Which expression is equivalent to (x^6y^8)^3\x^2y^2

Answer:

Step-by-step explanation:

The number of grains of wheat on the n(th) square is 2^(n-1), or 2 to  

the power of n-1.  This is because the first square has 2^0 = 1 grain,  

the second has 2^1 = 2, and the n(th) square has twice as many as the  

previous. Thus the total number of grains of wheat is

    S = 1 + 2 + 4 + 8 + ... + 2^63.

Since this is a geometric sequence with common ratio 2, the sum is

        2^64 - 1

    S = -------- = 2^64 - 1 = 18446744073709551615.

          2 - 1

Answer:

Range = (-∞, 5)

Step-by-step explanation:

This is the absolute value function with transformation.

The parent function is f(x) = |x|

This function has a "negative" in front, so it makes it reflect about x axis

The -4 after x makes horizontal translation of 4 units right

the +5 at the end makes the function translate 5 units UP

The graph is shown in the attached picture.

Looking at the graph, we can clearly see the range. The range is the allowed y-values. Hence, we can see that the range is  -infinity to 5

answer is not properly given, so i can't choose from the options, but the answer is -∞, 5 to 5

Answer:

Answer is  x=328 .

Step-by-step explanation:

solution= (4x-16)^1/2=36

squaring both sides we get

 4x-16=129

 4x=1296+16

 x=(1296+16)/4

  x=328 .

Answer:

x = 328

Step-by-step explanation:

The given equation is

[tex](4x-16)^{\frac{1}{2}}=36[/tex]

We need to find the solution of the given equation.

Taking square on both sides.

[tex]((4x-16)^{\frac{1}{2}})^2=(36)^2[/tex]

[tex](4x-16)^{\frac{2}{2}}=1296[/tex]

[tex]4x-16=1296[/tex]

Add 16 on both sides.

[tex]4x-16+16=1296+16[/tex]

[tex]4x=1312[/tex]

Divide both sides by 4.

[tex]x=\dfrac{1312}{4}[/tex]

[tex]x=328[/tex]

Therefore, the value of x is 328.

Answer:

[tex]4x[/tex]

Step-by-step explanation:

We want to find the simplest rational exponent form of

[tex]\sqrt{x} \cdot 4\sqrt{x}[/tex]

Recall that: [tex]\sqrt{a}=a^{\frac{1}{2} }[/tex]

We rewrite the expression in the exponent form to get:

[tex]x^{\frac{1}{2}}\cdot 4x^{\frac{1}{2}[/tex]

We can regroup the product to get:

[tex]4 x^{\frac{1}{2}\cdot x^{\frac{1}{2}[/tex]

We apply the rule: [tex]a^m\cdot a^n=a6{m+n}[/tex] to get:

[tex]4 x^{\frac{1}{2}}\cdot x^{\frac{1}{2}=4 x^{\frac{1}{2}+\frac{1}{2}}[/tex]

[tex]4 x^{\frac{1}{2}}\cdot x^{\frac{1}{2}=4 x^{1}[/tex]

[tex]4 x^{\frac{1}{2}}\cdot x^{\frac{1}{2}=4x[/tex]

Answer:

The length is 16.1 ft and the width is 4.7 ft

Step-by-step explanation:

Let

x -----> the total length of the tables

y -----> the width of the tables

we know that

The area is equal to

[tex]A=xy[/tex]

[tex]A=75\ ft^{2}[/tex]

so

[tex]75=xy[/tex] -----> equation A

[tex]x=3y+2[/tex] -----> equation B

substitute equation B in equation A

[tex]75=(3y+2)y[/tex]

[tex]3y^{2} +2y-75=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]y=4.7\ ft[/tex]

Find the value of x

[tex]x=3(4.7)+2=16.1\ ft[/tex]

therefore

The length is 16.1 ft and the width is 4.7 ft

Answer:

The length and width of the serving table is 16.1 ft and 4.7 ft respectively.

Step-by-step explanation:

Consider the provided information.

Let the width of the table is x and length of the table is y.

The total length of the tables will be two more than three times the width.

This can be written as:

y = 2+3x

The area of the table is 75 ²ft

The area of rectangle is:

length × width = Area

Substitute width = x and length = 2+3x in above formula.

(x)(2+3x) = 75

2x+3x²-75 = 0

3x²+2x-75 = 0

The above equation is in the form of ax²+bx+c=0. Now use the quadratic formula to find the root of the equation.

[tex]x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Substitute a=3, b=2 and c=-75 in above formula.

[tex]x_{1,2}=\frac{-2\pm\sqrt{2^2-4(3)(-75)}}{2(3)}[/tex]

[tex]x_{1,2}=\frac{-2\pm\sqrt{904}}{6}[/tex]

[tex]x_{1,2}=\frac{-2\pm30.07}{6}[/tex]

[tex]x_{1}=\frac{-2+30.07}{6}[/tex]

Ignore the negative value of x as width should be a positive number.

[tex]x=4.7\ ft[/tex]

Now substitute the value of x in y = 2+3x.

y = 2+3(4.7)

y = 16.1 ft

Hence, the length and width of the serving table is 16.1 ft and 4.7 ft respectively.

The measurement of angle RST is 105

Answer:

Option C). 105°

Step-by-step explanation:

From the figure we can see a cyclic quadrilateral QRST

To find the measure of <RST

From the figure we can see that, angle RST is an obtuse angle.

The measure of angle RST is nearer to a right angle that is nearer to 90°

From the options we get the measure of angle RST = 105°

Answer:

a. [tex]c(x) = 2x + 105[/tex]

b.  [tex]c(50) =\$205[/tex]

Step-by-step explanation:

The variable cost of $ 2 implies that for each manufactured calculator the total cost increases $ 2.

The fixed cost of $ 105 implies that regardless of the number of manufactured calculators there will always be a cost of $ 105.

If we call x the number of manufactured calculators then the total cost c(x) will be:

[tex]c(x) = 2x + 105[/tex]

Then, the cost of manufactured 50 calculators a day is:

[tex]c(50) = 2(50) + 105[/tex]

[tex]c(50) = 100 + 105[/tex]

[tex]c(50) =\$205[/tex]

Answer:

1180 cans

Step-by-step explanation:

Heywards collected = 980 cans

Ballards collected 200 fewer cans than Heywards.

Total cans collected by Ballard = ?

Therefore the sum of Heywards collected cans and Ballards fewer cans will give us the total cans collected by Ballard.

=980+200

=1180

Ballard collected 1180 cans....

Answer:

b

Step-by-step explanation:

any set times the radius will give you the answer

Answer:

The function is defined when x > 0

Step-by-step explanation:

Functions with radicals are only undefined when the value in the radical is negative, because the root of a negative number is imaginary.  

We know the function is undefined when the denominator is equal to zero.  [tex]\sqrt{2x}[/tex] is equal to zero when x=0.

We also know that functions with radicals are undefined when the value in the radicals are negative, because the root of a negative number is imaginary.  .  [tex]8x^{2}[/tex] will always be positive, but [tex]2x[/tex] is negative when x < 0.

So the function is undefined when x = 0, and when x < 0.

Therefore it is defined when x > 0

Answer:

Part 1) The ordered pair is (0,0)

Part 2) The ordered pair is (-2,-4)

Part 3) The ordered pair is (4,8)

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem we have a direct variation

[tex]y=2x[/tex]

Complete the ordered pairs

Part 1) we have (0,?)

For x=0

Substitute in the equation and solve for y

[tex]y=2(0)=0[/tex]

therefore

The ordered pair is (0,0)

Part 2) we have (-2,?)

For x=-2

Substitute in the equation and solve for y

[tex]y=2(-2)=-4[/tex]

therefore

The ordered pair is (-2,-4)

Part 3) we have (4,?)

For x=4

Substitute in the equation and solve for y

[tex]y=2(4)=8[/tex]

therefore

The ordered pair is (4,8)

Answer:

Yes, it is a function.

Step-by-step explanation:

Since each x-value is used only once, the relation is a function.

Yes, The relation represented in table is a function.

A relation between a set of inputs having one output each is called a function.

Given that;

The table is,

x |  5  10  15

y | 3    8    8

Now,

Clearly, Each inputs having one output in the table as;

⇒ f (5) = 3

⇒ f (10) = 8

⇒ f (15) = 8

So, The table represent the function.

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Answer:

Option B [tex]y> 0[/tex]

Step-by-step explanation:

we have

[tex]f(x)=9(2^{x})[/tex]

This is a exponential function of the form

[tex]y=a(b^{x})[/tex]

where

a is the initial value

b is the base

r is the rate

b=1+r

In this problem

a=9

b=2

r=2-1=1=100%

The domain for x is the interval ------> (-∞,∞)

All real real numbers

The range is the interval -----> (0,∞)

[tex]y> 0[/tex]

All real numbers greater than zero

see the attached figure to better understand the problem

Answer:

No.

Step-by-step explanation:

Direction variation is of the form y = kx.

This is not direct variation.

The equation 3y = 5x + 4 does not represent a direct variation because it includes a constant term '+4'. A direct variation would only have the form y = kx without any added or subtracted constants.

The equation 3y=5x+4 represents a direct variation, and if so, to find the constant of variation. A direct variation is when one variable is a constant multiple of another, expressed in the form y = kx, where k is the constant of variation. In this case, the equation 3y = 5x + 4 is not a direct variation because of the additional constant term '+4'. For it to be a direct variation, y must be alone on one side of the equation, and there should be no constant term added or subtracted with the term that is a multiple of x.

To be a direct variation, the equation needs to have the form y = kx. In the practice equation y + 7 = 3x, if we solve for y, we get y = 3x - 7 which still would not be a direct variation because of the -7. The other example equation 4y = 8 is not in the form of direct variation either since it has no variable x in it; it represents a horizontal line where y is a constant.

Answer:

Jagdish is 27 years old

Step-by-step explanation:

Jagdish=x

Resham=x+3

Rajesh=x+5

(x+3)(x+5) = 960

x²+8x+15=960

x²+8x=945

x²+8x-945=0

now factor this to solve

(x-27)=0 (x+35)=0

which means

x=27 and x=-35

obviously, we cannot have negative ages so we use x=27

so, Jagdish=27

Resham=30

Rajesh=32

and we can check this by doing 30x32 which does equal 960 so it is correct

The age of Jagdish for the condition is 27 years.

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:

ax² + bx + c = 0

Given Jagdish is 3 years younger than Resham

and  Rajesh is 5 years older than Jagdish

let age of Jagdish be x

Resham = x + 3

Rajesh = x + 5

according to conditions,

(x + 3)(x + 5) = 960

x² + 8x + 15 = 960

x² + 8x = 945

x² + 8x- 945=0

now factor this to solve

(x - 27)(x + 35) = 0

(x - 27) = 0, (x + 35) = 0

which means

x=27 and x=-35

obviously, we cannot have negative ages so we use x = 27

Therefore, the age of Jagdish is 27 years.

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Answer:

y = 3x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3)

m = [tex]\frac{3-0}{0+1}[/tex] = 3

We are given the y- intercept, that is c = 3

y = 3x + 3 ← equation of line

Answer:

rotated

Step-by-step explanation:

The triangle MNO has already been dilated and therefore, the answers were left to 3: rotated, reflected and translated. Triangle YHQ is not an image of triangle MNO. Thus, leaving only 2 choices: rotated and translated. If triangle MNO was translated, triangle YHQ was supposed to be in the same position as triangle MNO is and leaving only 1 option which is rotated.

Answer:

rotated

Step-by-step explanation:

the correct answer is rotated

when triangle Δ M N O was dilated to create Triangle Δ Y H Q

we can clearly see that the length of the sides of the triangle is increased and from the figure we can clearly see that the largest side is rotated.

marked angle is also rotated.

so, we can clearly say that to make  Triangle Δ Y H Q triangle Δ M N O is dilated and rotated.

Answer:

Option C is correct.

Step-by-step explanation:

Points given are

(1,2) and (3,8)

The formula used for slope is:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

x₁ = 1, x₂=3, y₁=2 and y₂=8

[tex]m=\frac{8-2}{3-1}\\m=\frac{6}{2}\\m=3[/tex]

So, slope =3

Option C is correct.

Answer:

The slope of the line passing through (1,2) and (3,8) is 3.

Step-by-step explanation:

Slope formula is y2-y1/x2-x1

y2=8

y1=2

x2=3

x1=1

8-2/3-1

8-2=6

3-1=2

6/2=3

Answer:

9 is (2/9) of the way from A = 5 to B = 23.

Step-by-step explanation:

Note that there are 23-5, or 18, units separating 5 and 23.

2/9 of that distance is (2/9)(18), or 4.

Adding 4 to 5, we get 9.

9 is (2/9) of the way from A = 5 to B = 23.

If this is not clear, I'd suggest you draw this situation and prove to yourself that 9 is (2/9) of the way from A = 5 to B = 23.

Answer:

9

Step-by-step explanation:

The equation is A+K (B-A). So 5+ 2/9 (23-5) = 9

Answer:

Step-by-step explanation:

[tex]8(x-2)=64\qquad\text{distributive property}\\8x-(8)(2)=64\\8x-16=64\qquad\text{add 16 to both sides}\\8x-16+16=64+16\qquad\text{addition property of equality}\\8x=80\qquad\text{divide both sides by 8}\\\dfrac{8x}{8}=\dfrac{80}{8}\qquad\text{division property of equality}\\x=10[/tex]

Answer:

ANSWER WOULD BE D . division property of equality

Step-by-step explanation:

Took the test the math is quite simple

Answer:

D is 36080

Step-by-step explanation:

D is the largest since A is 3.608, B is 360.8, C is 36.08

When dividing, the smaller decimal points will be larger, but if you multiple, the numbers shrink.

ANSWER

[tex]x = - 1 \: or \: x = - \frac{1}{ 3} [/tex]

EXPLANATION

The given equation is:

[tex] {x}^{ - 2} + 4 {x}^{ - 1} + 3 = 0[/tex]

Recall that:

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

[tex] \frac{1}{ {x}^{2} } + \frac{4}{x} + 3 = 0[/tex]

Or

[tex] {( \frac{1}{x} )}^{2} + 4( \frac{1}{x} ) + 3 = 0[/tex]

Let

[tex]u = \frac{1}{x} [/tex]

Our equation then becomes:

[tex] {u}^{2} + 4u + 3 = 0[/tex]

The factors of 3 that add up to 4 are:

[tex] {u}^{2} + 3u + u + 3[/tex]

[tex]u(u + 3) + 1(u + 3) = 0[/tex]

[tex](u + 1)(u + 3) = 0[/tex]

[tex]u + 1 = 0 \: or \: u + 3 = 0[/tex]

[tex]u = - 1 \: or \: u = - 3[/tex]

This implies that:

[tex] \frac{1}{x} = - 1 \: or \: \frac{1}{x} = - 3[/tex]

[tex]x = - 1 \: or \: x = - \frac{1}{ 3} [/tex]

Answer:

second option

Step-by-step explanation:

We are going to use the acronym:

"Soh Cah Toa".

Why? It tells us the right-triangle definitions of sine, cosine, and tangent.

sine is opposite over hypotenuse.

cosine is adjacent over hypotenuse.

tangent is opposite over adjacent.

So looking at our triangle with respect to B tells us that 3 is the opposite measurement and 6 is the adjacent.  No matter what angle we are looking for in this triangle, the hypotenuse is constantly going to by [tex]3\sqrt{5}[/tex].

So let's look at cos(B).

[tex]\cos(B)=\frac{6}{3\sqrt{5}}[/tex]

We need to rationalize the denominator by multiplying top and bottom by sqrt(5):

[tex]\cos(B)=\frac{6\sqrt{5}}{3(5)}=\frac{2\sqrt{5}}{5}[/tex]

So now looking at sin(B).

[tex]\sin(B)=\frac{3}{3\sqrt{5}}[/tex]

We have to rationalize again by multiplying top and bottom by sqrt(5):

[tex]\sin(B)=\frac{3\sqrt{5}}{3(5)}=\frac{\sqrt{5}}{5}[/tex].

So looking at our triangle with respect to A tells us that 3 is the adjacent measurement and 6 is the opposite.  No matter what angle we are looking for in this triangle, the hypotenuse is constantly going to by [tex]3\sqrt{5}[/tex].

We don't have to use any trigonometric ratios with A.

Answer:

2 Square 5/ 5

Step-by-step explanation:

I got it right on the test

Answer:

C x= 0   greater than

E x= 10 greater than

Step-by-step explanation:

4(2 – x) > –2x – 3(4x + 1)

Distribute

8 –4x > –2x – 12x -3

Combine like terms

8 –4x > – 14x -3

Add 14x to each side

8 –4x+14x > – 14x+14x -3

8 +10x >  -3

Subtract 8 from each side

8-8+10x>-3-8

10x > -11

Divide each side by 10

10x/10 >-11/10

x >-1.1

Any number greater than -1.1 is a solution

A x= -1.1   not greater than

B x= -2.2   not greater than

C x= 0   greater than

D x=-10  not greater than

E x= 10 greater than

Answer:

C & E

Step-by-step explanation:

Answer: C

Step-by-step explanation:

Probability: the outcome you want (2) over the total number of outcomes (6).

Probability= 2/6= 1/3.

The probability of landing on 2 is 1/6 if the total number of outcomes is 6 and favorable outcomes are 1 option (C) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have a spinner shown in the picture.

Total number of outcomes = 6

{1, 2, 3, 4, 5, 6}

Total number of favorable outcomes = 1

{2}

P(landing on 2) = 1/6

Thus, the probability of landing on 2 is 1/6 if the total number of outcomes is 6 and favorable outcomes are 1 option (C) is correct.

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Answer:

[tex]\large\boxed{(2b+3)\times(5b-1)\times(5b+1)}[/tex]

Step-by-step explanation:

The formula of a volume of a rectangular box:

[tex]V=lwh[/tex]

l - lenght

w - width

h - height

[tex]V=50b^3+75b^2-2b-3=25b^2(2b+3)-1(2b+3)\\\\=(2b+3)(25b^2-1)=(2b+3)(5^2b^2-1^2)\\\\=(2b+3)\bigg((5b)^2-1^2\bigg)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(2b+3)(5b-1)(5b+1)[/tex]

Therefore the dinemsions of thisp prism are:

[tex](2b+3)\times(5b-1)\times(5b+1)[/tex]

Answer:

the one with ++-

Step-by-step explanation:

Answer:

1-4x

Step-by-step explanation:

Answer:

Step-by-step explanation:

The product of four and a number x: 4 · x = 4x

One minus the product of four and a number x: 1 - 4x

Complementary angle add up to 90 degrees.

Angle A = x + 6

Angle B = x

They both add up to 90.

x + 6 + x = 90

2x + 6 = 90

2x = 90 - 6

2x = 84

x = 84/2

x = 42

Angle A = x + 6

Angle A = 42 + 6

Angle A = 48 degrees

Answer:C

Step-by-step explanation:4x _2y =64 because 8×8= 64

For this case we must find an equation equivalent to:

[tex]\frac {1} {4} x- \frac {1} {2} y = 8[/tex]

We add [tex]\frac {1} {2}[/tex] and on both sides of the equation:

[tex]\frac {1} {4} x = 8 + \frac {1} {2}y[/tex]

We multiply by 4 on both sides of the equation:

[tex]x = 32 + \frac {4} {2}y\\x = 32 + 2y[/tex]

Multiplying by 2 on both sides of the equation:

[tex]2x = 64 + 4y\\2x-4y = 64[/tex]

Answer:

Option B

Answer:

42.5 %

Step-by-step explanation:

You would multiply the probability of the couple having a girl and the test predicting it’s a girl.

0.85 x 0.5= 0.425 = 42.5%