10x 4 tens unit and standard form

The value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

To find the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80, we can use polynomial long division. Let's perform the division step by step:

Write the dividend and divisor in polynomial long division format:

_________________________

x + 3 │ x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ...

Divide the leading term of the dividend (x^(2n-1)) by the leading term of the divisor (x). The result is x^(2n-1)/x = x^(2n-2).

Multiply the divisor (x + 3) by the quotient obtained in the previous step (x^(2n-2)). The result is x^(2n-2) * (x + 3) = x^(2n-1) + 3x^(2n-2).

Subtract the result obtained in step 3 from the original dividend:

x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ... - (x^(2n-1) + 3x^(2n-2)) = -3x^(2n-2) + 0x^(2n-3) + ...

Bring down the next term of the dividend (which is 0x^(2n-3)) and repeat steps 2-4 until the remainder is constant.

Since we are given that the remainder is -80, we can set the remainder equal to -80 and solve for 'n'.

-3x^(2n-2) + 0x^(2n-3) + ... = -80

Since the remainder is constant (-80), it means that all the terms with x have been canceled out in the division process. Therefore, we can deduce that the highest power of x in the divisor (x + 3) is 0.

This implies that x^(2n-2) = 0, and for any value of 'n', the exponent 2n-2 should be equal to zero. Solving this equation:

2n-2 = 0

2n = 2

n = 1

Therefore, the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

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Answer:

Step-by-step explanation:

Answer:

4x² + 24x + 36

Step-by-step explanation:

(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36

Answer:

What is Poly in gender. Gender is Gender "Female" "Non-binary" "Male". Poly is Triangle gender which means random gender.

Answer: Explanation: To find the degree of the polynomial, add up the exponents of each term and select the highest sum.

Step-by-step explanation:

Answer:

option d

Step-by-step explanation:

6-,|-2|,|-4|,5,|9|

Answer:

-6,-4,-2,5,9 =a

the answer is a

he ran a mile in 8.4 minutes. Step-by-step explanation:

Kimberly had 2 times as many marshmallows as Chris. After eating 15 each, Kimberly had 3 times as many marshmallows as Chris. Kimberly had 60 marshmallows at first.

Generally, Let's call the number of marshmallows that Kimberly had at first X.

We know that Kimberly had 2 times as many marshmallows as Chris at first, so Chris had X/2 marshmallows.

After eating 15 each, Kimberly had X - 15 marshmallows, and Chris had X/2 - 15 marshmallows.

We also know that Kimberly had 3 times as many marshmallows as Chris after eating 15 each, so

(X - 15) = 3 * (X/2 - 15).

(X - 15) - 3 * (X/2 - 15) = 0

Then, we can simplify the left side of the equation:

X - 15 - 3 * X/2 + 45 = 0

Combining like terms, we get:

-3 * X/2 + X - 15 + 45 = 0

Simplifying further:

-X/2 =-30

X = 60

Therefore, Kimberly had 60 marshmallows at first.

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Answer:160

Step-by-step explanation:

it is 160 because when you add the 1 make the 2 then add

Answer:

1,280

Step-by-step explanation:

Answer:

6x

Step-by-step explanation:

2x-5x=-3x+9x=6x

espero que esto ayude por favor marque el más inteligente

Answer:

That would be 6x :)

Step-by-step explanation:

2x-5x=-3x+9x=6x

Based on the number of upgrade options that the pickup truck can be made with by the truck company, the number of different versions that can be produced is 2,048 versions.

The number of versions of the truck that can be produced can be found by the formula:

= 2 ^ number of upgrade options available

Solving for the number of different versions of the truck that can be produced gives:

= 2¹¹

= 2,048 versions

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Answer:

the answer is c.

$85,274.94

Step-by-step explanation:

on edge

The functions are illustrations of trigonometry ratios

\(\mathbf{(a)\ cos\theta = \frac{\sqrt{15}}{5}}\)

The sine of an angle is calculated as follows

\(\mathbf{sin\theta = \sqrt{1 - cos^2\theta}}\)

So, we have:

\(\mathbf{sin\theta = \sqrt{1 - (\sqrt{15}/5)}}\)

\(\mathbf{sin\theta = \sqrt{1 - (15/25)}}\)

Take LCM

\(\mathbf{sin\theta = \sqrt{\frac{10}{25}}}\)

\(\mathbf{sin\theta = \frac{\sqrt{10}}{5}}\)

\(\mathbf{(b)\ tan\theta = \frac{\sqrt{10}}{2}}\)

The tangent of an angle is:

\(\mathbf{\ tan\theta = \frac{Opposite}{Adjacent}}\)

Using Pythagoras theorem, we have:

\(\mathbf{Hypotenuse^2 = Opposite^2 + Adjacent^2}\)

So, we have:

\(\mathbf{Hypotenuse^2 = (\sqrt{10})^2 + 2^2}\)

\(\mathbf{Hypotenuse^2 = 10 + 4}\)

\(\mathbf{Hypotenuse^2 = 14}\)

Take square roots

\(\mathbf{Hypotenuse = \sqrt{14}}\)

So, the sine of the angle is:

\(\mathbf{\ sin\theta = \frac{Opposite}{Hypotenuse}}\)

\(\mathbf{\ sin\theta = \frac{\sqrt{10}}{\sqrt{14}}}\)

Rationalize

\(\mathbf{\ sin\theta = \frac{\sqrt{140}}{14}}\)

\(\mathbf{(c)\ csc\theta = \frac{\sqrt{15}}{3}}\)

The sine of the angles is:

\(\mathbf{sin \theta = \frac{1}{csc\theta}}\)

So, we have:

\(\mathbf{sin \theta = \frac{1}{\sqrt{15}/3}}\)

\(\mathbf{sin \theta = \frac{3}{\sqrt{15}}}\)

Rationalize

\(\mathbf{sin \theta = \frac{3\sqrt{15}}{15}}\)

\(\mathbf{sin \theta = \frac{\sqrt{15}}{5}}\)

\(\mathbf{(d)\ sec\theta =\frac{\sqrt 6}{3}}}\)

The sine of an angle is calculated as follows

\(\mathbf{sin\theta = \sqrt{1 - (1/sec\theta)^2}}\)

So, we have:

\(\mathbf{sin\theta = \sqrt{1 - (3/\sqrt 6)^2}}\)

\(\mathbf{sin\theta = \sqrt{(1 - 9/6)}}\)

\(\mathbf{sin\theta = \sqrt{( - 3/6)}}\)

The sine of the angle does not have a real value

\(\mathbf{(e)\ cot\theta = \frac{\sqrt 6}{2}}\)

Start by calculating the tangent of the angle

\(\mathbf{tan\theta = \frac{1}{cot\theta}}\)

So, we have:

\(\mathbf{tan\theta = \frac{1}{\sqrt 6/2}}\)

\(\mathbf{tan\theta = \frac{2}{\sqrt 6}}\)

Rationalize

\(\mathbf{tan\theta = \frac{2\sqrt 6}{6}}\)

\(\mathbf{tan\theta = \frac{\sqrt 6}{3}}\)

The tangent of an angle is:

\(\mathbf{\ tan\theta = \frac{Opposite}{Adjacent}}\)

Using Pythagoras theorem, we have:

\(\mathbf{Hypotenuse^2 = Opposite^2 + Adjacent^2}\)

So, we have:

\(\mathbf{Hypotenuse^2 = (\sqrt{6})^2 + 3^2}\)

\(\mathbf{Hypotenuse^2 = 6 + 9}\)

\(\mathbf{Hypotenuse^2 = 15}\)

Take square roots

\(\mathbf{Hypotenuse = \sqrt{15}}\)

So, the sine of the angle is:

\(\mathbf{\ sin\theta = \frac{Opposite}{Hypotenuse}}\)

\(\mathbf{\ sin\theta = \frac{\sqrt{6}}{\sqrt{15}}}\)

Rationalize

\(\mathbf{\ sin\theta = \frac{\sqrt{90}}{15}}\)

Rewrite as:

\(\mathbf{\ sin\theta = \frac{3\sqrt{10}}{15}}\)

\(\mathbf{\ sin\theta = \frac{\sqrt{10}}{5}}\)

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Using simple interest, it is found that the principal loan amount was of $156,491.6.

The amount of money after t years in simple interest is modeled by:

\(A(t) = A(0)(1 + rt)\)

In which:

In this problem, she paid $984 monthly for 22 years, hence:

\(t = 22, A(t) = 984(22)(12) = 259776\)

Interest rate of 3%, hence \(r = 0.03\)

Then:

\(A(t) = A(0)(1 + rt)\)

\(259776 = A(0)[1 + 0.03(22)]\)

\(A(0) = \frac{259776}{1 + 0.03(22)}\)

\(A(0) = 156491.6\)

The principal loan amount was of $156,491.6.

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Expected Sales for a store with the competitor's previous day's sale of $5000 is 561.2 thousand

An equation is an expression that shows the relationship between two or more numbers and variables.

We have been given that Regression line :

y'= 50 - 3x + 20x² + 10x³

where,

x: competitor's previous day's sales (in $1000s)

x²: population within 1 mile (in 1000s)

x³: ​1 if any radio advertising was used and 0 otherwise.

y' = sales (in $1000s)

Also, x (competitors) = 3 ,

x² (population) = 5100 = 5.1 thousands ,

x³ (nodrive-upp window) = 0

Therefore, we get;

y = 50 - 3(3) + 20(5.1)² + 10(0)³

y = 50 - 9 + 520.2

y = 561.2 thousand

y [ Expected Sales ] is 561.2 thousand

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The input is 8, the output of the function f(x) would be -5.

What is the function?

Function is a relationship or expression involving one or more variables.  It has a set of input and outputs.

Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet

To find the output of the function f(x) when x is 8, we substitute x = 8 into the function and simplify:

f(x) = 8/x - 6

f(8) = 8/8 - 6

f(8) = 1 - 6

f(8) = -5

Hence, if the input is 8, the output of the function f(x) would be -5.

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Answer:

Step-by-step explanation:

Answer:

5,040,300 is the standard form

Step-by-step explanation:

Answer:

-4.4c+1.1

Step-by-step explanation:

There are a total of 3 forwards on the team.

A fraction represents a part of the whole or group of objects.In a fraction, numerator and denominator are separated by a horizontal bar known as the fractional bar

Given:

2/8 of the players are forwards.

Total number of players on the team = 12

We will determine the total number of forwards on the team by multiplying the total number of players by the fraction representing the forwards.

Fraction representing the forwards:

= 2/8

= 1/4

Total forwards on the team:

= 12 * (1/4)

= 3.

Translated question:

Of the 12 players on the team, 2/8 are forwards. What are the total forward in the team?

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Answer:

(3x-2)(X+4)

X=2/3,-4

Step-by-step explanation:

3x^2 + 10x = 8

3x^2+12x-2x-8=0

3x(X+4)-2(X+4)=0

(3x-2)(X+4)=0

X=2/3,-4

So the solution is 2/3,-4

Answer:

answer attached

Step-by-step explanation:

answer attached

hope this helps!

Answer:

she filled 80 pages with 5 left over

Step-by-step explanation:

Answer:

(2a^3a^4)^5 simplifies to 32a^35.

Step-by-step explanation:

To simplify (2a^3a^4)^5, we can use the properties of exponents which states that when we raise a power to another power, we can multiply the exponents. Therefore, we can rewrite the expression as:

(2a^3a^4)^5 = 2^5 * (a^3a^4)^5

Next, we can simplify the expression inside the parentheses by multiplying the exponents:

a^3a^4 = a^(3+4) = a^7

Substituting this into our expression, we get:

(2a^3a^4)^5 = 2^5 * (a^3a^4)^5 = 2^5 * a^35

Finally, we can simplify this expression by using the property of exponents that states that when we multiply two powers with the same base, we can add their exponents. Therefore, we can rewrite the expression as:

2^5 * a^35 = 32a^35

Therefore, (2a^3a^4)^5 simplifies to 32a^35.

To calculate the mean, median, and mode, we first need to know what each of these terms represents. The mean, also known as the average, is the sum of all the values divided by the total number of values. To find the mean, add up all of the values and divide by the number of values. The median is the middle value in a set of data when it is arranged in order from least to greatest. The mode is the value that occurs most frequently in a set of data. Here's an example to illustrate these concepts:

Let's say we have a set of data consisting of the following values: 2, 5, 5, 7, 8, 10, 12. To find the mean, we add up all of the values and divide by the number of values. In this case, the sum of the values is 49 (2+5+5+7+8+10+12) and there are 7 values, so we divide 49 by 7 to get the mean, which is approximately 7. To find the median, we first need to arrange the data in order from least to greatest: 2, 5, 5, 7, 8, 10, 12. The middle value is 7, so that is the median. To find the mode, we look for the value that occurs most frequently. In this case, 5 occurs twice, which is more than any other value, so the mode is 5.
In conclusion, the mean, median, and mode are all measures of central tendency that can be used to describe a set of data. The mean is the average value, the median is the middle value, and the mode is the value that occurs most frequently. When calculating these measures, it is important to carefully consider the data and choose the appropriate method for finding each value.

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The fraction of the area of the tray occupied by the blondies is 1/9.

To find the fraction of the area of the tray occupied by blondies, we need to determine the area occupied by the blondies and compare it to the total area of the tray.

Let's calculate the area of each individual blondie:

The blondies are squares with 3-inch sides, so the area of each blondie is 3 inches × 3 inches = 9 square inches.

Now, let's calculate the area occupied by the blondies in each row:

Since there are 4 rows of blondies and each row contains 4 blondies, the total number of blondies is 4 rows × 4 blondies per row = 16 blondies.

So, the total area occupied by the blondies is 16 blondies × 9 square inches per blondie = 144 square inches.

Next, let's determine the area occupied by the brownies:

The brownies are squares with 6-inch sides, so the area of each brownie is 6 inches × 6 inches = 36 square inches.

Since there are also 4 rows of brownies and each row contains 4 brownies, the total number of brownies is 4 rows × 4 brownies per row = 16 brownies.

Therefore, the total area occupied by the brownies is 16 brownies × 36 square inches per brownie = 576 square inches.

Now, let's calculate the total area of the tray:

Given that the tray is completely full and has an area of 648 square inches, we can subtract the area occupied by the brownies from the total area to find the remaining area occupied by the blondies:

Total area of the tray - Area occupied by the brownies = Area occupied by the blondies

648 square inches - 576 square inches = 72 square inches.

So, the fraction of the area of the tray occupied by the blondies is:

Area occupied by the blondies / Total area of the tray = 72 square inches / 648 square inches.

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 72 in this case:

72 square inches / 648 square inches = 1/9.

Therefore, the blondies' percentage of the tray's surface area is 1/9.

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a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)

b. The increase in cost between 12 noon and 3 pm is $2.

c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.

The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.

We can represent it as (8am, 9am) U (11am, 12pm).

It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).

And stays constant at : (9am, 10am) U (10am, 11am)

We simply deduct the 12pm's cost from 3pm's cost.

So, we have

Cost increase = $3.5 - $1.5

Evaluate the difference

Cost increase = $2

Hence, the cost increase is $2

When you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

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The required equation of the function shown in the graph is y = |x - 4|.

Given that,
To determine the equation of the function shown in the graph.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
As we can see, the graph is of the aboslute value function,
y = |x|
And it is vertex is located at (4, 0)
So the transformation in the function is given as,
y - 0 = |x - 4|
y = |x - 4|

Thus, the required equation of the function shown in the graph is y = |x - 4|.

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Step-by-step explanation:

The probability that Becky's proportion of poses held for over a minute is greater than Carla's is 0.741.

This can be determined by using the z-table, which shows the probability that a random variable is in the range that is a certain distance away from the mean.

In this case, we are looking at the probability that a random variable is greater than C, so we use the z-value for 0.741.