PLEASE!?!?!? 11 points and brainliest
Match the expression to the exponent property that you use first to simplify the expression.
Answers
[tex](a^m)^n = a^{mn} \rightarrow (p^\frac{1}{4})^\frac{2}{3}[/tex]
[tex]a^m\cdot a^n = a^{m+n} \rightarrow z^{\frac{3}{4}} \times z^\frac{5}{6}[/tex]
[tex](\frac{a}{b})^n = \frac{a^n}{b^n} \rightarrow (\frac{x^2}{y})^\frac{1}{3}[/tex]
Please give brainliest :P
Step-by-step explanation:
[tex](p^\frac{1}{4})^{\frac{2}{3}}[/tex]
[tex]\frac{a^m}{a^n} =a^{m-n} --------------> \frac{h^\frac{3}{2}}{h^\frac{4}{3} } = h^{\frac{3}{2}-\frac{4}{3} }=h^{\frac{1}{3}}[/tex]
[tex](a^m)^n= a^{mn}-------> (p^\frac{1}{4})^{\frac{2}{3}}=p^\frac{1}{6}[/tex]
[tex]a^m * a^n= a^{m+n}------->z^\frac{3}{4} *z^\frac{5}{6} =z^{\frac{19}{12}}[/tex]
[tex](\frac{a}{b})^n=\frac{a^n}{b^n}-------> (\frac{x^2}{y})^{\frac{1}{3}} =(\frac{x\frac{2}{3} }{y^\frac{1}{3} })[/tex]
Related Questions
Write the sum using summation notation, assuming the suggested pattern continues. -9 - 3 + 3 + 9 + ... + 81
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Honestly I believe this is correct:
∑ 15 at the top, n =0 (-9+6n)
The perimeter of a square is in p inches. Write expressions, in terms of p, for the length of the side of the square and the area of the square.
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if the side length is p then the perimiter (distance around) is 4 times the length of the side or 4 times p or 4p
the area is side times side but since all sides are equal length, side^2 is the aera
perimiter=4p
area=p²
Which choices are real numbers? Check all that apply.
A. (-131072)^1/7
B. (-531441)^1/12
C. (-1024)^1/5
D. (-256)^1/8
Answers
[tex] \sqrt{x} [/tex]
That can be written as
x^(1/2)
...and when you take an even root of a negative number, there is no real answer. (2 is an even number).
Looking at the answer choices here, we can see that B and D use even roots, so they will give non-real answers.
So, A and C are the answer choices to select.
The real numbers are:
A. [tex]\((-131072)^{1/7}\)[/tex]
C. [tex]\((-1024)^{1/5}\)[/tex]
These have odd roots, resulting in real numbers.
To determine which of the given expressions are real numbers, we need to check if the roots of negative numbers are defined within the set of real numbers.
A. [tex]\((-131072)^{1/7}\)[/tex]
The expression [tex]\((-131072)^{1/7}\)[/tex] is the 7th root of [tex]\(-131072\)[/tex]. Since 7 is an odd number, the 7th root of a negative number is defined and is a real number.
So, [tex]\((-131072)^{1/7}\)[/tex] is a real number.
B. [tex]\((-531441)^{1/12}\)[/tex]
The expression [tex]\((-531441)^{1/12}\)[/tex] is the 12th root of [tex]\(-531441\)[/tex]. Since 12 is an even number, the 12th root of a negative number is not defined within the set of real numbers.
So, [tex]\((-531441)^{1/12}\)[/tex] is not a real number.
C. [tex]\((-1024)^{1/5}\)[/tex]
The expression [tex]\((-1024)^{1/5}\)[/tex] is the 5th root of [tex]\(-1024\)[/tex]. Since 5 is an odd number, the 5th root of a negative number is defined and is a real number.
So, [tex]\((-1024)^{1/5}\)[/tex] is a real number.
D. [tex]\((-256)^{1/8}\)[/tex]
The expression [tex]\((-256)^{1/8}\)[/tex] is the 8th root of [tex]\(-256\)[/tex]. Since 8 is an even number, the 8th root of a negative number is not defined within the set of real numbers.
So, [tex]\((-256)^{1/8}\)[/tex] is not a real number.
Summary:
- A. [tex]\((-131072)^{1/7}\)[/tex] is a real number.
- B. [tex]\((-531441)^{1/12}\)[/tex] is not a real number.
- C. [tex]\((-1024)^{1/5}\)[/tex] is a real number.
- D. [tex]\((-256)^{1/8}\)[/tex] is not a real number.
A regular pyramid has a height of 12 centimeters and a square base. if the volume of the pyramid is 256 cubic centimeters, how many centimeters are in the length of one side of its base
Answers
The Volume of a pyramid is [tex] \frac{1}{3}*area_b_a_s_e *height[/tex]
the area of the base is a^2,
we apply the formula
[tex]256= \frac{1}{3}*a^{2}*12 [/tex]
[tex]256= 4a^{2} [/tex]
[tex]256= (2a)^{2} [/tex]
[tex]2a= \sqrt{256}=16[/tex]
a=8 (cm)
Answer: 8 cm
In the triangle below, what is the side opposite the 30 degree angle
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How long does it take to drive 160 miles at 70mph?
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time=[Distance]/[Speed]
Distance=160 miles
Time=70 mph
thus;
time=160/70
=2 2/7 hours
Final answer:
To calculate the travel time to drive 160 miles at 70mph, use the formula Time = Distance ÷ Speed. The result is approximately 2.2857 hours, or about 2 hours and 17 minutes.
Explanation:
To calculate how long it takes to drive 160 miles at a constant speed of 70 miles per hour (mph), you can use the basic formula for time, which is Time = Distance ÷ Speed.
Distance to be traveled is 160 miles.
Speed of travel is 70 mph.
By plugging the numbers into the formula, we get:
Time = 160 miles ÷ 70 mph = 2.2857 hours.
To convert this time into minutes, we multiply by 60 (the number of minutes in an hour), so:
2.2857 hours × 60 minutes/hour = 137.1428 minutes, which is approximately 2 hours and 17 minutes.
any ideas friends? cant seem to figure this out
Answers
Io = 10^(-12), which is a constant usually shown in a table or in your book
Plug in those values to get
B = 10*log(I/Io)
B = 10*log((7.6*10^(-4))/(10^(-12)))
B = 88.808135922808
B = 88.81
Answer: Approximately 88.81 decibels
how would you prove two circles are similar
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GOOD LUCK!
Answer:
it is by similarity transformations
Step-by-step explanation:
so like it would be a rigid transformation then a dilation
EX- A translation then a dilation of R/r
Help with geometry...
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[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ 1}}\quad ,&{{ 2}})\quad % (c,d) G&({{ -4}}\quad ,&{{ 2}})\\ B&({{ 2}}\quad ,&{{ 3}})\quad % (c,d) H&({{ -3}}\quad ,&{{ 3}})\\ C&({{ 3}}\quad ,&{{ 1}})\quad % (c,d) G&({{ -2}}\quad ,&{{ 1}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}\\\\[/tex]
[tex]\bf -------------------------------\\\\ AG=\sqrt{(-4-1)^2+(2-2)^2} \\\\\\ BH=\sqrt{(-3-2)^2+(3-3)^2} \\\\\\ CG=\sqrt{(-2-3)^2+(1-1)^2}[/tex]
and doing the distances from ABC to DEF
[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ 1}}\quad ,&{{ 2}})\quad % (c,d) D&({{ 1}}\quad ,&{{ -1}})\\ B&({{ 2}}\quad ,&{{ 3}})\quad % (c,d) E&({{ 2}}\quad ,&{{ 0}})\\ C&({{ 3}}\quad ,&{{ 1}})\quad % (c,d) F&({{ 3}}\quad ,&{{ -2}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}[/tex]
[tex]\bf -------------------------------\\\\ AD=\sqrt{(1-1)^2+(-1-2)^2} \\\\\\ BE=\sqrt{(2-2)^2+(0-3)^2} \\\\\\ CF=\sqrt{(3-3)^2+(-2-1)^2}[/tex]
now... the ABC to JKL... surely you'd know how to do... the same way, just use the distance formula
Jan is twice as old as her sister betty, but half of joe's age. betty just got married. how old is joe most likely to be?
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x = 2y and x = 0.5z
Equating this two yields 2y = 0.5z. There are two variables but only one equation. Therefore, you have to specify one of the variables to be able to solve this problem. It was mentioned that Betty just got married. Let's assume that Betty's age was around 30 years old. Then, it follows that y=30. Substituting this to the final equation,
2(30) = 0.5z
z = 120 years old
This is impossible. Betty must have been married at an early age. Let's assume that Betty is 18 years old, then
2(18) = 0.5z
z = 72 years old
If Betty was 18 years old, then Joe is 72 years old. This is only an illustration to the problem. You must have introduced Betty's age to know the exact answer for Joe's age.
A hypothesis is only tentative: to make sure it's valid, you have to ___________.
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Solve log 1/100 = log(10^x+2)
A.) x= 0
B.) x= -2
C.) x= -4
D.) x= 4
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Write the equation of a circle with center (-2,3) and a radius of 4. Show all work to receive credit.
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(x-a)^2+(y-b)^2=r^2
where:
(a,b) is the center of the circle
given that the center of our circle is (-2,3) with the radius of 4, the equation will be:
(x+2)^2+(y-3)^2=4^2
expanding the above we get:
x^2+4x+4+y^2-6y+9=16
this can be simplified to be:
x^2+4x+y^2-6y=16-13
x^2+y^2+4x-6y=3
Find three positive numbers x, y, and z that satisfy the given conditions. the sum is 180 and the product is maximum.
Answers
Mario and Luigi want to purchase some extra controllers for their friends.each controller costs 29.99. Use an algebraic expression to describe how much they spend in total,before sales tax,based on purchasing the console(299.00)the number of games(59.99 each) and the number of extra controllers
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What is the answer??
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hope this helps!
Which equation illustrates the additive inverse property?Select one of the options below as your answer:A. c + d = d + cB. c × d = d × cC. -c + (-c) = 0D. d + (-d) = 0
Answers
The correct option is A
c + d = d + c
I hope that helps!
so answer is
d + (-d) = 0 (last choice)
Is the number of fish caught during a fishing tournamentnumber of fish caught during a fishing tournament discrete or continuous?
Answers
The number of fish caught in a fishing tournament is a discrete variable, as it can only take specific or separate values which are whole numbers, not fractions or decimals.
Explanation:The number of fish caught during a fishing tournament would be considered a discrete variable in mathematics. This is because discrete variables are variables that can only take specific or separate values.
In this case, you can't catch half a fish or 2.3 fish in a tournament, you can only catch whole fish. This makes the number of fish caught a discrete variable because the count can only be in whole numbers. This is different from a continuous variable, such as the amount of time spent fishing or the weight of the fish caught, which could take on any value within a given range.
Learn more about Discrete Variable here:https://brainly.com/question/28397043
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Bob is driving along a straight and level road toward a mountain. At some point on his trip, he measures the angle of elevation to the top of the mountain and finds it to be 21°44'. Find the height of the mountain to the nearest foot if Bob is 13,428.7 feet from the center of the mountain at the base.
A. 5453 ft
B. 5353 ft
C. 53,534 ft
D. 535,342 ft
Answers
h = 13428.7 * tan 21 44
Height = 5353 feet
Answer:
Option B is the correct answer.
Step-by-step explanation:
The arrangement is given in the below figure.
We have height of the mountain = x
We also have
[tex]tan(21^044')=\frac{x}{13428.7}\\x=5352.98ft[/tex]
Height of the mountain to the nearest foot = 5353 ft
Option B is the correct answer.
solve for y. 8x+y=15
Answers
y = 15 - 8x
8x = 15 + -1y
x = 1.875 + -0.125y
x = 1.875 + -0.125y
0=2x+3(3x-4)-(-x+14)
Fraction answer need help!!!
Answers
Follow BEDMAS
0=2x+9x-12-(-x+14)
0=2x+9x-12+x-14
Add like terms
0=11x-12+x-14
0=12x-12-14
0=12x-26
Flip the eqaution
12x-26=0
Move -26 across the equal sign
12x=0+26
12x=26
x=26/12
x=13/6
Hope this helps! A thanks/brainiest answer would be appreciated :)
A diner asked its customers, 'Did you cook dinner last night?' The results on the survey are shown in the table below: Male Female Cooked dinner 305 279 Did not cook dinner 152 459 What is the probability that one of the customers chosen from this survey was a female and cooked dinner? 0.23 0.38 0.47 0.61
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Answer:
0.23
Step-by-step explanation:
(07.03 LC)
The steps below show the incomplete solution to find the value of p for the equation 4p − 2p + 4 = −1 + 21:
Step 1: 4p − 2p + 4 = −1 + 21
Step 2: 4p − 2p + 4 = 20
Step 3: 2p + 4 = 20
Which of these is most likely the next step?
2p = 5
2p = 8
2p = 16
2p = 24
Answers
First they combined like terms on one side.
Step 2: 4p − 2p + 4 = 20
Then they combined like terms on the other side.
Step 3: 2p + 4 = 20
Now you have to subtract 4 from both sides.
Step 4: 2p = 16
So the answer is C. 2p = 16
2p+4=20
-4=-4
2p = 16
B is the midpoint of AC, D is the midpoint of CE. BD=10, and AE =2x. Find the length of CE if CD =3x
Answers
Since B is midpoint of AC and D is midpoint of CE, therefore, BD is parallel to AE and BD = 0.5 AE
AE = 2 BD = 2 x 10 = 2x
Therefore, x= 10
D is the midpoint of CE and CD = 3x, therefore CE = 6x where x = 10
Based on this, CE = 6 x 10 = 60 units of length
In how many ways can 50 cards be chosen from a standard deck of 52 cards?
Answers
The number of ways you can draw 50 cards from 52 is 52*51*50*49*48*47*...4*3 (it ends in 3).
,
But the number of ways that those 50 cards form the same set repeats is 50! = 50*49*49*47*....3*2*1
So, the answer is (52*51*50*49*48*....*3) / (50*49*48*...*3*2*1) = (52*51) / 2 = 1,326.
Note that you obtain that same result when you use the formula for combinations of 50 cards taken from a set of 52 cards:
C(52,50) = 52! / [(50)! (52-50)!] = (52*51*50!) / [50! * 2!] = (52*51) / (2) = 1,326.
Answer: 1,326
Question 6 jessica drive 380 miles using 14 gallons of gas. at this rate, how many gallons of gas would she need to drive 418 miles
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Factor out the largest possible term.
12x^5-4x^2+16x^3= ?
(Please include steps if you can)
Answers
---------------------------------------------------------------------
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Work Shown:
The GCF of the coefficients 12,-4,16 is 4
The GCF of the variable terms is x^2 since this is the smallest variable term that is found in each of x^5, x^2 and x^3
Overall, the GCF is 4x^2.
Factor each term in terms of the GCF
12x^5 = (12)*(x^5)
12x^5 = (4*3)*(x^3*x^2)
12x^5 = (4x^2)*(3x^3) <--- call this equation (1)
-------------
4x^2 = (4x^2)*(1) <--- call this equation (2)
-------------
16x^3 = (4*4)*(x^2*x)
16x^3 = (4x^2)*(4x) <--- call this equation (3)
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Using those individual factorizations, we can apply the distributive property to factor out the GCF
12x^5 - 4x^2 + 16x^3
(4x^2)*(3x^3) - 4x^2 + 16x^3 ... substitute equation (1)
(4x^2)*(3x^3) - (4x^2)*(1) + 16x^3 ... substitute equation (2)
(4x^2)*(3x^3) - (4x^2)*(1) + (4x^2)*(4x) ... substitute equation (3)
4x^2*(3x^3 - 1 + 4x) ... use the distributive property
Therefore, 12x^5 - 4x^2 + 16x^3 factors to 4x^2*(3x^3 - 1 + 4x)
This means, 12x^5 - 4x^2 + 16x^3 = 4x^2*(3x^3 - 1 + 4x) is a true equation for all real numbers x.
Simplify 15 to the 18th power over 15 to the 3rd power.
Answers
If the exponents you're dividing have the same base, you subtract them.
18 - 3 = 15
15^15
ΔZAP has coordinates Z (−1, 5), A (1, 3), and P (−2, 4). A translation maps point Z to Z' (1, 1). Find the coordinates of A' and P' under this translation.
Answers
To solve this problem, we should first identify the number of units that point Z was translated. The number of units of movement of point Z should be similar to the number of units of movement of points A and P.
Let us say that the movement is Δx and Δy for horizontal and vertical translations respectively.
From Z to Z’:
Δx = 1 – (-1) = 2
Δy = 1 - 5 = - 4
Therefore the translation is in the form of (x + 2 , y – 4). Points A and P then becomes:
A’ = (1 + 2 , 3 – 4)
A’ = (3, -1)
P’ = (-2 + 2, 4 – 4)
P’ = (0, 0)
Answers:
A’ = (3, -1)
P’ = (0, 0)
Answer:
Step-by-step explanation:
lets be honest whos reading this when theres an expert answer
how to factor 6x^2+5x+1