Simplify the expression. Assume that x is nonzero. Your answer should have only positive exponents.
Equation:
x^-10 · x^6
Please help me out.

Answer: O A.52 cubic yards

Step-by-step explanation: if u add 3+9+4+8+6+22= 52 cubic yards in the total volume of the figure :>

5/3 (a)(x)(b)(xx)(c)(a^3)

5/3 (a^4)(b)(c)(x^3)

-2.07 (a^2)(x^3)(a^2)(b)

-2.07 (a^4)(b)(x^3)

-7/6 (a^2)(x^3)(c)(a^2)(b)

-7/6 (a^4)(b)(c)(x^3)

Notice that only the first and third monomials (when simplified) contain the exact same variables with the same exponents. Therefore, those are the only two monomials we can add together.

(10/6 - 7/6)(a^4)(b)(c)(x^3) - 2.07(a^4)(b)(x^3)

(1/2)(a^4)(b)(c)(x^3) - (2.07)(a^4)(b)(x^3)

(a^4bx^3)(1/2c - 2.07) --- Factored form

Since this expression has two terms, it is a binomial.

Hope this helps!! :)

when the time is between 0 and 15 minutes, the distance depends on the time on a relation: d =(1/10)t

when the time is between 15 and 40 minutes, the distance is independent of the time, it is fixed d = 1.5 miles

when the time is between 40 and 50 minutes, the distance depends on the time on the relation: d = 1.5 + (1/10)(t - 40)

If a bicycle is traveling at 12 miles per hour, then it will cover a distance of 704 feet in 40 seconds.

To find the distance covered in feet in 40 seconds, follow these steps:

Hence, the bicycle will cover 704 feet in 40 seconds

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Answer:

3.9 hours

Step-by-step explanation:

3 2/5 + 1/2 = 39/10

3 9/10 =

3.9 hours

Based on the stem- and-leaf plot which indicates the scores of 50 students, the number of students that scored 22 is 1. (Option B).

A stem and leaf plot is a simple type of graph composed entirely of integers.

It is a method of illustrating the major characteristics of a distribution.

When a stem and leaf plot is flipped over, it resembles a bar graph or histogram and provides similar visual information.

A stem and leaf plot divides each data value into a leaf (the final number) and a stem (the other digits).

For instance, 12 on the stem and 7 on the leaf read as 127, and 127 is written using the stem and leaf plot key 12 I 7.

So, in this situation, in search of 22, we have:

The number of pupils who scored 22 is given as 2 on the stem and 2 on the leaf on the right side.

The total number of digits on the right also tells us how many students there were.

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Given the following equation:

You can solve for "x" by following these steps:

1. You must distribute the negative sign of the left side of the equation:

2. Now you need to add the like terms of the left side of the equation:

3. Apply the Subtraction property of equality by subtracting 7 from both sides of the equation:

4. Finally, you can apply the Division property of equality by dividing both sides of the equation by -2:

The answer is:

See attachment for the graph of the function g(x)=log4(x-1)+2

The equation of the logarithmic function is given as

g(x)=log4(x-1)+2

The parent function of the above logarithmic function is

f(x) = log4(x)

This means that the parent function is translated right by 1 unit and translated up by 2 units

Next, we plot the graph of the function g(x)=log4(x-1)+2

See attachment for the graph of the function g(x)=log4(x-1)+2

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a) the series converges when |x| < 1, the interval of convergence is (-1, 1) in interval notation.
b) the series converges for all x, the interval of convergence is (-∞, ∞) in interval notation.

c) both the Ratio Test and the Root Test yield the same result for the radius of convergence, but the Root Test is simpler to use

What does convergence mean?

The ability to go closer to a limit as a function's argument changes or grows or as the number of terms in the series does is a property (exhibited by some infinite series and functions).

(a) Using the Ratio Test:

We have the series\(∑(k=0)^{\infty} x^k / (4k(k+7)).\)

Let's apply the Ratio Test:

\(lim(k - > \infty) |(x^{(k+1)} / (4(k+1)((k+1)+7))) / (x^k / (4k(k+7)))|\)

Simplifying the expression, we get:

\(lim(k - > \infty) |x^{(k+1)} / (4(k+1)(k+8))| * |4k(k+7) / x^k|\)

The absolute values and constants cancel out, resulting in:

\(lim(k- > \infty) |x / ((k+1)(k+8))|\)

As k approaches infinity, both (k+1) and (k+8) approach infinity, and the expression becomes:

\(lim(k - > \infty) |x / (k^2 + 9k + 8)|\)

To find the limit, we can focus on the highest power term in the denominator, which is k². Dividing both the numerator and denominator by k², we get:

lim(k→∞) |x / (1 + 9/k + 8/k²)|

As k approaches infinity, the terms 9/k and 8/k² both approach zero, and the expression becomes:

lim(k→∞) |x / 1| = |x|

For the series to converge, |x| must be less than 1. Therefore, the radius of convergence, R, is 1.

To find the interval of convergence, we consider the values of x for which the series converges.

Since the series converges when |x| < 1, the interval of convergence is (-1, 1) in interval notation.

(b) Using the Root Test:

We have the series ∑(k=0)^(∞) x^k / (4k(k+7)).

Let's apply the Root Test:

lim(k→∞) (|x^k / (4k(k+7))|)^(1/k)

Simplifying the expression, we get:

lim(k→∞) (|x / (4k(k+7))|)^(1/k) * |x / (4k(k+7))|^(1/k)

The limit of (1/k) as k approaches infinity is 0, so the expression becomes:

lim(k→∞) (|x / (4k(k+7))|)^(0) * |x / (4k(k+7))|

Simplifying further:

lim(k→∞) |x / (4k(k+7))|

As k approaches infinity, the denominator becomes large, and the expression approaches zero. Thus, the limit is:

lim(k→∞) |x / (4k(k+7))| = 0

For the series to converge, the limit must be less than 1. However, the limit is always 0, which is less than 1 for all values of x. Therefore, according to the Root Test, the radius of convergence, R, is infinite (∞).

Since the series converges for all x, the interval of convergence is (-∞, ∞) in interval notation.

(c) In this case, both the Ratio Test and the Root Test yield the same result for the radius of convergence, but the Root Test is simpler to use.

The Root Test only involves taking the limit of the absolute value of the terms raised to the power of 1/k, whereas the Ratio Test requires taking the ratio of consecutive terms and evaluating a limit involving

hence, a) the series converges when |x| < 1, the interval of convergence is (-1, 1) in interval notation.
b) the series converges for all x, the interval of convergence is (-∞, ∞) in interval notation.

c) both the Ratio Test and the Root Test yield the same result for the radius of convergence, but the Root Test is simpler to use

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Answer:

507.79cm^3

Step-by-step explanation:

Diameter=9.9 cm

Radius=diameter/2

=9.9/2

=4.95 cm

Volume of a sphere=4/3πr^3

=4/3×3.14×4.95^3

=4/3×3.14×121.287375

=1,523.36943/3

=507.78981 cm^3

Approximately

507.79cm^3

Answer:

508.0 cm ^3

Step-by-step explanation: 4/3π(4.95)^3=508

Answer:

36

Step-by-step explanation:

12 x 3 =36

Answer:

36 kilometers or 22.4 miles

Step-by-step explanation:

12 kmh times 3 equals 36

Where the above conditions are given,  the correct option is: Plan 1 is a better deal for more than 5 cards purchased.

To determine   which pricing plan is a better deal,we need to compare the total cost for a certain number of game cards purchased.

Let's calculate the   total cost for different numbers  of game cards.

For Plan 1  -

- Admission fee  - $5 (fixed)

- Cost per game card  - $1

For Plan 2  -

- Admission fee  - $2.50 (fixed)

- Cost per game card  - $1.50

Now, let's compare the total cost for different numbers of game cards  -

1. If you purchase 1 game card  -

  - Plan 1  - $5 (admission fee) + $1 (cost per game card) = $6

  - Plan 2  - $2.50 (admission fee) + $1.50 (cost per game card) = $4

2. If you purchase 5 game cards  -

  - Plan 1  - $5 (admission fee) + $5 (cost for 5 game cards) = $10

  - Plan 2  - $2.50 (admission fee) + $7.50 (cost for 5 game cards) = $10

3. If you purchase 8 game cards  -

  - Plan 1  - $5 (admission fee) + $8 (cost for 8 game cards) = $13

  - Plan 2  - $2.50 (admission fee) + $12 (cost for 8 game cards) = $14.50

Based on these calculations, we can conclude that  -

- Plan 1 is a better deal for more than 5 cards purchased.

- Plan 2 is a better deal for more than 8 cards purchased.

Therefore, the correct option is  - Plan 1 is a better deal for more than 5 cards purchased.

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Answer:

1st answer choice

no because there is no whole number that when multiplied by itself gives 125

Step-by-step explanation:

125 is a perfect cube

5 times 5 times 5 = 125

Answer:

Option A

Step-by-step explanation:

125 is NOT a perfect square, because there is no whole number that multiplies by itself to give 125.

To check the perfectness of a square, take the square root:

\(\sqrt{125} =\) 11.1803399

The above number is NOT a whole number

∴125 is NOT a perfect square

The total amount of time Martina spent doing these two assignments will be 13/20 Hr.

Total time taken by Martina to complete her chemistry assignment = (2/5) Hr.

Total time taken by the Martina to complete her maths assignment = (1/4) Hr.

One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.

So, for determining the total amount of time martina spent doing these two assignment, we need to add the value of time taken by her in completing both the assignment.

So, the value of total amount of time taken by Martina for completing both the assignment will be = (2/5)+)1/4) Hr.

=(8+5)(20)=13/20 Hr.

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Answer:

\(P=\frac{1}{8}\)

Step-by-step explanation:

You're given your variables, you just need to put them in the correct spot. X is on top, and x =1, replace x with 1. Y is on the bottom and y=8, replace y with 8.

If I helped, a brainliest answer would be greatly appreciated!

Answer:

a = 10, b = 5, c = 14, d = 25

Step-by-step explanation:

Plug in -2 for x ....

y = 2(-2)^2 + -2 + 4

y = 2(4) + 2

y = 10

Plug in -1 for x ....

y = 2(-1)^2 + -1 + 4

y = 2(1) + 3

y = 5

Plug in 2 for x ....

y = 2(2)^2 + 2 + 4

y = 2(4) + 6

y = 8 + 6

y = 14

Plug in 3 for x ....

y = 2(3)^2 + 3 + 4

y = 2(9) + 7

y = 18 + 7

y = 25

Answer:

I believe its 3.4-?

Step-by-step explanation:

When a 3-by-3-inch square is placed next to a 10-by-10-inch square, the resulting region will have a surface area of 109 inches².

The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.

Here,

length of side=3 inch

length of side=10 inch

Total area= area of square 1 + area of square 2

=(3*3)+(10*10)

=9+100

=109 inch²

The area of resulted region will be 109 inch² when 3 inch by 3 inch square adjoins a 10-inch by 10-inch square.

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the matches are

-2(2x+5) ≤ -7(x+4)         x<=-6

4x-3x-1                          x<=-1

5(x-3)9(x+1)                   x>=-6

3(x-4)+5 2x-9                x>=-2

Generally, Inequality is a mathematical statement that compares two values or expressions and indicates whether they are equal or not equal, or which one is greater or smaller. Inequalities are expressed using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

For example, 5 < 8 is an inequality that indicates that 5 is less than 8, and x + 3 ≥ 7 is an inequality that indicates that the value of x plus 3 is greater than or equal to 7.

Inequalities are commonly used in algebra and other branches of mathematics to represent relationships between quantities.

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The correct matching of the inequalities can be shown from the calculations below

Inequalities are an important tool in mathematical modeling and optimization problems, where they are used to express constraints and objective functions.

Using the principle of inequalities we have;

1) -2(2x + 5) ≤ - 7(x + 4)

-4x -10 ≤ -7x -28

-4x +7x ≤ -28 + 10

3x ≤ -18

x ≤ -6

2) 4x - 6/2 ≥ 3x - 1

4x - 6 ≥ 6x - 2

4x - 6x ≥ -2 + 6

-2x ≥ 4

x  ≤ -2

3) 5(x - 3) ≤ 9(x + 1)

5x - 15  ≤ 9x + 9

5x - 9x  ≤ 9 + 15

-4x  ≤ 24

x ≥ -6

4) 3(x - 4) + 5 ≥ 2x - 9

3x - 12 + 5≥ 2x - 9

3x - 2x ≥ -9 + 12 -5

x ≥ -2

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Answer:

d. 20°

Step-by-step explanation:

First, we need to solve for m<Q

m<Q+m<R+m<S=180°

where m<R=90° and m<S=70°

m<Q+90°+70°=180°

m<Q=20°

Since m<Q=m<M

Then, m<M=20°

Answer:

he starts with 22 eats 2

22-2=20

he can give each friend 4 cookies because 4*5 is 20

Answer: about 2.2 times 8^8

Step-by-step explanation:

Pay the money x=y^2

Answer:

1) 6.438km 2)818,700m 3)6750cm

Answer:

.

Step-by-step explanation:

we are asked to write an expression that shows how to multiply 4 and 362 using place value ans expanded form. The expanded form of 362 is 300 + 60+ 2. IN this case, the expression is 4*(300 +60+ 2) that is we distribute 4 to the numbers inside that is 1200 + 240 + 8 equal to 1448

Answer:

x = - 3/2

(the dash by the 3/2 is to show that it is negative, and is part of the answer)

Answer:

x= -3/2

Step-by-step explanation:

Answer:

The final balance is $4,353.56.

The total compound interest is $1,153.56.

Step-by-step explanation:

Shimano Pty Ltd needs to sell a minimum of 300 fishing rods in 2021.

In 2021, Shimano Pty Ltd, a custom fishing rod manufacturer, sells each rod for $900. The variable costs associated with producing each rod amount to 60% of the selling price, which is $540 per rod. Additionally, the business incurs fixed costs of $108,000 for the year.

To calculate the total cost per rod, we need to consider both the variable and fixed costs. The variable cost per rod is $540, and the fixed costs for the year are $108,000. Since the fixed costs are independent of the number of rods produced, they can be spread across the total number of rods manufactured.

To determine the breakeven point, we need to find the number of rods that need to be sold to cover the total costs. The breakeven point can be calculated by dividing the total fixed costs by the contribution margin, which is the selling price minus the variable cost per unit. In this case, the contribution margin is $360 ($900 - $540).

Breakeven Point = Total Fixed Costs / Contribution Margin

Breakeven Point = $108,000 / $360

Breakeven Point = 300 rods

To cover the fixed costs and start generating a profit, Shimano Pty Ltd needs to sell a minimum of 300 fishing rods in 2021.

It's important for the company to keep track of its costs, particularly the variable costs, and carefully consider its pricing strategy to ensure profitability and sustainability in the market.

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55 pounds is approximately equal to 25 kilograms.

To convert 55 pounds to kilograms, we can use the fact that 1 pound is approximately equal to 0.453592 kilograms:

55 pounds ≈ 55 × 0.453592 kilograms/pound

≈ 24.94756 kilograms

Rounding this value to the nearest kilogram gives:

≈ 25 kilograms

what is kilograms?

Kilogram is a unit of measurement for mass in the metric system. It is defined as the mass of a particular cylinder of platinum-iridium alloy that is kept at the International Bureau of Weights and Measures in France. This definition of the kilogram was adopted in 1889 and is still in use today.

The kilogram is commonly used to measure the mass of objects, such as people, animals, and products, in many countries around the world. It is abbreviated as "kg".

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Answer:

\(\sqrt{9}+\sqrt{25}=8\)

Step-by-step explanation:

\(\sqrt{9}+\sqrt{25}\)

\(3+5\)

\(8\)

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

The given expression is equivalent to :

\( \large \boxed{ \mathfrak{Step\;\: by\:\; Step \:\:Explanation}}\)

\(\mathrm{✌TeeNForeveR✌}\)

Answer:

angle between the ladder and the ground = 89.1°

Step-by-step explanation:

Go to the image below to get the visualisation for what's actually happening in the question and what they have asked for.

We are provided with adjacent which is 1.75 meters and hypotenuse with 110m and asked to find angle between the ladder and the ground.

Here, we will take angle between ground and ladder as x.

using sohcahtoa method,

\(\frac{adjacent}{hypotenuse} = cosx\)

\(\frac{1.75}{110} = cosx\)

\(x = cos^{-1} (\frac{1.75}{110}) \)

x = 89.1°