What is the vertex of the absolute value function below?
(4, –1)

(1, –4)

(1, 4)

(4, 1)

Answer:

Hey I am also taking the k12 interim right now and I also think the answer is a.

Step-by-step explanation:

The starting balance was at $50 then it gradually started to increase by $100 with each deposit. So you're answer is a.

Check it out yourself and see that the balance is increasing by $100 dollars with each deposit.

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:)

Answer:

C. [tex]\sqrt{x}+3=13[/tex]

Step-by-step explanation:

We know that,

A radical equation is the equation in which the variable is under the radical.

According to the options, we see that,

In the equation [tex]\sqrt{x}+3=13[/tex], the variable is under the radical.

All other equations have constant number under the radical.

Thus, we get,

Equation C i.e. [tex]\sqrt{x}+3=13[/tex] is a radical equation.

[tex]\fbox{\text{Option C}}[/tex] is correct as [tex]\sqrt x+3 = 13[/tex] is radical equation because the variable is under the radical and the radicand is [tex]x[/tex].

Further explanation:

Radical can be describing as a square root, a cube root, a fourth root or higher root.

Radical equation can be defined as any equation that contains a radical on the variable is known as the radical equation.

The term under the radical symbol is known as radicand.

Option A is not correct.

Here, [tex]x\sqrt 3= 13[/tex] is not radical equation because the radical is on a constant term 3 not on the variable.

Option B is not correct.

Here, [tex]x+\sqrt 3=13[/tex] is not radical equation because the radical is on a constant term 3 not on the variable.

Option C is correct.

Here, [tex]\sqrt x+3=13[/tex] is radical equation because the variable is under the radical and the radicand is  .

Option D is not correct.

Here,  [tex]x+3 =\sqrt {13}[/tex] is not radical equation because the variable is not under the radical.

The equation [tex]\sqrt x+3=13[/tex] is a radical equation. Therefore [tex]\fbox{\text{Option C}}[/tex] is correct.

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Number system

Keywords: functions, equation, radical equation, radical, square root, cube root, fourth root, variable, radicand, term, under, contains describe.

Final answer:

Compound interest and exponential growth both involve the concept of compounding, where growth is based on previous amounts. Compound interest refers to interest earned on past interest, causing savings to grow over time. Similarly, compound growth rates result in exponential growth.

Explanation:

The relationship between compound interest and exponential growth is that they both involve the concept of compounding, where the growth or increase is based on previous amounts. Compound interest refers to the interest earned on past interest, causing the total amount of financial savings to grow over time. Similarly, compound growth rates mean that the rate of growth is multiplied by a base that includes past growth, resulting in an exponential growth curve.

For example, if you have $1,000 in a bank account with a compound interest rate of 5% per year, the interest earned each year is added to the principal amount and becomes part of the new base for calculating future interest. As a result, the amount of money in the account grows exponentially over time. This relationship can also be seen in other areas, such as population growth or economic growth rates.

Final answer:

Mt. McKinley is 20,318 feet tall. This is found by adding Mt. Whitney's height of 14,492 feet to the additional 5,826 feet that Mt. McKinley is taller by.

Explanation:

The question asks how tall Mt. McKinley is. First, we know Mt. Whitney has a height of 14,492 feet. According to the question, Mt. McKinley is 5,826 feet taller than Mt. Whitney. To find the height of Mt. McKinley, we need to add these two measurements together.

Step 1: Write down the height of Mt. Whitney: 14,492 feet.

Step 2: Add the additional height of Mt. McKinley to Mt. Whitney's height: 14,492 feet + 5,826 feet.

Step 3: Perform the addition: 14,492 + 5,826 = 20,318 feet.

Therefore, Mt. McKinley is 20,318 feet tall.

Answer:

less than -3 and greater than 5

Step-by-step explanation:

The Expression  [tex](3p^{3} q)^{\frac{3}{4} }[/tex] in radical form is [tex]p^{2} \sqrt[4]{27pq^{3} }[/tex]

An expression is a combination of numbers, operator and variables.

The given expression is [tex](3p^{3} q)^{\frac{3}{4} }[/tex]

We know that

[tex]a^{\frac{p}{q} } =\sqrt[q]{a^{p} }[/tex]

So let us use same form to solve the given expression to radical form.

[tex](3p^{3} q)^{\frac{3}{4} }[/tex]=[tex]\sqrt[4]{(3p^{3} q)^{3} }[/tex]

Simplify the terms in root,

=[tex]\sqrt[4]{(3^{3}p^{3.3}q^{3} }[/tex]

=[tex]\sqrt[4]{27p^{9}q^{3} }[/tex]

[tex]\sqrt[4]{27p^{4}p^{4}pq^{3} }[/tex]

=[tex]p.p\sqrt[4]{27pq^{3} }[/tex]

=[tex]p^{2} \sqrt[4]{27pq^{3} }[/tex]

Hence the Expression  [tex](3p^{3} q)^{\frac{3}{4} }[/tex] in radical form is [tex]p^{2} \sqrt[4]{27pq^{3} }[/tex]

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Using Newton's Second Law of Motion, and the principle that acceleration is directly proportional to the applied force, a force of approximately 86.15 newtons will cause an acceleration of 8 m/s².

The question relates to the principle stated in Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In this case, we can assume the mass of the object remains unchanged.

To find the force that will cause an acceleration of 8 m/s², we can set up a direct proportion based on the given data (70 N correlates with 6.5 m/s²):

70 N / 6.5 m/s² = X N / 8 m/s²

Solving this for X gives X = (70 N * 8 m/s²) / 6.5 m/s². Round your answer to the nearest hundredth, you get approximately 86.15 N.

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divide 6 3/5 by  2 1/5

6 3/5 = 33/5

2 1/5 = 11/5

33/5 / 11/5 = 3

 the temperature dropped 3 degrees per hour

Answer:

[tex]f^{-1}(x)=\frac{x+10}{2}[/tex]

Step-by-step explanation:

We ate asked to find the inverse of the given function [tex]f(x)=2x-10[/tex].

To find the inverse of function, first of all we will replace [tex]f(x)=y[/tex] and then interchange x and y values as shown below:

[tex]y=2x-10[/tex]

Inter-change x and y variables:

[tex]x=2y-10[/tex]

Solve for y using opposite operations:

[tex]x+10=2y-10+10[/tex]

[tex]x+10=2y[/tex]

Switch sides:

[tex]2y=x+10[/tex]

Divide both sides by 2:

[tex]\frac{2y}{2}=\frac{x+10}{2}[/tex]

[tex]y=\frac{x+10}{2}[/tex]

We will inverse function notation [tex]f^{-1}(x)[/tex] to write the inverse function as:

[tex]f^{-1}(x)=\frac{x+10}{2}[/tex]

Therefore, our required inverse function would be [tex]f^{-1}(x)=\frac{x+10}{2}[/tex].

Answer:

Step-by-step explanation:

(5x2)+3

=13  

This how you work the problem:

(5x2)+3   (5x2=10) 10+3=13. :)

The number of persons who have taken the ride is 60.

According to the question, a halloween fair with a big ferris wheel. The wheel has 10 chairs and people are seated [tex]2/chair[/tex].

Also, every minute a chair passes the exit platform and the wheel opens at 11 am for thirty minutes so, the rate at which the chair passes the exit platform is [tex]1\;chair\;per\;minute[/tex].

Now, number of persons who have taken the ride is calculated as-

[tex]n= minutes \times (1\;chair\;per\;minute)\times (2\;persons\;per\;chair)\\n=30\times 2\times 1\\n=60[/tex]

Hence, the number of persons who have taken the ride is 60.

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The domain restrictions of the expression (h² + 3h −10) / (h² − 12h + 20) are h≠2 and h≠10. which are the correct answers would be options (A) and (C).

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

The expression is given in the question as

(h² + 3h −10) / (h² − 12h + 20)

(h² + 5h - 2h−10) / (h² − 10h - 2h + 20)

(h(h + 5) - 2(h+5)) / (h(h − 10) - 2(h - 10))

(h + 5)(h - 2) / (h − 10)(h - 2)

We know that the denominator cannot be zero

Here (h-2)(h-10)=0

h= 2 or h = 10

Therefore, h cannot be 2 or 10 i.e. in the notation h≠2 and h≠10.

The domain restrictions of the expression (h² + 3h −10) / (h² − 12h + 20) are

h≠2 and h≠10.

Hence, the correct answers would be options (A) and (C).

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