Answer:
Volume = 264 cm³Step-by-step explanation:
Formula:
Let b be the base (circle) of the cone
and h be the height of the cone
[tex]\text{volume of the cone} =\frac{1}{3} \times b\times h[/tex]
……………………………………………
→ b = π × r²
= π × 6²
= (22÷7) × 36
= 113.142857142857 cm²
→ h = 7
[tex]\text{volume of the cone} =\frac{1}{3} \times b\times h[/tex]
The volume = (1÷3)×(113,142857142857)×(7)
= 264 cm³
===================
METHOD 2 :
Volume = (1÷3)×(22÷7)×36×7
= (1÷3)×22×36
= 22×12
= 264
write 2(3x+5)+4(2x-1) in the form of a(bx+c)
The equivalent expression of 2(3x+5)+4(2x-1) is 2(7x + 3)
How to rewrite the expression?The expression is given as:
2(3x+5)+4(2x-1)
Open the brackets
6x + 10 + 8x - 4
Evaluate the like terms
14x + 6
Factor out 2
2(7x + 3)
Hence, the equivalent expression of 2(3x+5)+4(2x-1) is 2(7x + 3)
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solve for x in the diagram below
Multiply:
(5x−1)(5x+4)
Answer: 25x^2+15x-4
Step-by-step explanation:
Multply 5x by the other 5x
25x^2
Multiply 5x by 4
20x
Multiply -1 by 5x
-5x
Multiply -1 by 4
-4
Add them together
25x^2+20x-5x-4
Combine like terms
20x-5x=15x
25x^2+15x-4
Use the strategy to simplify 4√576
Write the prime factorization of the radicand.
[tex]\begin{array}{r|l}576&2\\288&2\\144&2\\72&2\\36&2\\18&2\\9&3\\3&3\\1\end{array}[/tex]
[tex]576=2^6\cdot3^2[/tex]
Therefore
[tex]4\sqrt{576}=4\sqrt{2^6\cdot3^2}[/tex]
which expression represents the following calculation? subtract 1.9 from the product of 7.4 and 3.
A (7.4 + 3) - 1.9
B 7.4 x (3 - 1.9)
C (7.4 x 3) - 1.9
D (7.4 x 1.9) - 3
Answer:
The answer to the question is C
Step-by-step explanation:
as the question state that 1.9 is subtracted from the 7.4×3 so tge 1.9 will be removed ffrom it .
Which function is represented by the graph?
Answer:
D. f(x) = -|x+4| +3
The graph is flipped over the x-axis (facing down) so there's a negative sign in front of the function. It's shifted to the left 4 units so it'll be |x+4|. Finally, it's shifted up 3 units so it'll be +3 outside of the absolute bracket.
NOTE: if there's a change to the x value then it's inside the bracket or parenthesis, if there's a change to the y value then it's outside of the bracket or parenthesis
The ratio of the one leg of the right triangle to the other leg of the right triangle must be 8:7. Determine the greatest length of one leg of the right triangle given the other leg of the right triangle is 10.5 feet.
Answer:
534
Step-by-step explanation:
12. Find the value of x.
HELP PLS HELP
Answer:
x = 16
Step-by-step explanation:
SR = ST ⇒ Two sides are equal. So, ΔSRT is an isosceles triangle.
The angles opposite to equal sides are equal.
⇒ ∠STR = ∠R
∠STR = 4x - 28
Linear pair: If a ray stands on a line, then the adjacent angles are supplementary and they are called linear pair
∠STR + ∠STU = 180° {linear pair}
4x - 28 + 9x = 180
4x + 9x - 28 = 180 {Combine like terms}
13x- 28 = 180
Add 28 to both the sides
13x = 180 + 28
13x = 208
Divide both sides by 13
x = 208/13
[tex]\sf \boxed{x = 16}[/tex]
Answer:
x = 16
Step-by-step explanation:
since SR = ST , then Δ RST is isosceles with the 2 base angles congruent.
∠ STR = ∠ SRT = 4x - 28
∠ STR and ∠ STU are a linear pair and sum to 180° , that is
9x + 4x - 28 = 180
13x - 28 = 180 ( add 28 to both sides )
13x = 208 ( divide both sides by 13 )
x = 16
If f(x)=2x²+x-2, then f(-2)
Answer:
f(-2)=4
Step-by-step explanation:
put -2 where x is
f(x)=2x²+x-2
f(-2)=2(-2)²+(-2)-2
f(-2)=(2*4)-4
f(-2)=8-4
f(-2)=4
You purchase a new car today.the value of that car depreciates based on the function f(t)=12,000(0.96)^t, where t is measured in years after purchase. How much is the car worth after 3/2 years, rounded to the nearest dollar
Considering the definition of exponential function, the value of the car is 11,287.25 dollars.
What is exponential functionAn exponential function is one in which the independent variable x appears in the exponent and has a constant a as its base. Its expression is:
f(x)= aˣ
Being a a positive real, a > 0, and different from 1, a ≠ 1.
When 0 < a < 1, then the exponential function is a decreasing function and when a > 1, it is an increasing function.
What is the price of the carIn this case, the value of that car depreciates based on the function f(t)=12,000×[tex]0.96^{t}[/tex] where t is measured in years after purchase.
After 3/2 years, the value of the car is calculated as:
f(3/2)=12,000×[tex]0.96^{3/2}[/tex]
Solving:
f(3/2)= 11,287.25
Finally, the value of the car is 11,287.25 dollars.
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If sine of the quantity x plus y end quantity equals one half times sine of x plus radical 3 over 2 times cosine of x. What is the value of y?
A. pi over 2
B. pi over 3
C. pi over 4
D. pi over 6
The value of y from the given trig expression is pi/3 rad
Trigonometry identityThese identities are expressed in terms of sine, cosine and tangent
Given the expression
[tex]sin(x+y)=\frac{1}{2}sinx+\frac{\sqrt{3}}{2} cosx[/tex]
Expand sin(x+y)
sin(x+y) = sinxcosy + cosxsiny
Compare both equations
cosy = 1/2
y = arccos(1/2)
y = 60 degrees
y = pi/3 rad
Hence the value of y from the given trig expression is pi/3 rad
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Answer:
The answer is pi/4
When you input all the other values into the equation, they aren't true. When you input pi/4 the equation is true.
D^2=290^2+2030^2
How Do i simplify this
Answer:
Step-by-step explanation:
D²=290²+2030²
=290²+(290×7)²
=290²+290²×7²
=290²(1+7²)
=290²(1+49)
=290²×50
=290²×25×2
=290²×5²×2
D=290×5×√2
D=1450√2
A circle has a radius of 18 ft. Find the length s of the arc intercepted by a central angle of 1.1 radians.
Do not round any intermediate computations, and round your answer to the nearest tenth.
The length of the arc of the circle will be 19.8 ft.
What is an arc of the circle?The arc of the circle is the distance of the circumference of the circle formed sector of the circle at a particular angle.
The formula for the length of the arc of the circle will be given as:-
Arc = Angle x radius
We have Angle = 1.1 radians Radius = 18ft
Arc = 1.1 x 18
Arc = 19.8 ft.
Therefore the length of the arc of the circle will be 19.8 ft.
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Solve the following equations for 0 ≤ theta ≤ 360º cosec(2 — 45°) = 2
Step-by-step explanation:
here ,
[tex]cosec \alpha = \frac{1}{ \sin( \alpha ) } [/tex]
now,
cosec(2-45°)=2
or,
1/sin(2-45°) =2
or,
1/sin2cos45°-cos2sin45=2
or,
[tex] \frac{1}{ \sin(2) \frac{1}{2} - \cos(2) \frac{1}{2} } = 2[/tex]
or,
sorry I have that much qualifications to work on this question and hoping this much will make bit easy for you to solve it further
5. Use an inequality symbol (<, >,=, S) to compare -3 +7-10-2
A. >
B.<
C. ≤
D. =
If the question should read as the following, then I hope my answer will help; -3 +7 _ -10 - 2
Answer: A. >
Step-by-step explanation:
Given:
-3 + 7 _ -10 - 2
Simplify both sides by combining like terms:
4 _ -12
Compare, knowing that 4 is greater than -12:
4 _ -12
4 > -12
A. >
solve the system of equations y=5x-1 y=9x-9
Answer:
Look at the equations:
y
=
−
9
x
−
21
and
y
=
5
x
+
7
Because both equations equal (y), they both equal the same.
If an equations says "
y
=
−
9
x
−
21
" , that means we can replace (y) with
−
9
x
−
21
.
Therefore when i take the equation:
y
=
5
x
+
7
, we can replace (y) to get:
−
9
x
−
21
=
5
x
+
7
Now isolate (x):
−
9
x
−
21
=
5
x
+
7
⇔
−
21
=
14
x
+
7
⇔
−
28
=
14
x
⇔
x
=
−
2
What is the answer to 9!= and 12!=
Answer:
permutation is multiplying numbers from the number given to its last end. so that 9*8*7*6*5*4*3*2*1=is answer. thesame for 12!
Answer:
9! = 362,880
12!=479,001,600
Step-by-step explanation:
the symbol ! simply means factorial
9! = 9×8×7×6×5×4×3×2×1= 362,880
12! = 12×11×10×9×8×7×6×5×4×3×2×1=479,001,600
The shaded shape is a square. What are the coordinates of A and B?
the length of the bottom side is 17-3 = 10
to be a square all sides need to be 10 units.
A(7,13)
B (17,13)
if y=4 when x= -4, find y when x=7
Answer:
Answer:y=-7
Step-by-step explanation:
When x=-4 then y=4 and if x=7 then y=-7
Because y=-x
How many points marked on this graph are solutions?
Answer:
2 points are solutions
Step-by-step explanation:
A solution is a value that makes the equation true, meaning the points fall on the line. For example, the point (0,1) is on the line, which means that for the equation, when x=0, y=1. This also applies for a second point, which is about (-3.5,-1.5).
Hope this helps! :)
PLSSS HELPP Match the value to the correct image. Not all values will be used.
Find the approximate surface area of each right regular prism.
arrowRight
arrowRight
arrowRight
Answer:
open your book and start reading, you should study before the open your book and find it yourself
(03.04 MC) Two pieces of bread, banana and whole wheat, were left out on a kitchen counter and mold began to grow on them. The area of mold growth B(t), in mm2, on the piece of banana bread present after time t weeks, can be represented by the equation B(t) = 20(1.06)t. The area of mold growth W(t), in mm2, present on the piece of whole wheat bread after t weeks is represented in the table. t (in weeks) 1 2 3 4 W(t) (in mm2) 40.8 41.62 42.45 43.30 Which statement best compares the mold growth rates of the banana bread and the whole wheat bread? Question 16 options: The mold growth rate of the banana bread was three times the mold growth rate of the whole wheat bread. The mold growth rate of the banana bread was twice the mold growth rate of the whole wheat bread. The mold growth rate of the banana bread was half the mold growth rate of the whole wheat bread. The mold growth rate of the banana bread was a third the mold growth rate of the whole wheat bread.
Answer:
(a) The mold growth rate of the banana bread was three times the mold growth rate of the whole wheat bread
Step-by-step explanation:
The equation for exponential growth can be written in the form ...
f(t) = a·b^t
where a is the initial value, and b is the growth factor for time period t. The growth factor is related to the growth rate by ...
b = 1 +r . . . . . where r is the growth rate in time period t
__
banana breadThe equation for the area of mold on the banana bread is given as ...
B(t) = 20·1.06^t
Comparing to our generic equation, we see ...
a = 20b = 1.06 = 1 + 0.06The growth rate of the mold on the banana bread is given as 0.06 = 6% per week.
__
whole wheat breadWe are given some values of t and area that we can use to find the growth rate of mold on the whole wheat bread.
W(1) = 40.8 = a·b^1
W(4) = 43.30 = a·b^4
The ratio is ...
W(4)/W(1) = (a·b^4)/(a·b^1) = b^3 = 43.30/40.8
Then the value of b can be found to be ...
b = ∛(43.30/40.8) ≈ 1.02002 ≈ 1 + 0.02
The growth rate of mold on the whole wheat bread is about 0.02 = 2% per week.
__
comparison of growth ratesThe mold growth rate on the banana bread compared to that on the whole wheat bread is ...
(banana bread growth rate)/(whole wheat bread growth rate) = 6%/2% = 3
We can conclude ...
The mold growth rate of the banana bread was three times the mold growth rate of the whole wheat bread
EASY POINTS Which of the following is best defined as segments that intersect at a right
angle?
A. Intersecting segments
B. Perpendicular segments
C. Parallel segments
D. Coplanar segments
Answer:
I would say B.
Step-by-step explanation:
Perpendicular lines meet at a right angle.
Answer: B
Step-by-step explanation:
Instructions
Choose the best answer. If necessary, use the paper you were given.
Question
Last month Simon repaired 45 refrigerators at the Ace Appliance
Company. This month he repaired 20 percent more refrigerators than
last month. How many refrigerators did he repair this month?
Answer:
54 refrigerators
Step-by-step explanation:
In order to find the amount of refrigerators this month, we can do it in one of 2 ways.
The easier way is to multiply 45 by 1.20:
(45)(1.20) = 54
1.20 represents a 120%. This is because 45 refrigerators is 100% of last month, and Simon repaired 20% more, so 100 + 20 = 120.
The next way would be to multiply 45 by 0.20, and then add it to 45.
(45)(0.20) = 9
45 + 9 = 54
Both of the ways result in 54. So, Simon repaired 54 refrigerators this month.
Hope this helps! If you have any questions about my work, please let me know in the comments below!
Which is the best estimate of the distance between the point (-25, 10) and the origin?
O 8 units
O 15 units
O23 units
O 27 units
(Please answer!)
Answer:
27 Units
Step-by-step explanation:
To find the distance using x and y components, use the Pythagorean theory [tex]a^2 + b^2 = c^2[/tex]. Set a as your x-coordinate and b as your y-coordinate (although you can flip them if you so desire). The result will you the square of your distance, so take the square root.
Alternatively, we can solve for C and find that [tex]c = \sqrt{a^2 + b^2}[/tex] or in this case [tex]distance = \sqrt{-25^2 + 10^2}[/tex].
This shows us that distance = 26.93 which is close enough to 27.
For more information: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-theorem/v/the-pythagorean-theorem
evaluate 10 + 8÷4 - 12
Answer:
0
Step-by-step explanation:
evaluate 10 + (8÷4) - 12
Answer:
0
Step-by-step explanation:
First of all we need to divide then add then only subtract
write the function for the graph. a. f(x) = 4 • (12)x b. f(x) = 3 • (4)x c. f(x) = 4 • (3)x d. f(x) = 3 • (12)x
The function of the graph is y = 4(3)^x
How to determine the function of the graph?The graph is an exponential function with the following points
(x,y)= (0,4) and (1,12)
An exponential function is represented as:
y = ab^x
Substitute (0,4) in the equation
4 = a * b^0
a = 4
Substitute a = 4 in y = ab^x
y = 4b^x
Substitute (1,12) in the equation
12 = 4b^1
12 = 4b
Divide by 4
b = 3
Substitute b = 3 in y = 4b^x
y = 4(3)^x
Hence, the function of the graph is y = 4(3)^x
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what is the median data set 25, 17, 38, 11,
Answer:
21
Step-by-step explanation:
Answer:
Median = 21
Step-by-step explanation:
Arrange in ascending order,
→ 11, 17, 25, 38
Now take the middle two,
→ 17 & 25
Then the median data will be,
→ (17 + 25)/2
→ 42/2 = 21
Hence, the median is 21.
Find the value of (1/2)^3 A. 1/6 B. 3/6 C. 1/8 D. 1/2
Answer:
I think it's letter C.
Step-by-step explanation:
not sure correct me if I'm wrong.
We are going to multiply the fraction 1/2, to the power of 3.
This means that:
1 will be multiplied 3 times.2 will multiply 3 timesTherefore:
[tex]\bf{\left(\dfrac{1}{2}\right)^{3}=\dfrac{1\times1\times1}{2\times2\times2}=\dfrac{1}{8} }[/tex]
Therefore, the answer of the fraction (1/2)^3, is equal to 1/8.
The correct option is C.[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
Joe is a carpenter and needs a ladder long enough to reach to a second story window that is 17 ft. from the ground. If he sets the ladder three feet from the base of the building, to the nearest tenth of a foot, how tall must the ladder be in order to reach the frame of the window? Explain your answer.
triangle - left side 17 feel, bottom 3 feet, right side - ladder
A- 17.3 ft
B- 16.7 ft
C- 20 ft
D- 25 ft