Which interval for the graphed function contains the local
maximum?
O
O [1, 2]
O[2,3]
O[3, 4]
[-1, 0]

Answer:

[tex]d = 441[/tex]

Step-by-step explanation:

We know that [tex]d = 49t^2[/tex].

We also know that it takes 3 seconds to reach the bottom of the well, meaning that if we substituted [tex]t = 3s[/tex] in the formula, we'd get the height of the well.

[tex]d = 49 \times 3^2 \to 49 \times 9 \to 441[/tex]

[tex]\begin{array}{ccll} miles&gallons\\ \cline{1-2} 350 & 20\\ 875& g \end{array} \implies \cfrac{350}{875}~~=~~\cfrac{20}{g} \\\\\\ \cfrac{2}{5}=\cfrac{20}{g}\implies 2g=100\implies g=\cfrac{100}{2}\implies g=50[/tex]

The domain is all real numbers of x that makes the expression defined.

Set-builder notation: { x| x ≥ 0 }.

Interval notation: [0,∞).

Given the function in the question;

f(x) = 3√3x - 3

To determine the domain, we find where the expression is defined by setting the radicand √3x to be greater than or equal to zero and solve for x.

3x ≥ 0

Divide both sides by 3

3x ≥ 0

3x/3 ≥ 0/3

x ≥ 0/3

x ≥ 0

The domain is all real numbers of x that makes the expression defined.

Set-builder notation: { x| x ≥ 0 }.

Interval notation: [0,∞).

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The graph of the piecewise function is given at the end of the answer. From the graph, and from it's concepts, we have that:

A piecewise-defined function is a function that has different definitions, depending on the input of the function.

For this problem, the function has two definitions, as follows:

Both are decreasing linear functions, with the definition opening a space at x = 0, between y = 0 and y = -2, as shown in the graph. The closed interval, due to the equal sign, is at x = 0.

In a graph, the domain and the range are found as follows:

Hence, for the function in this problem, we have that:

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The value of the side length n is 15 units.

According to the question we have been given that ΔABC ≈ ΔQRS

And we know that when two triangles are similar then their corresponding sides are proportional to each other that is

           [tex]\frac{AB}{QR} = \frac{BC}{RS} = \frac{AC}{QS}[/tex]          (1)

Now we need to find the value of n which is the length of RS

To find the value of n we will use the above equation (1), we get

  The values that we have been given are :

   AC = 2 ,  BC = 6  and   QS = 5 , RS = n

We use the proportion,

              [tex]\frac{BC}{RS} = \frac{AC}{QS}[/tex]

                [tex]\frac{6}{n} = \frac{2}{5}\\n = \frac{6}{2} * 5\\n = 15[/tex]

Hence the value of the side length n is 15 units.

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In the given function if csc = 13/5 then:

So,

cscθ = 13/5 ⇒ 1/sinθ = 13/5

When both sides are flipped:

Tangent is found by knowing that 13 is the hypotenuse because it is the longest side, and 5 is "opposite," so 12 is "adjacent."

And because cosine is adjacent/ hypotenuse, the equation is:

Secθ is the inverse of cos theta, so it is as follows:

So, (B) sin= 5/13 and (D) tan=5/12 are correct.

Therefore, in the given function if csc = 13/5 then:

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Answer:lm

Step-by-step explanation:

the formula by using x=-2 in the other direction.

Reversing equation is what?

The goal of equation solving is to get the variable by itself on one side of the equation and a number on the other side. To isolate the variable, we must turn around the processes that effect it. To achieve this, w, we carry out each operation's inverse on both sides of the equation.

based on the provided statement;

Eliminate the biggest shared variable on both sides of the equation:

3x+2=-4

Unknown terms should be moved to the left side of the equation:

3x=-4-2

Determine the total or difference:

3x=-6

Add the variable's coefficient to both sides of the equation, then subtract it:

x=-6/3

x=-2

Calculate the product or quotient x=-2

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The slope of the line with equation - 6y = 2x + 7 is - 1/3.

The slope of a line is the rise-to-run ratio or the rise divided by the run. It gives information about a line's slope in the coordinate plane.

The general equation of a straight line is y = mx +c where m is the slope of the line.

Now,

Consider the equation of the line,

- 6y = 2x + 7

Dividing each side of the equation by 6.

( - 6y/ 6 ) = ( 2x / 6 ) + ( 7/6 )

- y = x/ 3 + 7/ 6

Multiplying each side of the equation by - 1,

- y × - 1 = x/ 3 × -1 + 7/ 6 × - 1

y = - x/3 - 7/6

y = - (1/3) × (x) - 7/6

Now comparing the equation with the general equation y = mx + c.

We get, the slope of the line as:

m = - 1/3

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The value of k that makes the statement true is: k = -4.

If we are given an equation that has an unknown variable, to find the value of the variable, solve to isolate the variable. The value of the variable is what will make the equation a true statement.

Given the equation:

-k + 12 = 16

Subtract 12 from both sides

-k + 12 - 12 = 16 - 12 [subtraction property]

-k = 4

Divide both sides by -1

-k/-1 = 4/-1 [division property]

k = -4

Check: substitute k = -4 into the equation

-k + 12 = 16

-(-4) + 12 = 16

4 + 12 = 16

16 = 16 [true]

Therefore, the value of k that makes the statement true is: k = -4.

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The simplified form of the expression which is as described by the word phrase given in the task content is; 83.4.

In order words, when the sum of 5.5 and 4.3 all divided by the quantity 4 end quantity times the quantity 2 minus 6 end quantity squared plus 5 is being simplified, it gives 83.4

According to the task content, it follows that the expression given by the word phrase and required to be simplified is;

{(5.5 + 4.3)/4} × (2-6)² + 5.

Hence, it follows from PEMDAS guidelines that the parentheses be solved first as follows;

{(9.8)/2} × (-4)² + 5

= 4.9 × 16 + 5

Hence, by multiplying first, we have;

= 78.4 + 5

= 83.4.

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The simplified form of the expression which is as described by the word phrase given in the task content is; 83.4.

In order words, when the sum of 5.5 and 4.3 all divided by the quantity 4 end quantity times the quantity 2 minus 6 end quantity squared plus 5 is being simplified, it gives 83.4

What is the simplified form of the word phrase given in the task content?

According to the task content, it follows that the expression given by the word phrase and required to be simplified is;

{(5.5 + 4.3)/4} × (2-6)² + 5.

Hence, it follows from PEMDAS guidelines that the parentheses be solved first as follows;

{(9.8)/2} × (-4)² + 5

= 4.9 × 16 + 5

Hence, by multiplying first, we have;

= 78.4 + 5

= 83.4.

We will have $ 672.97 in the account if no money is added or withdrawn from the account.

Amount deposited in the account = $ 600

Interest rate = 3.9 % annually

Time period = 3 years.

No money is added or withdrawn.

So, we will use the Compound Interest to calculate the amount after 3 years.

We have:

Compound interest formula:

A = P ( 1 + r )ⁿ

Here, P = $ 600

r = 3.9 %

n = 3 years

Substituting the values in the formula, we get that:

Compound interest = $ 600 ( 1 + 0.039 )³

Amount = $ 600 ( 1.039 )³

Amount = $ 600 ( 1.122)

Amount after 3 years = $ 672.97

Therefore, we will have $ 672.97 in the account if no money is added or withdrawn from the account.

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The result of simplifying each number 16¹.⁵ using the exponent rules is 2⁽²⁰⁾

To solve this exercise we have to resolve algebraic operations following the exponent rules.

16¹.⁵

Base= 16=  2⁴

The base number 16 is the same as: 2⁴, then we get:

(2⁴)¹.⁵

Using the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:

4⁽⁴*¹*⁵⁾

4⁽⁴*⁵⁾

2⁽²⁰⁾

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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Answer:

2x^2-x-6 (A.)

Step-by-step explanation:

Hope this helps buddy!

Answer:

The inequality that describes the problem for the given equation that is 12 + x ≤ 21 is x = 9.

Step-by-step explanation:

It is given that a shuttle bus to Willow Creek Mall has enough seats for 21 people to ride. Right now, there are 12 people on the bus.

It is further provided that,  let x represent how many more people can ride on the bus and we need to find which inequality describes the problem for the given equation that is 12 + x ≤ 21.

Now,

based on the above-mentioned conditions it can be formulated that;

=> 12 + x = 21

After rearranging the terms;

=> x = 21 - 12

=> x = 9

Therefore, the inequality that describes the problem for the given equation that is 12 + x ≤ 21 is x = 9.

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Answer:

"6a = 9"
"x × y = 9"

→ Variables can also be factors in the instance that they are multiplied by a number or another variable.

Check the picture below.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(~~-1 - (-3)~~)^2 + (~~-1 - 1~~)^2} \implies AB=\sqrt{(-1 +3)^2 + (-1 -1)^2} \\\\\\ AB=\sqrt{( 2 )^2 + ( -2 )^2} \implies AB=\sqrt{ 4 + 4 } \implies AB=\sqrt{ 8 }\implies AB\approx 2.8[/tex]

The function e(x) = 8/3x - 8 is a linear function and the zeros of the function is x = 3

The function is given as

e(x) = 8/3x - 8

Set the function to 0

So, we have

8/3x - 8 = 0

Add 8 to both sides of the equations

So, we have

8/3x = 8

Divide both sides of the equation by 8

So, we have

1/3x= 1

Multiply both sides of the equation by 3

So, we have

x = 3

Hence, the zeros of the function is x = 3

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1 yard is added to the field position on average for each running play.

In plain English, an average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group. For instance, based on the information provided, the average of the digits 2, 3, 4, 7, and 9 is 5.

Detailed explanation:

A data set's average can be calculated by:

Average = sum of data values/ total number of values

Given: The total number of plays =6

Sum of the change in field position resulting from each play is given by :-

sum =-3+2+(-1)+(-2)+(-3)+(1)

         =-6

Now, the average change in field position per running play is given by :-

Average = sum/total plays

               =-6/6

               =-1

Hence, the average change in field position per running play is -1 yard per play.

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The tax due for a single taxpayer by virtue of the tax rate for single filers; 22% as required in the task content is; 14,459.5.

It follows from the task content that the taxable income of the single taxpayer as discussed in the task content is; 65,725.

Since, the tax rate which is alloted to such individual single filers is; 22%.

It simply follows that the tax due on the individual can be determined as follows;

Tax due = 22% of 65, 725

= (22/100) × 65,725

= 14,459.5

Ultimately, the tax due for a single taxpayer by virtue of the tax rate for single filers; 22% as required in the task content is; 14,459.5.

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Answer:

Your answer is 39.8

You basically add all the numbers and divide by how many numbers there are.

Answer:

Step-by-step explanation:

55

The result of simplifying the expression  y⁵/₇ / y³/₁₄  using the exponent rules is [tex]\sqrt{}[/tex](y)

To solve this exercise we have to resolve algebraic operations following the exponent rules.

[(y)⁵/₇] / [(y)³/₁₄]

Using the quotient that indicates that: the exponent result will be the subtraction of these exponents, we have:

(y)⁵/₇ ⁻ ³/₁₄

(y) ⁽¹⁰⁻³⁾/¹⁴

(y) ⁽⁷/¹⁴)

(y) ¹/²

As we have a fractional exponent, you must convert the exponent to root:

[tex]\sqrt{}[/tex](y)

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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4√5 and 12√5 are like radicals as they have the same radicand.

An expression that has a root, typically a square or cube root, is referred to as a radical.

Radicals with the same root number and radicand are like radicals. (expression under the root).

Radicand is the one whose root you are finding.

Given: 4√5 + 12√5 +4

To identify the like radicals.

As we know, like radicals are those having the same radicand.

In the given expression,  4√5 and 12√5 are like as they have the same expression under the root.

Therefore, 4√5 and 12√5 are like radicals.

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Answer: Each person can get 12 cookies, or 12.2

Step-by-step explanation:

All you have to do is divide 61 by 5, your answer would 12 remainder 1, you would then divide 1 by 5 to get 0.2 . Add 12 and .2 to get your answer. The quotient would be 12 and the remainder 1.

Using a proportional relationship, it is found that:

A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx

From point (1.5, 45) on the graph, the constant is given as follows:

k = 45/1.5

k = 30.

Hence the equation is:

y = 30x.

In which:

Hence, point (1.5, 45) means that the 1.5 hours, he traveled 45 miles.

From the constant k = 30, we have that in one hour, Larry traveled 30 miles, also meaning that:

His distance changed at a unit rate of 30 miles per hour, so Larry's speed was of 30 miles per hour.

The slope of the graph is the velocity, hence:

If Larry had driven more slowly, the slope of the graph would be less than 30.

For this problem, the graph is missing, and is given by the image at the end of the answer.

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Answer:

9. 5/10
12. 4/10
15. 1/2

Step-by-step explanation:

1/2 = 5/10 --> 10 ÷ 5 = 2 --> 5+5 = 10 || Basically half
4/10 = 40/100 --> Multiply 10 more
6/12 = 1/2 --> 6+6 = 12 || Half again

Answer:

0.

Step-by-step explanation:

None of the sides colored yellow (1, 3, 5) have an even number that corresponds.