Answers
After demonstrating the procedure by algebraic means, the expression [tex](2\sqrt[3]{12} )\cdot (3\sqrt[3]{2} )[/tex] is equivalent to [tex]6\cdot \sqrt[3]{24}[/tex].
In this question we proceed to simplify [tex](2\sqrt[3]{12} )\cdot (3\sqrt[3]{2} )[/tex] by algebraic means into a single radical expression when possible, whose procedure is shown below and explained by appropriate definitions and theorems:
[tex](2\sqrt[3]{12} )\cdot (3\sqrt[3]{2} )[/tex] Given. [tex](2\cdot 3) \cdot (\sqrt[3]{12} \cdot \sqrt[3]{2} )[/tex] Commutative property/ Associative property. [tex]6\cdot \sqrt[3]{24}[/tex] Definition of cubic root/[tex]\sqrt[n]{a} = \sqrt[n]{b}[/tex]/ResultAfter demonstrating the procedure by algebraic means, the expression [tex](2\sqrt[3]{12} )\cdot (3\sqrt[3]{2} )[/tex] is equivalent to [tex]6\cdot \sqrt[3]{24}[/tex].
To learn more on radical expressions, we kindly invite to check this verified question: https://brainly.com/question/1810591
Related Questions
I need to know the area of this triangle and I would like to have an explanation because I dont know how to do it I know the formula just not how to get the height
Answers
Answer:
18 square units
Step-by-step explanation:
When one side is vertical or horizontal, it is convenient to find the height from the opposite vertex to that side. It is generally an integer number of grid squares.
Here, the height is 4 -(-2) = 6. The base length is 1 -(-5) = 6. That means the area is ...
A = 1/2bh
A = 1/2(6)(6) = 18 . . . . square units
_____
Alternate solution
If you want to go at this the hard way, you can find the length of LK and the distance of J to that line.
The length of LK is ...
d = √((x2 -x1)^2 +(y2 -y1)^2) = √((4 -(-2))^2 +(3 -(-5))^2) = √(36 +64) = 10
The distance to line LK can be found by writing the equation of the line LK in general form:
4x -3y -7 = 0
Then the distance formula for point (x, y) is ...
d = |4x -3y -7|/√(4^2 +3^2)
d = |4(-2) -3(1) -7|/5 = |-8 -3 -7|/5 = 3.6
Using the area formula with these dimensions gives ...
A = 1/2bh = 1/2(10)(3.6) = 18 . . . . square units
Answer:
18 square units
Step-by-step explanation:
pls pls pls mark me as brainliest
13/83.2, I have the answer but not the work
Answers
Answer:
6.4 is the correct answer
The 20th term from the end of the AP, 3, 8 , 13,. ..... ,253 is
Answers
Given A.P = 3,8,13,...,253
Common difference = 8-3 = 5
The AP from the end = 253, 248,245,...,13,8,3
First term from the end = 253
Common difference = 248-253 = -5
We know that
an = a+(n-1)d
t20 = 253+(20-1)(-5)
→ t 20 = 253 +(19)(-5)
→ t 20 = 253-95
→ t 20 = 158
20th term from the end of the AP = 158
I need help with this question
Answers
I can explain further in a reply, if needed.
Your school made it to the playoffs
in football and is selling t-shirts to
Celebrate their success for $10 each. The cost
to make the shirts is 5 each plus a one
time set ur fee of $20.
Answers
Answer:
I dont quite understand the question could you clarify? What are you trying to ask? how many shirts to break even? Im not quite understanding I'd be more than happy to help if you re worded the question!
Step-by-step explanation:
QUESTION 1
A conical cup is 4 cm across and 6 cm deep. Water leaks out of the bottom at the rate of 2 cm/sec. How fast (in cm/sec) is the water level dropping
when the height of the water is 3 cm?(Round your answer two (2) decimal places)
Answers
The water level will be dropping at the rate of [tex]0.64 cm/sec[/tex] when the height of the water reaches [tex]3cm[/tex]
We are give a cone with dimensions as seen in the diagram in the attached image.
The volume changes at the rate
[tex]\frac{dV}{dt}=-2cm^2/sec[/tex]
the negative sign is used because the volume of water is reducing.
what we need to know is the rate the height is changing when [tex]h=3cm[/tex]. That is, we need to evaluate
[tex]\frac{dh}{dt}|_{h=3cm}[/tex]
The relationship between the volume and the height is given by
[tex]V=\frac{1}{3}\pi r^2h[/tex]
but both [tex]h[/tex] and [tex]r[/tex] are changing when [tex]V[/tex] changes. So we need to eliminate [tex]r[/tex] somehow. From the diagram, we can use the similar triangle property to accomplish this
[tex]\frac{r}{2}=\frac{h}{6}\\\\\implies r=\frac{h}{3}[/tex]
substitute into the volume formula to eliminate [tex]r[/tex]
[tex]V=\frac{\pi h^3}{27}[/tex]
differentiate both sides with respect to time, [tex]t[/tex], since both the volume and height are functions of time. They will both be differentiated implicitly
[tex]\frac{dV}{dt}=\frac{\pi h^2}{9}\frac{dh}{dt}[/tex]
to find [tex]\frac{dh}{dt}|_{h=3cm}[/tex], substitute the values for [tex]\frac{dV}{dt}[/tex] and [tex]h[/tex]
[tex]-2=\frac{\pi 3^2}{9}\frac{dh}{dt}\\\\\frac{dh}{dt}=-\frac{2}{\pi}\\\\\approx -0.64 cm/sec[/tex]
So the rate at which the height is reducing when it reaches [tex]3cm[/tex] is [tex]0.64cm/sec[/tex]
Learn more about related rate of change here: https://brainly.com/question/15576763
Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-3, 1) and point (4, 2) rounded to the nearest tenth?
Answers
Answer:
√(4 - ( - 3))^2 + (2 - 1)^2
√(4 + 3)^2 + (2 - 1)^2
√49 + 1
√50
7.07 = 7.1 units
A group of pupils calculated their average score for a Mathematics
test. If one of them scored 9 marks more, their average score would
be 81. If one of them scored 3 marks less, their average score would
be 78. How many pupils were there in the group?
Answers
Answer: 4
Step-by-step explanation: +9-(-3)=12
81-78=3
so 12/3=4
It’s number 5 what is the domain and range plz help urgent
Answers
Answer:
Domain: -2,-1,0,3 Range: -2,-1,0,3
Step-by-step explanation:
The x values (horizontal) is the domain and the dots on the x values are -2,-1,0,3. The y values is the range and the dots on the y values are -2,-1,0,3. Hope this helps :)
House of Mohammed sells packaged lunches, where their finance department has established a
weekly relationship between its Revenue R, in dollars and the number of lunches x, as R=x(82−x)
(a) Write the revenue R, in the form R=ax2+bx+c (b) What is the revenue when 35 lunches are sold? (c) Explain why the graph of R has a maximum.
(d) Write R in the form a(x−h)2+k
(e) How many lunches must be sold for them to achieve their maximum revenue?
(f) State the company's maximum revenue.
(2 marks) (2 marks) (2 marks)
(5 marks)
(2 marks) (2 marks)
(g) Complete the following table of values and graph the Revenue equation using the ordered pairs
(x , R). Label the coordinates of the vertex.
x
10
20
30
40
50
60
70
80
90
R
( 10 marks)
Answers
The revenue function is a quadratic equation and the graph of the function
has the shape of a parabola that is concave downwards.
The correct responses are;
(a) R = -x² + 82·x(b) $1,645(c) The graph of R has a maximum because the leading coefficient of the quadratic function for R is negative.(d) R = -1·(x - 41)² + 1,681(e) 41(f) $1,681Reasons:
The given function that gives the weekly revenue is; R = x·(82 - x)
Where;
R = The revenue in dollars
x = The number of lunches
(a) The revenue can be written in the form R = a·x² + b·x + c by expansion of the given function as follows;
R = x·(82 - x) = 82·x - x²
Which gives;
R = -x² + 82·xWhere, the constant term, c = 0
(b) When 35 launches are sold, we have;
x = 35
Which by plugging in the value of x = 35, gives;
R = 35 × (82 - 35) = 1,645
The revenue when 35 lunches are sold, R = $1,645
(c) The given function for R is R = x·(82 - x) = -x² + 82·x
Given that the leading coefficient is negative, the shape of graph of the
function R is concave downward, and therefore, the graph has only a
maximum point.
(d) The form a·(x - h)² + k is the vertex form of quadratic equation, where;
(h, k) = The vertex of the equation
a = The leading coefficient
The function, R = x·(82 - x), can be expressed in the form a·(x - h)² + k, as follows;
R = x·(82 - x) = -x² + 82·x
At the vertex, of the equation; f(x) = a·x² + b·x + c, we have;
[tex]\displaystyle x = \mathbf{-\frac{b}{2 \cdot a}}[/tex]
Therefore, for the revenue function, the x-value of the vertex, is; [tex]\displaystyle x = -\frac{82}{2 \times (-1)} = \mathbf{41}[/tex]
The revenue at the vertex is; [tex]R_{max}[/tex] = 41×(82 - 41) = 1,681
Which gives;
(h, k) = (41, 1,681)
a = -1 (The coefficient of x² in -x² + 82·x)
The revenue equation in the form, a·(x - h)² + k is; R = -1·(x - 41)² + 1,681(e) The number of lunches that must be sold to achieve the maximum revenue is given by the x-value at the vertex, which is; x = 41
Therefore;
The number of lunches that must be sold for the maximum revenue to be achieved is 41 lunches(f) The maximum revenue is given by the revenue at the vertex point where x = 41, which is; R = $1,681
The maximum revenue of the company is $1,681Learn more about the quadratic function here:
https://brainly.com/question/2814100
Pls help I’ll brainlest ASAP and add extra points I’m failing
Answers
Step-by-step explanation:
you drew already the right things, you have everything.
so, what is the problem ?
the most common form of line equation is
y = ax + b
a is the slope of the line. it is expressed as the ratio
y coordinate change / x coordinate change
when going from one point to the other.
b is the y-intercept (the y value when x = 0).
once we have the slope, we get b by using the coordinates of one of the given points as x and y in the equation and solve for b.
so, for the 2 marked points you showed correctly the differences :
x changes by +8 (from -4 to 4).
y changes by -2 (from 3 to 1).
so the slope is -2/+8 = -1/4
the y-intercept we also see directly in the chart : +2.
Prime number after 167, 118, 82, 57, 41,
Answers
The prime numbers after 167, 118, 82, 57, 41 are 37, 31, 29, 23, 19, 17, 13, 11, 7, 5, 3, 2.
Prime numbers are numbers that are divisible by 1 and itself.
This are number greater than one with only two factors which are 1 and itself.
In other words, this number, when they are divided by another number other
than 1 or itself , one will get a remainder that is not zero.
Example of prime numbers are 2, 5, 7, 11, 13 etc.
The prime numbers after 167, 118, 82, 57, 41 are as follows:
37, 31, 29, 23, 19, 17, 13, 11, 7, 5, 3, 2.
learn more about prime number here: https://brainly.com/question/26013414
The distance between a 16 foot tall flagpole and a 40 foot tall tree is equal to the sum of the lengths of their shadows. If the flagpole casts a 18 foot shadow, find the distance from the flagpole to the tree.
Answers
Answer:
The distance from the flagpole to the tree is 27 ft
Step-by-step explanation:
a store have a 12.7% discount on $2002 furniture. what is the new price
Answers
Answer:
$1,747.75
Step-by-step explanation:
(12.7% = 0.127)
$2,002 x 0.127 = 254.25
$2,002 - 254.25 = $1,747.75
in an exam,Kianna scored 80% out of a total of 520 how may marks did she score?
Answers
Answer:
416
Step-by-step explanation:
you take 520 times .80
Types of Angle Relationships
Listen
Question
If two angles are supplementary, then the sum of their measures is _[blank] degrees.
Question
ol
What number correctly fills in the blank in the previous sentence?
Question
Enter your answer as a number, like this: 42
а
Answers
Answer: The answer is 180°.
Explanation: Two angles are called supplementary when their measures add up to 180 degrees, therefore the answer is 180 degrees.
Which function is graphed below?
Answers
Answer:
y=arcsec(x) (C)
Step-by-step explanation:
The graph of y=arcsec(x) is equal to the graph shown in the question
please help me with this!
•
•
•
Answers
Answer:
y=-2 is y intercept, graph opens upward like a smiley face
a=3 ,b=1, c=-2
Step-by-step explanation:
1.the graph opens upward since 3x^2 is positive
2.the graph corsses the Y axis when x is zero, so setting x equal to zero we find...
3(0)^2 + (0) -2 =y so y=-2 is y intercept
y=ax+bx+c
y=3x^2+x-2
a is represented by 3
b is 1 since x is positive
c is -2
f(x) = 1/3x + 1 if x=-18
Answers
Answer:
7
Step-by-step explanation:
1/3*(-18) + 1 = 7
Just plug in the x which is -18, and solve with a calculator.
Hope this helps!
1) Solve for x (11 - 2*) 7 = 21
Answers
ok done. Thank to me :>
f(x)=2x 2 +8x Find f(−1)
Answers
Answer:
-6
Step-by-step explanation:
f(x)=2x^2+8x
f(-1)=2(-1)^2+8(-1)
f(-1)=2(-1)(-1)-8
f(-1)=2(1)-8
f(-1)=2-8
f(-1)=-6
50 * 20 - 10 + 4 = ?
Answers
Answer: 994
Step-by-step explanation:
50 * 20 = 1000 - 10 = 990 + 4 = 994
The low temperature on a certain day is 56°F. The low temperature is 14°F lower than the high temperature, h.
Which equation can be used to find the high temperature for that day?
56=h−14
56 = 14h
56 = h + 14
h + 56 = 14
Answers
Answer:10.9
Step-by-step explanation:
Please help. Due in 30 mins!!
Answers
1: 1.645
2. 1.28
4: 95% confidence level (12.93, 13.87)
3: No Idea
5: sorry im a bit rusty
Im so sorry for not answering all you questions
if f(x)=3^x+10 and g(x)=2x-4, find (f+g)(x)
Answers
Answer:
4
Step-by-step explanation:
find the total amount due on the simple interest loan if the principle is $3000 with a rate of 5% for 10 years
Answers
Step-by-step explanation:
hope it will help you......
Solve the following equation for d:cd – 8 = f
Answers
Answer: Well my friend, there is not enough info to sole the equation..
Step-by-step explanation:
A buyer of a new sedan can custom order the car by choosing from 5
different exterior colors, 3 different interior colors, 2 sound systems, 3
motor designs, and either manual or automatic transmission. How many
choices does the buyer have? /(10 pts)
Answers
Using the Fundamental Counting Theorem, it is found that the buyer has 180 choices.
Fundamental counting theorem:
States that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this question:
The options are independent.There are 5 different exterior colors, hence [tex]n_1 = 5[/tex].There are 3 different interior colors, hence [tex]n_2 = 3[/tex].There are 2 sound systems, hence [tex]n_3 = 2[/tex].There are 3 motor designs, hence [tex]n_4 = 3[/tex].There are 2 transmission options, hence [tex]n_5 = 2[/tex].Then:
[tex]N = 5 \times 3 \times 2 \times 3 \times 2 = 180[/tex]
The buyer has 180 choices.
To learn more about the Fundamental Counting Theorem, you can take a look at https://brainly.com/question/25799621
Simplify 1/3 (5x-8)+2/3x
Answers
Answer:
7x-8
3
Step-by-step explanation:
Answer:
2 1/3x - 2 2/3
Step-by-step explanation:
1/3 x 5
1/3 x -8
and add 2/3x to the mix
so
1 2/3x - 2 2/3x + 2/3x = 2 1/3x - 2 2/3
PLEASE HELPPP
ILL GIVE 5 STARS TY
Answers
Answer:
14
Step-by-step explanation:
4^2=16
16/2=8
8+6=14
Answer:
[tex]14[/tex]
Step-by-step explanation:
This equation would be easier to do if it was: [tex]6+\frac{4^2}{2}[/tex]
So first you have to cancel out: [tex]\frac{4^2}{2}[/tex] so that would become [tex]6+8[/tex]
Finally [tex]6+8=14[/tex]
There you go brainliest pls
