Answer:
Answer is C
Step-by-step explanation:
The result of product [tex]\sqrt[3]{24} \times \sqrt[3]{45}[/tex] is [tex]6\sqrt[3]{5}[/tex].
The product is represented as:
[tex]\sqrt[3]{24} \times \sqrt[3]{45}[/tex]
Multiply the roots
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= \sqrt[3]{24\times 45}[/tex]
Rewrite the above expression as:
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= (24\times 45)^{1/3}[/tex]
Expand 24
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= (3 \times 8 \times 45)^{1/3}[/tex]
Express 8 as 2^3
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= (3 \times 2^3 \times 45)^{1/3}[/tex]
So, we have:
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= 2(3 \times 45)^{1/3}[/tex]
Express 45 as 9 * 5
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= 2(3 \times 9 \times 5)^{1/3}[/tex]
Express 9 as 3^2
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= 2(3 \times 3^2 \times 5)^{1/3}[/tex]
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= 2(3^3 \times 5)^{1/3}[/tex]
So, we have:
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= 2\times 3(5)^{1/3}[/tex]
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= 6(5)^{1/3}[/tex]
Rewrite as:
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= 6\sqrt[3]{5}[/tex]
Hence, the result of product [tex]\sqrt[3]{24} \times \sqrt[3]{45}[/tex] is [tex]6\sqrt[3]{5}[/tex]
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A beach ball has a radius of 10 inches. Round to the nearest tenth
Find the coordinates of the point for the reflection.
(−4, 8) across the x-axis
The coordinates of the reflection are
Answer:
The point after the reflection: [tex](-4,-8)[/tex]
Step-by-step explanation:
-Statement: If you reflect the point [tex](x,y)[/tex] across x-axis or the y-axis, then the [tex]x[/tex] and the [tex]y[/tex] of the point can change either positive, negative or the same, depending on where the point is located on a graph.
-So, if you reflect the point [tex](-4,8)[/tex] across x-axis, then the point after the reflection, would be [tex](-4, -8)[/tex] :
The following point: [tex](-4, 8)[/tex]
The point after the reflection: [tex](-4,-8)[/tex]
f(x) = 3^x; find f(0)
Answer:
f(0)=1
Step-by-step explanation:
The question asks us to find f(0). We want to find what f(x), or y is, when x is equal to 0.
f(x)=3^x
Therefore, we can substitute 0 in for x.
f(0)=3^0
Evaluate the exponent, 3^0.
Any number raised to the power of zero is equal to 1.
f(0)=1
Answer:
1
Step-by-step explanation:
f(0) = 3^0
f(0) = 1
anything to the 0th power = 1
f (x) = 3x^2 - 7x - 32
What is the value of f(-4)?
Answer:
f (-4) = 3x(-4)^2 - 7x(-4) - 32 = 44
Step-by-step explanation:
you should replace every x with the number given which is here equals -4
Please help!! Thank you!
Answer: 84 ft
Step-by-step explanation:
A taxi cab company charges a flat amount of $5.00 plus a rate of $3.00 per mile traveled. Part A: If the total cost of the fare was $41.00, then which of the following equations can be used to determine the number of miles traveled, x?What is the total number of miles traveled, x, if the fare was $41.00?
Answer:
5 + 3x = 41
x = 12 miles
Step-by-step explanation:
A taxi cab company charges a flat amount of $5.00 plus a rate of $3.00 per mile traveled.
Let x is the number of miles traveled.
If the total cost of the fare was $41.00 then
5 + 3x = 41 eq. 1
The above equation can be used to determine the number of miles traveled.
Solving the equation for x,
5 + 3x = 41
3x = 41 - 5
3x = 36
x = 36/3
x = 12 miles
Therefore, 12 is the total number of miles traveled if the fare was $41.00.
6/7 times 3/4=?????????
Answer:
[tex] \frac{9}{14} [/tex]
Step-by-step explanation:
times top numbers and bottom numbers
6 × 3 = 18
7 × 4 = 28
18/28
*simplify*
9/14
Select the correct answer.
If a six-sided die is rolled 30 times, how many times can you expect to get a 6?
Answer:
5
Step-by-step explanation:
the probability of getting a 6 every time you roll the die once is just 1/6. multiply that by 30 and we get our answer, which is 5 times.
A container shapes like an inverted cone holds 96 cubic centimeters of water. The height of the cup is 14 centimeters. Find the length of the diameter?
Answer:
Cone Volume = (PI * radius^2 * height) / 3
96 cc = (PI * radius^2 * 14) / 3
(96 * 3) / (PI * 14) = radius^2
radius ^ 2 = 6.5480890872
radius = 2.5589234235
diameter = radius *2 = 5.117846847 cm
diameter = 5.12 cm (rounded)
Step-by-step explanation:
Enrollment in a dance studio has grown exponentially since the studio opened. A graph depicting this growth is shown. Determine the percentage rate of growth.
0.25%
1.25%
2.5%
25%
Answer:
Option (4). 25%
Step-by-step explanation:
The graph attached shows the exponential growth.
Let the graphed function is y = [tex](1+\frac{r}{100})^{t}[/tex]
Here 'r' = Rate of growth
t = Duration of time in years
y = enrollments after time 't' years
Graph shows at time 't' = 0 or initially number of enrollments = 20
After 8 years number of enrollments will be
120 = [tex]20(1+\frac{r}{100})^{8}[/tex]
[tex]\frac{120}{20}=(1+\frac{r}{100})^{8}[/tex]
6 = [tex](1+\frac{r}{100})^{8}[/tex]
log 6 = [tex]8\text{log}(1+\frac{r}{100})[/tex]
0.77815 = [tex]8\text{log}(1+\frac{r}{100})[/tex]
[tex]\text{log}(1+\frac{r}{100})[/tex] = 0.0972689
[tex](1+\frac{r}{100})=1.251[/tex]
[tex]\frac{r}{100}=0.251[/tex]
r = 25.1%
r ≈ 25%
Therefore, Option (4) will be the answer.
Answer:
25%
Step-by-step explanation:
did test and it was right
Is every trapezoid a rectangle
Answer:
No, a trapezoid is not a rectangle.
This is because trapezoids by definition have only one pair of parallel sides while rectangles must have at least two sets of opposite parallel sides. Also, trapezoids do not have 90 degrees at every angle like rectangles do.
the radius of a circle is 2 in what is the length of the 45 arc?
Answer:
1.5707
Step-by-step explanation:
i solved it using the formula :
[tex]2\pi \times r \frac{45}{360} [/tex]
The base of a right triangle is 13 less than 2 times the height. The area of the triangle is 12 square cm. What is the height of the triangle in cm? *
Answer:
The height of the triangle is 8 cm
Step-by-step explanation:
First we need to write down the question in a mathematical format and then solve.
let b be the base of the triangle and h be the height of the triangle
"The base of a right triangle is 13 less than 2 times the height" can be written as
b = 2h - 13 -----------------------------------------------------(1)
"The area of the triangle is 12 square cm" can be written as;
area of the triangle = 12 cm²
but area of a triangle = [tex]\frac{1}{2}[/tex] ×b × h
This implies that
[tex]\frac{1}{2}[/tex] ×b × h = 12 cm²
bh = 24 cm² --------------------------------------------------(2)
substitute equation (1) in equation (2)
(2h - 13)h = 24
2h² - 13h = 24
2h² - 13h - 24 = 0 ----------------------------------------------(3)
The above is now a quadratic equation, so we will solve by completing the square method.
Find two numbers such that its product will give -48 and its sum will give -13
The two numbers are -16 and 3
Replace -13h by (-16h + 3h) in equation (3)
2h² - 13h - 24 = 0
2h² - 16h + 3h - 24 = 0
2h(h - 8) + 3(h-8) = 0
(h-8)(2h+3) = 0
either h-8 = 0
h = 8
OR
2h + 3 = 0
2h = -3
h =-3/8
There is no such thing as negative length, therefore h= 8 is the answer
The height of the triangle is 8 cm
What’s the answer to this
Answer B
Step-by-step explanation:
2x+1+14
Answer:
B.)
Step-by-step explanation:
B)2x+15
h(x)=x-4 Determine whether it is in the domain of h or not.
Answer:
-4
Step-by-step explanation:
Answer: im pretty sure it is a domain
Step-by-step explanation:
The function h ( x ) = 1 x − 1 h ( x ) = 1 x - 1 can be expressed in the form f ( g ( x ) ) f ( g ( x ) ) , where g ( x ) = ( x − 1 ) g ( x ) = ( x - 1 ) , and f ( x ) f ( x ) is defined as:
Answer: f(x) = 1^(x + 1)
Step-by-step explanation:
we have that h(x) = 1^x
and h(x) = f(g(x))
This mean that we are evaluating the function f(y) in the point y = g(x)
where g(x) = x - 1
then:
f(g(x) = f(x - 1) = h(x) = 1^x
then we should have that:
f(x) = 1^(x + 1)
then:
f(x - 1) = 1^(x - 1 + 1) = 1^x
Which equation can be used for x in the following diagram?
Answer:
x+ 4x-85 = 90
Step-by-step explanation:
The two angles are complementary so they add to 90 degrees
x+ 4x-85 = 90
Combine like terms
5x - 85 = 90
Add 85 to each side
5x = 175
Divide by 5
5x/5 =175/5
x =35
Answer:
x (4-85) = -81x
Step-by-step explanation:
Equation: x (4-85)
Answer: x (4-85)
1: Find the missing side
2: add the other numbers
Hope this helps.
Write an equation of the line that passes through (2,−3) and is perpendicular to the line y=−2x−3.
i dont understand your question
Explain how you would create an equation from a graph of a line representing a scenario.
Answer:
Find two points on the line and write them out: (x1,y1) (x2,y2)
Use this formula: y2-y1/x2-x1
The answer you get is the slope which is "m" in y=mx+b
Now in y=mx+b plug in one point's y into y and x into x.
Find b
Answer:
Use points from the graph to create a table of data points. Then find a rule for the data in the table and write an equation that represents that rule. Lastly, check that the equation holds true for other data points in the table or graph.
Step-by-step explanation:
What is the value of x?
What is the volume of the cube shown? 2 1/4
Volume of a cube is Volume = S^3, where S is the length of one side.
Volume = 2 1/4^3 = 2 1/4 x 2 1/4 x 2 1/4 = 11 25/64 in^3
The answer is D.
Answer: 30 3/8
Step-by-step explanation:
which expression is equivalent to 100n2-1
Answer:
10 x 10n^2 -1
Step-by-step explanation:
any expression as long as they equal the same as your equation (100n^2-1)
Answer:
(10n + 1)(10n - 1)
Step-by-step explanation:
solve for x 6000=-2x^2+20x-42
Answer:
3 or 7
Step-by-step explanation:
[tex]-2x^2+20x-42=0\\-2(x^2-10x+21)=0\\-2(x-7)(x-3)=0\\x=7, 3[/tex]
Hope this helps!
Nguyen is decorating the room for her sister’s baby shower party. She is wrapping Vietnamese conical hats in baby prints tissue paper to decorate the tables and some shelves in the wall. Each hat has a diameter of 16 inches and a height of 9 inches. If she wants to wrap 21 Vietnamese hats, how much tissue paper will she need?
Answer:
She needs 301.8 in² of tissue paper.
Step-by-step explanation:
In order to calculate the amount of tissue paper she needs to make 21 hats, we need to find the area of each hat and multiply it by the total number of hats she wants to make.
Since the Vietnamese conical hats are hollow and don't have a base, we need to find the area of the it's lateral walls, this is given by the following expression:
lateral area = pi*r*l
r = d/2 = 16/2 = 8 in
We were given the height, but we need the slant height, therefore:
l = sqrt(r² + h²) = sqrt(8² + 9²) = sqrt(64 + 81) = sqrt(145) = 12.041 in
Then the lateral area is:
lateral area = pi*8*12.0141 = 301.8 in²
She needs 301.8 in² of tissue paper.
4 + d = -12
I need work and answer
WILL GIVE BRAINLIEST
Answer:
d= -16
Step-by-step explanation:
-16 +4=-12
Answer:
d=−16
Step-by-step explanation:
d+4−4=−12−4
d=−16
Determine the center and radius of the following circle equation:
x2 + y2 - 4x + 20y + 55 = 0
Step-by-step explanation:
x2 - 4x +4 -4 + y2 + 20y +100 -100 + 55=0
(x-2)2 + (y+10)2 =49
center:(2,-10)
r=7
Find the volume of a right circular cone that has a height of 10.5 in and a base with a circumference of 7.1 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
14 cubic inches
Step-by-step explanation:
First, we have to find the radius from the circumference. We know that the circumference can be found using the equation c = 2pi(r). Set c equal to 7.1, and solve for r by dividing by 2pi.
Now, we have a radius of 1.13. Using this, we can plug the radius and the height into the equation used to find the volume of a cone: v = pi(r^2)(h/3)
This leads us to 14.04, or 14, when rounded to the nearest tenth of a cubic inch.
Let p=x^2-2p=x 2 −2p, equals, x, squared, minus, 2. Which equation is equivalent to (x^2-2)^2+18=9x^2-18(x 2 −2) 2 +18=9x 2 −18left parenthesis, x, squared, minus, 2, right parenthesis, squared, plus, 18, equals, 9, x, squared, minus, 18 in terms of ppp ?
Question:
Let [tex]p=x^2-2[/tex] .
Which equation is equivalent to in terms of p ?
Answer:
[tex]p^2+18=9p[/tex] or [tex]p^2+18 - 9p = 0[/tex]
Step-by-step explanation:
Given
[tex]p=x^2-2[/tex] .
Required
Find the equation equivalent to [tex](x^2-2)^2+18=9x^2-18[/tex]
To get the equation equivalent to the given expression, we simply simplify [tex](x^2-2)^2+18=9x^2-18[/tex] and solve in terms of p
[tex](x^2-2)^2+18=9x^2-18[/tex]
Factorize expression on the right hand side
[tex](x^2-2)^2+18=9(x^2-2)[/tex]
Substitute [tex]x^2 - 2[/tex] for p
[tex](x^2-2)^2+18=9(x^2-2)[/tex] becomes
[tex]p^2+18=9p[/tex]
Hence, equation [tex]p^2+18=9p[/tex] is equivalent to [tex](x^2-2)^2+18=9x^2-18[/tex]
Solving further to get the value of p
[tex]p^2+18=9p[/tex]
Subtract 9p from both sides
[tex]p^2+18 - 9p = 9p - 9p[/tex]
[tex]p^2+18 - 9p = 0[/tex]
Rearrange
[tex]p^2 - 9p +18 = 0[/tex]
Factorize
[tex]p^2 - 6p - 3p +18 = 0[/tex]
[tex]p(p - 6) - 3(p -6) = 0[/tex]
[tex](p - 3)(p -6) = 0[/tex]
p - 3 = 0 or p - 6 = 0
p = 3 or p = 6
Answer:
p^2-18+9p=0
Step-by-step explanation:
Khan
f(x) = (x+2)^2+4 . what are the coordinates of the vertex?
Answer:
[tex](-2,\, 4)[/tex].
Step-by-step explanation:
To find the vertex of this parabola, start by rewriting it in the vertex form [tex]f(x) = a\, (x - h)^2 + k[/tex].
Start with the original expression:
[tex]f(x) = (x + 2)^2 + 4[/tex].
Note that in the vertex form, the sign in front of [tex]h[/tex] should be a minus. However, in [tex]f(x) = (x + 2)^2 + 4[/tex], the sign in front of [tex]2[/tex] is a plus. Since adding
[tex]f(x) = (x - (-2))^2 + 4[/tex].
Therefore:
[tex]h = -2[/tex],[tex]k = 4[/tex].Hence, [tex](-2,\, 4)[/tex] is the vertex of this parabola.
What is the mean of the given data set. 39,82,74,96,64,52,74
Hey there!
Another word for the mean is the average. To find the mean in a set of numbers, you add up the numbers and then divide by the number of numbers!
39+82+74+96+64+52+74=481
Now, we see that we have seven numbers. So, we divide by seven!
481/7≈68.71 (rounded to nearest hundredth)
I hope that this helps!