what would 6x-4=10 be?

By evaluating each function in -x, we will see that the only odd one is:

f(x) = -x

We say that a function is odd if:

f(-x) = f(x)

Then we just need to check that for the given functions, let's see what we get:

1) f(-x) = (-x)^3 + 5*(-x)^2 + (-x) = -x^3 + 5x^2 - x ≠ -f(x)

2) f(-x) = (-x)^2 - x= x^2 - x ≠ -f(x)

3) f(-x) = -(-x) = x = -f(x)

So the only odd function is the third one, one useful thing that you may need to know is that usually when you see even exponents, that function will not be odd.

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The length of the rectangle is 33.5 feet.

To find the length of the rectangle, we can use the formula for the area of a rectangle:

Area = length * width

Given:

Area = 402 ft^2

Width = 12 ft

Let's solve for the length:

402 ft^2 = length * 12 ft

To find the length, divide both sides by 12 ft:

length = 402 ft^2 / 12 ft

length = 33.5 ft

So, the length of the rectangle is 33.5 feet.

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We can solve this problem by setting up a system of equations using the given information and using algebraic methods to solve for each variable, which represent the cost of the individual items.

This question can be solved by using the method of linear equations. Let's denote the cost of a small pizza as P, a liter of soda as S, and a salad as A. From the given information, we can create three equations:

By solving these equations, we can determine the prices of the individual items. The details of solving these equations may vary based on your level of comfort with algebra and systems of equations, but the general method involves isolating one variable in one equation and then substituting it into the other equations to eventually solve for each variable.

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Answer:

$2280

Step-by-step explanation:

Answer:

9600 square inches.

Step-by-step explanation:

We have been given that a puzzle contains a triangular piece with a base of 3 in. and a height of 4 in.

The would used for each triangular piece would be equal to area of triangle.

[tex]\frac{1}{2}\times 3\text{ in}\times 4\text{ in}=3\text{ in}\times 2\text{ in}=6\text{ in}^2[/tex]

Each puzzle contains 20 triangular pieces, so wood used for each piece of puzzle would be 20 times 6 square inches.

[tex]\text{Wood used for each puzzle}=20\times 6\text{ in}^2[/tex]

[tex]\text{Wood used for each puzzle}=120\text{ in}^2[/tex]

[tex]\text{Wood used for 80 puzzles}=80\times 120\text{ in}^2[/tex]

[tex]\text{Wood used for 80 puzzles}=9600\text{ in}^2[/tex]

Therefore, 9600 square inches of wood is needed to make 80 puzzles.

The solution for y of the given equation is y = (d - 5x)/ 5.

Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.

The operator that performs the arithmetic operations are called arithmetic operators.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

Given that the equation as

⇒ d = 5x + 5y

Rearrange the terms in the above equation

⇒ 5y = d - 5x

Divided by 5 both sides of the equation

⇒  y = (d - 5x)/ 5

Hence, the solution for y of the given equation is y = (d - 5x)/ 5.

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Answer:

Dustin has 17 nickels and 32 quarters.

Explanation:

Let's denote the number of nickels as [tex]\(n\)[/tex] and the number of quarters as [tex]\(q\).[/tex]

We can set up a system of equations based on the given information:

1. The total number of coins: [tex]\(n + q = 49\)[/tex]

2. The total value of the coins: [tex]\(0.05n + 0.25q = 8.85\)[/tex]

We can solve this system of equations to find the values of [tex]\(n\) and \(q\).[/tex]

From equation (1), we can express [tex]\(n\)[/tex] in terms of [tex]\(q\):[/tex]

[tex]\[n = 49 - q\][/tex]

Now, substitute this expression for [tex]\(n\)[/tex] into equation (2):

[tex]\[0.05(49 - q) + 0.25q = 8.85\][/tex]

[tex]\[2.45 - 0.05q + 0.25q = 8.85\][/tex]

Combine like terms:

[tex]\[0.20q + 2.45 = 8.85\][/tex]

Subtract 2.45 from both sides:

[tex]\[0.20q = 6.40\][/tex]

Now, divide both sides by 0.20:

[tex]\[q = \frac{6.40}{0.20} = 32\][/tex]

So, Dustin has 32 quarters.

To find the number of nickels, we can substitute the value of \(q\) into the equation [tex]\(n + q = 49\):[/tex]

[tex]\[n + 32 = 49\][/tex]

[tex]\[n = 49 - 32\][/tex]

[tex]\[n = 17\][/tex]

So, Dustin has 17 nickels.

Answer:

[tex]n=0\text{ or }n=\frac{4}{5}[/tex]

Step-by-step explanation:

We have been given an equation [tex]-n(5n-4)=0[/tex]. We are asked to solve our given equation using zero product property.

Zero product property states that the product of two expressions are zero, if and only if, one of them is zero.

Using zero product property, we will set each factor of our equation to zero as:

[tex]-n=0\text{ or }(5n-4)=0[/tex]

[tex]n=0\text{ or }5n-4=0[/tex]

[tex]n=0\text{ or }5n-4+4=0+4[/tex]

[tex]n=0\text{ or }5n=4[/tex]

[tex]n=0\text{ or }\frac{5n}{5}=\frac{4}{5}[/tex]

[tex]n=0\text{ or }n=\frac{4}{5}[/tex]

Therefore, the solutions for our given equation are [tex]n=0\text{ or }n=\frac{4}{5}[/tex].

The coordinates of the midpoint of the segment that has endpoints as (14,-8) and (4,12) are (9,2).

Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.

Suppose we've two endpoints of a line segment:

A(p,q), and B(m,n)

Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:

x = (p+m) / 2

and

y = (q+n) / 2

Given that a segment has an endpoint (14,-8) and (4,12). Therefore, The coordinates of the midpoint of the segment can be written as,

X- coordinate = (14+ 4)/2

                      = 18/2

                      = 9

Y- coordinate = (-8+12)/2

                      = 4/2

                      = 2

Hence, the coordinate of the midpoint of the segment that has endpoints as (14,-8) and (4,12) is (9,2).

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9.75 / 1.25 = 7.8

10^6 - 10^2 = 10^4

= 7.8 x 10^4 greater

Final answer:

The 5% represents the annual interest rate on Loretta's investment in a simple interest account.

Explanation:

The 5% represents the annual interest rate on Loretta's investment. In simple interest, the interest is calculated as a percentage of the initial investment. So, if Loretta invested $1000, and after 2 years her account has grown to $1100, the interest earned would be $100 (1100 - 1000).

To find the interest rate, we can use the formula:

Interest = Principal * Rate * Time

Using the given information, we can plug in the values and solve for the rate:

100 = 1000 * Rate * 2

Simplifying the equation, we get:

Rate = 100 / (1000 * 2) = 0.05 or 5%

Therefore, the 5% represents the annual interest rate in this scenario.