Answer:
The volume of the cone is [tex]27cm^3[/tex]
Step-by-step explanation:
We know that formulas
Volume of cylinder is
[tex]V_1=\pi r^2 h[/tex]
Volume of cone is
[tex]V_2=\frac{1}{3}\pi r^2 h[/tex]
we are given
A cone and cylinder have the same height and the same base radius
So, both will have same radius and height
now, we can find ratios
[tex]\frac{V_2}{V_1}=\frac{\frac{1}{3}\pi r^2h }{\pi r^2h}[/tex]
now, we can simplify it
[tex]\frac{V_2}{V_1}=\frac{1}{3}[/tex]
we are given
the volume of the cylinder is 81 cm^3
so, [tex]V_1=81[/tex]
now, we can plug it and solve for V2
[tex]\frac{V_2}{81}=\frac{1}{3}[/tex]
[tex]81\times \frac{V_2}{81}=81\times\frac{1}{3}[/tex]
[tex]V_2=27[/tex]
So, the volume of the cone is [tex]27cm^3[/tex]
The volume of the cone, which has the same height and base radius as the cylinder with a volume of 81 cm³, is one-third that of the cylinder, equating to 27 cm³.
For a cone with the same height and base radius as the cylinder, the volume formula is V = ⅓πr²h, which is one-third of the volume of the cylinder. Given that the volume of the cylinder is 81 cm³, the volume of the cone can be found by dividing this value by 3, resulting in a volume of 27 cm³ for the cone. Therefore, the correct answer is B) 27 cm³.
enrico buys 3/8 pound of cheddar cheese and 4/8 pound swiss cheese how many cheese does enrico buy in all
Answer:
They buy [tex]\frac{7}{8}[/tex] of cheese.
Step-by-step explanation:
When adding two fractions with the same denominator, you simply add the two numerators (numbers on top):
[tex]\frac{3}{8} + \frac{4}{8} = \frac{7}{8}[/tex]
So they buy [tex]\frac{7}{8}[/tex] of cheese.
The Gonzalez family has three children on summer break they want to an amusement park they bought three child tickets for $18.50 and two adult tickets if they spent a total of $104.50 how much was the price of each adult ticket
Answer:
Each adult ticket was $43
Step-by-step explanation:
2x+18.5 = 104.5
Simplify
2x = 86
x = $43
The surface area of a cube is 18 3/8 m square. Find its volume.
Answer:
[tex]5\frac{23}{64}\approx 5.36 [/tex] cubic meters.
Step-by-step explanation:
We have been given that the surface area of a cube is [tex]18\frac{3}{8}[/tex] square meters and we are asked to find the volume of the cube.
Since we know that surface area of a cube with each edge equals a units is:
[tex]\text{Total surface area of cube}=6a^2[/tex]
Let us find length of each edge using surface area formula.
[tex]18\frac{3}{8}=6a^2[/tex]
Let us convert our given area into mixed fraction.
[tex]\frac{147}{8}=6a^2[/tex]
Upon dividing both sides of our equation by 6 we will get,
[tex]\frac{147}{8*6}=a^2[/tex]
[tex]\frac{147}{48}=a^2[/tex]
Upon taking square root of both sides we will get,
[tex]\frac{7\sqrt{3}}{4\sqrt{3}}=a[/tex]
[tex]\frac{7}{4}=a[/tex]
Now we will use volume of cube formula with each side length 'a'.
[tex]\text{Volume of cube}=a^3[/tex]
[tex]\text{Volume of cube}=(\frac{7}{4})^3[/tex]
[tex]\text{Volume of cube}=\frac{343}{64}[/tex]
[tex]\text{Volume of cube}=5\frac{23}{64}[/tex]
[tex]\text{Volume of cube}=5.359375\approx 5.36[/tex]
Therefore, the volume of cube will be [tex]5\frac{23}{64}[/tex] cubic meters.
Apply the Pythagorean Theorem to find the distance between points A and B.
A)
11
units
B)
50
units
C)
61
units
D)
72
units
Answer:
c 61 units but it should be under a square root
Step-by-step explanation:
CA=6
CB=5
5^2+6^2=AB^2
61=AB^2
The Option C is partially correct , the answer must be under a square root as [tex]\;\sqrt {61} {\text{ units}}[/tex].
Further explanation:
The pythagorean theorem is used in the right angle triangle and it states that the square of the hypotenuse is equal to the sum of the squares of the perpendicular and base.
It can be mathematically expressed as,
[tex]{h^2} = {p^2} + {b^2}[/tex]
Here, [tex]h[/tex] is the hypotenuse, [tex]p[/tex] is the perpendicular and [tex]b[/tex] is the base.
Step by step explanation:
Step 1:
It is observed from given figure that after joining the points [tex]A,B{\text{ and C}}[/tex] it is established as right angle triangle.
First determine the perpendicular and the base of the triangle.
It can be seen that there are 5 boxes between the point [tex]A{\text{ and }}C[/tex] and 6 boxes between the point [tex]{\text{B and C}}[/tex].
Therefore, the perpendicular of the triangle [tex]AC[/tex] is [tex]{\text{6 units}}[/tex] and the perpendicular of the triangle [tex]AB[/tex] is .
Step 2:
Now use the Pythagoras theorem to find the distance between [tex]B{\text{ and }}A[/tex].
The distance between [tex]B{\text{ and }}A[/tex] is the length of the hypotenuse of the triangle [tex]ABC[/tex].
The length of the hypotenuse [tex]AB[/tex] can be calculated as,
[tex]\begin{aligned}{h^2}&= {p^2} + {b^2}\\{h^2} &= {6^2} + {5^2}\\{h^2} &= 61\\h &= \sqrt {61}\\\end{aligned}[/tex]
Therefore, the distance between [tex]B{\text{ and }}C[/tex] is [tex]\sqrt {61}[/tex] units.
Thus, option C is partially correct , the answer must be under a square root as [tex]\sqrt {61}[/tex] units.
Learn more:
Learn more about the distance between two points on the number linehttps://brainly.com/question/6278187 Learn more about the distance between two coordinates of the linehttps://brainly.com/question/10135690 Learn more about midpoint of the segment https://brainly.com/question/3269852Answer details:
Grade: Junior school
Subject: Mathematics
Chapter: Pythagoras theorem.
Keywords: Distance, Pythagoras theorem, points, base, perpendicular, hypotenuse, right angle triangle, boxes, units, squares, sum
in the figure L1 L2 and L3 is a traversal what is the value of q-p
Answer:
q=135 degrees
p=45 degrees
Step-by-step explanation:
For q:
q is 135 degrees because alternate exterior angles are congruent when L1 is parallel to L2 intersected by L3.
For p:
p is 45 degrees because L2 is a straight line so it has a measurement of 180 degrees. So to find p you do 180 degrees-q.
Which is 180-135=45 degrees
Please help with my math homework :(
Answer:
8x-12=6x-2 x=5
Step-by-step explanation:
Nolan made lanps to sell at the school art show. He made 9 lamps each week for 4 weeks. How many lamps did Nolan make?
Answer: The answer would be 36
Step-by-step explanation:
9×4=36
Find a cubic function that has the roots 5 and 3-2i
Answer:
[tex]P(x)=x^3-11x^2+43x-65[/tex]
Step-by-step explanation:
If the complex number [tex]3-2i[/tex] is a root of a cubic function, then the complex number [tex]3+2i[/tex] is a root too. Thus, the cubic function has three known roots [tex]5,\ 3-2i,\ 3+2i[/tex] and can be written as
[tex]P(x)=(x-5)(x-(3-2i))(x-(3+2i)),\\ \\P(x)=(x-5)(x^2-x(3-2i+3+2i)+(3-2i)(3+2i)),\\ \\P(x)=(x-5)(x^2-6x+9-4i^2),\\ \\P(x)=(x-5)(x^2-6x+9+4),\\ \\P(x)=(x-5)(x^2-6x+13),\\ \\P(x)=x^3-11x^2+43x-65.[/tex]
What is the solution to
-x+3y=2
X+y=-2
Answer:
(-2, 0)
Step-by-step explanation:
Use elimination: add the two systems. Because the left is equal to right, you are adding the same thing and it's legal.
-x+3y=2
+ (x+y=-2)
Add each term
-x+x + 3y+y = 2+ -2
4y=0
y=0
x+y=-2
x+0=-2
x=-2
Answer:
x=-2, y=0
Step-by-step explanation:
-x+3y=2
X+y=-2
We can add these two equations together to eliminate x
-x+3y=2
x+y=-2
--------------
4y = 0
Divide each side by 4
4y/4 = 0/4
y=0
Now we still need to find x
x+y = -2
Substitute x=0
0+y = -2
y= -2
if f(x)=3x-2 and g(x)=f(x)+3, write the equation for g(x)
g(x) = f(x) + 3
Since you know f(x) = 3x - 2, you can plug in (3x - 2) for "f(x)" in the equation:
g(x) = f(x) + 3
g(x) = (3x - 2) + 3
g(x) = 3x - 2 + 3
g(x) = 3x + 1
Identify a pattern in the given list of numbers. Then use this pattern to find the next number 5,9,14,20,27,35,____
Answer:
the answer is 44
Step-by-step explanation:
the pattern is 4,5,6,7,8 so then you would add 9 to get 44
Final answer:
The pattern in the given list of numbers is that each number increases by consecutively larger increments of 1. By continuing this pattern, adding 9 to the last number (35), we determine the next number in the series to be 44.
Explanation:
The given list of numbers is 5, 9, 14, 20, 27, 35, and we are asked to identify the pattern to find the next number in the series.
Let's look at the differences between consecutive terms: 9 - 5 = 4, 14 - 9 = 5, 20 - 14 = 6, 27 - 20 = 7, 35 - 27 = 8.
We can see that with each step, the difference increases by 1. This pattern suggests that the next difference should be 9.
To find the next number, we add 9 to the last number in the series: 35 + 9 = 44. Therefore, the next number in the series is 44.
The number in the middle of a data set best describes
help me to solve this question...easier
Answer:
x = - 3 and x = - 4
Step-by-step explanation:
(a)
The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.
solve x + 3 = 0 ⇒ x = - 3
(b)
Equate f(x) to 5, that is
[tex]\frac{2x+3}{x+3}[/tex] = 5 ( cross- multiply )
5(x + 3) = 2x + 3 ( distribute left side )
5x + 15 = 2x + 3 ( subtract 2x from both sides )
3x + 15 = 3 ( subtract 15 from both sides )
3x = - 12 ( divide both sides by 3 )
x = - 4
it cost $270 for 3 people to go on a fishing trip how much does it cost for 10 people to go on a fishing trip
Answer:
$900
Step-by-step explanation:
It cost each person $90 to go on the trip when you divide 270/3. You can find out how much it would cost for 10 people to go on the trip by multiply 10X90.
What is the equation of the line passing through the points (2, –1) and (5, –10) in slope-intercept form?
A)
Y=3x-5
B)
Y=3x+5
C)
Y=3x-5
D)
Y=3+5
Answer:
y = -3x+5 This has a negative slope
Step-by-step explanation:
The first step is to find the slope. We can use the formula
slope = (y2-y1)/(x2-x1)
= (-10--1)/(5-2)
= (-10+1)/3
= -9/3
=-3
Next we will use the point slope form of the equation of a line
y-y1 = m(x-x1)
y--1 = -3(x-2)
y+1 = -3(x-2)
Distribute the -3
y+1 = -3x -3*(-2)
y+1 = -3x+6
Subtract 1 from each side
y+1-1 = -3x+6-1
y = -3x+5
This is in the slope intercept form of the equation.
My answer differs from the options because I have a negative slope
One evening 1400 concert tickets were sold for the Fairmont Summer Jazz Festival. Tickets cost $20 for covered pavilion seats and $15 for lawn seats. Total receipts were $24,000. How many tickets of each type were sold?
To determine how many tickets of each type were sold, two equations were formulated and the system was solved using the elimination method, resulting in 600 covered pavilion seats and 800 lawn seats sold.
To solve this problem we need to set up a system of equations based on the information provided. Let's define two variables: x for the number of covered pavilion seats sold, and y for the number of lawn seats sold. We know that together, a total of 1400 tickets were sold and the total receipts from these sales were $24,000. We can set up the following equations:
1) x + y = 1400 (total number of tickets sold)
2) 20x + 15y = 24,000 (total revenue from ticket sales)
To solve the system of equations, you can use either substitution or elimination method. Let's use the elimination method by multiplying the first equation by -15 and adding it to the second equation to eliminate y.
-15x - 15y = -21,000
20x + 15y = 24,000
Add the two equations:
5x = 3,000
Divide both sides by 5:
x = 600
Now we can substitute x back into the first equation to solve for y:
600 + y = 1400
y = 800
Therefore, 600 covered pavilion seats and 800 lawn seats were sold.
Point Y is the midpoint of segment XZ. If XY = 2(3x +1) and YZ = 5x + 22, find the value of x. x = 20 x = 24 x = 18 x =11
Answer:x=20
Step-by-step explanation:
2(3x+1) = 6x+2
since xy and yz are the parts of a midpoint they are equal to eachother
so 6x+2=5x+22
if you subtract 5x from both sides you get x+2 = 22 then you subtract 2 from both sides so you have x=20
which of the binomials below is a factor of this trinomial 5x^2-18x+9
Answer:
5x-3 or x-3
Step-by-step explanation:
I don't know what are the choices, so I'll just factor the whole thing. Choose the ones that fit.
-3 + -15 = -18
-3 * -15 = 9*5
5x^2-15x-3x+9
5x(x-3)-3(x-3)
(5x-3)(x-3)
Answer:
5x - 3
Step-by-step explanation:
APEX
I need help with his problem.
Mario made six batches of cookies. His friends asked him to make an extra batch. He used 15 3/4 cups of sugar and needs another 5/8 cup for the extra batch. How many cups of sugar will Mario use altogether? Show work.
The cups of sugar mario use would be 16 3/8 cup
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
We are given that Mario made six batches of cookies. His friends asked him to make an extra batch.
He used 15 3/4 cups of sugar
15 3/4 cup = 126/8 cup
then he needs another 5/8 cup for the extra batch.
126/8 + 5/8 = 131/8 cup
Mario use altogether;
131/8 = 16 3/8 cup
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Kiara downloaded 264 pictures from her cell phone to her computer. These pictures took up 528 megabytes of space on her computer. Each picture took up the same amount of space. How many megabytes do 35 of these pictures take up?
Hello!
Divide 528 and 264. It will give you 2.
Now, multiply 35 and 2.
Answer: 70
Hope this helps! ~Pooch ♥
what is the slope of the line that passes through the points (2, 5) and (7, 3)?
ANSWER: [tex]\frac{2}{-5}[/tex]
EXPLANATION:
We can use the slope formula and input the x and y values to solve for the slope.
[tex]\text{Slope Formula}: \frac{y_{2}-y_{1} }{x_{2}-x_{1}}=m[/tex]
[tex]\frac{5-3}{2-7}=m\\\text{Simplify.}\\\frac{2}{-5} =m[/tex]
The slope of the line is [tex]\frac{2}{-5}[/tex]
The slope of the line that passes through the points (2, 5) and (7, 3) is -2/5.
Explanation:To find the slope of the line passing through the points (2, 5) and (7, 3), we can use the formula for slope:
The slope of the line that passes through the points (2, 5) and (7, 3) can be calculated using the formula:
Slope (m) = (y2 - y1) / (x2 - x1)
Plugging in the values, we get:
Slope (m) = (3 - 5) / (7 - 2) = -2/5
Therefore, the slope of the line is -2/5.
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Find the product of 83 and 3.
Hello!
Answer:
249
Step-by-step explanation:
83
3 x
___
249
Hope this helps! ~Pooch ♥
The cost of belonging to a gym can be modeled by C(m)= 50m + 79.50, where C(m) is the total cost for m months of membership. State the meaning of the slope and y-intercept of this function with respect to the cost associated with the gym membership.
Answer:
The slope is 50, which is the cost per month of the gym membership, and 79.50 is the y intercept. It represents the initial cost to join the gym.
Step-by-step explanation:
C(m)= 50m + 79.50,
This is written in the form y= mx+b where m is the slope and b is the y intercept.
The slope is 50, which is the cost per month of the gym membership, and 79.50 is the y intercept. It represents the initial cost to join the gym.
The slope of the function represents the cost of each additional month of membership, while the y-intercept represents the initial cost of joining the gym.
Explanation:The slope of the function C(m) = 50m + 79.50 represents the cost of each additional month of gym membership. In this case, the slope is 50, meaning that for every additional month of membership, the cost increases by $50.
The y-intercept of the function, which is 79.50, represents the initial cost of joining the gym. This can be considered as the one-time fee or the cost for 0 months of membership.
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The wholesale price of a lamp is $44 and will be marked up by 40 percent. What is the retail price of the lamp?
Answer:
61.60
Step-by-step explanation:
Answer:
The answer is $61.60
Step-by-step explanation
The wholesale price is 44$, but it will be marked up 40% which in decimal form is .40. You multiply that by 44 to get 17.6, and since its mark up you add that number to 44 to get $61.6
factor trinomial 28x^3+27x^2+5x
Answer:
Hello, Gayleayers!! The answer is x(4x+1)(7x+5)
Step-by-step explanation:
To check your answer, use the box method or foil, whichever you prefer. When you use it, leave out the x in front of the parenthesis. The answer will come to x(28x^2+27x+5), then distribute the x. You will get your original answer.
Have a great night and Happy New Year!!
Answer: x(7x + 5)(4x + 1)
Step-by-step explanation:
28x³ + 27x² + 5x
= x(28x² + 27x + 5)
= x(28x² + 7x + 20x + 5)
= x[7x(4x + 1) + 5(4x + 1)]
= x(7x + 5)(4x + 1)
Out of 25 students in Mrs. Green’s class, 12 have a pet. What percent of the students in Mrs. Green’s class have a pet?
Answer by YourHope:
Hi! :)
Out of 25 students in Mrs. Green’s class, 12 have a pet. What percent of the students in Mrs. Green’s class have a pet?
76% of the students in Mrs. Green’s class have a pet!
I also love your profile pic! :)
Write an equation for the line that is parallel to the given line and passes through the given point.
Given line: y= 2x + 4 Given Point: (3, 8)
A.) y = 2x + 2
B.) y = 2x + 6
C.) y = -2x + 6
D.) y = - 1/2x + 2
Parallel lines have the same slope.
If y = 2x + 4, then parallel line has equal y = 2x + b.
The line passes throught the point (3, 8). Put the coordinates of the point to the equation of a line:
8 = 2(3) + b
8 = 6 + b subtract 6 from both sides
2 = b
Answer: A) y = 2x + 2Find an exact value. sine of seventeen pi divided by twelve.
Answer:
4.45058959259........
And it still goes
The exact value of sin(17π/12) is -(√2 + √6)/4.
To find the exact value of sin(17π/12), we need to express 17π/12 as a sum or difference of angles for which we know the sine values. Since 17π/12 is not a standard angle, we'll use the angle addition formula.
17π/12 = (3π/4) + (2π/3)
Now, we'll use the sine addition formula:
sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
Here, A = 3π/4 and B = 2π/3:
sin(3π/4 + 2π/3) = sin(3π/4)cos(2π/3) + cos(3π/4)sin(2π/3)
Now, we need to find the sine and cosine values of 3π/4 and 2π/3:
sin(3π/4) = √2/2, cos(3π/4) = -√2/2
sin(2π/3) = √3/2, cos(2π/3) = -1/2
Plugging these values into the formula:
sin(17π/12) = (√2/2 * -1/2) + (-√2/2 * √3/2)
= -√2/4 - √6/4
= -(√2 + √6)/4
So, the exact value of sin(17π/12) is -(√2 + √6)/4.
-4/40c+12/30 factor each expression completely
Answer:
[tex]\frac{4}{10}(-\frac{1}{4} c+1)[/tex]
Step-by-step explanation:
To factor the expression [tex]\frac{-4}{40}c+\frac{12}{30}[/tex] we use the GCF or greatest common factor. The greatest common factor is the greatest number that will divide into the values. We start to find it by factoring each term's coefficient:
[tex]\frac{2*2}{2*2*2*5}[/tex]
[tex]\frac{2*2*3}{2*3*5}[/tex]
We notice both have 2*2 in the numerator and 2*5 in the denominator. This is our GCF.
[tex]\frac{2*2}{2*5}=\frac{4}{10}[/tex]
We now write the expression 4/10(____+_____). We find the inside of the parenthesis by dividing the coefficients by the GCF. This is also the remaining factors which are not part of the GCF.
[tex]\frac{1}{2*2}=\frac{1}{4}[/tex]
[tex]\frac{3}{3}=1[/tex]
So the answer is [tex]\frac{4}{10}(-\frac{1}{4} c+1)[/tex]