4641
w=4641/l
Plug into the other equation...
2l+2(4641/l)=284
Solve
l*(2l+9282/l)=284
2l^2+9282=284l
2l^2-284l+9282=0
Factor the trinomial:
2(l−51)(l−91)=0
l−51=0 or l−91=0(Set factors equal to 0)
l=51 or l=91
now, lets plug it into one of the equations to find w
51*w=4641
w=91, l=51
or...
91*w=4641
w=51, l=91
Answer:
91 ft × 51 ft
Step-by-step explanation:
while the other answer is basically correct, it makes a to at the beginning of the calculation (but the continues correctly).
and it assumes you can find the right factoring of the expression.
so, I will show you here how to generally solve this, even if you cannot find the right factorization :
l×w = 4,641 ft²
w = 4641/l
2l + 2w = 284
2l + 2(4641/l) = 284
2l + 9282/l = 284
2l² + 9282 = 284l
2l² - 284l + 9282 = 0
to make things easier let's divide everything by 2
l² - 142l + 4641 = 0
the general solution to a squared equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = l
a = 1
b = -142
c = 4641
l = (142 ± sqrt((-142)² - 4×1×4641))/(2×1) =
= (142 ± sqrt(20,164 - 18,564))/2 =
= (142 ± sqrt(1600))/2 = (142 ± 40)/2 = 71 ± 20
l1 = 71 + 20 = 91
l2 = 71 - 20 = 51
w1 = 4641/91 = 51
w2 = 4641/51 = 91
so, they are interchangeable (it does not matter which we call length and which width).
the dimensions are 91 ft × 51 ft
Paint costs $3.99 per can and brushes cost $2.50 each. The sales tax rate is 5%. Which expression represents the total cost of p cans of paint and b paint brushes
Multiply the price of each by the quantity purchased, add those together, then multiy the total by the sales tax.
Total = 1.05(3.99p + 2.50b)
I would just like to know what this means and how to do it consistently. Thanks (:
Answer:
This question is asking for you to determine if the tables represent linear functions, functions in y=mx+b form, and to find the equation for the line.
If something is a linear function, each of the input values will have it's own corresponding y value, therefore c cannot be linear, as -1 and 1 both have 10 as the output.
I hope this helps, but if you need more clarification, please tell me in the comments!
For every pizza Caron's family ate, Caron ate 2 of the 8 slices. If Caron's family brought 4 pizzas, write the ratio of the total number of slices Caron ate to the total number of slices the family ate.
Answer:
[tex]\frac{8}{32}[/tex]
Step-by-step explanation:
2×4=8
Caron are a total of 8 slices.
8×4=32
There were 32 slices between all 4 pizzas.
A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 feet from the base of the pole. A right triangle with side length 10 feet, hypotenuse of 22 feet, and side of h. What is the height of the pole? Round to the nearest hundredth. 12. 00 feet 19. 60 feet 24. 17 feet 38. 40 feet.
The height of the pole from the ground is 19.60 feet round to the nearest hundredth.
How to find the length of longest side in right angle triangle?To find the lenght of longest side in right angle triangle, the Pythagoras theorem is used.
According to this theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.
A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 feet from the base of the pole.
A right triangle with side length 10 feet, hypotenuse of 22 feet, and side of h. Thus, the length of side of h by the Pythagoras theorem can be given as,
[tex]h^2=22^2-10^2\\h=\sqrt{484-100}\\h=\sqrt{384}\\h=19.60\rm\; ft[/tex]
Thus, the height of the pole from the ground is 19.60 feet round to the nearest hundredth.
Learn more about the Pythagoras theorem here;
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PLS HELP :How is energy causing motion or creating a change in this image? (2 points)
(leaves of a plant in the sunlight)
1.Energy from fuel allows the plant to grow and make its own food.
2.Energy from the sun allows the plant to grow and make its own food.
3.Energy from the wind allows the plant to grow and make its own food.
4.Energy from the water allows the plant to grow and make its own food
Answer:
Not entirely sure but im sure its no. 2
Step-by-step explanation:
Answer:
I think it's 2
Step-by-step explanation:
what is the area of this triangle?
Write the y-intercept of the graph of 8x − 4y = 2?
Answer:
b= -1/2
Step-by-step explanation:
-2/4 is simplified to -1/2 as the y-intercept
y= -4x - 1/2
What is the volume of this figure? Enter your answer in the box. ft³
Answer:
75 ft³ for K12
Based on her results, what is the probability that a student randomly picked in her class chose comedy as their favorite?
1. 1/14
2. 2/7
3. 1/2
4. 1/7
Explanation:
8 people picked comedy out of 14+8+2+4 = 28 people total.
8/28 = (4*2)/(4*7) = 2/7 is the probability of randomly selecting someone who picked comedy as their favorite.
Is (2,10) a solution to this system of equations?
y = 4x + 2
y = x + 8
Yes or no
Answer:
yes, it is
Step-by-step explanation:
10 = 4(2) + 2
10 = 8 +2
10 = 10
10 = 2 + 8
10 = 10
Answer:
The answer is yes
*View the attached graph to check your answer graphically.*
Step-by-step explanation:
y = 4x + 2
y = x + 8
For this problem, I will be using substitution, since the second equation is already in the slope-intercept form.
First, I will substitute the second equation, for y, in the first equation:
y = 4x + 2
y = x + 8
x + 8 = 4x + 2
Next, subtract 4x from both sides to isolate x:
x + 8 = 4x + 2
-4x -4x
-3x + 8 = 2
Then, subtract 8 from both sides:
-3x + 8 = 2
- 8 - 8
-3x = -6
Now, divide both sides by -3:
-3x = -6
/-3 /-3
x = 2
Now, we find the value of y by substituting 2 for x:
y = 4x + 2
y = 4(2) + 2
y = 8 + 2
y = 10
(x, y) ==> (2, 10)
Therefore, yes (2,10) is a solution to this system of equations.
*View the attached graph to check your answer graphically.*
Hope this helps!
1. for his birthday, you buy your dad a package of tennis balls that come in a
cylindrical container with diameter 6.9 cm and height 20.6 cm. you cover
the container in wrapping paper before giving it to him. what is the area
of the wrapping paper? assume there is no overlap. round to the nearest
whole number.
a. 447 cm b. 521 cm
c. 1192 cm d. 3111 cm
Answer:
Why is it so important to know the area of wrapping paper it's just paper?
But anyways the answer is b 521 cm
Step-by-step explanation:
Hong purchased n notebooks. They were 5 dollars each. Write an equation to represent the total cost c that Hong paid.
Answer:
5n=c
Step-by-step explanation:
the equation 5n=c can represent the total cost Hong would have paid for the notebooks because given that each notebook costs $5, you would multiply 5 by the number of notebooks (n) that Hong would be purchasing, which would bring you to the cost (c) of the notebooks all together
sorry for the delay. hope this helps
On Melissa's 6th birthday, she gets a $6000 CD that earns 7% interest, compounded semiannually. If the CD matures on her 14th birthday, how much money will be available?
if the CD matures on her 14th birthday, that means 8 years after she got it, since she got it in her 6th birthday, so
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &8 \end{cases} \\\\\\ A=6000\left(1+\frac{0.07}{2}\right)^{2\cdot 8}\implies A=6000(1.035)^{16}\implies A\approx 10403.92[/tex]
*prove de/ae = bd/ce*
triangle proportionality.
i am able to find that the triangles are similar but don’t know how to prove the parallel sides are proportional to the side segments
Explanation:
You can use the definition of similarity to show that corresponding sides are proportional. You cannot prove anything about the proportionality of non-corresponding sides.
Statement . . . . Reason1. BD║CE . . . . given
2. ∠A≅∠A . . . . reflexive property of congruence
3. ∠ABD≅∠ACE . . . . corresponding angles theorem
4. ΔABD ~ ΔACE . . . . AA similarity postulate
5. BD/CE = AD/AE . . . . definition of similarity
_____
Additional comment
Length DE is related to BC in the same way that AD is related to AB. There is no way to prove the ratio you show in your problem statement. You can show that ...
DE/AE = (CE -BD)/CE = 1 -(BD/CE) . . . . the difference is proportional to the corresponding longer side
Describe the relationship between pi and circles.
Answer:
The circumference (C) of a circle is found by the equation C = 2*[tex]\pi[/tex]*radius
There is a second relationship between [tex]\pi[/tex] and circles. That of the area (A) of the circle which is found by the formula A = [tex]\pi*radius^{2}[/tex]
Step-by-step explanation:
What is the expected probability of spinning a 1 on the following spinner?
a spinner with 5 equal sections labeled 1 through 5.
enter your answer as a fraction, like this: 42/53
Answer:
1/5
Step-by-step explanation:
Miranda deposits $100 into a savings account. she decides that she will make one deposit at the end of each month and that she will increase the amount that she deposits by 10% each month.
a. complete the table to show the amount of money miranda deposits at the end of each month for the first 4 months
Using an exponential function, it is found that the amounts deposited at the end of each month are given by:
At the end of the first month, she deposits $110.At the end of the second month, she deposits $121.At the end of the third month, she deposits $133.1.At the end of the fourth month, she deposits $146.41.What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, we have that A(0) = 100, r = 0.1, hence the equation for the amount deposited after t months is:
[tex]A(t) = 100(1.1)^t[/tex]
Then, for each of the first four months:
[tex]A(1) = 100(1.1)^1 = 110[/tex][tex]A(2) = 100(1.1)^2 = 121[/tex][tex]A(3) = 100(1.1)^3 = 133.1[/tex][tex]A(4) = 100(1.1)^4 = 146.41[/tex]More can be learned about exponential functions at https://brainly.com/question/25537936
The circumference of a circle is 15pi centimeters. What is the area of the circle in terms of pi?
Answer: [tex]56.25\pi[/tex]
Step-by-step explanation:
The circumference of a circle can be found using [tex]d\pi[/tex], where d is the diameter. In this case, we can clearly see the diameter is 15.
Next, we must find the radius as the formula for the area of a circle is [tex]\pi r^2[/tex]
The radius is half of the diameter. [tex]\frac{15}{2} =7.5[/tex]
Now sub in this value for the formula of the area of a circle
[tex]\pi r^2\\\\\pi (7.5)^2\\\\56.25\pi[/tex]
Answer:
56.25[tex]\pi[/tex]
Step-by-step explanation:
circumference=2[tex]\pi r[/tex]
15[tex]\pi[/tex]=2[tex]\pi r[/tex]
r=7.5
Area=[tex]\pi r^{2}[/tex]
=[tex]\pi * 7.5^{2}[/tex]
= 56.25[tex]\pi[/tex]
Phillip is going to a college where tuition is $7,000 per year. He has a scholarship that pays 75% of tuition. He has a grant that pays $1,500 per year. How much will he need to borrow to pay tuition each year?
please help??????????????????????????????? so confused
8s-11s+6s
Answer: = 3 seconds
Step-by-step explanation: combine the like terms Hope it helps !!
To simplify: 8s - 11s + 6s. Simplify the like terms by combining them
Simplifying 8s - 11s + 6s will give 3s.
Given,
8s - 11s + 6s
Now,
Expression : 8s-11s+6s
To simplify the expression combine like terms. So, all the terms consists of variable s.
Combine all terms having same sign,
So,
Firstly apply addition
8s + 6s
= 14s
Now,
Apply subtraction,
14s - 11s
= 3s
Therefore the simplified version is 3s.
Know more about expressions,
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Express the decimal as a percent. 1.276
60 points.
To change a decimal to a percentage, all that we have to do is multiply the decimal by 100 (or move the decimal point to the right two places).
1.276 x 100 = 127.6
Percentage: 127.6%
Hope this helps!
Please I really need help!? NOW!! Will give brainest!!
Answer:
the figure is a rectangle with a side of trapezium
according to my calculation the answer is
196m²
explanationArea of trapezium =½(10+8)×4=36
Area of rectangle =10×16=160
add=160+36
therefore the answer is 196m²PLEASE HELP!! 100 POINTS
Consider this dilation.
(a) Is the image of the dilation a reduction or an enlargement of the original figure? Explain.
(b)What is the scale factor? Explain and show your work.
The red figure is the original and the green the dilation. We know this because the dilated points are marked with '.
Therefore, we can see that the dilation is a reduction of the original figure. The figure got smaller in size after the dilation.
To find the scale factor, we'll need to look at a few of the points before and after the dilation.
A = (-4, 4)
A' = (-2, 2)
C = (0, 4)
C' = (0, 2)
---The scale factor will be the same on all the points, which is why I have selected only 2 sets of points to look at.
Now, we can figure out the scale factor by thinking about how -4 got to -2, how 4 got to 2. In this case, it is simply dividing by 2. The scale factor must be in multiplication, so we cannot use division in reporting the scale factor, it must be a fraction.
2 / 4 = 1 / 2
The scale factor, therefore, is 1/2.
Hope this helps!
Answer:
a) A reduction.
b) 0.5 or 1/2
Step-by-step explanation:
a) The new points are indicated by the ' next to the letters. By observing the graph, we can see that new points have lessened, and therefore shrank the dialtion, so it is a reduction.
b) On each point, it is reducted by 0.5.
Point A went down from 4 to 2, which is half of 4.
Point B went down from -2 to -1, which is half of -2.
Point C went down from 4 to 2, which is half of 4.
Point D went down from 8 to 4, which is half of 8.
hope this helps!