Answer:
The volume of the cone is approximately 453.0 cm³
Step-by-step explanation:
The volume of a cone is one third that of a cylinder with the same height and radius. That gives us 1/3 πr²h, where r is radius and h is height.
However, we are not given the height of the cone, but the side length. We can work out the height using the Pythagorean theorem, as we have a right triangle with the height, base radius, and length. You may recall that the Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of it's other two sides:
[tex]a^2 = b^2 + c^2[/tex]
So we can find the height of the cone with that:
[tex]10.8^2 = 7.4^2 + h^2\\h^2 = 10.8^2 - 7.4^2\\h^2 = 116.64 - 54.76\\h^2 = 61.88\\h = \sqrt{61.88}\\h \approx 7.9[/tex]
Now that we have the cone's height, we can solve for its volume:
[tex]v = \frac{1}{3} \pi r^2 h\\v = \frac{1}{3} \pi \times 7.4^2 \times 7.9\\v = \frac{1}{3} \pi \times 54.76 \times 7.9\\v = \frac{1}{3} \pi \times 432.6\\v = \pi \times 144.2\\v \approx 453.0 cm^3[/tex]
Answer:
c = 490/3
Step-by-step explanation:
Triangle DEF is a right triangle. The length of the legs are 7 cm and 10 cm, how long is the hypotenuse? Round to the nearest tenth if possible.
A.
7.1 unit
B.
9.0 units
C.
12.2 units
D.
17.0 units
Answer:
C
Step-by-step explanation:
Answer:
C. 12.2
Step-by-step explanation:
7^2 + 10^ = 49 + 100
Square root of 149 = 12.2
Long Divison : 3 divided by 2,284 = and don't forget the remainder of it all
2,284 divided by 3,what is the remainder??
Answer :2,284÷3=761 and remainer=1
Answer:
761 R1
Step-by-step explanation:
Can someone help please
Plz help with these 3:)
Answer: 1) 2
2) 7/10
3) -1/3
What is the value of 5k + m when k = -3 and m = -9
A. -60
B. -30
C. -24
D. -6
Answer:
-24
Step-by-step explanation:
5(-3) + -9 =
-15 + -9 =
-24
c
5×-3+-9
15+9=24
i think
What is the area of the triangle that has a base of 12 and a height of 23.
Pls help with this
Answer:
138
Step-by-step explanation:
Answer:
138
Step-by-step explanation:
Area of a triangle = ½×base×height
Base=12
Height=23
Area=½×12×23
=1×6×23
=138cm²
12 can be divided exactly by 2 that's why we have 6.
I have been stuck on this question for the past five minutes I am confused.
Answer: hahahah don't
Step-by-step explanation:
Ali was asked to simplify the expression 3(x - 6) + (4x + 12) - 6x. His work is shown below.
3(x - 6) + (4x + 12) - 6x
3x - 9 + 4x + 12 - 6x
(3x + 4x - 6x) + (-9 + 12)
x + 3
Answer:
Step 2 is wrong.
It should be 3x – 18 + 4x + 12 – 6x
Explanation:
3(x – 6) + (4x + 12) – 6x →
3x – 18 + 4x + 12 – 6x →
(3x + 4x – 6x) + (-18 + 12) →
x – 6
solve eight and two fourths minus three and one third
Answer:
5 1/6
Step-by-step explanation:
Rewriting our equation with parts separated
=8+2/4−3−1/3
Solving the whole number parts
8−3=5
Solving the fraction parts
2/4−1/3=?
Find the LCD of 2/4 and 1/3 and rewrite to solve with the equivalent fractions.
LCD = 12
6/12−4/12=2/12
Reducing the fraction part, 2/12,
2/12=1/6
Combining the whole and fraction parts
5+1/6=5 1/6
The objective when solving an equation is to....
Answer:
to get the variable by itself on one side of the equation and a number on the other side of the equation. To isolate the variable, you have to reverse the operations acting on the variable.
Step-by-step explanation:
A bird can fly at a speed of 50 miles/h. If the bird flies for 90 minutes, what distance will it have flown?
Answer:
75 miles
Step-by-step explanation:
If the bird flies for 90 minutes at 50 mph (miles per hour), we need to calculate how many hours 90 minutes is.
One hour is 60 minutes. Our equation will be: 90/60 = 1.5
This mean the bird flies 1.5 hours at 50 mph. To find the distance, we multiply 1.5 by 50.
1.5 × 50 = 75
The bird has flown 75 miles.
please answer this:
3n + 2 = 17
Ren was trying to solve a system of linear equations. He correctly argued that he could replace one equation by the sum of that equation and multiple of the other. He stated that this would produce a system that has the same solution as the original system.
To show this, Ren wrote down a system of equations. He them determined wich othe system of equations would have the same solution as the original system. Ren's original system is shown below.
Answer:
This what I got.
Hope it helps!
The solution of 1st and 2nd system of equations have solutions same as the main system of equations and 3rd is not same.
What is a system of equations?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
The given equations are;
-2x-5y = -47........(i)
4x-2y = -2
We can simply it, and write;
2x-y = -1
y = 2x+1.....(ii)
Put equation (ii) in (i)
-2x-5(2x+1) = -47
-2x-10x-5 = -47
-12x = -42
x = 7/2
Put value of x in eq (ii)
y = 2(7/2)+1
y = 8
Therefore, the solution of main equation is (7/2, 8)
Solving the other three equations,
1) -14x+y = -41
or, y = -41+14x......(i)
2) 4x-2y = -2
or, 2x-y = -1
y = 2x+1....(ii)
Solving the equations,
2x+1 = -41+14x
12x = 42
x = 7/2
Put x = 7/2, in (ii)
y = 8
Therefore, the solution is (7/2, 8)
We get the solution of main equation is equal to this system of equation.
2) -2x-5y = -47......(i)
6x+3y = 45
or, 2x+y = 15.......(ii)
Solving the equation by elimination,
-4y = -32
y = 8
Put y = 8 in equation (ii)
2x+8 = 15
x = 7/2
Therefore, the solution is (7/2, 8)
Again, we get the solution of main equation is equal to this system of equation.
3) -2x-5y = -47.........(i)
8x-5y = -8.......(ii)
Solving the equations by elimination,
-10x = -39
x = 39/10
Since, value of x is not same as the value of x in main equation, that means, both the system of the equation do not have same solution.
Hence, we get that, the solution of 1st and 2nd system of equations have solutions same as the main system of equations and 3rd is not same.
For more references on system of equations, click;
https://brainly.com/question/12895249
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factor using x method and foil to prove
Can someone plz help me with those two I’m being timed !!!
Answer:
The first one is (-4,3) The second one is (-1,3)
Does the graph represent a function?
Yes Or No
Answer:
Yes.
Step-by-step explanation:
First, draw a vertical line. Then check the interception between the graph and a vertical line.
If the line intercepts the graph only one point, then it is a function. Otherwise, it is not. That includes two or more.
The graph shown in the picture is a function (Cubic Function).
URGENT!! PLEASE HELP 30 POINTS! FAKE ANSWERS REPORTED
Answer:
X=1÷2,Y=32°
Step-by-step explanation:
in right angled traingleRST
<R+<T<S=180(INTERIOR ANGLE OF TRAINGLE)
Y-2+90+60=180(S=60°BEING ONE ANGLE OF EQUILATERAL TRAINGLE)
Y+148=180
Y=180-148=32
NOW,
UT=5X(RT BISECTS TS AND UT EQUALLY)
RU=US(SIDE OF EQUILITERAL TRAINGLE IS EQUAL)
8X+1=UT+TS
8X+1=5X+5X
1=10X-8X
1=2X
X=1/2
Solve: 2(3x + 4) = 44
Answer: x=6
Step-by-step explanation:
What is the image of (3,-7) after a reflection over the line y =x
Answer:
Image: (-7,3)
Step-by-step explanation:
Reflections In The Coordinate Plane
Reflect over the line y = x:
When reflecting a point across the line y = x, the x-coordinate, and y-coordinate change places.
Thus, the point (3,-7) maps to the point (-7,3) when reflected over y=x.
I need help with this
Answer:
B is ur answer! Divide 8 by 3
Step-by-step explanation:
PEMDAS
Please help Find x
====================================================
Explanation:
The hexagon is broken up into 6 congruent or identical equilateral triangles. If we find the area of one triangle, then we multiply by 6 to get the area of the hexagon.
Going in reverse, we divide the hexagon's area by 6 to get the area of one equilateral triangle
We're told the hexagon has an area of [tex]18\sqrt{3}[/tex] square inches. Divide this by 6 and you should get the result [tex]3\sqrt{3}[/tex]. So each of the six equilateral triangles has area of [tex]3\sqrt{3}[/tex] square inches.
-------------------------------------
Each triangle has a base of [tex]2(\sqrt{3})^{x/12}[/tex] and a height of [tex](\sqrt{3})^{x/6}[/tex]
The x/12 and x/6 are exponents.
Let [tex]b = 2(\sqrt{3})^{x/12}[/tex] and [tex]h = (\sqrt{3})^{x/6}[/tex] be the base and height respectively.
Also, let [tex]A = 3\sqrt{3}[/tex] be the area of the triangle
We can then solve for x like so:
[tex]A = 0.5*b*h\\\\3\sqrt{3} = 0.5*2(\sqrt{3})^{x/12}*(\sqrt{3})^{x/6}\\\\3*3^{1/2} = (\sqrt{3})^{x/12+x/6}\\\\3^1*3^{1/2} = (\sqrt{3})^{x/12+2x/12}\\\\3^{1+1/2} = (\sqrt{3})^{3x/12}\\\\3^{3/2} = (3^{1/2})^{x/4}\\\\3^{3/2} = 3^{(1/2)*(x/4)}\\\\3^{3/2} = 3^{x/8}\\\\[/tex]
Since the bases are equal to 3, this means the exponents must be equal as well (for both sides overall to be equal)
3/2 = x/8
3*8 = 2*x ... cross multiply
24 = 2x
2x = 24
x = 24/2
x = 12
Express as a trinomial.
(2 – 4)(2x + 3)
Answer:
-2(2x+3)
Step-by-step explanation:
Answer:
-2 (2x + 3)
Step-by-step explanation:
We need to use FOIL
Multiply the FIRST terms of each set together
Then the OUTSIDE terms
Then the INSIDE terms
and then the LAST terms
Thus:
[tex]2*2x = 4x[/tex]
[tex]2*3 = 6[/tex]
[tex]-4*3 = -12[/tex]
[tex]-4*2x = -8x[/tex]
So finally we end up with 4x + 6 - 12 - 8x
Simplifying this gives us -4x - 6
We can then factor out -2 from each factor, giving: -2(2x+3)
Hope this helps!
Can anyone help me with this please :( ?
Don’t answer if you do not know.
I will mark you as a brainliest:) !
Answer:
y=200x
Step-by-step explanation:
the y intercept is 0 so it does not need to be added
the line rises 200 every time
don´t really know how else to explain hope this helps
The length and breadth of rectangular field are 240m and 200m respectively. Find the cost of digging the field at Rs 10 per m^2
Answer:
Please check the explanation.
Step-by-step explanation:
Given
The length of rectangular field = l = 240mThe breadth of rectangular field = w = 200mWe can determine the area of the rectangular field using the equation
[tex]A=wl[/tex]
where
[tex]l[/tex] is the length [tex]w[/tex] is the widthsubstituting l = 240m, and w = 200m in the formula
[tex]A=wl[/tex]
A = 240 × 200
A = 48000 m²
Given that the cost of digging the field at Rs 10 per m².
Thus,
The cost of digging the field of the area 48000 m² = 10 × 48000
= 480000 Rs
Therefore, the total cost of digging = 480000 Rs
So on my math hw I got asked this. I don't understand can someone help?
Answer:
A
Step-by-step explanation:
A proportional relationship is basically just a pattern between numbers.
Hence the correct option is A
Help plzzzzz.............
Answer:
a) 3 b) y = 3x + 11
Step-by-step explanation:
a)
In order to find the gradient (slope), find the change in y or change in x (rise/run).
-2 - 2 / 7 - (-5)
-2 - 2 / 7 + 5
-4/12 = -1/3
Now that we know the gradient of line AB is -1/3, take the opposite reciprocal of that to find the gradient perpendicular to line AB.
-1/3 ⇒ 3
b)
Take point C's values and the perpendicular gradient found earlier and substitute them into the point-slope form equation.
y - 5 = 3(x - (-2))
y - 5 = 3(x + 2)
y - 5 = 3x + 6
y = 3x + 11
for each system, determine whether the given ordered pair is a solution (help fast)
(3,1 ) is a solution
X+Y=4
X-Y=2
X=4-y
4-y-y=-2
4-2y=-2
-2y=-2
y=1
X+1=4
X=4-1
X=3
if £2000 is placed into a bank account that pays 3% compound interest per year how much will be in account after 2 years?
Answer:
£2121.80
Step-by-step explanation:
Year 1 -> 2000 + (3% of 2000) = 2000 + (60) = 2060
Year 2 -> 2060 + (3% of 2060) = 2060 + (61.80) = 2121.80
Which one of these dishes would make the food dish the warmest when placed on top of it?
HELP THIS IS WORTH 100 POINTS WILL MARK BRAINLIEST
Answer:
I cant see it
Step-by-step explanation: