Answers
Answer:
The equivalent expression for this equation is x²¹ × y⁻²¹
Step-by-step explanation:
When you are multiplying exponents that are in parentheses, you multiply the exponential numbers together. So, for this problem, we will multiply the exponents together so we can get our final equivalent expression.
(x⁻³ × y³)⁻⁷
So, we will multiply -3 by -7 and we will also multiply 3 by -7 because those are our exponential numbers.
x²¹ × y⁻²¹
So, this is the final expression that is equivalent to our equation.
The expression (x⁻³.y³)⁻⁷ is equivalent to x ²¹ . y ⁻²¹.
What is algebra?Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.
The given expression is,
(x⁻³.y³)⁻⁷
To find the solution for the expression,
Simplify the power terms,
x⁽⁻³ˣ⁻⁷⁾ . y ³ˣ⁻⁷
x ²¹ . y ⁻²¹
The simplified form of the expression (x⁻³.y³)⁻⁷ is x ²¹ . y ⁻²¹.
Hence, option (A) is correct.
To know more about Algebra on:
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Related Questions
PLEASE HELP!! what is the equation of a line that is perpendicular to y = 2x + 4 and passes through the point (4, 6)?
Answers
Answer:
The answer is B)
[tex]y = - \frac{1}{2}x + 8[/tex]
Answer:
B. y = -[tex]\frac{1}{2}[/tex]x + 8
Step-by-step explanation:
The line is perpendicular to line whose equation is:
y = 2x + 4 and;
passes through point (4,6) .
The product slopes of two perpendicular lines is -1.
The slope of the line whose equation is y = 2x + 4 is; 2
Let the slope of the perpendicular line (l2) be [tex]m_{l2}[/tex]
[tex]m_{l2} * 2 = -1[/tex]
[tex]m_{l2}[/tex] = [tex]-\frac{1}{2}[/tex]
Taking another point xy on line l2;
[tex]\frac{y - 6}{x - 4} = -\frac{1}{2}[/tex]
Cross multiplying this gives;
y = -[tex]\frac{1}{2}[/tex]x + 8 which is the equation of the perpendicular line!
andy is making floor plans for a tree house using a scale 1in to 2ft he wants to make the floor of the tree house have a length of 8ft. how many inches should he show for this distance on his floor plan
Answers
Answer:
Andy should represent the 8 feet long floor on the floor plan with a dimension of 4 inches
Step-by-step explanation:
The scale of the tree house plan is given as 1 in. to 2 ft,
Therefore we have a scale of 1/2 in. of the floor plane is equivalent to 1 ft. in actual dimensions
Given that Andy wants the floor to make the tree house floor to have a length of 8 ft., let the dimension of the floor plan of the house floor be x, we have;
[tex]\dfrac{\frac{1}{2} \ inches \ plan }{1 \ feet \ actual} =\dfrac{x \ inches \ plan}{8 \ feet \ actual}[/tex]
[tex]x \ inches \ plan =\dfrac{\frac{1}{2} \ inches \ plan }{1 \ feet \ actual} \times 8 \ feet \ actual = 4 \ inches[/tex]
Therefore, Andy should represent the 8 feet long floor on the floor plan with a dimension of 4 inches.
James conducted an experiment with 4 possible outcomes. He determined that the experimental probability of event A happening is 10 out of 50. The theoretical probability of event A happening is 1 out of 4. Which action is most likely to cause the experimental probability and theoretical probabilities for each event in the experiment to become closer? removing the last 10 trials from the experimental data completing the experiment many more times and combining the results to the trials already done including a fifth possible outcome performing the experiment again, stopping immediately after each event occurs once
Answers
Answer:
Completing the experiment a few more times and combining the results to the trails already done.
Answer:
Completing the experiment a few more times and combining the results to the trails already done.
Step-by-step explanation:
Every year the Lee family has a big family dinner, and everyone brings a mug to exchange. The mugs are put on wooden hangers on the wall, and each wooden hanger can hold 12 mugs. Last year the family had 15 mugs to hang up. This year the Lee family filled three wooden hangers. How many more mugs were brought to the Lee family dinner this year compared to the previous year? *
Answers
Answer:
21 more mugs were brought this year than last year.
Step-by-step explanation:
We can solve by subtracting the initial amount of mugs from the final amount of mugs.
To find the amount of mugs hung up this year, we will use the equation: m = 12w where m = the number of mugs & w = the number of wooden hangers. The 12 represents the amount of mugs per wooden hanger.
We can plug in 3 for w since 3 wooden hangers were filled up and we would get 12(3) = m = 36 mugs
Now we subtract last year's total mugs hung up from this year's total mugs hung up.
We end up with 36 - 15 = 21
daniel thinks of a number and subtracts 2
from it. He divides 32 by the result. If
his answer is 4, what number does he
think of
Answers
Answer:
the number is 126
Step-by-step explanation:
1) multiply each side by 32: (n-2) / 32 = 4
2) subtract 2 from each side: n-2 = 128
3) n = 126
Answer:
130
Step-by-step explanation:
So basically this number, minus 2, divided by 32 is 4, so lets write the unknown number as x.
So, (x-2)/32 = 4.
First multiply both sides by 32 to get rid of the denominator.
(32)(x-2)/32 = 4(32) x-2 = 128
Now the -2 remains to figure out x, so you add 2 to both sides to get rid of the -2.
So, x-2+2 = 128+2, -2 +2 is 0, and 128 +2 is 130, so you have x = 130.
the first four terms of the sequence an=2n+3are
answer
5,8,11,14
3,5,7,9
1,3,5,7
5,7,9,11
Answers
Step-by-step explanation:
Hey, there!!!
Your required answer is optionD.
checking,
The 1st sequences are,
5,8,11,14
here,
now, use formula,
(an = 2n+3) in the sequences,
a1 = 2×1+3=5 = matching
a2= 2×2+3=7 = not matched
a3= 2×3+3= 9 = not matched
a4= 2×4+3=11 = not matched.
For 2nd sequences
3,5,7,9
Use the formula of an term,
a1 = 2×1+3=5 = not matched
a2 =2×2+3=7not matched
a3 = 2×3+3=9= not matched.
For 3rd sequences,
1,3,5,7
a1=2×1+3=5= not matched
a2=2×2+3=7= not matched
a3=2×3+3=9= not matched
a4=2×4+3=11= not matched
Now, for 4th sequences,
5,79,11
a1=2×1+3=5= matching
a2=2×2+3=7= matching
a3= 2×3+3=9= matching
a4=2×4+4=11= matching
Therefore, the answer is option D.
Hope it helps..
Is this a function or no?
Answers
Function
It is a function
Twice the difference between a number and 4 is twenty. Find the number.
А. 8
B. 9
C. 12
D. 14
Please help!!!
Answers
Answer:
D 14
Step-by-step explanation:
Let x be the number
2(x-4) = 20
Divide each side by 2
2/2(x-4) = 20/2
x-4 = 10
Add 4 to each side
x-4+4 = 10+4
x = 14
Answer:
The number is 14
Step-by-step explanation:
Let's call this unknown number of x:
2×(x – 4) = 20
2x – 8 = 20
2x = 20 + 8
2x = 28
x = 28/2
x = 14
Find the domain for the rational function f of x equals quantity x plus 1 end quantity divided by quantity x minus 2 end quantity.
(−[infinity], 2) (2, [infinity])
(−[infinity], −2) (−2, [infinity])
(−[infinity], 1) (1, [infinity])
(−[infinity], −1) (−1, [infinity])
Answers
Answer:
[tex](- \infty, 2), (2, \infty)[/tex]
Step-by-step explanation:
Given the function:
[tex]f(x) = \dfrac{x+1}{x-2}[/tex]
To find:
Domain of the function.
Solution:
First of all, let us learn about definition of domain of a function.
Domain of a function is the valid input values that can be provided to the function for which output is defined.
OR
Domain of a function [tex]f(x)[/tex] are the values of [tex]x[/tex] for which the output [tex]f(x)[/tex] is a valid value.
i.e. The function does not tend to [tex]\infty[/tex] or does not have [tex]\frac{0}0[/tex] form.
So, we will check for the values of [tex]x[/tex] for which [tex]f(x)[/tex] is not defined.
For value to tend to [tex]\infty[/tex], denominator will be 0.
[tex]x-2\neq 0 \\\Rightarrow x \neq 2[/tex]
So, the domain can not have x = 2
Any other value of x does not have any undefined value for the function [tex]f(x)[/tex].
Hence, the answer is:
[tex]\bold{(- \infty, 2), (2, \infty)}[/tex] [2 is not included in the domain].
Nathan, a tutor, buys 5 calculators for $7.50 each at a store, planning to provide one to each of his clients. However, the next day, he discovers that the same calculators has gone on sale for $5.00 and also discovers that he will only have three tutoring clients instead of five. He returns the five calculators and purchases three calculators at the new sale price. He uses the following expression to determine the amount he should receive back from the store. (5 x $7.50) - (3 x $5.00) Which of the following expressions could Nathan have used. 5 ($7.50 - $5.00). $7.50 - $5.00. (5 x $7.50) - $5.00. (5 x $7.50) - $5.00. 3 ($7.50 - $5.00) +2 x $7.50
Answers
Answer: 5 (7.50-3 )
Step-by-step explanation:
Given: Previous price of calculator = $7.50
Number of client =5
Total price = (Number of calculators) x (Price for each calculator)
Total price of 5 calculators = (5 x $7.50)
New price of calculator = $5.00
Number of client =3
Total price of 3 calculators = (3 x $5)
Price will receive = (Total price of 5 calculators) -(Total price of 3 calculators )
= (5 x $7.50) - (3 x $5)
= 5 (7.50-3 )
Required expression: 5 (7.50-3 )
Find the x-intercept(s) of the equation: y =3x^2-3x-6
a. x-intercepts: (-1,0) and (2,0)
b. x-intercepts:(0,-3) and (0,2)
c. x-intercept: (-6,0)
d. x-intercept: (0,-6)
Answers
Answer:
(2,0) ( -1,0)
Step-by-step explanation:
y =3x^2-3x-6
Let y = 0 and solve for x to find the x intercepts
0 =3x^2-3x-6
Factor out a 3
0 =3(x^2-x-2)
Factor inside the parentheses
0 = 3( x-2) (x+1)
Using the zero product property
x-2 =0 x+1 = 0
x=2 x = -1
(2,0) ( -1,0)
Answer:
[tex]\large \boxed{\mathrm{a. \ x-intercepts: (-1,0) \ and \ (2,0)}}[/tex]
Step-by-step explanation:
The x-intercept(s) is when y = 0.
3x² - 3x - 6 = 0
Factor left side of the equation.
3(x + 1)(x - 2) = 0
Set factors equal to 0.
x + 1 = 0
x = -1
x - 2 = 0
x = 2
The x-intercepts are (-1, 0) and (2, 0).
What are the solutions to 3( x + 2)(x – 9) = 0
Answers
Mark Brainliest if correct:
x = -2, 9
Step-by-step explanation:
x2: x + 2 = 0
x = -2
x1: x - 9 = 0
x = 9
x = -2, 9
An office supply store recently sold a black printer ink cartridge for $14.99 and a color printer ink cartridge for $20.99. At start of a recent fall semester, a total of 42 of these cartidges was sold for a total of $695.58. How many of each type were purchased?
Answers
Answer:
B = 31, C = 11
Step-by-step explanation:
Let B be the number of Black printer ink cartridges and C be the number of color printer ink cartridges.
42 were sold in total, hence,
B+C= 42 ------------(1)
Also, its given that
14.99 B+20.99C= 695.58 ------(2)
Multiplying (1) by 20.99,
14.99 B+14.99 C= 629.58 ------(3)
Now, subtracting (3) from (2),
14.99 B+20.99C= 695.58
14.99 B+14.99 C= 629.58
------------------------------------
6 C = 66
C= 66/6
C = 11
We know, B+ C= 49
Hence B = 42- 11 = 31
B = 31
Hence, number of Black printer ink cartridges = 31 and color printer ink cartridges = 11 .
Hong buys candy that costs $5 per pound. He will buy at least 7 lbs of candy. What are the possible amounts he will spend on candy? Use c for the amount (in dollars) Hong will spend on candy. Write your answer as an inequality solved for c.
Answers
Step-by-step explanation:
if he buys 7 pounds, it will cost 7×5 = $35
he might buy more than that (and it will then also cost more than that) , but not less than that.
so,
c >= $35
what is the volume of a cube with and edge length of 4 cm
Answers
Answer:
V = 64 cm^3
Step-by-step explanation:
Volume of a cube is given by
V = s^3 where s is the side length
V = 4^3
V = 64 cm^3
Answer:
64
Step-by-step explanation:
i guess so as the volume is 4×4×4
sinx =căn 2/3
sinx=5/4
sinx =1
sin3x=can3/2
sin(x-60)=-1/2
sin3x=1/2
Answers
Answer:
Correct option is
B
0
D
−1
sinx+sin2x+sin3x
=sin(2x−x)+sin2x+sin(2x+x)
=2sin2xcosx+sin2x [ by using sin(A+B)=sinAcosB+sinBcosA and sin(A−B)=sinAcosB−sinBcosA ]
=sin2x(2cosx+1)........(i)
cosx+cos2x+cos3x
=cos(2x−x)+cos2x+cos(2x+x)
=2cos2xcosx+cos2x [By using cos(a−b)=cosa⋅cosb+sina⋅sinb and cos(a+b)=cosa⋅cosb−sina⋅sinb]
=cos2x(2cosx+1).....(ii)
∴(sinx+sin2x+sin3x)
2
+(cosx+cos2x+cos3x)
2
=1
sin
2
2x(2cosx+1)
2
+cos
2
2x(2cosx+1)
2
=1.......[From(i)(ii)]
⇒(2cosx+1)
2
=1
⇒2cosx+1=±1
∴cosx=0or−1
Solve for a.
-4a – 2a – 7 = 11
a =
[?]
Answers
a = [-3]
Step-by-step explanation:
-4a - 2a - 7 = 11
Combine like terms
-4a - 2a = -6a
-6a - 7 = 11
Add 7 to both sides
-6a = 18
Solve for a
a = 18/-6
••••••••••••••••••••••••••••••
doomdabomb:
All brainliest and thanks
are appreciated and
would mean a lot to me,
thanks!
a = -3
••••••
Answer:
or, -4a - 2a -7 = 11
or, -4a -2a =11 +7
or, - 6a = 18
or, a= 18÷ -6
a= -3
Find the length of the third side. If necessary, round to the nearest tenth.
20
28
Answer:
Submit Answer
attempt 1 out of 2
PLS HELP ASAP
Answers
Answer:
b = 19.6
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
20^2+ b^2 = 28^2
400 + b^2 = 784
b^2 = 784-400
b^2 =384
Taking the square root of each side
sqrt( b^2) = sqrt(384)
b =19.59591794
To the nearest tenth
b = 19.6
Answer:
19.6
Step-by-step explanation:
It is a right triangle so use the pythagorean theorem; a^2 + b^2 = c^2
a=20
b=?
c=28 - c is the hypotenuse because it is across from the right angle
20^2 + b^2 = 28^2
400+ b^2 =784
b^2=384
b= 19.595917... or 19.6 (rounded to nearest tenth)
Calculate the volume and surface area of a cone with the base of 20cm, the vertical hieght of 34cm and 35.6cm leaning height.
Answers
Answer:
Step-by-step explanation:
Volume = 1/3πr²h
Surface Area = πr(r+√(h²+r²))
V = 1/3π(10)²(34) = 3560 .5 cm³
SA = π(10)(10 + √(34²+10²)) = 1427.5 cm²
7th Grade Math Answer ASAP Please <3
Answers
Answer:
Hey there!
Andrew made a mistake in the last step. -11.8+9.8=2, not -21.6.
Let me know if this helps :)
if line y bisects line AC, AB = 4 - 5x, and BC = 2x+25, find AC
Answers
Answer:
4-5x = 2x+25
-5x+4 = 2x+25
-7x = 21
x = -3
4 - 5(-3)
4 + 15
19
AC = 2 x 19
AC = 38
Let me know if this helps!
Find the perimeter of this figure. (Image down below)
Answers
Answer:
The answer is
44 ftStep-by-step explanation:
The figure above is a rectangle
To find the perimeter of a rectangle we use the formula
Perimeter of a rectangle = 2l + 2w
where
l is the length of the rectangle
w is the width of the rectangle
From the question
length = 14 ft
width = 8ft
Substituting the values into the above formula we have
Perimeter = 2(14) + 2(8)
= 28 + 16
We have the final answer as
Perimeter = 44 ftHope this helps you
A car is averaging 50 miles per hour. If the car maintains this speed, how many minutes less would a 450-mile trip take than a 475-mile trip?
Answers
Answer:
1/2 a minute (30 seconds)
Step-by-step explanation:
475/50=9.5
450/50=9
9-9.5=.5
17. ralph is 3 times as old as sarah. in 4 years ralph will only be twice as old as sara will be then. find ralph’s age now.
Answers
Answer:
Sara is now 4, will be 8 in 4 years. Ralph is now 12, will be 16 in 4 years.
Please help answer!!!!
Answers
Answer:
? = 4
Step-by-step explanation:
You are in the third quadrant. You want the answer to come out to the equivalent of 225o or pi + pi/ 4 = 5/4 * pi
x - pi/2 = 5/4 pi
x = 5/4 pi + pi/2
x = 5/4 pi + 2*pi / 4
x = 7/4 pi
? = 4
Help please, thanks :)
Answers
Answer:
х=6
Step-by-step explanation:
[tex]7 + 5(x -3 ) = 22 \\ 7 + 5x - 15 = 22 \\ 5x = 22 - 7 + 15 \\ 5x = 30 \\ x = 6[/tex]
Answer:
C
x=6
Step-by-step explanation:
What is the range of the given function?
{(-2, 0), (-4, -3), (2, -9), (0,5), (-5, 7)}
O {x | x = -5, 4, -2, 0, 2}
{yly = -9, -3, 0, 5, 7}
{x | x = -9, -5, 4, -3, -2,0, 2, 5, 7}
{yl y = -9, -5, 4, -3, -2, 0, 2, 5, 7}
Answers
9514 1404 393
Answer:
(b) {yly = -9, -3, 0, 5, 7}
Step-by-step explanation:
The range is the set of y-values in the ordered pairs. It is usually convenient to list a set in alphanumeric order.
The second values of the ordered pairs are 0, -3, -9, 5, 7. So, the range is ...
y ∈ {-9, -3, 0, 5, 7} . . . . . matches the second choice
1/4(8x-4)=
need help please answer
Answers
Answer:
2x-1 is the answer (or if you're trying to multiply it, the answer is -8.)
Step-by-step explanation:
1. Dada a função exponencial abaixo, se x=1, qual valor de imagem? * a) 1 b) -2 c) 0 d) -1
Answers
Complete question:
Dada a função exponencial abaixo, se x=1, qual valor de imagem? * a) 1 b) -2 c) 0 d) -1
The function in the image is f(x) = 3^x-1
Answer:
A) 1
Step-by-step explanation:
To solve the exponential function above given that x = 1;
Substitute x = 1 into the exponential function
If x = 1
f(x) = 3^(x - 1)
f(1) = 3^(1 - 1)
f(1) = 3^0
f(1) = 1
For the polynomial, (((x^3)+3x+2)/5)+((5x^2)/2)-(x^6)
a. Determine the coefficient of x^3.
b. Determine the coefficient of x^6.
c. Determine the constant of the term
polynomial.
d. Determine the degree of the polynomial.
Answers
Answer:
Hello,
Step-by-step explanation:
[tex](((x^3)+3x+2)/5)+((5x^2)/2)-(x^6)\\\\=\dfrac{x^3}{5} +\dfrac{3*x}{5} +\dfrac{2}{5} +\dfrac{5*x^2}{2} -x^6\\\\\\=-x^6+0x^5+0x^4+\dfrac{x^3}{5} +\dfrac{5*x^2}{2} +\dfrac{3*x}{5}+\dfrac{2}{5} \\\\\\a)\ \dfrac{3}{5} \\\\b)\ -1\\\\c)\\degree=6\\[/tex]