The correct way by using the power of a power property we can write as;
⇒ x¹⁵ = (x³)⁵
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ x¹⁵
Now,
Since, The expression is,
⇒ x¹⁵
We can write the expression as by using the power of a power property as;
⇒ x¹⁵ = (x³)⁵
Thus, The correct way by using the power of a power property we can write as;
⇒ x¹⁵ = (x³)⁵
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Select the correct answer. Which expression is equivalent to , if x ≠ 0 and y ≠ 0? A. B. C. D.
see image below:
The expression similar to [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex] obtained by using the laws of indices is option A.
A. [tex]2\cdot x^2 \cdot y\sqrt[3]{7\cdot x \cdot y^2}[/tex]
What are the laws of indices?According to some of the laws of indices, we have;
[tex]\dfrac{1}{x^n} =x^{-n}[/tex]
[tex]x^m \cdot x^n = x^{m+n}[/tex]
[tex]\sqrt[m]{x^n} =x^{\frac{n}{m} }[/tex]
The expression can be presented as follows; [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex]
Simplifying the above expression gives;
[tex]\sqrt[3]{56\cdot x^7\cdot y^5 } = \sqrt[3]{8 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 }[/tex]
[tex]\sqrt[3]{8 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 } = \sqrt[3]{2^3 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 }[/tex]
Collecting terms with an index of a multiple of 3 gives;
[tex]\sqrt[3]{2^3 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 } = \sqrt[3]{2^3\cdot x^6 \cdot y^3 \times 7\cdot x \times y^2 }[/tex]
[tex]\sqrt[3]{2^3\cdot x^6 \cdot y^3 \times 7\cdot x \times y^2 } = 2\cdot x^2 \cdot y \times \sqrt[3]{ 7\cdot x \cdot y^2 }[/tex]
The expression that is equivalent to [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex]is option A.
A. [tex]2\cdot x^2 \cdot y \times \sqrt[3]{ 7\cdot x \cdot y^2 }[/tex]
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Algebra 2 please help!
Which table of values would produce the graph shown above?
The table (D) values would produce the same graph as shown.
What is a Graph?Mathematical structures known as graphs are used to describe pairwise relationships between things. Graph theory is the study of these mathematical structures. Vertices (also known as nodes or points) and edges are what make up a graph in this sense (also called links or lines). It is possible to distinguish between directed and undirected graphs, where edges connect two vertices asymmetrically and symmetrically, respectively. One of the primary topics in discrete mathematics is graphs.
From the graph, find the intercepts,
At x = 0, the value of y is -1.
At, y = 0, the value of x is 4
So, from the given options, we can see that the values are given in table (D).
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Hi I'm honestly really confused on this problem and have no idea what I'm meant to do. It'd be helpful if someone could explain this
As corresponding angles ∠5 and ∠8 are equal. Hence line x is parallel to line z by converse of corresponding angles theorem.
What does converse of corresponding angles theorem states?
If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.
How can we show two lines are parallel to each other?
We can show lines are parallel by finding a pair of corresponding angles that are congruent.
Proving if two lines are parallel then third line is parallel too.
According to the given data:
It is given in the question that line x is parallel to line yTherefore, ∠5 ≅ ∠7 (i.e. corresponding angles)
∠5 = ∠7
Similarly as given line y is parallel to line z∠6 ≅ ∠8 (Corresponding angles are equal)
∴ Measure of angles is also equal ⇒ ∠6 = ∠8
∠5 = ∠8 (transitive property of equality of angles which says if
∠a = ∠b and ∠b = ∠c then ∠a = ∠c)
∠5 ≅ ∠8 (If measure of angles is same then they are congruent)
Therefore, line x || line z
(Converse of the Corresponding Angles Theorem).
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help meeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The length of the shorter leg is 9 mm.
The length of the longer leg is 12 mm.
The length of the hypotenuse is 15 mm.
Pythagoras theory applies to every right triangle. If
The shorter leg = aThe longer leg = bThe hypotenuse = c[tex]a^2 + b^2 = c^2[/tex]Step-by-step explanation:
Known
Longer leg = shorter leg +3 mmAsked
a?b?c?Answer
[tex]a^2 + b^2 = c^2[/tex]
[tex]a^2 + (a+3)^2 = (a+6)^2[/tex]
[tex]a^2 + a^2 + (2 \times a \times 3) + 3^2 = a^2 + (2 \times a \times 6) + 6^2[/tex]
[tex]2a^2 + 6a + 9 = a^2 + 12a + 36[/tex]
[tex]2a^2 - a^2 + 6a - 12a + 9 - 36 = 0[/tex]
[tex]a^2 - 6a - 27 = 0[/tex]
[tex]a^2 - 9a + 3a - 27 = 0[/tex]
[tex]a \times (a - 9) + 3 \times (a - 9) = 0[/tex]
(a-9) (a+3)=0
a-9=0 or a+3= 0
a=9 or a=-3 (impossible)
Shorter leg
a=9 mm
Longer leg
b = a+3
b = 9+3
b = 12 mm
Hypotenuse
c = a+6
c = 9+6
c = 15 mm
Mason, a hardwood flooring installer, needs to calculate the amount of hardwood flooring needed to cover a floor that’s 3 3/4 yards Wide and 5 1/2 yards Long. How many square yards of hardwood flooring are needed? (Area= Length x Width). A) 20 5/8 B)15 3/8 C)18 3/4 D)16 1/2
A floor that is 3 3/4 yards wide and 5 1/2 yards long requires 20 5/8 square yards of hardwood flooring area.
length = 5 1/2 yd, breadth = 3 3/4 yd.
Make fractions out of both measurements first.
3 3/4 = 3 + 3/4
= 12/4 + 3/4
= 15/4
5 1/2 = 5 + ½
= 10/2 + ½
= 11/2
Area = (15 * 11)/(4 * 2) yd2
Area = 165/8 yd2
They essentially believed that 165/8 = 20 leftover 5 area = 20 5/8 yd2.
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15. Write the factored form of 9+24 by pulling out the GCF?*
There are 2 common factors of 9 and 24, that are 1 and 3. Therefore, the greatest common factor of 9 and 24 is 3.
What is GCF ?In mathematics, the greatest common divisor of two or more nonzero integers is the largest positive integer that divides each integer
. The greatest common divisor (GCF) of a set of numbers is the greatest factor of division of all numbers.
CalculationGCF by listing factor method :-
Factors of 9: 1, 3, 9
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
There are 2 common factors of 9 and 24, that are 1 and 3. Therefore, the greatest common factor of 9 and 24 is 3.
other two methods are attached below .
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very stuck please help
The equation of the line through (3,1) and is perpendicular to a line through (6, -2) and (-8 ,5) is y = 2x - 5 .
In the question ,
it is given that
the required line is perpendicular to the line passing through (6, -2) and (-8 ,5) .
the slope is = (5 -(-2))/(-8 -6)
= 7/(-14)
= -1/2
so , the slope of the required line is = 2 .
The equation of the line passing through the point (3,1) with slope 2 is
(y - 1) = 2*(x-3)
y -1 = 2x - 6
y = 2x - 6 + 1
y = 2x - 5
the equation of line is y [tex]=[/tex] 2x - 5
the perpendicular slope is = 2
the y intercept is -5 .
Therefore , The equation of the line through (3,1) and is perpendicular to a line through (6, -2) and (-8 ,5) is y = 2x - 5 .
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Compare the two functions described below.
Function 1: Originally there were 60 people living in Schondel City. The city’s population is growing and the amount of people living in the city is double what it was from the day before!
Function 2:
x y
0 32
1 25.6
2 20.48
3 16.384
4 13.1072
Answer:zh 0 89 1 87.6
Step-by-step explanation: 0 89 1 87.6
is y=4x-8, continuous or discrete?
The equation y = 4x - 8 is discrete
What are discrete data?Discrete data is a sort of numerical information that consists of full, concrete numbers with predetermined, set values that can be counted.
While complex numbers and fluctuating data values taken over a predetermined period of time are examples of continuous data.
The difference between discrete and continuous dataThe main distinction between continuous and discrete data is that the former has a finite value that can be counted while the latter has an endless number of possible values that can be measured.
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rationalise the denominator [tex]\frac{1}{4-\sqrt-{11} }[/tex]
Answer:
[tex]\frac{4+\sqrt{11} }{5}[/tex]
Step-by-step explanation:
to rationalise the denominator, multiply the numerator and denominator by the conjugate of the denominator.
the conjugate of 4 - [tex]\sqrt{11}[/tex] is 4 + [tex]\sqrt{11}[/tex] , then
[tex]\frac{1(4+\sqrt{11}) }{(4-\sqrt{11})(4+\sqrt{11}) }[/tex] ← expand denominator using FOIL
= [tex]\frac{4+\sqrt{11} }{16-11}[/tex]
= [tex]\frac{4+\sqrt{11} }{5}[/tex]
Please help me I need this I'm behind
Answer:
25.5 feet because of some
Step-by-step explanation:
.,........
Answer:
Step-by-step explanation:
divide 14 7/8 by 6 because you want to find out how much 6 inches is their in 14 7/8 because that the giving inchwhen you do 6 ÷ 14 7/8 you get 2.47916666667now you multiply by 3 1/2 with is the same as 3.5 and you get 8.67708333333 and that rounds to 8.68.Answer: 8.68 feetPlease help me with this question. the m is 6 and the d is 8
Step-by-step explanation:
so, we have
6x² + 8xy + 8y²
and
5x² + 3xy + 16y²
we can combine only terms of the same kind (defined by the type and exponent of the used variables).
this is like adding fruit.
e.g. when we have a mixture of 3 apples, 4 oranges and 5 plums, and we add a mixture of 6 apples, 2 oranges and 3 plums - what do we get ?
we get a new mixture of
3+6 = 9 apples
4+2 = 6 oranges
5+3 = 8 plums
and exactly the same thing happens with mixing terms when adding them up.
so, we get
6+5 = 11x²
8+3 = 11xy
8+16 = 24y²
so, the result is
11x² + 11xy + 24y²
it is really that simple.
The geometric mean of a number and nine times the number is 30. What is the number?
For the given geometric mean of a required number and nine times the required number is 30 then the required number is equal to 10.
As given in the question,
Geometric mean GM = 30
Let us assume the first number is x
and second number i.e. 9 times of the first number is 9x
By the formula GM = [tex]\sqrt{x.y}[/tex]
Now putting the value
30 = [tex]\sqrt{x.9x}[/tex]
30 = [tex]\sqrt{9x^{2} }[/tex]
30 = 3x (∴ square root of 9 is 3 and sq root of x² is x)
10 = x (by dividing both the side by 3)
Therefore, for the given geometric mean of a required number and nine times the required number is 30 then the required number is equal to 10.
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find the inequality 2x/3 <4
Answer:
x<6
Step-by-step explanation:
2x/3<4
2x<12
x<6
Answer:
x < 6
Step-by-step explanation:
[tex]\frac{2x}{3}[/tex] < 4 ( multiply both sides by 3 to clear the fraction )
2x < 12 ( divide both sides by 2 )
x < 6
2.8x + 10 + 5.7x = 70+x
Answer:
Step-by-step explanation a=0.32
The required simplified value of x in the given expression is 8.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
2.8x + 10 + 5.7x = 70+x
Simplifying,
8.5x + 10 = 70 + x
8.5x - x = 70 - 10
7.5x = 60
x = 60 / 7.5
x = 8
Thus, the required simplified value of x in the given expression is 8.
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You go out to eat with 3 friends and your meal was $72.50. There is 6.75% sales tax and you plan to tip the server 15%. How much should each person pay?
The amount that each person should pay is $22.06 .
in the question ,
it is given that
total number of persons = 3 person + 1 = 4 persons
cost of the meal = $72.50
sales tax percent = 6.75%
tip percent = 15%
So , the amount of sales tax = 6.75% of cost = 0.0675 * 72.50 = $4.89
and , the amount of tip is = 15% of cost
= 0.15 * 72.50
= 10.87
So , the total amount payable is = cost + sales tax + tip
= 72.50 + 4.89 + 10.87
= 88.26
since the total number of persons is 4 ,
the amount per person is = 88.26/4 = 22.06
Therefore , The amount that each person should pay is $22.06 .
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The wholesale cost for a purse in a department store is $12. 50. The store plans to mark up the purse by 140%. What will be the selling price of
the purse to the nearest cent?
Give me the right anwser
The selling price of the the purse in a department store is cents.
Define the term selling price?A product's or service's selling price is the seller's final price, or how much the buyer pays for anything. The trade can be for a certain proportion, quantity, or measure of a commodity or service.The price at which you sell anything must be sufficient to generate a profit. It must also establish a market position.For the given question-
A purse in such a department store costs $12.50 at wholesale.
The purse will be 140% more expensive at the store.
Then,
140% of 12.50 = 140 x 12.50 / 100
140% of 12.50 = 17.5
Selling price = percent increase + cost price
Selling price = 17.5 + 12.5
Selling price = $30.0
Selling price = 3000 cents
Thus, the selling price of the the purse in a department store is cents.
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A car originally is worth $3000. It is decreasing in value by 3% every year. How much is it worth in 3 years.
(Round to the nearest cent)
Answer:
$2825,32
Step-by-step explanation:
Value of the car after 1 year
$3000 * 3% = 3000 * 0.03 = 90
3000 - 90 = $2910
Value of the car after 2 year
$2910 * 3% = 2910 * 0.03 = 87.3
2910 - 87.3 = $2912,7
Value of the car after 3 year
$2912,7 * 3% = 2912,7 * 0.03 = 87.381
2912,7 - 87.381 = $2825,319
"Round to the nearest cent"
$2825,32
Betsie is going to buy 250 envelopes.
Here is some information about the cost of envelopes in two shops.
Value World
Pack of 10 envelopes for £1.99
Buy 2 packs get 1 pack free
Letters2go
Pack of 25 envelopes for £3.19
Betsie wants to buy the envelopes for the best possible price.
Which shop should Betsie buy the 250 envelopes from?
You must show how you get your answer.
Betsie should buy the 250 envelopes from the shop Letter2go.
As, 250 envelopes will cost £31.9 in Shop Letter2go whereas will cost £33.17 in Shop Value World.
Given, that Betsie is going to buy 250 envelopes.
the cost of envelopes in two shops:
Value World:
Pack of 10 envelopes for £1.99
Buy 2 packs get 1 pack free
Letters2go:
Pack of 25 envelopes for £3.19
Now, if we see the cost of envelopes in shop 1 i.e. Value World
Cost of Pack of 10 envelopes = £1.99
Also, 1 pack is free for 2 packs
1 pack = £1.99
2 packs = 2×£1.99 = £3.98
Also, with 2 packs Betsie get 1 pack free
so, Betsie gets 3 packs for £3.98.
1 pack = 10 envelopes
3 packs = 30 envelopes.
Hence, In shop Value World:
30 envelopes = £3.98
1 envelope = £3.98/30
250 envelopes = (3.98/30)×250
So, 250 envelopes will cost £33.17 in Shop Value World.
And in shop Letter2go:
25 envelopes = £3.19
1 envelope = £3.19/25
250 envelopes = (3.19/25)×250
So, 250 envelopes will cost £31.9 in Shop Letter2go.
Hence, 250 envelopes will cost £33.17 in Shop Value World and £31.9 in Shop Letter2go.
So, Betsie should buy the 250 envelopes from the shop Letter2go.
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please help fast algebra 2
I need this answer as soon as possible.It will be nice if you do it in a paper.
Answer:
as shown in underline ^^
Step-by-step explanation:
Fill in the missing words:
When a solid mixes with a liquid and becomes part of the liquid it dissolves.
A solid that dissolves in a liquid is soluble.
A solid that does not dissolve in a liquid is insoluble.
question 1 a sample random sample of 6 bulbs was selected from a lot of 100 for the purpose of estimating its quality. the life of each bulb selected was measured by letting the bulb until it burned out. the results from the test are as follows: bulb number life duration (hours) 1 950 2 1210 3 1070 4 840 5 1420 6 980 a.) estimate the average life of the bulbs in the lot. b.) estimate the total life bulbs in the lot c.) estimate the proportion of bulbs in the lot with life exceeding 1000 d.) estimate the number of bulbs in the lot with life exceeding 1000
a) The average life of the lot is 1078.33 hrs, b) the total life is 107833.33 hours, c) a proportion of 1/2 bulbs have a life exceeding 1000 hrs while d) an estimation of 50 bulbs have a life exceeding 1000 hours.
It is given that the number of bulbs in a given lot is 100.
The number of bulbs in the sample selected is 6
The life of the sample bulbs was
no. life (hours)
1 950
2 1210
3 1070
4 840
5 1420
6 980
a)
The average life of the bulbs can be calculated by
the sum of the lives of the sample/ no. of samples
= (950 + 1210 + 1070 + 840 + 1420 + 980) / 6
= 1078.3333 hrs
b) The total lives of the bulbs in the lot will be
average life X no. of bulbs
= 1078.3333 X 100
= 107833.33 hrs
c)
We can gain the proportion of the bulbs that have a life exceeding 1000 hrs by the given sample
The bulbs
2, 3, and 5 have lives exceeding 1000 hrs.
Hence, out of 6 bulbs, 3 have lives exceeding 1000 hrs.
Therefore the proportion
= 3/6
= 1/2
d)
The number of bulbs in the lot with a life exceeding 1000 will be
proportion X no. of bulbs
= 1/2 X 100
= 50 bulbs
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evaluate (-3)^3 x (-5/3)^-4
Answer:
answer. {-2187x}/{625}
The local craft fair charges the vendors a flat rate of $15 plus $10 for each hour that they splend at the fair. If the vendor owed $65, how many hours did he remain at the craft fair?
Answer:
5 hours
Step-by-step explanation:
$65 - $15 = $50
$50/$10 = 5
What is the zero of g?
(-6,0)
(-3, -4.5)
(-8, 0)
(0,-9)
Answer: Either C. or D.But I'm sure it's D.
Step-by-step explanation:
6 in each of these numbers: 364 346 which sentence correctly compares the values? a. the value of the 6 in 364 is the value of the 6 in 346. b. the value of the 6 in 364 is 100 times the value of the 6 in 346. c. the value of the 6 in 364 is the value of the 6 in 346. d. the value of the 6 in 364 is 10 times the value of the 6 in 346.
The correct answer to this question is d. the value of the 6 in 364 is 10 times the value of the 6 in 346.
The place value of the 6 in 346 is six because it is in the place of ones, whereas the place value of the sixth in 364 is 60 because it is in the place of tens. As a result, the value of 60 is ten times that of the value of 6.
The value of each digit in a number is known as place value. Every digit in a number has a distinct value depending on where it is located. The value of a digit depends on its position in the number, which can result in a number having two similar digits with different values.
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1/2x-7=1/3(x-12) Explain or show your reasoning.
Answer: x=18
Step-by-step explanation:
It just does ok
help meeeeeeeeeeeeeee pleaseee
Answer: See the image below for the table and graph
==========================================================
Explanation:
We replace x with the values mentioned. Do so one at a time to compute the corresponding y value.
For instance, if x = -2, then...
[tex]\text{y} = 2\text{x}^2\\\\\text{y} = 2(-2)^2\\\\\text{y} = 2(4)\\\\\text{y} = 8\\\\[/tex]
If x = -2, then y = 8. This produces the point (-2,8) which is on the parabola.
We'll write "8" without quotes into the box next to x = -2, as shown in the table diagram below.
Repeat for x values x = -1 through x = 2.
Once we determine those point coordinates, we then plot said points to form the parabola shown below. The more points, the better accurate picture you'll have of the curve. I used GeoGebra to make the graph and table. Desmos is another good option which I recommend.
Karla drank a 15-fluid-ounce bottle of water before tennis practice. After practice, she drank 4 cups of water. What is the total amount of water Karla drank?
a 7 c and 9 fl oz
b 7 c and 7 fl oz
c 5 c and 9 fl oz
d 5 c and 7 fl oz
The total amount of water Karla drank before and after the tennis practice is 5 cups and 9 fluid ounces.
The correct answer option is option C.
What is the total amount of water Karla drank?Volume of water Karla drank before tennis practice = 15-fluid-ounceVolume of water Karla drank after tennis practice = 4 cupsConvert fluid ounces to cups:
1 fluid ounces = 0.125 cups
15 fluid ounces = 1.875 cups
Total volume of water Kayla drank = Volume of water Karla drank before tennis practice + Volume of water Karla drank after tennis practice
= 1.875 cups + 4 cups
= 5.875 cups
Approximately,
5 cups and 9 fluid ounces
Therefore, the total volume of water Karla drank is approximately 5 cups and 9 fluid ounce
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I NEED THIS GRAPH SOLVED ASAP
I need either the function in factored form or the roots(with multiplicity) or standard form thank you and please!!!
Answer:
if the root is 10 then the function is ²✓5