Which expression is equivalent to (startfraction 4 m n over m superscript negative 2 baseline n superscript 6 baseline endfraction) superscript negative 2? assume m not-equals 0, n not-equals 0.

Answers

Answer 1

The equivalent expression to [tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex] is given by [tex]=\mathbf{\frac{n^{10}}{16m^6}}[/tex].

From the principle of indices we get,

Addition of exponent, [tex]a^{m+n}=a^m.a^n[/tex]

Subtraction, [tex]a^{m-n}=\frac{a^m}{a^n}[/tex]

Multiplication, [tex]a^{mn}=(a^m)^n[/tex]

negative exponent, [tex]a^{-m}=\frac{1}{a^m}[/tex]

Here in the problem given expression is [tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex]

Calculating we get,

[tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex]

[tex]=\left(4m^{1-(-2)}n^{1-6}\right)^{-2}[/tex], using addition and subtraction of indices formulae

[tex]=\left(4m^3n^{-5}\right)^{-2}[/tex]

[tex]=16^{-1}m^{-6}n^{10}[/tex], using multiplication of indices

[tex]=\frac{n^{10}}{16m^6}[/tex], using negative exponent formula

Hence the equivalent required expression is [tex]=\frac{n^{10}}{16m^6}[/tex].

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Answer 2

Answer:

b

Step-by-step explanation:

edge 23


Related Questions

The directrix and vertex of a parabola are shown on the graph. What is the vertex form of the equation for the associated parabola?

Answers

Considering the directrix and vertex given in the graph, the equation of the parabola is:

B. [tex]x = -\frac{1}{4}(y + 2)^2 - 2[/tex]

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

(y - k)² = 4p(x - h).

In which the directrix is the line x = h - p.

Looking at the graph, we have that:

The vertex is (-2,-2), hence h = k = -2.The directrix is x = -1, hence -1 = -2 - p -> p = -1.

Thus the equation is:

(y + 2)² = -4(x + 2).

Writing x as a function of y:

B. [tex]x = -\frac{1}{4}(y + 2)^2 - 2[/tex]

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One of the five quadratics below has a repeated root. (The other four have distinct roots.) What is the repeated root?


$\begin{align*}

&-x^2 + 18x + 81 \\

&3x^2 - 6x + 9 \\

&8x^2 - 32x + 32 \\

&25x^2 - 30x - 9 \\

&x^2 - 14x + 196

\end{align*}$

Answers

Answer:

Step-by-step explanation:

The quadratic expression having repeated root is 8x² - 32x + 32.

What are Quadratic Expressions?

Quadratic expressions are polynomial expressions of second degree.

The general form of a quadratic expression is ax² + b x + c.

We have to find the root of each quadratic expression.

-x² + 18x + 81 = 0

x² - 18x - 81 = 0

Discriminant = [tex]\sqrt{(-18)^2-(4*-81)}[/tex] = [tex]\sqrt{648}[/tex]

x = (18 + √648) / 2 or x = (18 - √648) / 2

Distinct roots

3x² - 6x + 9

x² - 2x + 3

Discriminant = [tex]\sqrt{(-2)^{2}-(4*3) }[/tex] = [tex]\sqrt{-8}[/tex]

x = (2 + [tex]\sqrt{-8}[/tex]) / 2 or x =  (2 - [tex]\sqrt{-8}[/tex]) / 2

Distinct roots

8x² - 32x + 32

x² - 4x + 4

Discriminant = [tex]\sqrt{(-4)^{2}-(4*4) }[/tex] = 0

x = (4 + 0)/ 2 or x = (4 - 0) / 2

x = 2 or x = 2

Repeated roots

Hence the quadratic expression having repeated roots is 8x² - 32x + 32.

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Can you answer the question

Answers

well if its asking for an exponent then its (-5)⁴

The correct answer would be (-5)^4.

Explanation : (-5) to the power of 4, or, 625.

Toby has $31 to buy t-shirts for his bowling team. each t-shirt costs $5. how many t-shirts can he buy?

Answers

Answer:

6 because 30 divided by 5 is 6 so he would have 1$ change

Answer:

Toby can buy 6 T-shirts with 1 extra dollar leftover

Step-by-step explanation:

Hook me up with a 5 star and a thanks :)

If m < 0 and b > 0, the graph of y = mx + b does not pass through which quadrant?
Quadrant I
Quadrant II
Quadrant III
Quadrant IV

Answers

Answer: Quadrant III

Step-by-step explanation:

The slope is negative and the y-intercept is positive.

This means that it is impossible for both x and y to be negative, and thus it does not pass through Quadrant III

Please help me with this question!

Answers

The diameter of the sphere is 14 cm.

What is a sphere ?

Sphere is a three dimensional object , it has no edges or vertices and is round in shape.

The surface area of the sphere is given by 4πr²

As radius = diameter /2

Surface area =  4π r²

196 π = 4π *(d/2)²

196/4 = d²/4

49 *4 = d²

d = 14 cm

Therefore the diameter of the sphere is 14 cm.

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4 2/3 ÷ 2 1/3 ? what is the quotient?​

Answers

Answer: 42/21 or 2

Step-by-step explanation:

you first convert them to improper fractions, which is 14/3 and 7/3. Then, you multiply the reciprocal and get 14/3x3/7, and get 42/21. Simplify, and you get 2.

Graph the result of the following transformation on f(x)​

Answers

The graph would be the normal parent function of f(x) but all points would be 6 units up.

There's an upward vertical shift of 6. To graph this, you need to graph the function f(x) and then add 6 units to all the y values.

0.33632287 to 3sf please

Answers

Answer:

.

Step-by-step explanation:

The answer is 0.336

Bao says: "i can prove this using the fact that opposite sides in a parallelogram are congruent, and by establishing the congruence of a single pair of triangles." which pair of triangles is bao referring to, and which criterion should he use for establishing congruence?

Answers

The pair of triangle formed are congruent using the side-side-side congruency theorem.

What are congruent triangles?

Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent.

Since the opposite sides of a parallelogram are congruent, if the parallelogram is cut through the diagonal, the pair of triangle formed are congruent using the side-side-side congruency theorem.

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find the area of quadrilateral​

Answers

Using the formula u should get 302.3

Answer:

here is answer try this type

What is the measure of \angle x∠xangle, x?
Angles are not necessarily drawn to scale.

Answers

Answer:

Step-by-step explanation:

Comment

x and 133 sit on the the same straight line with MO in common. Therefore they are supplementary which means that the add to 180o.

Equation

x + 133 = 180

Solution

Subtract 133 from both sides

x + 133 = 180                    

x + 133 - 133 = 180 - 133

x = 47 degrees.

Answer

x = 47

Brandon is a running back for his local high school football team. In the last game, he carried the ball 8 times. In the first 5 carries, he gained 6 yards, 12 yards, and 4 yards before losing 2 yards and then losing additional yards. His last 7 carries combined for yards. What was his total net yardage for the game?

Answers

Using it's concept, it is found that Brandon's net yardage for the game was of 26.

How to find the net yardage?

The total net yardage is the sum of all the yardage they gain, that is, the positive gains are added with a plus signal, while the negative gains are added with a negative signal.

Hence, his net yardage, considering that he gained 20 yards on his last 7 carries, is given by:

6 + 20 = 26.

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Help anyone? Simple problem ​

Answers

Answer:x>7

Step-by-step explanation:

Its saying a nuber greater than 7 and 3 plus 8 would be 11

Simplify each expression
3+8b+4+7b-3

Answers

Answer:

9. 15b + 4

10. 4y + 6

11. 15r+72

12. 130n + 20

Step-by-step explanation:

9. Combine Like terms

10. Combine Like terms

11. Distribute the 8 into (r + 9) then combine like terms

12. Distribute 10 into (3n + 2 + 10n) then combine like terms

Answer:

[tex]\mathsf {9) 15b + 4}\\\mathsf {10) 4y + 6}\\\mathsf {11) 15r + 72}\\\mathsf {12) 130n + 20}[/tex]

Step-by-step explanation:

[tex]\textsf {Question 9}[/tex]

[tex]\mathsf {3 + 8b + 4 + 7b - 3}[/tex]

[tex]\mathsf {8b + 7b + 4 + 3 - 3}[/tex]

[tex]\mathsf {15b + 4}[/tex]

[tex]\textsf {Question 10}[/tex]

[tex]\mathsf {8 + 7y - 3y + 2 - 4}[/tex]

[tex]\mathsf {7y - 3y + 8 + 2 - 4}[/tex]

[tex]\mathsf {4y + 6}[/tex]

[tex]\textsf {Question 11}[/tex]

[tex]\mathsf {8(r + 9) + 7r}[/tex]

[tex]\mathsf {8r + 8(9) + 7r}[/tex]

[tex]\mathsf {8r + 7r + 72}[/tex]

[tex]\mathsf {15r + 72}[/tex]

[tex]\textsf {Question 12}[/tex]

[tex]\mathsf {10(3n + 2 + 10n)}[/tex]

[tex]\mathsf {10(13n + 2)}[/tex]

[tex]\mathsf {10(13n) + 10(2)}[/tex]

[tex]\mathsf {130n + 20}[/tex]

What is the missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x? 1. The distributive property: 4x – 12 + 4 < 10 + 6x 2. Combine like terms: 4x – 8 < 10 + 6x 3. The addition property of inequality: 4x < 18 + 6x 4. The subtraction property of inequality: –2x < 18 5. The division property of inequality: ________ x < –9 x > –9 x < x is less than or equal to negative StartFraction 1 Over 9 EndFraction. x > –x is greater than or equal to negative StartFraction 1 Over 9 EndFraction.

Answers

The inequality 4(x – 3) + 4 < 10 + 6x is solved as x > -9. Then the variable x is greater than the negative 9. Then the correct option is B.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign.

The inequality equation is given below.

4(x – 3) + 4 < 10 + 6x

Then the steps of solving are given below.

1. The distributive property: 4x – 12 + 4 < 10 + 6x

2. Combine like terms: 4x – 8 < 10 + 6x

3. The addition property of inequality: 4x < 18 + 6x

4. The subtraction property of inequality: –2x < 18

5. The division property of inequality: x > –9

Then x is greater than the negative 9.

Then the correct option is B.

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If the diagonal of the rectangle is 10.5 inches and the length of the rectangle is 7.25, what is the width of the rectangle?

Answers

Answer:

w≈7.6in

Step-by-step explanation:

L= 7.25

D= 10.5

Using the formula    [tex]d=\sqrt{w^{2} + l^{2} } \\[/tex]Solving for w          [tex]w=\sqrt{d^{2} -l^{2} }[/tex]                                    [tex]\sqrt{10.52^{2}-7.25^{2} } = 7.59523in[/tex]

Answer:-

The width of this rectangle is = 7.59

Given:-

In this question, it is given that -

The diagonal of this rectangle is = 10.5

the length of this rectangle is = 7.25

To find:-

We have to find the width of this rectangle.

Solution:-

We can easily solve this problem using the Pythagorean theorem.

In this problem, it is given that the length of this rectangle is = 7.25 and the diagonal is =10.5

so by the Pythagorean theorem, we can get-

(length)² + (width)² = (diagonal)²

or, (7.25)² + (width)² = (10.5)²

or, (width)² = (10.5)² - (7.25)²

= 17.75 × 3.25

= 57.6875

or, width = 7.59

So, the width of the rectangle is 7.59.

A rectangle has perimeter 16 m. Express the area A (in m2) of the rectangle as a function of the length, L, of one of its sides.

Answers

The area A of the rectangle as a function of the length, L of one of its sides is A = 8L - L²

What is the perimeter of a rectangle?

The perimeter of a rectangle is P = 2(L + W) where

L = length of the rectangle and W = width of the rectangle

Given that P = 16 m,

P = 2(L + W)

16 = 2(L + W)

16/2 = L + W

L + W = 8

So, W = 8 - L

What is the area of the rectangle?

The area of the rectangle, A = LW where

L = length of the rectangle and W = width of the rectangle

Since W = 8 - L, substituting W into the equation for A, we have

A = LW

A = L(8 - L)

A = 8L - L²

So, the area A of the rectangle as a function of the length, L of one of its sides is A = 8L - L²

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All else being equal, if you cut the sample size in half, how does this affect the margin of error when using the sample to make a statistical inference about the mean of the normally distributed population from which it was drawn? m e = startfraction z times s over startroot n endroot endfraction.

Answers

Simple the fraction into the population of the x and times it by Z

Find the interest rate for a principal of $8635 and charged $33549 in interest for 11 years.
Round your answer to 1 decimal place.

Answers

Answer:

rate = 0.4 %

Step-by-step explanation:

Interest = principal x rate x time

33549 = 8635 x r x 11

33549 = 94985r

r = 33549/94985

r = 0.3532

r = 0.4

rate = 0.4 %

Could someone do this question for me? Thanks

Answers

Answer:

20 counters/box

Step-by-step explanation:

Missing counters(m)= 8

Total number of counters available (t-m)= 132

Required number of counters(t):

=(t-m) + m

= 132 + 8 = 140

Total number of boxes(tB) = 7( 6 full and one with eight missing)

Total Counters/Boxes= t/tB

= 140/7

= 20

What is the value of y? 17.5ft 12.5ft 11.6ft 16.5ft

Answers

Answer:

y = 16.5 ft

Step-by-step explanation:

• in the right triangle BCD :

cos(∠BCD) = 8/14

________

• In the right triangle ABC :

cos(∠BCA) = 14/(8+y)

________

Since ∠BCD and ∠BCA are the same one

then

cos(∠BCD) = cos(∠BCA)

Therefore

[tex]\frac{8}{14} =\frac{14}{y+8}[/tex]

[tex]\Longleftrightarrow 8(y+8)=14^2[/tex]

[tex]\Longleftrightarrow 8y+64=196[/tex]

[tex]\Longleftrightarrow 8y=196-64[/tex]

[tex]\Longleftrightarrow 8y=132[/tex]

[tex]\Longleftrightarrow y=\frac{132}{8}[/tex]

[tex]\Longleftrightarrow y=16.5[/tex]

Name the property of equality or congruence that justifies going from the first statement to the second statement.

3x+x+7=23

4x+7=23

Answers

Answer:

Reflexive Property



What are the solutions to the quadratic equation below in factored form?
(10x + 5)(11x - 44) = 0
= ½, x = 4
0x=
0 x = 2, x = -4
0x = 2, x = 4
○ x = − ½, x = 4

Answers

Answer:

D.) x = − ½, x = 4

Explanation:

[tex]\rightarrow \sf (10x + 5)(11x - 44) = 0[/tex]

set the factors to zero

[tex]\rightarrow \sf 10x + 5 = 0, \ 11x - 44 = 0[/tex]

exchange the sides

[tex]\rightarrow \sf 10x = -5, \ 11x = 44[/tex]

exchange the sides

[tex]\rightarrow \sf x = -\dfrac{5}{10} , \ x = \dfrac{44}{11}[/tex]

simplify the following

[tex]\rightarrow \sf x = -\dfrac{1}{2} , \ x =4[/tex]

(10x+5)(11x-44)=010x(11x-44)+5(11x-44)=0110x²-440x+55x-220=0110x²-385x-220=0

On solving

x=-1/2 or x=4

The product of 2 more than 3 times a number and 6 less than 4 times the number (z)

Answers

Answer:

[tex]12z^{2} -10z -12[/tex]

Step-by-step explanation:

Let the number be z

2 more than 3 times z ==> 3z + 2

6 less than 4 times z ==> 4z - 6

Product of the above two is
[tex](3z + 2) (4z - 6) \\= (3z)(4z) + (3z)(-6) + (4z)(2) + (2)(-6)\\= 12z^{2} -18z + 8z - 12\\= 12z^{2} -10z -12[/tex]

PLSS HELP WIT 4 QUESTIONNN

Answers

Answer:

1. Statement C is not true.

2. Option B is correct

3. Option C is correct

4.Option C is correct

Step-by-step explanation:

1. There are 5 Platonic solids : The tetrahedron, cube

,octahedron, dodecahedron ,icosahedron.

The faces of cube and dodecahedron are not triangles.

therefore statement C is incorrect.

2. Polyhedron formula : Vertices - Edges + Faces = 2

now put the values

12 - 18 + F= 2

F = 8.

3. Polyhedron formula : Vertices - Edges + Faces = 2

now put the values

V - 30 + 12 = 2

V = 20.

4. Probability is the number of favourable or unfavourable event divided by total events.

therefore denominator always greater than numinator.

so [tex]\frac{8}{7}[/tex] cannot represent the probability

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What is this function written in vertex form? f(x) = (x 2)2 3 f(x) = (x2 2x)2 3 f(x) = (x 1)2 2 f(x) = (x 3)2 2x

Answers

The vertex form of the give quadratic equation is f(x) = (x+1)² + 2

Vertex form of an equation

The standard vertex form of a quadratic equation is expressed as

y = a(x -h)² + k

where (h, k) is the vertex

Given the quadratic equation

f(x) = x^2 + 2x + 3

Complete the question

f(x) = (x^2+2x) + 3

f(x) = (x^2+2x+1)-1 + 3

f(x) = (x+1)² + 2

Hence the vertex form of the give quadratic equation is f(x) = (x+1)² + 2

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Pls help quickly!!!

Find the coordinates of the vertex of the graph of the function.
y=3x^2-4x+3

Answers

Answer:

vertex = ( [tex]\frac{2}{3}[/tex], [tex]\frac{8}{3}[/tex] )

Step-by-step explanation:

given the equation of a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = 3x² - 4x + 3 ← is in standard form

with a = 3 , b = - 4 , then

x = - [tex]\frac{-4}{6}[/tex] = [tex]\frac{2}{3}[/tex]

substitute x = [tex]\frac{2}{3}[/tex] into the equation for corresponding y- coordinate of vertex

y = 3([tex]\frac{2}{3}[/tex] )² - 4([tex]\frac{2}{3}[/tex] ) + 3

  = 3([tex]\frac{4}{9}[/tex] ) - [tex]\frac{8}{3}[/tex] + 3

  = [tex]\frac{4}{3}[/tex] - [tex]\frac{8}{3}[/tex] + [tex]\frac{12}{3}[/tex]

  = [tex]\frac{8}{3}[/tex]

vertex = ( [tex]\frac{2}{3}[/tex], [tex]\frac{8}{3}[/tex] )

Vertex ( 2/3 , 8/3 )

Need to know asap thanks

Answers

Answer:

[tex]\large \boxed{\sf 16}[/tex]

Explanation:

[tex]\Rightarrow \sf \sqrt{121} + \sqrt[3]{125}[/tex]

[tex]\Rightarrow \sf{ \sqrt{11 \ x \ 11} + \sqrt[3] {\sf5 \ x \ 5 \ x \ 5}[/tex]

[tex]\Rightarrow \sf{ \sqrt{11^2} + \sqrt[\sf 3] {\sf 5^3}[/tex]

[tex]\Rightarrow \sf 11 + 5[/tex]

[tex]\Rightarrow \sf 16[/tex]

I hope this help you . the concept of sure and cube roo

lateral surface for a triangular prism l=8 w=4 h=6

Answers

Answer:

? i need help

Step-by-step explanation:

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