Factor completely:

7r^2− 64r + 64

An integer is a whole number that's not a fraction, thus a positive integer for 45, would be 45.

What are  integers?

Natural numbers are: 1, 2, 3, ....

Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )

Rational numbers are numbers which can be written in the form of a/b where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5) etc.

Irrational numbers are those real numbers which are not rational numbers.

Know that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.

We have to write an integer for: a deposit of $45 *

A deposit is positive, therefore the integer will be positive.

An integer is a whole number that's not a fraction, thus a positive integer for 45, would be 45.

Learn more about numbers here;

brainly.com/question/3151755

#SPJ2

Answer:

$45

Step-by-step explanation:

1. A deposit is positive, so the integer will be positive.
2. An integer is a whole number that's not a fraction, so a positive integer for 45, would be 45.

I hope this helps!

(x+12)=110

Subtract 12 from both sides.

x=110−12

Subtract 12 from 110 to get 98.

x=98

The squareroot of a negative number is notdefined in the realm of real numbers.

We have,

The squareroot of a negative number is not defined in the realm of real numbers.

The square root function is only defined for non-negative real numbers.

In this case, the expression "negative 9 squared" means the square of negative 9, which is positive 81.

However, taking the square root of the negative of positive 81 would involve imaginary numbers.

If we consider the square root of -81 in the realm of complex numbers, it can be represented as ±9i, where i is the imaginary unit (√-1).

Thus,

The squareroot of a negative number is not defined in the realm of real numbers.

Learn more about imaginarynumbers here:

brainly.com/question/6748860

#SPJ6

Answer:

Step-by-step explanation:

Let x be the random variable representing the height of players on the football team. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = standard deviation

n = number of samples

From the information given,

µ = 74 inches

σ = 1 inch

n = 50

x = 74 inches

the probability that a player is less than 74 inches tall is expressed as

P(x < 74)

For x = 74,

z = (74 - 74)/(1/√50) = 0

Looking at the normal distribution table, the probability corresponding to the z score is 0.5

Therefore,

P(x < 74)

The players less than 74 inches is

0.5 × 50 = 25 players

Answer:

260

Step-by-step explanation:

7 shelves containing 37 cans of pineapples each would give you 259 cans of pineapple. Then, round to the nearest ten would give you 260.

Option c) x² + 11x - 1 = 0 is the correct quadratic equation that can be used to determine the thickness of the frame.

In this problem, Emily wants to hang a painting in a gallery, and she needs to determine the thickness of the frame, denoted by "x," surrounding the painting. The painting and frame together should have an area of 31 square feet. The dimensions of the painting are given as 5 feet in width and 6 feet in length. To find the equation that will help us determine the thickness of the frame, we need to set up a quadratic equation based on the given information.

Let's start by visualizing the problem. The painting is a rectangle, and the frame around it will also form a rectangle. So, we can find the area of the frame by subtracting the area of the painting from the total area of the painting and the frame.

The area of a rectangle can be calculated by multiplying its length and width. For the painting, we have:

Painting's area  = Length * Width

                          = 6 feet * 5 feet

                          = 30 square feet

Now, we know that the total area of the painting and frame together is 31 square feet. So, we can set up the following equation:

Total area (painting + frame) = Painting's area + Frame's area

31 square feet = 30 square feet + Frame's area

Frame's area = 31 square feet - 30 square feet = 1 square foot

The frame's area is given by the product of its width (which is the thickness "x") and the length of the painting (6 feet):

Frame's area = x * 6 feet

Since the frame's area is equal to 1 square foot, we can write:

x * 6 = 1

Now, let's rearrange the equation to set it to zero on one side:

6x - 1 = 0

We have now derived the quadratic equation that represents the problem:

6x - 1 = 0

The correct answer is not directly provided among the options. However, let's manipulate the equation to put it in standard quadratic form (ax² + bx + c = 0):

Multiply the equation by -1 to change the sign of each term:

-6x + 1 = 0

Now, it matches option c) x² + 11x - 1 = 0.

Thus, option c) is the correct quadratic equation that can be used to determine the thickness of the frame, "x," for the given problem.

To know more about Quadratic Equation here

brainly.com/question/17177510

#SPJ2

The correct answer is 4x2 + 22x − 1 = 0  

That's what you get when you (5 + 2x)(6 + 2x) = 31

And you get to expand that based on the data that is already provided in the question.