Rewrite the polynomial .22 – 52 + 6 as 2? + m2 + n2 +6, where m. n = 6 and m +n=-5. What are the values of m and n?

The expression which is equivalent to the given expression; (ab²)³/b⁵ as given in the task content is; a³b.

It follows from the task content that the expression which is equivalent to; (ab²)³/b⁵ be determined.

Hence, since the given expression is; (ab²)³/b⁵.

By first applying the power of power law of indices; we have;

(ab²)³/b⁵ = a³b⁶/b⁵.

Also, by applying the quotient of powers rule of indices; we have;

a³ b^(6 - 5)

= a³b¹

= a³b

Ultimately, the expression which is equivalent to; (ab²)³/b⁵ as required in the task content is; a³b.

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First step, derivative of the constant:

Second step, the chain rule:

Where we applied that the derivative of tangent is the secant^2.

Hence the answer is:

From the graph below, the domain is

From the given figure

The 2 triangles have one equal angle of measure 88

The side of length 3 and the side of length 1 have a ratio 3: 1

The side of length 6 and the side of length 2 have a ratio 6: 2, when we divide both terms of the ratio by 1, it becomes 3: 1

That means we have one equal angle and two proportional sides

Since the angle is between the proportional sides, then

The 2 triangles are similar by the SAS postulate

Answer B

To answer this question, it is a good practice to order the data in ascending order as follows:

We need to check for the total number of data. In this case, we have 30 observations.

To find the mean, we need to find the sum of all the observations and then divide this result by the total of observations (30). Then, we have:

Then, the value for the mean is:

The range is the result of subtracting the greatest number and the lowest number in the data:

The mode is the observation that is repeated the most (appears the most).

We can see that we have two values that appear six times in the list: 11 and 15.

Therefore, we can see that there is not a unique element, so there is no mode.

In summary, we have:

• Mean = 12.73333...

• Range = 8

• Mode = None.

The finance charge on Daniyar's May statement is $4.45.

What is finance charge?

The cost of consumer credit expressed as a dollar amount is the financing charge. It includes any fee imposed by the creditor as an incident to or a requirement of the credit extension that is directly or indirectly payable by the customer. It excludes any fee that would be paid in an equivalent cash transaction.

The finance charge is equal to the product of the average daily balance and the monthly periodic rate.

So,

$270.31 x 1.65%

= $270.31 x 0.0165

= $4.45

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Let t be the time, in hours, elapsed till the buses are 791 miles apart, then we can set the following equation:

Solving the above equation for t we get:

Answer: 7 hours.

Using a regression calculator, the line of best fit for the given set of data is:

where y = mass of the rope and x = length of the rope.

To estimate the length of the rope if its mass is 4.25 kilograms, let's replace "y" in the equation above with 4.25, and then solve for x.

Subtract 0.168088 on both sides of the equation.

Then, divide both sides of the equation by 0.34121.

Therefore, the length of the rope having a mass of 4.25 kilograms is approximately 11.96 meters.

Step-by-step explanation:

6×(4 + x) = 7

24 + 6x = 7

6x = -17

x = -17/6 = -2.833333333... = -2 5/6

Let x represent the number of pounds of coffee that she bought.

From the information given,

cost per pound of coffee = $8.73

Cost of x pounds of coffee = 8.73 * x = 8.73x

Initial amount that she had = $90

After spencing $8.73x, the amount left is $63.81. This means that

90 - 8.73x = 63.81

8.73x = 90 - 63.81

8.73x = 26.19

x = 26.19/8.73

x = 3

She bought 3 pounds of coffee

Answer:

This is an isosceles right triangle, so

x = 45°.

Answer:

$194.69

Step-by-step explanation:

The best way to predict the amount of tips is using this formula:

[tex]100(\frac{Tips(total)}{Customers(total)} )[/tex]

This finds the average tip per customer with all of the data, and multiplies it by 100 to get the predicted amount of tips for 100 customers.

Plugging in the data from the table gives you this equation:

[tex]100(\frac{1174}{603} )[/tex]

This equals $194.69.

It will take 80 seconds for both tank 1 and tank 2 to have the same amount of water

Water in the tank 1 = 120 gallons

Drainage rate of tank 1 = 1/2 gallon each second

Water in tank 2 = 100 gallons

Drainage rate of tank 2 = 1/4 gallon each second

Let x represent the number of seconds it will take for both tanks to have the same amount of water

Formulating the equation we get the following:

Water in tank 1 - Drainage rate of tank 1*x = Water in tank 2 - Drainage rate of tank 2*x

120 - 1/2x = 100 - 1/4x

20 = 1/2x - 1/4x

20 = 1/4x

x = 80

So, it will take 80 seconds

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Answer:

the probability is 2/8

Step-by-step explanation:

Answer:

Step-by-step explanation:

V = 4/3.pi.r^3

36 = 4/3 pi r^3

8.6 = r^3

r = 2 in

---------------------

Area of sphere :

A = 4.pi.r^2

A = 4 . Pi . 2^2

A = 16 Pi

A = 50.26 in

Answer:

See below

Step-by-step explanation:

Rotate rectangle A 90 ° clockwise with the center being the lower right hand corner.  Then translate down and right until rectangle A in over rectangle B

4x -2 = 3(x-3)

4x - 2 = 3x - 9

bring like terms together

4x-3x = -9 +2

x = -7

The given algebraic expression would be equivalent to the expression [tex]\dfrac{1}{4(x)^\frac{2}{9} }[/tex] which is the correct answer would be an option (B)

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The given algebraic expression is:

[tex](64x^{\frac{2}{3} })^{-\frac{1}{3} }[/tex]

Apply the property of a⁻ˣ = 1/aˣ in the above term,

[tex]\dfrac{1}{ (64x^{\frac{2}{3} })^{\frac{1}{3} }}[/tex]

Here 64 = 4×4×4 = 4³

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

Apply the cube root property and Multiply the exponent of the variable x to 1/3

[tex]\dfrac{1}{ 4x^{\frac{2}{3} }^\times^{\frac{1}{3} }}[/tex]

Apply the multiplication operation to the exponent of the variable x to get the solution.

[tex]\dfrac{1}{4(x)^\frac{2}{9} }[/tex]

Hence, the correct answer would be an option (B)

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Answer: [tex]y < \frac{1}{3}x+2, y < -2x+2[/tex]

Step-by-step explanation:

The equations of the lines are [tex]y=\frac{1}{3}x+2[/tex] and [tex]y=2-2x[/tex].

Since the line [tex]y=\frac{1}{3}x+2[/tex] has a dotted boundary and is shaded below, it represents the inequality [tex]y < \frac{1}{3}x+2[/tex].

Since the line [tex]y=2-2x[/tex] has a dotted boundary and is shaded below, it represents the inequality [tex]y < 2-2x[/tex].

The stock witness an total average decrease in stock of $80 in the 8 weeks

The given parameters are:

Average decrease per week = 10 dollars

Also, we have the number of weeks to be

Number of  Weeks = 8 weeks

So, the total average decrease in the stock is calculated using the following equation

Total = Average decrease per week x Number of weeks

Substitute the known values in the above equation

So, we have the following equation

Total = 10 x 8

Evaluate the products in the above equation

So, we have the following equation

Total = 80

Hence, the total average decrease in the stock is $80

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Given:

• AD = 3

• DC = 27

• BD = x + 3

Let's solve for x.

To solve for x, apply the altitude formula:

Where BD is the altitude.

Cross multiply:

Plug in the values and solve for x:

Take the square root of both sides:

Therefore, the value of x is 6 .

ANSWER:

d. 6

Answer: Linear

Step-by-step explanation:

Each time [tex]x[/tex] increases by [tex]1[/tex], [tex]y[/tex] decreases by [tex]8[/tex]. Since the value of y changes at a constant rate, the relationship is linear.

1) Looking at that table, we can pick the points

(1,9) (3,23)

2) Note that every time x increases by 2 units y increases by 14

3) Considering this a linear function we can find the rule by plugging in

23-9/3-1=14/2 = 7

9=7(1)+b

9=7 +b

2 =b

So we can write the rule as y =7x+2

Answer:

 65 pairs

Step-by-step explanation:

Black makes up 5/(5+8) = 5/13 of the total order, so ...

 (5/13)(169 pairs) = 65 pairs

Vinny will order 65 pairs of black high tops.

Equation for the line in point-slope form is 5x + 6y = 6.

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.

Given Data

P(6, -3)

y =1/2 x + 2

When the equation has been solved for y, the line in slope intercept form with slope = m = 1/2 = the coefficient of the x term is represented by the equation y= (1/2)x + 2. 2 represents the y coordinate of the location (0, 2) where the line intersects the y axis as the y intercept.

So, the points are (6,-3) and (0,2)

Formula

y₂ - y₁ = m(x₂ - x₁)

slope of the line (m) = [tex]\frac{x-x}{y-y}[/tex]₁¹

m= [tex]\frac{2-(-3)}{0-6}[/tex]

m = -[tex]\frac{5}{6}[/tex]

Equation

y- (-3) = -[tex]\frac{5}{6}[/tex](x- 6)

y +5 = -[tex]\frac{5}{6}[/tex]x + 6

y + 5 = -[tex]\frac{5+36 }{6}[/tex]

6y + 30 = -5x + 36

5x + 6y = 6

Equation for the line in point-slope form is 5x + 6y = 6.

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Answer: x < -4

Step-by-step explanation:

➜ First thing we notice is the open circle. This means we will use either < or >

➜ The next thing we notice is that the values are pointing to the left of the circle, this means we will be using <

➜ The last part we notice is that the dot is on -4. This is the value we'll use to write our inequtliy.

    The last thing to do is to write the inequality using the parts we pointed out above:

x < -4

A perpendicular bisector is a segment which intersects another segment on its midpoint and with a right angle.

First, we have to find the midpoint between X(-9,1) and Y(3,5), as follows

This means the perpendicular bisector must pass through (-3,3). Now, with the given points we find the slope of XY

Then, we apply the rule of perpendicularity to find the slope of the perpendicular bisector.

Now, we use the slope-point formula to find the equation for the perpendicular bisector.

Where we replace the slope -3 and the point (-3,3).

Answer:

70

Step-by-step explanation:

14 x 10 is 140.

Since a triangle is just half a square, we multiply the two sides we have and then divide it.

140 ÷ 10 = 70.

Answer = 70.

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