Answers
For this case we must find an expression equivalent to:
[tex](x ^ {\frac {4} {3}} * x ^ {\frac {2} {3}}) ^ {\frac {1} {3}}[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
So, rewriting the expression we have:
[tex]x ^ {\frac {4} {3 * 3}} * x ^ {\frac {2} {3 * 3}} =[/tex]
[tex]x ^ {\frac {4} {9}} * x ^ {\frac {2} {9}} =[/tex]
By definition of multiplication of powers of the same base, we put the same base and add the exponents:
[tex]x ^ {\frac {4} {9} + \frac {2} {9}} =\\x ^ {\frac {4 + 2} {9}} =\\x ^ {\frac {6} {9}} =\\x ^ {\frac {2} {3}}[/tex]
Answer:
Option B
Answer:
[tex]x^{2/3}[/tex]
Step-by-step explanation:
The question is on rules of rational exponents
Here we apply the formulae for product rule where;
[tex]= a^{n} *a^{t} = a^{n+t} \\\\\\\\=(x^{4/3} *x^{2/3} ) = x^{4/3 + 2/3} = x^{6/3} = x^{2} \\\\\\=(x^2)^{1/3} \\\\\\=\sqrt[3]{x^2}[/tex]
[tex]=x^{2/3}[/tex]
Related Questions
(r^3+6r^2-21r-18) ÷ (r-3)
Show in Synthetic Division
Answers
Answer:
r² + 9r + 6
Step-by-step explanation:
+3| +1 +6 -21 -18
| +3 +27 +18
+1 +9 +6 0
Answer:
=1r² +9r + 6 + 0
=r² +9r + 6 (simplified)
Read on if you want to know how it was done.
To do synthetic division, you first need to get the constant of the divisor and change the sign.
Then list the coefficients of the dividend.
Drop the first coefficient.
Multiply it by the divisor, and write the answer under the next coefficient and add. Repeat till the end.
The answer should be one degree less, the original polynomial.
For this case we must build a quotient such that when multiplied by the divisor, it eliminates the terms of the dividend until it reaches the remainder.
According to the figure we have that the quotient is:
[tex]r ^ 2 + 9r + 6[/tex]
Answer:
Quotient:
[tex]r ^ 2 + 9r + 6[/tex]
See attached image
points A(-2,4), B(1,3), C(4,-1) and D form a parallelogram what are the coordinates of d?
Answers
Answer:
answer is (1,0)
Step-by-step explanation:
Let the coordinates of D be (a,b).The diagonals of a parallelogram bisect each other.The midpoint of AC should be the same as the midpoint of BD.Compare corresponding coordinatesThis implies that:, , , Therefore the coordinates of D are: (1,0)
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Which angles are corresponding angles? Check all that apply.
Answers
Answer:
Option 1 and 3 are correct.
Step-by-step explanation:
The corresponding angles are the matching angles when two lines are crossed by another line which is called traversal.
Looking in the figure following are corresponding angles
8 and 6
4 and 2
7 and 5
3 and 1
Now, looking at the options
Option 1 5 and 7
and Option 3 6 and 8 are only given corresponding angles.
So Option 1 and 3 are correct.
Lan pays a semiannual premium of $650 for automobile insurance, a monthly premium of $125 for health insurance, and an annual premium of $450 for life insurance.
The monthly expense is $? with explanation
Answers
Answer:
Monthly Expense = $270.83
Step-by-step explanation:
The semi-annual premium is paid twice a year so,
Automobile insurance premium for whole year = 650*2
= $1300
Monthly premium will be paid 12 times a year so,
Health insurance premium for whole year = 125*12 = $1500
Annual premium is only paid once a year.
So adding all the premiums will give us the total premiums for whole year.
Total amount of premium for a year = $1300+$1500+$450
= $3250
The premium amount for whole year is $3250. To find the monthly expense, we will divide it by 12.
So monthly expense is:
= 3250/12
= $270.83 ..
To find the monthly expense, calculate the total annual premium for each insurance and divide by 12. The monthly expense is $187.5.
Explanation:To find the monthly expense, we need to calculate the total annual premium for each insurance and divide it by 12 (since there are 12 months in a year).
For automobile insurance, the semiannual premium is $650, so the annual premium is $650 * 2 = $1300.
The monthly premium for health insurance is $125.
For life insurance, the annual premium is $450.
Now, let's calculate the total monthly expense: ($1300 + $125 + $450) / 12 = $187.5.
So, the monthly expense is $187.5.
2.043928 as a fraction
Answers
Answer: it can’t be converted to a fraction
Step-by-step explanation:
Does geometry nation help a lot with geometry eoc? Or the textbook helped more?
Answers
Answer: It depends on you if it seems easier for you, you should try both and see which one works better for you.
Answer:
Geometry nation helps when you need to go more in depth and need practice problems. While the textbook might give you good definitions it may seem more monotone.
if the standard deviation of data values in a sample is 17, what is the varience of the data values
Answers
Answer:
Step-by-step explanation:
The variance is the square of the standard deviation. Here, the variance is 17^2, or 289.
If a polynomial function f(x) has roots -4,2,1 and square root of 11 what must be also a root of f(x) ?
Answer choices:
- square root 11
-2
-1
4
Answers
Answer:
- [tex]\sqrt{11}[/tex]
Step-by-step explanation:
Radical roots occur in conjugate pairs
Thus if [tex]\sqrt{11}[/tex] is a root then
- [tex]\sqrt{11}[/tex] is also a root
The other root of the given polynomial is [tex]-\sqrt{11}[/tex].
What is the root of a polynomial?"Roots of a polynomial refer to the values of a variable for which the given polynomial is equal to zero."
Given roots of a polynomial f(x) are - 4, 2, 1, [tex]\sqrt{11}[/tex].
We know, for the root of an equation, radical roots are always in pair.
If a polynomial has two roots, one is [tex]\sqrt{x}[/tex] then the other one must be [tex]-\sqrt{x}[/tex].
Similarly, the root of the given polynomial is [tex]-\sqrt{11}[/tex].
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Please help picture is there
Answers
Answer:
B
Step-by-step explanation:
Using the rule of radicals/ exponents
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]
Given
[tex]\sqrt[3]{x^5 y}[/tex]
= [tex]\sqrt[3]{x^5}[/tex] × [tex]\sqrt[3]{y}[/tex]
= [tex]x^{\frac{5}{3} }[/tex] [tex]y^{\frac{1}{3} }[/tex] → B
given the eaquation y-4=3/4 (x+8) in the point-slope form, identify the equation of the same line in standard form.
Answers
Answer:
[tex]\large\boxed{3x-4y=-48}[/tex]
Step-by-step explanation:
The standard form of an equation of a line
[tex]Ax+By=C[/tex]
We have the eqution in the point-slope form:
[tex]y-4=\dfrac{3}{4}(x+8)[/tex]
Convert it to the standard form:
[tex]y-4=\dfrac{3}{4}(x+8)[/tex] multiply both sides by 4
[tex]4y-16=3(x+8)[/tex] use the distributive property
[tex]4y-16=3x+32[/tex] add 16 to both sides
[tex]4y=3x+48[/tex] subtract 3x from both sides
[tex]-3x+4y=48[/tex] change the signs
[tex]3x-4y=-48[/tex]
A 12 feet piece of wood is to be cut into two pieces. One piece must be 8 feet longer than the other. Find the length of each piece
Answers
Answer:
2 and 10
Step-by-step explanation:
In order to solve these types of problems, you should first subtract the difference of the two pieces. You get 4. Divide by 2 (two pieces) and there are 2 and 2. Add the 8 back to one of them, and you get 10 ad 2.
Prove by mathematical induction that 1+2+3+...+n= n(n+1)/2 please can someone help me with this ASAP. Thanks
Answers
Let
[tex]P(n):\ 1+2+\ldots+n = \dfrac{n(n+1)}{2}[/tex]
In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:
[tex]P(1):\ 1 = \dfrac{1\cdot 2}{2}=1[/tex]
So, the base case is ok. Now, we need to assume [tex]P(n)[/tex] and prove [tex]P(n+1)[/tex].
[tex]P(n+1)[/tex] states that
[tex]P(n+1):\ 1+2+\ldots+n+(n+1) = \dfrac{(n+1)(n+2)}{2}=\dfrac{n^2+3n+2}{2}[/tex]
Since we're assuming [tex]P(n)[/tex], we can substitute the sum of the first n terms with their expression:
[tex]\underbrace{1+2+\ldots+n}_{P(n)}+n+1 = \dfrac{n(n+1)}{2}+n+1=\dfrac{n(n+1)+2n+2}{2}=\dfrac{n^2+3n+2}{2}[/tex]
Which terminates the proof, since we showed that
[tex]P(n+1):\ 1+2+\ldots+n+(n+1) =\dfrac{n^2+3n+2}{2}[/tex]
as required
Which of the following is an equivalent form of the compound inequality −33 > −3x − 6 ≥ −6?
Answers
The given compound inequality doesn't have any solutions because it creates a contradictory situation where x needs to be both greater than 9 and less than 0 at the same time, which is not possible.
Explanation:The given compound inequality is −33 > −3x − 6 ≥ −6. To find the equivalent form, let's solve it step by step.
First, add 6 to all sides, resulting in -27 > -3x > 0.
Then, divide by -3. Remember that when dividing by a negative number, the direction of the inequality changes. So, we get 9 < x < 0.
This indicates that x is greater than 9 but x also needs to be less than 0. This, however, is a contradictory situation because a number cannot be both greater than 9 and less than 0 at the same time. So, there are no solutions for this inequality.
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An equivalent form of the compound inequality −33 > −3x − 6 ≥ −6 is x > 9.5 or x ≤ 0.
To find an equivalent form of the compound inequality −33 > −3x − 6 ≥ −6, we can break it down into two separate inequalities:
−33 > −3x − 6
−3x − 6 ≥ −6
To simplify the first inequality, we can add 6 to both sides: −27 > −3x. Then, we can divide both sides by -3, remembering to flip the inequality sign since we are dividing by a negative number: x > 9.5.
To simplify the second inequality, we can add 6 to both sides: −3x ≥ 0. Then, we can divide both sides by -3, remembering to flip the inequality sign: x ≤ 0.
Therefore, an equivalent form of the compound inequality −33 > −3x − 6 ≥ −6 is x > 9.5 or x ≤ 0.
Help!! Which angle is a vertical angle with ∠AOF??
(A)∠DOE
(B)∠COD
(C)∠BOC
(D)∠FOE
use the diagram.
Answers
Answer:
angle COD
Step-by-step explanation: vertical angles share the same vertacy and are opposite of each other. They are created by two intersecting lines.
What value of b will cause the system to have an infinite number of solutions? y = 6x – b –3x + y = –3 b =
(a)2
(b) 4
(c) 6
(d) 8
Answers
Answer with explanation:
Consider two linear equation in two variable,
ax + by =c
p x +q y=r
The equations have an infinite number of solutions , means the two lines are Coincident, when it follows the following law
[tex]\frac{a}{p}= \frac{b}{q}= \frac{c}{r}[/tex]
--------------------------------------(1)
Now, equation of two lines are
1. y= 6 x -b
→6 x -y -b=0
2. -3 x +y= -3
⇒-3 x+y+3=0
By the above law,that is law 1, the two lines will be coincident
[tex]\frac{6}{-3}=\frac{-1}{1}= \frac{-b}{3}\\\\2=1= \frac{b}{3}[/tex]
Which is not possible that is ,2≠1.
→→→Hence the two lines can never be coincident for any value of b.
What is the volume of the cylinder below?
Answers
Answer:
[tex]\large\boxed{D.\ 2160\pi\ units^3}[/tex]
Step-by-step explanation:
[tex]\text{The formula of a volume of a cylinder:}\\\\V=\pi r^2H\\\\r-radius\\\H-height\\\\\text{We have}\ r=12\ \text{and}\ H=15.\ \text{Substitute:}\\\\V=\pi(12^2)(15)=\pi(144)(15)=2160\pi[/tex]
The volume of the cylinder is [tex]\( 2160 \pi \)[/tex] units³.
To find the volume of the cylinder, we'll use the formula for the volume of a cylinder, which is given by:
[tex]\[ V = \pi r^2 h \][/tex]
Where:
- V is the volume of the cylinder,
- r is the radius of the cylinder, and
- h is the height of the cylinder.
Given:
- Height h = 15 units
- Radius r = 12 units
We'll substitute these values into the formula:
[tex]\[ V = \pi \times (12)^2 \times 15 \][/tex]
[tex]\[ V = \pi \times 144 \times 15 \][/tex]
[tex]\[ V = 2160 \pi \][/tex]
So, the volume of the cylinder is [tex]\( 2160 \pi \)[/tex] cubic units.
The correct answer is option D: [tex]\( 2160 \pi \)[/tex] units³.
Which of the following BEST summarizes how to use the multiplication property of equality to isolate the variable p below? -1/2 p = 4
Answers
Answer:
multiplication property of equality
Step-by-step explanation:
Given:
[tex]-\frac{1}{2}p = 4[/tex]
The rule is that whatever is done on one side of the equation is done on the other side of the equation two.
In order to isolate p, both sides of equation will be multiplied by -2.
This is called the multiplication property of equality ..
which statements are true?
Please see picture
Answers
Answer:
Following are the statements:
a. logₐb - logₐc = logₐb/logₐc
False.
b. logₐB - logₐc = logₐ(b/c)
True.
c. log₄(5x+16) = log₄5x+log₄16 = 2 +log₄5x
False.
d. log₄(5x*16) = log₄5x+log₄16 = 2 +log₄5x
True.
e. logₐ(3x)₂ = 2 logₐ3 + logₐx
False.
f. logₐ(3x)₂ = 2 logₐ3 + 2 logₐx
Answer:
a. False
b. True
c. False
d. True
e. False
f. True
Step-by-step explanation:
By properties of logarithms:
a. False: ㏒ₐb-㏒ₐc ≠ (㏒ₐb / ㏒ₐc) does not exists that property
b. True: (㏒ₐb)-(㏒ₐc) = ㏒ₐ(b/c) Logarithm of a Quotient
c. False: Does not exists the property: ㏒ₐ(c+b) = ㏒ₐc + ㏒ₐb
so
㏒₄(5x+16) ≠ ㏒₄5x + ㏒₄16 but, ㏒₄16 + ㏒₄5x = 2 + ㏒₄5x
because ㏒₄16 = 2.
d. True: Logarithm of a Product: ㏒ₐ(c×b) = ㏒ₐc + ㏒ₐb
so
㏒₄(16×5x) = ㏒₄16 + ㏒₄5x = 2 + ㏒₄5x
e. False: Logarithm of a Power: ㏒ₐ(c×b)ⁿ = n ㏒ₐ(c×b) = n (㏒ₐc + ㏒ₐb) = n ㏒ₐc + n ㏒ₐb
so
㏒ₐ(3x)² ≠ 2 ㏒ₐ3 + ㏒ₐx
f. Correct use of property in point e.
Use the properties of exponents to rewrite the expression
5e•5e•5e•5e
Answers
Answer:
(5e)^4
Step-by-step explanation:
5e•5e•5e•5e
There are 4 sets of 5e being multiplied together
(5e)^4
Answer:
thanks for the points
Step-by-step explanation:
What value for y makes this equation true?
(7xy)+(7x4=7x14
A.2
B.4
C.7
D.10
Answers
A 52 year-old father has a son and a daughter. The son is twice as old as the daughter. In 4 years the sum of all their ages will be 100. How old are the two siblings now? (RSM problem)
Answers
100= total years of age of all ppl in 4years but we want their age now
100=(52+4)+(2x+4)+(x+4)
3x=36
x=12
So daughter is 12 and son is 2x or 24
Any questions on how to set this up or how to arrive at the answer, please feel free to ask. Thanks!
Answer:The age of daughter is 12 years and age of son is 24 years
Step-by-step explanation:
Given :
Present age of father = 52 years
Let the present age of daughter be x
So according to the question son's age is twice that of daughter's
So present age of son =2x
Now after 4 years the sum of their ages = 100
i.e. x+4 + 2x+4 + 52 +4 =100
3x+ 64 = 100
Subtracting both sides by 64 we get
3x + 64 - 64=100 -64
3x = 36
Dividing LHS and RHS by 3 we get
x=12
i.e. Present age of daughter = x = 12 years
Present age of son = 2x = 2× 12= 24 years
Please help!! Local wildlife experts have begun to track the population of trout in their area. The function f represents the approximate population of trout in Sky Lake, and the function g represents the approximate population of trout in Lake Cyan, where t is the number of months since experts began tracking the populations.
f(t) = 1.5t + 50
g(t) = 0.1t^2 - 4t + 70
Find the expression that describes the total trout population in the area after t months, f(t) + g(t).
A. 0.1t^2 + 5.5t +120
B. 0.1t^2 - 5.5t +120
C. 0.1t^2 - 2.5t + 120
D. 0.1t^2 + 2.5t + 120
Answers
Answer:
Option C.
Step-by-step explanation:
We know that
f(t) = 1.5t + 50
represents the approximate population of trout in Sky Lake
And
g(t) = 0.1t^2 - 4t + 70
represents the approximate population of trout in Lake Cyan
The total trout population in the area is described as
f(t) + g(t)
f(t) + g(t) = [1.5t + 50] + [0.1t^2 - 4t + 70]
f(t) + g(t) = [1.5t + 50+ 0.1t^2 - 4t + 70]
f(t) + g(t) = [0.1t^2 -2.5t + 120]
f(t) + g(t) = 0.1t^2 -2.5t + 120
Option C.
what is 30% of $40 ?
Answers
Answer:
$12
Step-by-step explanation:
30 % × $40 = 30 ÷ 100 × 40 = $12
The value of the Percentage 30% of $40 is: $12
How to calculate the percentage?Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.
Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by:
Percentage = (value / total value) * 100%
Thus:
30% of $40 is calculated as:
30/100 * 40
= 1200/100
= $12
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The graph of the parent function f(x) = x3 is translated such that the resulting graph can be represented by the function g(x) = (x – 1)3 + 1. Which is the graph of g(x)?
Answers
Answer:
1st graph in edgnuity
Step-by-step explanation:
Answer:
1st graph
Step-by-step explanation:
i got it correct
A
passes through A(-3,0) and B(-6,5). What is the equation of the line that passes through the origin and is parallel to AB?
OA. 5x - 3y = 0
B. -* + 3y = 0
c. 5x - 3y = 0
D. 3x + 5y = 0
E. -3x + 5y = 0
Answers
Answer:
B. 5x + 3y = 0Step-by-step explanation:
Parallel lines have the same slope.
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points A(-3, 0) and B(-6, 5). Substitute:
[tex]m=\dfrac{5-0}{-6-(-3)}=\dfrac{5}{-3}=-\dfrac{5}{3}[/tex]
The line passes through the origin, therefore the y-intercept is equal to 0.
Therefore we have the equation:
[tex]y=-\dfrac{5}{3}x[/tex]
Convert to the standard form [tex]Ax+By=C[/tex]
[tex]y=-\dfrac{5}{3}x[/tex] multiply both sides by 3
[tex]3y=-5x[/tex] add 5x to both sides
[tex]5x+3y=0[/tex]
The equation of the line parallel to AB passing through the origin is 5x - 3y = 0.
The equation of the line that passes through the origin and is parallel to AB is 5x - 3y = 0.
To find the equation of a line parallel to AB passing through the origin, we first need to find the slope of AB, which is (5 - 0) / (-6 + 3) = 5 / -3 = -5/3.
Since the line passing through the origin and parallel to AB has the same slope, its equation will be of the form y = mx. Substituting the point (0, 0) into y = -5/3x gives us y = -5/3x, which simplifies to 5x - 3y = 0.
What is the slope of the line represented by the equation below?y=-2/3x+3 A-2/3 B. 2/3 C.2 D.x
Answers
ANSWER
A.
[tex] - \frac{2}{3} [/tex]
EXPLANATION
The given equation is
[tex]y = - \frac{2}{3}x + 3[/tex]
This equation is already in the form:
[tex]y =mx + b[/tex]
This is called the slope-intercept form.
The slope is
[tex]m = - \frac{2}{3} [/tex]
and the y-intercept is 3.
The correct answer is A.
In a situation where the line is not given in the slope intercept form, then you must rewrite in this form before comparing.
What kind of taxes are likely to pay for universities and police? a. local taxes b. state taxes c. federal taxes d. income taxes Please select the best answer from the choices provided
Answers
b. state taxes are the most likely to pay for universities and police.
Answer:
B
Step-by-step explanation:
a student measured the temperature in degrees celsius for several winter days and recorded the data in a list find the average of the temperatures listed 6,-7,-5,5,-8,3
Answers
Answer:
Average = -1°C
Step-by-step explanation:
The data recorded is;
6, -7, -5, 5, -8, 3 (in °C)
Average = [tex]\frac{6 - 7 - 5 + 5 - 8 + 3}{6}[/tex] = -1°C
Answer:
Average temperature listed will be (-1).
Step-by-step explanation:
As we know average of any given set of numbers is = [tex]\frac{\text{Sum of all the numbers}}{\text{Total numbers }}[/tex]
Now the given set of temperatures is 6, -7, -5, 5, -8, 3
Now Sum of all numbers = 6 + (-7) + (-5) + 5 + (-8) + 3
= (-6)
Total numbers = 6
Now average temperature will be = [tex]\frac{-6}{6}=(-1)[/tex]
Therefore, average temperature listed will be (-1).
solve for n 25/n = 5/8
Answers
Answer:
n=40
Step-by-step explanation:
25/n=5/8
25/5=5
n/5=8
n=40
Answer:
N= 40.
Hope that helps!
5x + 8y =2
4x -6y =9
Answers
Answer:
x = 42/31, y = -37/62
Step-by-step explanation:
5x + 8y =2
4x -6y =9
Multiply the first equation by 4
4(5x + 8y) =2*4
20x +32y = 8
Multiply this equation by -5
-5(4x -6y) =9*-5
-20x +30y = -45
Add them together
20x +32y = 8
-20x +30y = -45
-----------------------------
62y = -37
Divide by 62
62y/62 = -37/62
Multiply the first equation by 3
3(5x + 8y) =2*3
15x +24y =6
And the second equation by 4
4(4x -6y) =9*4
16x -24y = 36
Add them together
15x +24y =6
16x -24y = 36
-----------------
31x = 42
Divide by 31
31x/31 = 42/31
x = 42/31