Choose the correct simplification of x to the 2nd power over y to the 5th power all raised to the 4th power. (5 points)

x to the 8th power over y to the 9th power
y12
x12y8
x to the 8th power over y to the 20th power

Final answer:

The goal of solving equations with variables on both sides or multi-step equations is to isolate and solve for the variable. Operations such as addition, subtraction, multiplication, and division are used to maintain equation balance and eliminate terms, which is necessary for solving any algebraic equation. The process involves careful step-by-step simplification, including dealing with multiple variables when necessary.

Explanation:

The goal of solving equations with the variable on each side is essentially the same as solving multi-step equations because in both scenarios, we aim to isolate the variable to find its value. When we encounter an equation with variables on both sides, we usually perform operations to get all variable terms on one side and constant terms on the other. This often involves addition or subtraction to eliminate terms and then the use of multiplication or division to isolate the variable. This process aligns with the steps taken in solving multi-step equations, where we also combine like terms, use inverse operations, and apply the distributive property if necessary.

Multiplication or division by the same number on both sides of an equation maintains equality, which is a fundamental principle in algebra. For an equation with more than one term on either side, it is important to enclose the side with more terms in brackets before applying a multiplication or division operation to ensure the operation is distributed to each term within the brackets. By doing so, we preserve the balance of the equation while simplifying it step by step toward finding the unknown value.

When faced with an equation containing more than one variable, our objective is to use algebra to determine the remaining unknowns. This could involve solving simultaneous equations or manipulating a single equation to isolate the variable of interest. In more complex scenarios involving several unknowns, finding a set of equations that each contain only one unknown becomes essential, and careful consideration of physical principles or context may guide us in selecting the right equations to solve for the variables in question.

Answer:

[tex]\text{64 must be added to the expression }x^2 + 16x\text{ to make it a perfect-square trinomial}[/tex]

Step-by-step explanation:

Given the expression

[tex]x^2+16x[/tex]

we have to tell which value must be added to the above expression to make it a perfect-square trinomial.

Expression: [tex]x^2+16x[/tex]

By completing the square method,

The square of half of the coefficient of x must be added , we get

[tex]x^2+16x+64[/tex]

[tex]x^2+8x+8x+64[/tex]

[tex]x(x+8)+8(x+8)[/tex]

[tex](x+8)^2[/tex]

which is a perfect square.

[tex]\text{Hence, 64 must be added to the expression }x^2 + 16x\text{ to make it a perfect-square trinomial}[/tex]

Answer:

I believe it is The Multiplication Property of Equality

Step-by-step explanation:

Since "x" is being divided by 6, we need to do the opposite!

Answer:

multiplication

Step-by-step explanation:

since x/6 is a fraction and fractions represent division we would havw to do the opposite to isolate the x variable. pLeAsE mArK bRaInLiEsT

The inequality that represents the numbers of both kinds of CD players that can be sold to reach or exceed the sales target is:

[tex]\[ 72s + 90p \geq 360 \][/tex]

To write an inequality that represents the sales target, we need to consider the profit made from each type of CD player and the total profit required per day.

Let [tex]\( s \)[/tex] represent the number of standard CD players sold, and [tex]\( p \)[/tex] represent the number of portable CD players sold. According to the information given, the store makes a profit of $72 for every standard CD player and $90 for every portable CD player.

The manager's target is to make at least $360 a day from the sales of these CD players. To find out how many of each type of CD player need to be sold to meet this target, we can set up the following inequality:

[tex]\[ 72s + 90p \geq 360 \][/tex]

Here, [tex]\( 72s \)[/tex] represents the total profit from standard CD players, and [tex]\( 90p \)[/tex] represents the total profit from portable CD players. The sum of these two amounts must be greater than or equal to the target profit of $360.

This inequality accounts for all possible combinations of standard and portable CD players that can be sold to meet or exceed the daily profit target. It is important to note that the inequality uses the  greater than or equal to  symbol [tex](\( \geq \))[/tex] because the store wants to make at least $360, and any amount over that is also acceptable.

The answer is 22 add

The process of transformation under translation means that the figure is simply change into another position. That is, the angles, the lengths or any other characteristic is unchanged except for the position of the figure in the Cartesian coordinate alone.
We are given the function in the form of:

f(x) = x^2

Which can also be written as:

y = x^2

Since the translation made is to move the figure 7 units up, then this means that the y coordinate is increased by 7. The given equation is a parabola pointing up with vertex at (0, 0). So moving it up would move the vertex at point (0, 7). The vertex of y is represented by the variable b, therefore b = 7 which further gives us the function:

y' = x^2 + 7

or

g(x) = x^2 + 7

Answer:

Step-by-step explanation:

cot(x) can be written as

[tex]cot(x) =\frac{cosx}{sinx}[/tex]

Here we have [tex]cot(\frac{2x}{3}[/tex]

so It will be undefined whenever

[tex]sin(\frac{2x}{3}) = 0[/tex]

As we cannot have a 0 in the denominator .

so to point all the discontinuties we need to identify the x values where

[tex]sin (\frac{2x}{3} ) = 0[/tex]

[tex]\frac{2x}{3} = 0 + \pi k[/tex] where k is any integer

[tex]x= \frac{3\pi }{2} k[/tex]

It means f(x) is discontinuous at all the values of [tex]x = \frac{3\pi }{2}k[/tex]

for k = 0 , 1 ,2.....

You need to look at each term and find the degree by adding the exponents of each variable in it. The largest degree is the degree of the polynomial.

The polynomial has 2 terms, so it's binomial  ← classification 

25.

 answer is B since it is adding he amount of the bill with the amount of the tip.

 the other 3 will all calculate just the amount of the tip

26

3x-4 needs to equal or be below 8

rearrange the formula to 3x,=8+4

so 3x<=12

12/3 = 4

 so x <= 4 to satisfy the inequality

so answer is A

Answer:

(a) [tex]\text{New Price}=0.96\times \text{Original Price}[/tex]

(b) The new price of car is $43584.

Step-by-step explanation:'

(a)

The original price of car is $45400.

It is given that the car dealership decreased the price of a certain car by 4%.

[tex]\text{New Price}=\text{Original Price}-\frac{4}{100}\times \text{Original Price}[/tex]

[tex]\text{New Price}=(1-\frac{4}{100})\times \text{Original Price}[/tex]

[tex]\text{New Price}=\frac{96}{100}\times \text{Original Price}[/tex]\

[tex]\text{New Price}=0.96\times \text{Original Price}[/tex]

(b)

Using part (a), we get

[tex]\text{New Price}=0.96\times \text{45400}[/tex]

[tex]\text{New Price}=43584[/tex]

Therefore the new price of car is $43584.

The formula for the new price is New Price = 0.96 x 45400, while the value of the new price of the car is $43,584

From the question, we have:

Original price = $45,400

Rate decreased = 4%

The new price would be calculated using:

New Price = (1 - Rate) x Original price.

So, we have:

New Price = (1 - 4%) x Original price

Express the percentage as decimal

New Price = (1 - 0.04) x Original price.

So, we have:

New Price = 0.96 x 45400

In (a), we have:

New Price = 0.96 x 45400

Evaluate

New Price = 43584

Hence, the new price of the car is $43,584

Read more about percentage change at:

https://brainly.com/question/386302

PART A) the initial value of the function is 150 at 0 weeks, that means that there are still 150 songs to be downloaded at the beginning.
The rate of change is -30 songs each week, that is because the amount of songs left to be downloaded decrease by 30 each week.

PART B:
lets use 2 points of the graph p1(0, 150), p2(1, 120)
calculate the slope:
m = (y2- y1)/(x2 - x1) = (120 - 150)/(1 - 0)
m = -30
and now use line equation in form point-slope:
y - y1 = m(x - x1)
y - 150 = -30(x - 0)
y = -30x + 150

2nd picture: for bushels of corn

 Part A, looking at the line in the graph, you can see the line falls on 2 bushes cost $16, 4 bushels cost $31, etc., using that information you can calculate that 1 bushel of corn costs $8, ( 16/2 = 8, 32/4 = 8)

 PART B

 using the table for previous years you can calculate corn cost $6 a bushel ( 12/2=6)

 so corn cost $2 more this year.

Answer: 3125

Step-by-step explanation:

Given: A fair sortition trial is carried out, and one of the candidates is assigned the number = 32,041

If each digit can be chosen from 0-4, and if each of the possible sequences is assigned to a candidate, then the number of candidates (repetition of digits allowed)=[tex]5\times5\times5\times5\times5[/tex]

[tex]=3125[/tex]

Hence, the number of candidates there are = 3125.

The triangle with side lengths of 32, 60, and 68 is a right triangle is true.

A triangle is a three-sided polygon that consists of three edges and three vertices.

We can use the Pythagorean theorem to check if a triangle with side lengths of 32, 60, and 68 is a right triangle:

a² + b² = c²

where a, b, and c are the side lengths of the triangle and c is the hypotenuse.

Plugging in the values, we get:

32² + 60² = 68²

Simplifying:

1024 + 3600 = 4624

So, the equation holds true, which means that the triangle with side lengths of 32, 60, and 68 is a right triangle.

To learn more on Triangles click:

https://brainly.com/question/2773823

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Answer: Our required probability is 0.34.

Step-by-step explanation:

Since we have given that

Number of seventh grade student s= 21

Number of eight grade students = 14

Number of ninth grade students = 7

Total number of boys and girls = 42

Probability of an eigthth grader winning the competition would be

[tex]\dfrac{14}{42}\\\\=\dfra{1}{3}\\\\=0.3333333..................\\\\\approx 0.34[/tex]

Hence, our required probability is 0.34.

16g+4

4(4g+1)

49-14h

7(7-2h)