The volume of the cylinder with radius r = x - 3 and height h = 2x + 7 is given by the expression V = π ( 2x³ - 5x² - 24x + 63 )
What is a Cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is
Volume of Cylinder = πr²h
Surface area of cylinder = 2πr ( r + h )
where r is the radius of the cylinder
h is the height of the cylinder
Given data ,
Let the volume of the cylinder be represented as V
Now , the radius of the cylinder r = ( x - 3 ) units
Let the height of the cylinder be h = ( 2x + 7 ) units
And , Volume of Cylinder = πr²h
On simplifying the equation , we get
Volume of Cylinder = π ( x - 3 )² ( 2x + 7 )
Volume of Cylinder = π ( x² - 6x + 9 ) ( 2x + 7 )
On further simplification , we get
Volume of Cylinder = π ( 2x³ - 5x² - 24x + 63 )
Hence , the expression for the cylinder is V = π ( 2x³ - 5x² - 24x + 63 )
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Which type of transformation is the equivalent of two reflections across intersecting lines?
Answer:
Rotation
Step-by-step explanation:
Anthony, Josh, and Dominic worked a combined 7 hours today. Dominic worked twice as many hours as Anthony did with an extra hour. Dominic worked 5 more hours than Josh did. How many hours did each of them work?
The number of hours worked by Anthony , Josh and Dominic is 2 hours , 0 hours and 5 hours respectively
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of hours worked by Anthony = A
Let the number of hours worked by Josh = J
Let the number of hours worked by Dominic = D
Total number of hours worked by Anthony , Josh and Dominic = 7 hours
So , A + J + D = 7 be equation (1)
Now ,
Dominic worked twice as many hours as Anthony did with an extra hour
So , D = 2A + 1 be equation (2)
And ,
Dominic worked 5 more hours than Josh did
So , D = 5 + J be equation (3)
Simplifying be equation (2) and be equation (3) , we get
2A + 1 = 5 + J
Subtracting 5 on both sides , we get
J = 2A - 4 be equation (4)
Now ,
Substituting the values of equation (2) , equation (3) and equation (4) in equation (1) , we get
A + 2A - 4 + 2A + 1 = 7
5A - 3 = 7
Adding 3 on both sides , we get
5A = 10
Divide by 5 on both sides , we get
A = 2
Therefore , the number of hours Anthony worked is 2 hours
Now , Substituting the value of A in equation (4) , we get
J = 4 - 4
J = 0 hours
Therefore , the number of hours Josh worked is 0 hours
Now , Substituting the value of A in equation (2) , we get
D = 4 + 1
D = 5 hours
Therefore , the number of hours Dominic worked is 5 hours
Hence , The number of hours worked by Anthony , Josh and Dominic is 2 hours , 0 hours and 5 hours respectively
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What is the answer to 4x+8+6x+12=85
Answer:
= 10x + 20
Step-by-step explanation:
If I helped may I get brainliest?
Answer:
x=6.5
Step-by-step explanation:
1. simplify the equation to 10x + 20 +85
2. minus 20 from both sides to get 10x =65
3. divide 10 from both sides
4. x= 6.5
hope this helps!
What does negative 3 over 5 > −2 indicate about the positions of negative 3 over 5 and −2 on the number line?
So,
Ignore the negatives and just make them positives.
For now.
Then, you look at 3/5 and say... it's 3 ticks towards the number five,
meaning it's between 4 and 5. After you do that whats happens is you place back the negatives and you have -3/5 and -2.
-2 < 5 and -2 < 4
Meaning it goes more to the left.
I could be wrong but If I'm right please mark brainliest
A rectangular object is 3.0 cm long, 2.0 cm wide, and 4.0 cm high. Calculate the VOLUME of the object?
Answer:
V = length x width x height
V = 3 x 2 x 4
V = 24 cm^3
Rebecca Smith was the top scorer in a women's professional basketball league for the 2006 regular season, with a total of 863 points. The number of two-point field goals that Rebecca made was 80 less than double the number of three-point field goals she made. The number of free throws (each worth one point) she made was 13 less than the number of two-point field goals she made. Find how many free throws, two-point field goals, and three-point field goals Rebecca Smith made during the 2006 regular season.
Answer:
Number of free throws = 155,
Number of two-points field goals= 168
Number of two-points field goals= 124
Step-by-step explanation:
Let x,y, and z be the numbers of free throws, two-point field goals and three-point field goals she made.
As she scored a total of 863 points, so
x+2y+3z=863...(i)
As the number of two-point field goals that Rebecca made was 80 less than double the number of three-point field goals she made, so
2z-y=80
Or y=2z-80...(ii)
As the number of free throws (each worth one point) she made was 13 less than the number of two-point field goals she made, so
y-x=13
-x= 13-y
-x= 13-(2z-80)
-x= 93-2z
x=2z-93...(iii)
Now, put the values from equation (ii) and (iii) to equation (i), we have
(2z-93)+2(2z-80)+3z=863
2z-93+4z-160+3z=863
9z=863+93+160=1116
z=1116/9=124
From equation (ii)
y=2x124-80=168
and from equation (iii)
x=2x124-93=155.
Hence, the number of free throws, two-point field goals, and three-point field goals Rebecca Smith made during the 2006 regular season are 155, 168, and 124 respectively.
Write in simplest form. 12/15 Divided by 4/9
Answer:
9/5
Step-by-step explanation:
12/15 / 4/9
12/15 * 9/4
108/60
54/30
27/15
9/5
Please help I’ll give brainiest!!
A
0.50
B
1
C
3
D
2
Answer:
D.
Step-by-step explanation:
The slope/rate of change is 2.
Use long division to divide.
691 ÷ 9
Answer ⇒
= 76
Step - By - Step Explanation ⇒
It is not easy to write long division on a laptop as it paper, so I have attached an image from a calculator that I found online.
Instructions: Find the missing angle in the image below. Do not include spaces in your answers.
Answer:
im not the best in math but I think its 95 since a line segment is 180 degrees and you add tge two number and subtract what you have
hope this hells
graph the inequality plz help me solve this and explain how plzzzzzz x-y <4
Answer:
Step-by-step explanation:
first you have to get the inequality to a point where you can actually graph it
to do this you have to get the x to the same side of the less than symbol
you do this like any other equation, subtract x from the left and right sides because whatever you do to one side, you do to the other
this leaves you with -y < -x + 4
you have to multiply the entire thing by -1 because y cannot be negative
this gives you y < x - 4, now you can graph it
because x is isolated you just have to graph y < -4 like so
im not the best at explanations, i apologize
Question
Identify the correct graph and solution for the inequality.
10 a <25
(Look at pic)
Answer:
First option
Step-by-step explanation:
First, Solve the inequality:
Divide each side by 10 to cancel out the 10 next to a. It should now look like this: a < 2.5Find the inequality that matches the solution:
The first option (which literally writes the simplified version of the inequality) is correct, because it matches our simplified inequality above.Re-write the quadratic function below in Standard Form
y = 3(x - 2)2 – 2
Answer: Y=
A group of 7 people spent $33.50 on movie tickets. They paid $6.50 for each adult ticket and $3.50 for each child's ticket. We would like to determine how many of each type of ticket was purchased. A. Specifically define variables for this system B. Write a system of equations that reflects the relationships described in this situation
Answer:
Number of Adult tickets = 3
Number of student tickets = 4
Step-by-step explanation:
Let the number of Adults tickets = x
The number of students tickets = y
A. Specifically define variables for this system
x + y = 7...... Equation 1
They paid $6.50 for each adult ticket and $3.50 for each child's ticket.
$6.50 × x + $3.50 × y = $33.50
6.50x + 3.50y = 33.50.......Equation 2
B. Write a system of equations that reflects the relationships described in this situation
x + y = 7...... Equation 1
x = 7 - y
6.50x + 3.50y = 33.50.......Equation 2
6.50(7 - y) + 3.50y = 33.50
45.5 - 6.5y + 3.5y = 33.5
45.5 - 33.5 = 6.5y -3.5y
12 = 3y
y = 12/3
y = 4 tickets
x + y = 7...... Equation 1
x + 4 = 7
x = 7- 4
x = 3 tickets
Please identify the common angles and sides or if there are non. Explain all work please!
Answers:
Common angles: ΔBGC and ΔGDC
Common sides: ΔGE and ΔAG
A common angle is a triangle that exists in two or both of the triangles.
Here, the common angles should be ΔBGC and ΔGDC.
These two angles are triangles, and they consist in both triangles.
A common side is when two angles have one vertex in the same area.
Here, we see that the common sides are ΔGE, because they intersect.
Another common side we see here is ΔAG, because they also intersect.
Hope this answer helps you!
2/3x = 24 what does x equal?
Answer:
x=36
Step-by-step explanation:
Find the two integers, m and n,
make the equation (2x^ny2)m = 4x6y4 true.
Answer:
m = 2 and n = 3
Step-by-step explanation:
We want to find the value of the integers m and n that will make the given expression true
(2x^ny^2)^m = 4x^6y^4
We can rewrite the left hand side of the equation as follows;
(2x^3y^2)^2
we can proceed to use inspection to ind the value of m and n
Through inspection since the left hand side of the equation now looks like the right hand side;
Then;
m= 2 and n = 3
is 192 rational , why is it?
Answer: 192 IS IRRATIONAL. I HOPE THIS ANSWER HELPS.
Step-by-step explanation:
It is an irrational number if it is not a perfect square. Since 192 is not a perfect square, it is an irrational number. This means that the answer to "the square root of 192?" will have an infinite number of decimals. The decimals will not terminate and you cannot make it into an exact fraction.
Part 2 - What is the equation of the line?
Answer:
y = 3x + 3
Step-by-step explanation:
Hope This Helps!
Plz Mark Brainliets!
1/6 and 3/10 simplified
Answer:
They are already simplified..
Step-by-step explanation:
Help!!!!!!!!! Quick!!!!!
Answer:
<A obtuse
<B acute
<C obtuse
<D right
Step-by-step explanation:
what is the value of 1+(-7)-(-2.5)?
Anne plans to increase the prices of all the items in her store by 5%. To the nearest cent, how much will
an artist save if the artist buys a canvas and a frame that each measure 24 by 36 inches before the
price increase goes into effect
Answer:
Step-by-step explanation:
We don't know the first price?
what is x? in the equation x-21=6
Answer:
27
Step-by-step explanation:
You would turn the equation around, so it is 21+6=27 and checking, 27-21=6
Answer:
x = 27
Step-by-step explanation:
x- 21 = 6
add 21 to both sides:
x = 27
Check your work by substitution:
27 - 21 = 6
6= 6
x = 27
Interce
Determine the intercepts of the line.
Y=-9x-14
Answer:
y= -14 x= -1.556
Step-by-step explanation:
graphing calculator is good
is so eassy 2 puls 2
Answer:
4
Step-by-step explanation:
Answer:
22
Step-by-step explanation:
True or false? You can rely solely upon induction to prove that your conclusion is correct
Answer:
false
Step-by-step explanation:
Answer:
false you will need more info
Step-by-step explanation:
PLEASE HELP ME! Check Picture
Answer:
Are their any options on what to do??
Step-by-step explanation:
-)
Choose the symbol that goes in the blank to make the statement true.
163_136
Answer: 163>136
Step-by-step explanation:
encuentra el numero decimal equivalente a la fracción
7/10
198/100
85/100
45/100
1/4
3/2
3/8
1/9
7/10 = 0.7
198/100 = 1.98
85/100 = 0.85
45/100 = 0.45
1/4 = 0.25
3/2 = 1.5
3/8 = 0.375
1/9 = 0.11111111 ( goes on forever) ( sigue para siempre )
Hope it Helps!
¡Espero eso ayude!