A sphere has a radius of five units, and intersects the zy plane along the circle whose equation is (x-1)² + (y+4)2-9 If the coordinate of the center of the sphere is a positive number, determine the equation of the sphere. (2.) (10 pts) Determine a vector of length four that points in the same direction as u = (1,2,2)

The car was driven 105 miles.

What is rent?

An agreement where a fee is paid for the temporary use of a good, service, or property owned by another is known as renting, sometimes known as hiring, or letting.

In the given example the cost function is, c = 15 + 2m

Where, c is the total cost and m is the number of miles car driven.

The total cost was $225.

So, plug c = $225 in the above equation.

225 = 15 + 2m

210 = 2m

   m = 105

Therefore, the car was driven 105 miles.

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Answer:

p=1/4

Step-by-step explanation:

4(p+5)=21

4p+20=21

4p=1

p=1/4

Answer:

Choice A

The ratio of the rise to the run of the given triangle is \(\frac{1}{4}\)

The ratio of the rise to the run of the image triangle is \(\frac{1}{4}\)

Answer:

not D

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

The ponderal index cannot be computed without the value of the constant "a" in the formula. Therefore, the ponderal index for a person who is 76 inches tall and weighs 192 pounds cannot be determined.

To compute the ponderal index, we need the formula and the value of the constant "a."

a) The formula for the ponderal index is given as I = a, where I represents the ponderal index and a is a constant. However, the value of the constant "a" is missing in the provided information. Without knowing the value of "a," we cannot compute the ponderal index for a person who is 76 inches tall and weighs 192 pounds.

b) Similarly, without knowing the value of the constant "a," we cannot determine the weight of a man who is 77 inches tall and has a ponderal index of 11.56.

To compute the ponderal index or determine the weight, we need the specific value of the constant "a" in the given formula.

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The dependent variables in the following scenario are whether the bacon becomes moister and more flavorful and the independent variable is the cooking method.

In statistics, a dependent variable is one whose value is determined by another set of variables called independent variables. To put it simply, the dependent variable is the thing that is being tested or calculated. The dependent variable is sometimes known as the "outcome variable." In the given scenario, the chef was curious as to whether or not frying or microwaving the bacon would produce a moister and more flavorful final product. The bacon is the result of the experiment, hence it is a dependent variable.

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Amanda's answer correct is not correct. The correct answer is 4 R2, because she might have incorrectly divide the first digit of 34, which is 3, by 8. She should have moved on to the next digit instead

Amanda's answer, 3 R10, is not correct.

When we divide 34 by 8, we want to know how many times 8 goes into 34, and what is left over. We start by dividing 8 into the first digit of 34, which is 3. 8 cannot go into 3, so we move on to the next digit, which is 34.

We can see that 8 goes into 34 four times, because 8 x 4 = 32. This means that the whole number part of the answer is 4.

But there is still a remainder left over. To find the remainder, we subtract 32 from 34, which gives us 2.

Therefore, the correct answer is 4 R2.

Amanda's mistake may have been to incorrectly divide the first digit of 34, which is 3, by 8. She should have moved on to the next digit instead.

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Answer:

SLOPE: 1

Y-Intercept: (0,4)

Step-by-step explanation:

Answer:

m=1

Step-by-step explanation:

Answer:

A.) 4 x (y + 7)

Step-by-step explanation:

4 times means that you are going to be multiplying something by 4. It says 4 times the sum of y and 7. This means that you are going to multiply whatever y and 7 equal by 4. Sum means addition. So that's going to be that you are multiplying what the combined total of y and 7 is by 4.

I hope this helped :)

For the given equation i.e. y = 2\((3)^{t}\), the number of infected people reach 1,458 will be in 6 weeks.

We have,

Equation,

y = 2\((3)^{t}\)

Now,

According to the question,

It is given that,

y = number of infected people,

And,

t = time in weeks in which people get infected,

And,

Number of infected people i.e. y = 1452,

So,

Putting values in the given equation,

We get,

1458 = 2\((3)^{t}\)

On solving we get,

729 = \((3)^{t}\)  

Now,

We can rewrite the above equation as,

(3)⁶ = \((3)^{t}\)

Now, comparing the powers on both sides,

we get,

t = 6,

i.e.

It will take about 6 weeks, for 1458 number of people to get infected.

Hence we can say that for the given equation i.e. y = 2\((3)^{t}\), the number of infected people reach 1,458 will be in 6 weeks.

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Using the Factor Theorem, the length of one side of the garden is:

(3x - 4) feet.

The Factor Theorem states that a polynomial function with roots \(x_1, x_2, \codts, x_n\) is given by:

\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)

In which a is the leading coefficient.

The area of a rectangle is given by the multiplication of it's dimensions. In this problem, it is given by:

A = 9x² - 24x + 16.

The root of 9x² - 24x + 16 = 0 is x = 4/3 with multiplicity 2, hence:

\(x_1 = x_2 = \frac{4}{3}\)

Hence the area can be written as:

\(A = 9\left(x - \frac{4}{3}\right) \times \left(x - \frac{4}{3}\right)\)

Then, to find one side:

9(x - 4/3) = 9x - 12 = 3(3x - 4).

Hence (3x - 4) feet is one side.

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The solution to the given system of linear equations is x = 3, y = -2, and z = 1.

To solve the system of linear equations AX = B using the inverse matrix A^(-1), follow these steps:

1. Write the given system of equations in matrix form: A = | 1 2 5 | | 2 3 9 | | 4 7 17 | X = | x | | y | | z | B = | 1 | | 2 | | 1 |

2. Find the inverse of matrix A, A^(-1).

To do this, first calculate the determinant of A: d

et(A) = 1(3*17 - 7*9) - 2(2*17 - 7*4) + 5(2*3 - 2*4) = -12

Since det(A) ≠ 0, A has an inverse.

Now, find the adjugate of A and divide by det(A):

A^(-1) = (1/-12) * adj(A) = | (-6) 10 -1 | | 8 -3 -4 | | -4 2 1 |

3.Multiply A^(-1) by B to find the solution matrix X:

X = A^(-1) * B = | (-6) 10 -1 | | 1 | | 8 -3 -4 | | 2 | | -4 2 1 | | 1 | X = | (-6*1 + 10*2 + (-1)*1) | | (8*1 - 3*2 - 4*1) | | (-4*1 + 2*2 + 1*1) | X = | 3 | | -2 | | 1 |

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Answer:

38cm

Step-by-step explanation:

set 3x-5 and 19-x equal to eachother, since, given as its an isoscles triangle, they should be equal. After you work out the equation, you're left with x=6. So now you plug that it.

3(6)-5=13

19-(6)=13

2(6)=12

Now you add them all together, so the perimeter is 38 cm.

Answer:

x = 6

y = -5

Explanation:

substitute each of the following,

-3x + 13  = -x + 1

-3x + x = 1 - 13

-2x = -12

x = 6

Find y,

y = -x + 1

y = -6 + 1

y = -5

Step-by-step explanation:

please mark me as brainlest

Answer:

Step-by-step explanation:

You are given four responses to a question and are to identify which of those four are correct.  

The first one is FALSE, because the divisor -2 results in a non-zero remainder.

The second one is also FALSE.  The y-intercept is (0, -4).

The third one is TRUE.  Division by -2 results in a remainder of -6, which is the y-value of the function at -2.

The fourth is FALSE.

Answer: D. "none."

Step-by-step explanation: The complement of "at least one" is "none."

When we say "at least one," it means that there is a minimum of one of something. Therefore, the complement of "at least one" refers to the opposite condition, where there is no occurrence of that something.

Here's an example. Suppose you have a bag of marbles, and you are told that the bag contains at least one red marble. The complement of "at least one red marble" would mean that there are no red marbles in the bag.

Answer:

Step-by-step explanation:

1]Add 6 to both sides.

x/3=20+6

2] x/3=26

3]Multiply both sides by 3.

 x= 26*3

 x= 78

The standard form of the quadratic equation is:

y = 3x² + 24x + 45

To do it, we just need to expand the product in the right side of the given quadratic, here we start with:

y = 3(x + 3)(x + 5)

Expanding the product we will get:

y = 3*(x + 3)*(x + 5)

y = (3x + 9)*(x + 5)

y = 3x*x + 3x*5 + 9x + 9*5

y = 3x² + 15x + 9x + 45

y = 3x² + 24x + 45

That is the standard form.

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Answer:

7.47 more pounds

Stage 1: Subtract the numbers.

7.71 - 0.24 = 7.47

Stage 2: Write the solution.

7.47 is the solution.

Hope it helps!

Answer:

7.47

Step-by-step explanation:

Just subtract 7.71 and 0.24.

The linear model for this data is y = 0.63t + 4.922 and the estimated population of Greensboro in 2015 was 11,530

What is slope?

Slope is a measure of the steepness of a line. It is defined as the change in y-coordinate divided by the change in x-coordinate between any two points on the line.

a. To find the linear model for this data, we need to determine the equation of the line that passes through the two given points: (0, 4.922) and (6, 9.1). The slope of this line can be calculated as:

slope = (change in y) / (change in t)

slope = (9.1 - 4.922) / (6 - 0)

slope = 0.63

Using the point-slope form of a linear equation, we can write the equation of the line as:

y - 4.922 = 0.63(t - 0)

Simplifying, we get:

y = 0.63t + 4.922

Therefore, the linear model for this data is y = 0.63t + 4.922.

b. To estimate the population in 2015, we need to find the value of y when t = 11 (since 2015 is 11 years after 2004). Substituting t = 11 into the linear model, we get:

y = 0.63(11) + 4.922

y = 11.53

Therefore, the estimated population of Greensboro in 2015 was 11,530 (rounded to the nearest whole number).

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A simple random sample are numbers equally likely to be chosen from a large population of numbers.

This is defined as the total number of people or variables present in an area over a given period of time.

Numbers are usually chosen at random from a large population for different reasons and are referred to as simple random sample because they have an equal probability of being chosen.

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Limits function lim p(x) can be calculated if p is a polynomial function by:

To calculate the limits of a polynomial function, p(x), first identify the degree of the polynomial. Then, use the formula Lim p(x) = aₙ xⁿ + aₙ₋₁ xⁿ⁻¹ + ... + a₀, where an is the leading coefficient. For example, if the polynomial is of degree 3, then the formula would be:

Lim p(x) = a₃ x³ + a₂ x² + a₁ x + a₀.

Next, we need to subtitute the variable x with the defined limits. For example, if the defined limit of the function is 2, then the limit function would be:

Lim p(2) =  a₃ (2)³ + a₂ (2)² + a₁ (2) + a₀

Then, we just need to simplify our finding:

Lim p(2) =  8a₃ + 4a₂ + 2a₁ + a₀

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To create an equivalent system that will eliminate one variable when the equations are combined, we can use the method of elimination. The goal is to manipulate one or both of the equations to ensure that the coefficients of one variable in both equations are additive inverses (i.e., they add up to zero).

Let's take a look at the given system of equations:

Equation 1: 4x + y = 4

Equation 2: 2x + 6y = 24

To eliminate one variable, we need to make the coefficients of either "x" or "y" in both equations additive inverses. In this case, it would be convenient to eliminate "x." To do that, we can multiply Equation 1 by 2 and Equation 2 by -4:

Equation 1 (multiplied by 2): 8x + 2y = 8

Equation 2 (multiplied by -4): -8x - 24y = -96

Now, if we add the two equations together, the "x" terms will cancel each other out:

(8x + 2y) + (-8x - 24y) = 8 + (-96)

Simplifying the equation gives:

2y - 24y = -88

Combining like terms:

-22y = -88

Dividing both sides of the equation by -22:

y = 4

Now that we have the value of "y," we can substitute it back into one of the original equations (let's use Equation 1):

4x + y = 4

4x + 4 = 4

Simplifying:

4x = 0

Dividing both sides by 4:

x = 0

Therefore, the equivalent system of equations that eliminates one variable is:

x = 0

y = 4

equivalent system of equations:
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Answer:

I think it is - 1/2 by the way love ur profile picture and username

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Work Shown:

Use the compound interest formula

A = P*(1+r/n)^(n*t)

A = 10000(1+0.039/1)^(1*4)

A = 11,653.65589441

A = 11,653.66

That's the amount of money Tammy will have at the end of 4 years.

Subtract off the principal from this value to get the interest.

interest = A - P

interest = 11,653.66 - 10,000

interest = 1,653.66

Answer:0-ounce package of cashews costs $8.11 is better then a 16-ounce package of cashews costs $12 , because cost per ounce for the 10-ounce package of cashews = $ is greater then cost per ounce for the 16-ounce package of cashews = $

Step-by-step explanation:

The inequality, and we can't find a number of days that Michelle must read in order to read more pages than Jill.

What is inequality?

An inequality is a mathematical statement that compares two values, expressing that they are not equal.

Let "x" be the number of days that Michelle must read in order to read more pages than Jill.

The total number of pages Michelle reads can be represented as:

33 + 19x

The total number of pages Jill reads can be represented as:

45 + 23x

To write an inequality to represent the number of days that Michelle must read in order to read more pages than Jill, we need to compare the two expressions:

33 + 19x > 45 + 23x

Simplifying the inequality, we get:

-12 > 4x

Dividing both sides by 4 (and flipping the inequality because we're dividing by a negative number), we get:

x < -3

However, this solution doesn't make sense in the context of the problem because we can't have negative days of reading.

Hence, there is no solution to the inequality, and we can't find a number of days that Michelle must read in order to read more pages than Jill.

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The matrix can be diagonalized, and the correct choice is B. For P= ⎡⎣​3−110​11​⎤⎦, D= ⎡⎣​393​000​⎤⎦.

To diagonalize a matrix, we need to find its eigenvectors and use them to construct a matrix P, where the columns of P are the eigenvectors. The diagonal matrix D is formed by placing the eigenvalues on the diagonal.

First, we find the eigenvalues λ by solving the characteristic equation det(A - λI) = 0, where A is the given matrix and I is the identity matrix. By calculating the determinant, we have (33 - λ)(9 - λ) - (-3)(18) = 0, which simplifies to λ^2 - 42λ + 315 = 0. Solving this quadratic equation gives λ = 3 and λ = 9.

Next, we find the corresponding eigenvectors. For λ = 3, we solve the equation (A - 3I)v = 0, where v is the eigenvector. This leads to the eigenvector v = ⎡⎣​3−110​⎤⎦. For λ = 9, we solve (A - 9I)v = 0, which gives v = ⎡⎣​11​1​⎤⎦.

We construct matrix P by using the eigenvectors as columns: P = ⎡⎣​3−110​11​⎤⎦. The diagonal matrix D is formed by placing the eigenvalues on the diagonal: D = ⎡⎣​393​000​⎤⎦.

Therefore, the correct choice is B. For P= ⎡⎣​3−110​11​⎤⎦, D= ⎡⎣​393​000​⎤⎦.

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The expression 2^2020+2^2022=5.2^2020​ is proved below

From the question, we have the following parameters that can be used in our computation:

2^2020+2^2022=5.2^2020​

Express 2022 as 2020 + 2

So, we have the following representation

2^2020+2^(2020 + 2) = 5.2^2020​

When expanded, we have

2^2020+2^(2020) * 2^2 = 5.2^2020​

Factor out 2^2020

2^2020 * (1 + 2^2) = 5.2^2020​

Evaluate

2^2020​ * 5 = 5. 2^2020​

This implies that

5.2^2020​ = 5.2^2020​

HEnce, the expression has been proved

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Answer:

90 degree counter-clockwise

Step-by-step explanation: