Which expression is equal to 5 6 (6 is an exponent)

6x5
36x6x6x6
25x5x5x5
125x125

Answer:

?????

Step-by-step explanation:

The sum of the given expressions using the column method is 3a^2.

The sum of the given expressions can be found using the column method. Let's break it down step-by-step:
1. First, let's consider the expression a^2 + 2ab + b^2.
2. Write down the expression vertically, with each term aligned under its respective power of a:
      a^2
   + 2ab
   + b^2
3. Add the corresponding terms vertically:
    (a^2 + 2ab + b^2)
4. Next, let's consider the expression a^2 - 2ab - b^2.
5. Write down the expression vertically, with each term aligned under its respective power of a:
      a^2
   - 2ab
   - b^2
6. Add the corresponding terms vertically:
    (a^2 - 2ab - b^2)
7. Finally, let's consider the expression a^2 + b^2.
8. Write down the expression vertically, with each term aligned under its respective power of a:
      a^2
      b^2
9. Add the corresponding terms vertically:
    (a^2 + b^2)
10. Now, we can find the sum of all the expressions by adding the results from steps 3, 6, and 9:
    (a^2 + 2ab + b^2) + (a^2 - 2ab - b^2) + (a^2 + b^2)
11. Simplify the expression:
    a^2 + 2ab + b^2 + a^2 - 2ab - b^2 + a^2 + b^2
12. Combine like terms:
    3a^2
Therefore, the sum of the given expressions using the column method is 3a^2.

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-2

Answer:

Solution given:

|-3| -|5|=3-5=-2

since modules gives a value of any number alwats positive

Answer:

-2

Step-by-step explanation:

Absolute value means take the non-negative value

|-3| = 3

|5| =5

|-3| -|5| = 3 -5 = -2

The expressions to represent the length and width of Melissa’s vegetable garden in terms of x include the following:

y = 3x + 2.

y = x + 5

In order to write the expressions representing the length and width of Melissa’s vegetable garden, we would assign variables to its dimensions as follows;

Since Melissa wants the length of her rectangular vegetable garden to exceed three (3) times the length of the tomato square patch by 2 feet, the length of the rectangular vegetable garden with respect to its length is given by:

y = 3x + 2.

For the width, an expression for the rectangular vegetable garden's width with respect to the width of the tomato square patch is given by:

y = x + 5

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The complete solution is:

∫4\(sin^{-1}(2x) dx = sin^{-1}(2x)\) x 4x + √(1 - (2x)²) + C, where C is the constant of integration.

We have,

\(u = sin^{-1)}(2x)\)

dv = 4 dx

Taking the derivative of u, we get:

du/dx = 1 / √(1 - (2x)²)

Integrating dv, we get:

v = ∫4 dx = 4x

Now, applying the integration by parts formula:

∫4 \(sin^{-1}(2x) dx\) = uv - ∫vdu

Plugging in the values, we have:

∫4 \(sin^{-})(2x) dx = sin^{-1}(2x) \times\) 4x - ∫(4x / √(1 - (2x)²)) dx

At this point, we need to evaluate the integral on the right side.

Let's perform a substitution to simplify it:

Let u = 1 - (2x)²

Differentiating u with respect to x, we get:

du/dx = -4(2x) = -8x

Solving for dx, we have:

dx = -du / (8x)

Substituting these values, the integral becomes:

∫(4x / √(1 - (2x)²)) dx = ∫(-4x / (8x x √u)) (-du / (8x))

Simplifying, we get:

∫(4x / √(1 - (2x)²)) dx = ∫(-1 / (2√u)) du

= -∫(1 / (2√u)) du

= -√u + C

Substituting back the value of u, we have:

∫(4x / √(1 - (2x)²)) dx = -√(1 - (2x)²) + C

Therefore,

The complete solution is:

∫4\(sin^{-1}(2x) dx = sin^{-1}(2x)\) x 4x + √(1 - (2x)²) + C, where C is the constant of integration.

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The complete question:

a) Evaluate the integral ∫4 sin^(-1)(2x) dx using integration by parts.

Answer:

Step-by-step explanation:Samir should just paint better and quicker

Samir paints 1/3 of a fence in 2/3 hours. To find his rate per hour, you would divide the fraction of the fence painted by the time taken. Thus, the desired expression is (1/3) ÷ (2/3) = 1/2, meaning Samir paints half of the fence in one hour.

The question is about determining the rate at which Samir paints a fence. According to the question, Samir paints 1/3 or 13 of a fence in 2/3 or 23 hours. To find out how much fence Samir paints in 1 hour, or his rate, we divide the fraction of the fence painted by the time taken.

So the expression would be (1/3) ÷ (2/3). In essence, we're dividing the fraction of the fence painted by the corresponding time. When you divide fractions, you multiply the first fraction by the reciprocal of the second fraction. Thus, it becomes (1/3) * (3/2) = 1/2. So, Samir would be able to paint 1/2 of the fence in one hour if he continues to paint at the same rate.

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Answer:

x = 7

Step-by-step explanation:

9x+11 = 74 (As they are corresponding angles)

9x = 74-11

9x = 63

x = 63/9

x = 7

Answer: a=123

b=230

Step-by-step explanation:

Answer:

X+Y=172 OE X=172-Y

X=5Y-8

5Y-8=172-Y

5Y+Y=172+8

6Y=180

Y=180/6

Y=30 ANS

X=172-30

X=142 ANS.

Step-by-step explanation:

Answer: 72.5 degrees

Step-by-step explanation: Call smaller angle x, so larger angle is x+35, so 2x+35=180, subtract 35 from both sides, 2x=145, so x=72.5! I hope this helps you

Answer:

x =54

Step-by-step explanation:

68 - x = 14

find the difference of 68 and 14 to get X

68 - 14 = 54

X=54

(Sorry if it is incorrect or doesn’t make sense!)

Answer:

90

Step-by-step explanation:

210 divided by 7 is 30 and times 3 is 90

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{90 \: dollars}}}}}\)

Step-by-step explanation:

Total amount of money that Rob had = $ 210

Total amount of money that he spent = \( \sf{ \frac{4}{7} \times 210} = \: 120 \: dollars\)

Finding the amount of remaining money

\( \boxed{ \sf{total \: amount \: of \: money \: that \: he \: had \: - \: total \: amount \: of \: money \: that \: he \: spent}}\)

\( \dashrightarrow{ \sf{210 - 120}}\)

\( \dashrightarrow{ \sf{90 \: dollars}}\)

Hope I helped!

Best regards! :D

The width that maximizes the area is 45ft, the corresponding length is also 45ft, and the maximum area is 2025 square feet.

Let's solve the problem step by step:

1. Write the perimeter P and area A of the rectangle in terms of l and w:

  Perimeter P = 2l + 2w

  Area A = lw

2. Write A in terms of w only:

  We can use substitution to express A in terms of w only. Since we know that the perimeter is 180ft, we have the equation:

  2l + 2w = 180

  Solving this equation for l, we get:

  l = 90 - w

  Substitute this value of l into the area equation:

  A = (90 - w)w

  Simplifying, we have:

  A = 90w - w^2

3. Find w that maximizes the area:

  To find the value of w that maximizes the area, we can take the derivative of A with respect to w and set it equal to zero:

  dA/dw = 90 - 2w = 0

  Solving this equation, we find:

  2w = 90

  w = 45

4. Find the corresponding l that maximizes the area:

  Substitute the value of w = 45 into the equation l = 90 - w:

  l = 90 - 45

  l = 45

5. Find the maximum area:

  Substitute the values of l = 45 and w = 45 into the area equation:

  A = 90(45) - (45)^2

  A = 4050 - 2025

  A = 2025 square feet

Therefore, the width that maximizes the area is 45ft, the corresponding length is also 45ft, and the maximum area is 2025 square feet.

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(a) On scaling up by a factor of 2 , the equivalent fraction is 18/30.

(b) On scaling up by a factor of 3 , the equivalent fraction is 27/45.

(c) On scaling down by a factor of 3 , the equivalent fraction is 3/5 .

In the question ,

a fraction 9/15 is given ,

Part(a)

to scale up the fraction by a factor of 2 , we multiply the numerator and denominator by 2 .

On multiplying , we get

9/15 = (9*2)/(15*2) = 18/30 .

Part(c)

to scale up the fraction by a factor of 3 , we multiply the numerator and denominator by 3 .

On multiplying , we get

9/15 = (9*3)/(15*3) = 27/45 .

Part(c)

to scale down the fraction by a factor of 3 , we divide the denominator and numerator by 3 .

On dividing , we get

9/15 = (9/3)/(15/3) = 3/5 .

Therefore , (a) On scaling up by a factor of 2 , the equivalent fraction is 18/30.

(b) On scaling up by a factor of 3 , the equivalent fraction is 27/45.

(c) On scaling down by a factor of 3 , the equivalent fraction is 3/5 .

The given question is incomplete , the complete question is

Write three fractions equivalent to 9/15 .

Scale the numerator and denominator up for the first two and down for the third.

(a) Scale up by: __ Equivalent fraction: __

(b) Scale up by: __ Equivalent fraction: __

(c) Scale down by: __ Equivalent fraction: __

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Answer:

\((5x-1)(x+4)\)

Step-by-step explanation:

Given:

\(5x^2 +19x-4\)

Factor the expression by grouping. First, the expression needs to be rewritten as \(5x^2 +ax+bx-4\). To find a and b, set up a system to be solved.

\(a+b=19\)

\(ab=5(-4)=-20\)

Since \(ab\) is negative, a and b have the opposite signs. Since \(a+b\) is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product \(-20\).

\(-1,20\)

\(-2,10\)

\(-4,5\)

Calculate the sum for each pair.

\(-1+20=19\)

\(-2+10=8\)

\(-4+5=1\)

The solution is the pair that gives sum \(19\).

\(a=-1\)

\(b=20\)

Rewrite \(5x^2+19x-4\) as \((5x^2-x)+(20x-4)\).

Factor out x in the first and 4 in the second group.

\(x(5x-1)+4(5x-1)\)

Factor out common term \(5x-1\) by using distributive property.

\((5x-1)(x+4)\)

Therefore, \((5x-1)(x+4)\).

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Answer:

12.3693

Step-by-step explanation:

use distance formula

64*256*1,024=16,777,216

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3 quarts is equal to approximately 285 centilitres.

To Calculate this we have:

3 quarts is equal to 3 x 0.95 liters = 2.85 liters.

1 litre is equal to 100 centilitres, so 2.85 litres is equal to 2.85 x 100 = 285 centilitres.

Therefore, 3 quarts is equal to approximately 285 centilitres.

In detail, a quart is a unit of measurement in the Customary System Units and is defined as a quarter of a gallon. 1 quart is equal to 0.95 litres. To find out how many centilitres are in 3 quarts, we need to multiply the number of quarts (3) by the conversion factor (0.95 litres per quart). This gives us 2.85 litres. Since 1 litre is equal to 100 centilitres, we can multiply 2.85 litres by 100 to get 285 centilitres. Therefore, 3 quarts is equal to approximately 285 centilitres.

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Mia walked 7km/h so after 1 hour, she is 7 km north of the house of Julia

Samantha walked 11km/h so after 1 hour, she is 11 km west of the house of Julia.

The points where Mia and Samantha are after 1 hour , and the house of Julia form a right triangle with sides 7 and 11 km. The distance between the girls, is the hypotenuse of his triangle.

by the pythagorean theorem:

Answer: 13 km

Answer:

C

Step-by-step explanation:

The speed of current and average speed of paddling is 3 and 7 respectively.

Let p represents paddling speed of kayack guide  and c represents speed of current.

If paddling downstream, the total speed is p + c because you’re paddling with the current. Similarly, if paddling upstream, the total speed is p - c because you would be paddling against the current.

Since paddling downstream took  2 hours so distance covered 2*(p + c)

which is equal to 20 miles.

2*(p + c) =20.

p + c = 10. -----i

Paddling upstream took 4 hours so distance covered 4*(p-c).

which is equal to 16 miles.

4*(p-c) = 16.

p - c = 4.  -------ii

adding both equation c will be cancelled. 2*p=14 p =7.

put value of p in equation i.

7 + c = 10  ,c = 3.

So the speed of current and average speed of paddling is 3 and 7 respectively.

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The length and width of the plot that will maximize the area is 60 meters by 120 meters. The largest area that can be enclosed is 7200 square meters.

To maximize the area of the rectangular plot, Farmer Ed must use 9000 meters of fencing to enclose three sides of the plot. The fourth side, which borders the river, does not need to be fenced. To find the length and width of the plot that will maximize the area, the 9000 meters of fencing must be divided into two sides of equal length, with the remaining fencing used for the third side. This results in a length of 120 meters and a width of 60 meters, which maximizes the area of the plot. The largest area that can be enclosed is 7200 square meters.

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The dilation is centered at the origin and has a scale factor of 0.5.

Here are the steps to find the image coordinates using a dilation centered at the origin with a scale factor of 0.5:

Write down the coordinates of the pre-image points.

P(-4, 2), L(2, 4), A(2, -4), Y(-4, -2)

Multiply each coordinate by the scale factor of 0.5.

P' = (0.5 × -4, 0.5 × 2) = (-2, 1)

L' = (0.5 × 2, 0.5 × 4) = (1, 2)

A' = (0.5 × 2, 0.5 × -4) = (1, -2)

Y' = (0.5 × -4, 0.5 × -2) = (-2, -1)

Write down the image coordinates.

P'(-2, 1), L'(1, 2), A'(1, -2), Y'(-2, -1)

Therefore, the dilation centered at the origin with a scale factor of 0.5 maps the points P(-4, 2), L(2, 4), A(2, -4), Y(-4, -2) to their respective images P'(-2, 1), L'(1, 2), A'(1, -2), Y'(-2, -1).

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Image transcribed:

Use coordinate notation to describe the dilation. Express the scale factor as a decimal if necessary.

Answer:

43%

Step-by-step explanation:

(40.76 - 28.50) / 28.5 = .43 or 43%

Answer:

Step-by-step explanation:

Perimerter is 9.6ft

The estimated crop yield from the simulation is 443 (option b).

To estimate the crop yield from the given random numbers, we need to assign a specific meaning to each random number. Let's assume that each random number represents the crop yield for a particular year.

Given random numbers: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81

To find the estimated crop yield, we sum up all the random numbers:

37 + 23 + 92 + 01 + 69 + 50 + 72 + 12 + 46 + 81 = 443

Therefore, the estimated crop yield from the simulation is 443. The correct option is b.

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Answer:

B) \(\$8395.80\)

Step-by-step explanation:

\(A=P(1+rt)\\A=7996(1+0.06\cdot\frac{10}{12})\\A=7996(1+0.05)\\A=7996(1.05)\\A=\$8395.80\)

This is all assuming that r=6% is an annual rate, making t=10/12 years

Recapturing a higher percent of marked alligators affects the estimated total population by making it high enough to support an accurate estimate.

This is referred to as the total number of species or organisms in an area at a given period of time.

Recapture rates are high enough to support an accurate estimate. The Lincoln-Peterson calculation tends to overestimate the population size, especially if the number of recaptures is small.

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Answer:

-xy+y

Step-by-step explanation:

=2xy-3xy+y

=-xy+y

Answer: The answer is 16y I think

Step-by-step explanation: