The correct simplification of the expression is 4x¹⁴y¹⁷
Given,
The expression is (2x⁷ y)² (y⁵)³
To distribute the exponent, apply the power rule (ab)ⁿ = aⁿbⁿ
Implement the product rule to (2x⁷y)².
Here, we have a = 2x⁷ , b = y and n = 2
=(2x⁷)² y²(y⁵)³
= 2²(x⁷)² y²(y⁵)³
= 4(x⁷)² y²(y⁵)³
Now exponents should be multiplied while using the product rule.
The product rule is (aˣ)ⁿ = aˣⁿ
We apply this to (x⁷)² and (y⁵)³
So the expression becomes,
=4x⁷·² y² (y⁵·³)
= 4x¹⁴ y² y¹⁵
∵ In exponents we have a rule that if bases are same then powers are added i.e, aˣ aⁿ = aˣ⁺ⁿ
∴ 4x¹⁴ y¹⁵ ⁺ ²
= 4x¹⁴ y¹⁷
Hence we get the answer as 4x¹⁴ y¹⁷
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please help me with my math
Answer:
x = 115
z = 27
Step-by-step explanation:
x + 65 = 180 (same side interior angles)
x = 115
x = 3z +34 (alternate interior angles)
115 = 3z + 34
3z = 81
z = 27
What will be the percentage of profit per annum by which Tk.13000 will be Tk.18850 as profit-principal in 5 years?
The simple interest rate is 9% if the Tk 13000 will be Tk 18850 as profit-principal in 5 years.
What is simple interest?It is defined as the interest on based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount of borrowed amount.
We have given:
The principal amount, P = Tk 13000
Final amount A = Tk 18850
Number of years n = 5 years
Rate = r
I = A - P
I = 18850 - 13000 = Tk 5850
I = Pnr
5850 = 13000(5)(r)
r = 0.09
r = 9%
Thus, the simple interest rate is 9% if the Tk 13000 will be Tk 18850 as profit-principal in 5 years.
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What is the 17th term in the arithmetic sequence an=77+(n-1)(-5)
Answer:
a₁₇ = - 3
Step-by-step explanation:
substitute n = 17 into the nth term rule
a₁₇ = 77 + 16 × - 5 = 77 - 80 = - 3
If you vertically stretch the cubic parent function, f(x) = x3, what is the
equation of the new function?
Which ordered pair would form a proportional relationship with the point graphed below?
On a coordinate plane, a line goes through points (0, 0), (10, 40) and (negative 10, negative 40).
(40, 10)
(–5, –10)
(5, 20)
(–10, –20)
Answer:
(5, 20)
Step-by-step explanation:
The recursive formula for an arithmetic sequence is:
a1 = -10
an = an-1+3
What is the 3rd term in the sequence?
A. -16
B. -30
C. -7
D. -4
Answer:
D. -4
Step-by-step explanation:
a1 is the first term.
a1 = -10
an = an-1 + 3
The recursive formula means that each term after the first term is 3 more than the previous term.
a2 = a1 + 3 = -10 + 3 = -7
a3 = a2 + 3 = -7 + 3 = -4
Our school store buys a shipment of 1000
pencils for $65. If we sell each pencil for
10 cents, what is the markup percentage
of each pencil?
A. 28%
C. 54%
D. 65%
B. 43%
Answer:
54%
Step-by-step explanation:
65 / 1000 = 0.065. 0.10 / 0.065 = 1.538, so the markup would be C, 54%.
Which output in this table is incorrect
Answer:
B
Step-by-step explanation:
This is quite a trial and error question.
Given from the table
$1 cost of item = $0.08 tax on item
$2 cost of item = ($0.08x2) tax on item = $0.16 tax on item
$3 cost of item = ($0.08x3) tax on item = $0.24 tax on item
$8.50 cost of item = ($0.08x8.50) tax on item = $0.68 tax on item
$10 cost of item = ($0.08x10) tax on item = $0.80 tax on item
The only one that is different is the incorrect value therefore $0.64 is the incorrect one.
The radius of the water well is 2r inches. Find the area of the water well.
The area of the water well is [tex]4\pi r^2[/tex]
How to determine the area?The radius is given as:
Radius, R = 2r
The area of the water well is calculated using:
[tex]A = \pi R^2[/tex]
This gives
[tex]A = \pi (2r)^2\\\\\\[/tex]
Evaluate the expression
[tex]A = 4\pi r^2[/tex]
Hence, the area of the water well is [tex]4\pi r^2[/tex]
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a jacket is on sale for 30% of and its £42 after discount whats the original price
Answer:
£60
Step-by-step explanation:
70% of original price = £42
100% of original price = £42 * 10/7 = £6 * 10 = £60
Given parallelograms ABCD, AC=22, and AE=2x-5, find the value of x.
Answer:
D
Step-by-step explanation:
the diagonals of a parallelogram bisect each other , then
2 AE = AC ( substitute values )
2(2x - 5) = 22 ( divide both sides by 2 )
2x - 5 = 11 ( add 5 to both sides )
2x = 16 ( divide both sides by 2 )
x = 8
5
·?
16. Which of the following is equivalent to 49
05-7²
O 5(7²)
O 5(72)
1
5(7²)
O
Step-by-step explanation:
[tex] = 49[/tex]
[tex] = 7 \times 7[/tex]
[tex] = {7}^{1 + 1} [/tex]
[tex] = {7}^{2} [/tex]
Find the least common denominator for these
two rational expressions.
8
-9
3a²
-
a
The common denominator is 3a²
Someone please explain this step by step:
If\begin{align*}
2x-y&=3,\\
x+y &=1,
\end{align*}compute $8x-7y$.
Answer:
13
Step-by-step explanation:
Perhaps the most straightforward way to find the value of the given function is to first solve the equations for x and y. The results can be substituted into your expression to find the value you want.
__
solving the systemWe notice the y-coefficients are opposites, so we can eliminate the y-variable by adding the equations.
(2x -y) +(x +y) = (3) +(1)
3x = 4 . . . . . . simplify
x = 4/3 . . . . . divide by 3
The value of y can be found from the second equation:
4/3 +y = 1 . . . . substitute for x
y = -1/3 . . . . . . subtract 4/3
expression valueThe value of 8x-7y is found by substituting the x- and y-values into this expression:
8(4/3) -7(-1/3) = 32/3 +7/3 = 39/3 = 13
The value of 8x-7y is 13.
_____
Additional comment
You can also work out what combination of the two equations will give 8x -7y. That turns out to be 5 times the first minus 2 times the second:
5(2x -y) -2(x +y) = 5(3) -2(1)
10x -5y -2x -2y = 15 -2
8x -7y = 13
__
The coefficients 5 and -2 are found by solving the system of equations ...
a(2x -y) +b(x +y) ≡ 8x -7y ⇒ {2a +b = 8, -a +b = -7}
Which of the following is a like radical to 3√6x^2
x(3√6x)
6 (3√x²)
4 (3√6x²)
x(3√6)
Answer:
x(3√6)
Step-by-step explanation:
Radicals:
Take out a variable or number for every pair of the variable or number inside the radicals
[tex]\sf 3\sqrt{6x^2}=3*\sqrt{6*x*x}\\\\[/tex]
[tex]\sf = 3x \sqrt{6}[/tex]
The circuit is working, and all three bulbs are lit. If a switch at A is opened,
what will happen to the circuit?
•
A. All three bulbs will stay lit
B. All three bulbs will go out.
C. Bulbs 1 and 2 will go out, but bulb will remain lit.
D. Bulb 1 will go out, but bulbs 2 and 3 2 will remain lit.
Answer:
B.
Step-by-step explanation:
Since all bulbs are connected in series, by opening switch A, you break the series connection, and all bulbs go out.
The time spent dancing (minutes) and the amount of calories burned can be modeled by the equation c = 5.5t. Which table of values matches the equation and includes only viable solutions?
The table that matches the equation is:
Time Calories
-20 -110
-10 -55
-15 - 82.50
-5 -27.50
What is the correct table?The correct table would contain values that are multiples of 5.5t
For example:
Total calories burned at 20 seconds : 5.5 x 20 = 110
Total calories burned at 10 seconds : 5.5 x 10 = 55
Total calories burned at 15 seconds : 5.5 x 15 = 82.50
Total calories burned at 5 seconds : 5.5 x 5 = 27.50
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Answer:
The 2nd one
Step-by-step explanation:
its the right one
The least common denominator of 5/6, 2/3, and 3/5 is:
Answer:
30
Step-by-step explanation:
Select the correct answer.
Edwin graphs the relationship of the gallons of milk he buys in terms of dollars.
What must be the value of x so that lines a and b are parallel lines cut by transversal f? 10 20 22 32.
Answer: Option 3 or C. 22
Step-by-step explanation:
I got the answer correct on Edge 2022 quiz. Trust me the answer is correct I screenshot it using the prt sc key then uploaded it. The proof is in the pic below. :)
Hurrry 100 points both in elimination solving show your work
1) 7x - 9y =-30
-3x - 6y = 3
2) 3x +2y =9
2x +6y=6
Answer:
2
Step-by-step explanation:
6y=18. (3₁-2). 3) -2x +9y=-4. 2x+3y=-20. (-7,-2). 5) 2x + 5y = 0 ... -10x + 5y = 30. (-3,0). 15) 3x-2y = −6 x-2y=-10. (2,6). 17) 3x +9=-3y. 3y=-5x-11.
Answer:
[tex]1. \: x = \frac{9y - 30}{7} \: x = - 1 - 2y \\ \\ 2. \: x = \frac{9 - 2y}{3} \: x = 3 - 3y[/tex]
Step-by-step explanation:
[tex]1. \: 7x = - 30 + 9y \\ 7x = 9y - 30 \\ x = \frac{9y - 30}{7} \\ \\ - 3(x + 2y) = 3 \\ x + 2y = - 1 \\ x = - 1 - 2y \\ \\ 2. \: 3x = 9 - 2y \\ \\ (x + 3y) = 6 \\ x + 3y = \frac{6}{2} \\ x + 3y = 3[/tex]
can someone please help mee(20 points and i will give brainliest!!!)
Answer:
(5,2)
Maximum
5
Step-by-step explanation:
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\texttt{\:Coordinates of vertex = (5,2)}[/tex]
[tex]\texttt{The graph has a maximum} [/tex]
[tex]\tt \: Axis\:\: of \:\; symmetry : x = 5\ [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Coordinate of vertex is the point where there's a unique (only one) value of y for x :
[tex]\qquad \tt \rightarrow \: (5,2)[/tex]
Since it's a downward parabola, it doesn't have defined minima, as it's value reach [ - infinity ]
and hence, it has a maximum, at the vertex.
Axis of symmetry is the line that divides the parabola into two equal regions that are mirror images of each other.
it is the line passing through vertex and parallel to y - axis.
[tex]\qquad \tt \rightarrow \: x = 5[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Carter paid $201.75 for a camera and a memory card. if the 32 gb memory
card costs $12.35, and a discount of 20% is given to the camera, find the
regular price of the camera. estimate it to the nearest whole number.
The regular price of the camera is $227.
Given that, the total amount paid=$201.75 and the cost of the memory card=$12.35.
Cost of camera=201.75-12.35=$189.4
What is a discount?A discount is a deduction from the usual price of something. To discount means to deduct an amount from the price.
Discount is given to the camera=20%.
The regular price of the camera=189.4+20% of 189.4
=189.4+0.2×189.4=189.4+37.88=$227.28
The estimation to the nearest the whole number is $227.
Therefore, the regular price of the camera is $227.
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answer
yes do it your self
The __________ is the process of posing and answering research questions using controlled techniques that include systematic, orderly observation and the collection of data.
Answer:
Scientific Method:
Step-by-step explanation:
Scientific method is the set of basic rules that must be followed for the production of knowledge that has the rigor of science, that is, it is a method used for research and verification of a certain content. For several authors, the scientific method is the logic applied to science.
i hope this
Translate this sentence into an equation. the product of jenny's height and 4 is 52.
Answer:
4J = 52
Step-by-step explanation:
If Jenny's height is J:
4J = 52
HELP, FAST!!!
choose an equation for the graph
Answer:
The equation of the graph is y = -lx - 4l - 1.
Step-by-step explanation:
As the values of y are same before and after (4, -1)
the slope of the graph is change on point (4, -1)
the equation of first line is
y - (-1) = 1 (x -4)
the equation of the second line is:
y - (-1) = -1 (x - 4)
As value of y should remain same in both equations
therefore: y - (-1) = - lx - 4l
y = - lx - 4l -1
The equation of the graph is y = -lx - 4l - 1.
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please give me answer friend
Answer:
90°
Step-by-step explanation:
right angle - 90°
.....
Answer:
65
Step-by-step explanation:
Please help with a good explanation
(15-10)-(14+12+ (8+5)
Answer:
-34
Step-by-step explanation:
Remove all brackets by multiplying the existing math signs then take it from there
(15-10)-(14+12+ (8+5)
5 - (14 + 12 + (8 + 5)
5 - (14 + 12 + 13)
5 - 39
-34
Ted is trying to change 0.43 to a fraction. Evaluate teds method so far
Step-by-step explanation:
[tex] = 0,43[/tex]
[tex] = \frac{0,43}{1} [/tex]
[tex] = \frac{0,43}{1} \times \frac{100}{100} [/tex]
[tex] = \frac{43}{100} [/tex]
