3
3
Use exponent rules to explain why (√5)³ = √√5³.
Answers
Answer:
see image
Step-by-step explanation:
Use new exponent rules like:
A power raised to a power is the product of the powers. (power to a power, times the exponents)
and,
Square root is a half power. (Converting radicals to fractional exponents)
Also, you can multiply in any order, like since you learned multiplying (example: 2×6 is the same as 6×2)
see image.
Here's the plan:
Change the radical to a 1/2 exponent. Now 3 and 1/2 are both exponents. Rearrange the order. Rewrite in radical form again.
see image.
The proof of the equation (√5)³ = √(5³) is given below.
What is an exponent?Exponentiation is one of the mathematics operation.
Let mᵃ, where m and a are the real numbers.
And m is multiplied by a times to itself.
So, a is the exponent of m.
Given:
A radical equation,
(√5)³ = √(5³).
LHS = (√5)³
Simplifying,
(√5)³ = {(5[tex])^{1/2}[/tex]}³
= [tex]5^{3/2}[/tex]
= √(5³)
= RHS.
Therefore, (√5)³ = √(5³).
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The complete question:
Simplify and prove the equation (√5)³ = √(5³) by using exponent rules.
Related Questions
Can I get some help with this
Answers
The final velocity of a vehicle with a mass of 800kg is 20000 m/s.
What is velocity?The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity.The speed at which an object goes in one direction is known as its velocity. Speed may be used to calculate both the speed of the car traveling north on the major highway and the speed of the rocket bursting into space.So, calculate the final velocity as:
Formula: v = √u² + 2asWhere u is initial velocity, a is acceleration and s is displacement.Now, we know that:
u = 108 km/ha = 4 km/s²s = 50 kmInsert values in the formula and calculate as follows:
v = √u² + 2asv = √108² + 2(4)(50)v = √11,664 + 400v = √12,064v = 20000.022499991 m/sRounding off: v = 20000 m/s
Therefore, the final velocity of a vehicle with a mass of 800kg is 20000 m/s.
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How can I evaluate P = 3n+2r+t -1 when n=3, r=2, and t=5?
Answers
Answer:
p=17
Step-by-step explanation:
P = 3n+2r+t -1
when n=3, r=2, and t=5?
we will just substitute for the values
p=3(3)+2(2)+5-1
p=9+4+4
p=9+8
p=17
;- The value for p is 17
award as brainliest
p= 9 + 4+ 5 - 1
therefore p = 17
What is the slope of the line that contains these points?
Answers
The slope of the line that contains the the given points is 1/5 .
The slope of the line containing the two points (x₁ , y₁) and (x₂ , y₂) is calculated using the formula
slope = (y₂ - y₁)/(x₂ - x₁)
In the question ,
it is given that the
line contains the points x [tex]=[/tex] -4 , y [tex]=[/tex] -3
and x = 1 , y = -2 .
we need two points to find the slope of the line
Substituting the values in the formula for slope ,
we get
slope = (-2 -(-3))/(1-(-4))
= (-2+3)/(1+4)
= 1/5
Therefore , The slope of the line that contains the the given points is 1/5 .
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A cycle Wheel does 1645 full turns in 7 minutes
work out the number of full turns per minute
Answers
The number of full turns per minute is 235.
Given that, a cycle Wheel does 1645 full turns in 7 minutes.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here,
The number of full turns per minute = Number of full turns/Number of minutes
= 1645/7
= 235 full turns per minute
Therefore, the number of full turns per minute is 235.
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Eli is following this recipe to bake bread rolls.
He uses 900 g of flour.
How much of the other ingredients does he use?
Recipe: Makes 12 bread rolls
600 g flour
12 g salt
9 g yeast
45 ml oil
360 ml water
g salt
0
g yeast
0
ml oil
0
ml water
Answers
Answer:
1022
Step-by-step explanation:
360+600+12+45+9=1022
How many inches are in 5 1/4 feet?
Answers
Answer: 63 inches
Step-by-step explanation:
Answer:
63 inches
Hope this helps :)
Use the number line to plot –3, 1, and 3. Which statements are true? Select all that apply. –3 > 1 –3 = 3 1 < 3 –3 < 1
Answers
Answer:
The answer is –3 < 1
Step-by-step explanation:
-3 is below zero. 1 is above zero. therefore, -3 less than 1
after a bride has interviewed 6 djs to play at her wedding, her fiance tells her she needs to narrow it down to 3 djs. in how many ways can she rank the 3 djs? a) 20 b) 18 c) 720 d) 3 e) 120 f) none of the above.
Answers
The number of way in which bride can rank the three Djs out of 6 is 120.
Defined the word permutation?The number of possible arrangements for a given set is determined mathematically, and so this procedure is referred to as permutation. Simply said, a permutation is a concept that refers to the wide range of possible arrangements or orders. The arrangement's order is important if using permutations.There are several different ways we might rank the three DJs.
Therefore, we must identify the permutation P. (6,3).
Total number of DJs = 6Required number of DJs = 3ⁿPₓ = n!/(n - x)!
⁶P₃ = 6!(6-3)!
⁶P₃ = 6×5×4
⁶P₃ = 120
Thus, the number of way in which bride can select the three Djs out of 6 is 120.
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ets
d and simplify these
4(a + 8) =
Answers
4(a + 8)
multiply out:
= 4a + 32
Can you help me create a polynomial function from the diagram displayed below? My teacher never went over this in class.
Thanks!
Answers
Considering the dimensions of the rectangular prism and it's volume, it is found that:
The expression is: V(x) = 4x³ - 22x² + 30x.The degree is of 3, the number of terms is of 3, and the leading coefficient is of 4.How to obtain the volume of a rectangular prism?The volume of a rectangular prism is given by the multiplication of the dimensions of the prism, which are the width symbolized by w, the height symbolized by h and the length symbolized by l, that is:
V = l x w x h.
In the context of this problem, from the image, the dimensions are given as follows:
Length: l = 2x - 5.Width: w = x - 3.Height: h = 2x.Then the polynomial expression regarding the volume of the prism is obtained as follows:
V(x) = 2x(x - 3)(2x - 5)
V(x)= 2x(2x² - 11x + 15)
V(x) = 4x³ - 22x² + 30x.
The features of the polynomial expression V(x) = 4x³ - 22x² + 30x is obtained as follows:
Degree of 3, which is the highest exponent of the function V(x).Number of terms of 3, which are 4x³, 22x² and 30x.The leading coefficient is of 3, as it is the term that multiplies the term with the highest exponent x³.A similar problem, also about the volume of a rectangular prism, is presented at brainly.com/question/22070273
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Graph the function f(x)=−14x−2.
Use the line tool and select two points to graph.
Answers
The slope is negative so the function is decreasing.
Let’s find the intersection points of the function:
0=-14x-2
14x=-2
X≈-0.142
(-0.142,0)
Y=-14*0-2
Y=2
(0,2)
Here is the answer:
Lena made $60 babysitting for 3 hours on Sunday. He made $140 for 7 hours
on Tuesday. What is the rate of change?
Answers
Answer:20 dollars per hour
Step-by-step explanation:60/3 = 20
20 dollars per hour
7 x 20 = 140
What is the relationship between Za and Zb?
Choose 1 answer:
A
B
a
Vertical angles
b
Complementary angles
Answers
Answer:
A
Step-by-step explanation:
∠ A and ∠ B are vertically opposite angles and are congruent. that is
∠ A and ∠ B are vertical angles
A shelter has enough food to feed an average of 45 hungry people a day for 20 days. If an average of 18 peo
Answers
The number of days that the food will last when an average of 18 people are at the shelter everyday is 50 days.
How to calculate the number of people?From the information given, the shelter has enough food to feed an average of 45 hungry people a day for 20 days.
Let the number of days that the people can be fed when 18 people come be Illustrated as x.
Therefore, this will be illustrated as x. This will be:
x = (45 × 20) / 18
x = 900 / 18
x = 50
The number of days is 15 days.
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Complete question
A shelter has enough food to feed an average of 45 hungry people a day for 20 days. If an average of 18 people are at the shelter everyday, how long will the food last?
CARPENTRY A carpenter is building a podium. The side panel of the podium is cut from a rectangular piece of wood. The rectangle must be
sawed along the dashed line in the figure.
Answers
The measure of angle1 in the given rectangular figure is 64° .
In the question ,
it is given that ,
the one of the angle is 116° .
From the figure below ,
we can see that
the dashed line is a transversal to AB and CD ,
the angles on the line AB form a linear pair ,
So , angle2 + 116° = 180°
angle2 = 180° - 116°
angle2 = 64°
Since the side panel of the podium is cut from rectangular piece
the figure is representing two parallel lines , cut by the transversal .
By the property of transversal that alternate interior angles are equal in measure ,
angle 1 = angle 2
hence , angle 1 = 64° .
Therefore , The measure of angle1 in the given rectangular figure is 64° .
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Jerome tries to find the value of the expression 3 - 6 + 5 by first applying the commutative property. He rewrites the expression as 3 - 5 + 6. Explain, What is wrong with Jerome's approach?
Answers
The fault with Jerome's approach as required in the task content is; he tries to add 3 and 5 by switching 5 and 6, but, he forgets to switch the signs too.
What is the commutative property of addition?Commutative property of addition is a property of addition which posits that Changing the order of addends does not change the sum.
On this note, the use of the commutative property of addition on the given expression; 3 - 6 + 5 would yield the expression; 3 + 5 - 6.
Consequently, the fault with Jerome's approach is that; he tries to add 3 and 5 by switching 5 and 6, but, he forgets to switch the signs too.
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Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. He knows he
has the option of beginning repayment of the loan in 4.5 years. He also knows that during this non-payment time, interest will accrue at 4.29%.
If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period.
a. What will the new principal be when he begins making loan payments?
b. How much interest will he pay over the life of the loan?
Answers
a) The new principal (principal + capitalized interest) when Rich begins making loan payments will be $9,425.10.
b) The total interest that Rich will pay over the life of the loan is $4,914.20.
How is interest on student loans determined?The interest on student loans is based on simple interest.
The only interest capitalized is the interest during the non-payment period if the student does not pay the interest.
Some students elect to pay the interest during the non-payment period to reduce the capitalized interest and principal during the payment period.
Capitalization refers to the addition of interest to the principal amount.
Period of student loan = 10 years
The amount of the federal unsubsidized student loan = $7,900
Interest rate = 4.29%
Capitalized interest during the non-payment time = $1,525.10 ($7,900 x 4.29% x 4.5)
New principal when Rich begins making loan payments = $9,425.10 ($7,900 + $1,525.10)
Total interest for loan = $4,914.20 ($7,900 x 4.29% x 14.5)
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For each sequence, decide whether it could be arithmetic, geometric, or
neither.
1. 27, 9, 3, ...
2. 4, 8, 12,...
3. 50, 56, 60, ...
4. 36, 12, 4, ...
5. 4, 24,...
Answers
1. Therefore, the sequence is geometric.
2. Therefore, the sequence is arithmetic.
3. Therefore, the sequence is neither arithmetic nor geometric.
4. Therefore, the sequence is geometric.
5. Therefore, the sequence is neither arithmetic nor geometric.
Explain sequences and seriesFor the arithmetic, geometric, and harmonic sequences, a collection of sequences and series formulas is provided below. The sequence and series formulas presented here contain formulas for determining the sum of the n terms in a series as well as the nth term of the sequence.
A common difference exists between two succeeding terms in an arithmetic series. There is a typical ratio between succeeding terms in a geometric series.
1. Given sequence is 27, 9, 3, ...
As the difference between the number is large.
So, we will check for geometric sequence.
[tex]r = \frac{27}{9} = \frac{3}{3} = \frac{1}{3}[/tex]
Therefore, the sequence is geometric.
2. Given sequence is 4, 8, 12, ...
As we can see there is uniform difference of 4
Therefore, the sequence is arithmetic.
3. Given sequence is 50, 56, 60, ...
As the difference between the number is not uniform.
So, we will check for geometric sequence.
[tex]r = \frac{50}{56} \neq \frac{56}{60}[/tex]
There, the sequence is neither arithmetic nor geometric.
4. Given sequence is 36, 12, 4, ...
As the difference between the number is large.
So, we will check for geometric sequence.
[tex]r = \frac{36}{12} = \frac{12}{4} = 3[/tex]
Therefore, the sequence is geometric.
5. Given sequence is 4, 24, ...
The number of terms is very less and hence we can't decide.
There, the sequence is neither arithmetic nor geometric.
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The radius of a circle is 599 cm. What is the diameter of this circle?
Answers
Answer:
1,198 cm
Step-by-step explanation:
To find the diameter, use the formula d = 2r.
d = 2(599)
d = 1,198
i NEED HELP NOW dane is selling popcorn for a fundraiser if each bag of popcorn he sells cost $4.75 what equation can he use to calculate the total amount of money he raised if he sold x number of bags
Answers
Answer:
Step-by-step explanation:
Take the amount, $4.75, multiplied by x will give you the total amount of money raised and just put that into the equation format:
$4.75 (x) = total amount of money raised
the student council at westford high school is making t-shirts to sell for a fundraiser, at a price of $10 apiece. the costs, meanwhile, are $6 per shirt, plus a setup fee of $72. selling a certain number of shirts will allow the student council to cover their costs. what will the costs be? how many shirts must be sold?
Answers
Cost will be $180 and so will be the revenue.
What is linear equation ?Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on. Some of the examples of linear equations are 2x – 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x – y + z = 3.
CalculationCost: C=72+6s, where s is the number of shirts sold
Revenue: R=10s
Break-even is where they are equal
72 + 6s = 10s
72/4 = s
s = 18 shirt s
Cost will be $180 and so will be the revenue.
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Warren has 40 coins (all nickels, dimes, and quarters) worth $4.05. He has 7 more nickels than dimes. How many quarters does Warren have?
Please provide a detailed explanation and steps on how to do
Answers
If he has 7 more nickels than dimes. The number of quarters that Warren have is 7.
How to determine the number of quarters?Let coins be:
n + d + q = 40
Where;
n = nickels
d =dimes
q = quarters
Hence,
.05n + .10d + .25q = 4.05
n = d + 7
Substitute (d+7) for n
(d+7) + d + q = 40
2d + q = 40 - 7
2d + q = 33
q = (33-2d)
So,
.05(d+7) + .10d + .25q = 4.05
.05d + .35 + .10d + .25q = 4.05
15d + .25q = 4.05 - .35
.15d + .25d = 3.70
Substitute (33-2d) for q
.15d + .25(33-2d) = 3.70
.15d + 8.25 - .5d = 3.70
.15d -.5d = 3.70 - 8.25
-.35d = -4.55
Divide both side by -/35d
d = -4.55 / -.35
d = 13 dimes
Nickels
n = d+7 where d is 13
n = 13 + 7
n = 20 nickels
Quarters
q = (33-2d)
q = 33 - 2(13)
q = 33 - 26
q = 7 quarters
Therefore 7 is the quarters.
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How much of a radioactive kind of promethium will be left after 265 hours if the half-life is 53
hours and you start with 15,488 grams?
grams
Answers
265 hours and half life is 53 so 265/53=5, so you half 15488 5 times which gives you 484.
0.38 in standard form
Answers
Nick starts with 20
20
milligrams of a radioactive substance. The amount of the substance decreases by 12
1
2
each week for a number of weeks,
w
. He writes the expression 20(12)
20
(
1
2
)
w
to find the amount of radioactive substance remaining after
w
weeks.
Autumn starts with 1
1
milligram of a radioactive substance. The amount of the substance decreases by 50%
50
%
each week for a number of weeks,
w
. She writes the expression (1−0.5)
(
1
-
0
.
5
)
w
to find the amount of radioactive substance remaining after
w
weeks.
Use the drop-down menus to explain what each part of Nick's and Autumn's expressions mean.
Answers
Each part of Nick's and Autumn's expressions mean can be explained as follows;
Nick;
the amount of substance he begins with = 20the amount of substance left after each week = 1/2Autumn:
The one outside of parentheses = the initial amount of the substance.The one inside of parentheses = 100% of the original amount of the substance.0.5 represents the 50% of the substance that is lost each time periodHow to explain each variable in an expression?ler
Number of weeks = wNick expression:
[tex] {20( \frac{1}{2} })^{w} [/tex]
Where,
the amount of substance he begins with = 20
the amount of substance left after each week = 1/2
If w = 2
[tex] {20( \frac{1}{2} })^{w} [/tex]
[tex]{20( \frac{1}{2} })^{2} [/tex]
= 20(0.25)
= 5 milligrams
Autumn's expression:
[tex] {(1 - 0.5)}^{w} [/tex]
The one outside of parentheses = the initial amount of the substance.
The one inside of parentheses = 100% of the original amount of the substance.
0.5 represents the 50% of the substance that is lost each time period
If w = 2[tex] {(1 - 0.5)}^{w} [/tex]
[tex] {(1 - 0.5)}^{2} [/tex]
= (0.5)²
= 0.25 milligrams
Complete question:
Nick starts with 20 milligrams of a radioactive substance. The amount of the substance decreases by 1/2 each week for a number of weeks, w. He writes the expression 20(12)w to find the amount of radioactive substance remaining after w weeks. Autumn starts with 1 milligrams of a radioactive substance. The amount of the substance decreases by 50% each week for a number of weeks, w. She writes the expression (1-0.5)w to find the amount of radioactive substance remaining after w weeks. Use the drop-down menus to explain what each part of Nick's and Autumn's expressions mean.
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Please help now asap !!! Due tomorrow
Answers
Answer:
Step-by-step explanation:
it help by showinbng thta
Help me for this question
Answers
A bakery sells 4 dozen cupcakes every 3 hours. If the bakery is open 8 hours each day, how many days does it take to sell 640 cupcakes?
Answers
5 days does it take to sell 640 cupcakes.
Given:
A bakery sells 4 dozen cupcakes every 3 hours.
If the bakery is open 8 hours each day.
4 dozen cupcakes = 4*12 cupcakes
= 48 cupcakes
48 cupcakes = 3 hours
divide by 3 on both sides
3hours/3 = 48/3 cupcakes
1 hour = 16 cupcakes
Number of cupcakes for 8 hours = 8 * 16 = 128 cupcakes.
128 cupcakes sells in one day.
To sell 640 cupcakes = 640/128
= 5 days.
Therefore 5 days does it take to sell 640 cupcakes.
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please help me with this problem.
Answers
Answer:
(- 25, 5 )
Step-by-step explanation:
- 3x - 6y = 45 → (1)
- 5y = x → (2)
substitute x = - 5y into (1)
- 3(- 5y) - 6y = 45
15y - 6y = 45
9y = 45 ( divide both sides by 9 )
y = 5
substitute y = 5 into (2)
- 5(5) = x , then
x = - 25
solution is (- 25, 5 )
line that passes through the point (8,−3) and has a slope of 1/4
Answers
The equation of line having a slope of 1/4 which passes through point (8,-3) is y = (1/4)x - 5.
What is the equation of line with the given point and slope?The equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Point (8, -3 )
x = 8y = -3Slope m = 1/4Determine the y-intercept 'b'.
Substitute the point and slope into the equation of line formula and solve for b.
y = mx + b
-3 = (1/4)(8) + b
-3 = 8/4 + b
-3 = 2 + b
b = -3 - 2
b = -5
Now, substitute slope and y-intercept into y = mx + b to determine the equation of the line.
y = mx + b
y = (1/4)x + (-5)
y = (1/4)x - 5
Therefore, the equation of the line is y = (1/4)x - 5.
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