If the purchase price for a house is $445,500, what is the monthly payment if you put 5% down for a 30 year loan with a fixed rate of 6.25%?

Answer:

B

Step-by-step explanation:

Answer: $2657.1

Step-by-step explanation:

Given: The price of a riding mower = $2,746.00

The amount she received by manufacturer as rebate= $49.95

The amount she received by the store as rebate =  $38.95

The total amount she received as rebate =[tex]\$49.95+\$38.95=\$88.9[/tex]

Therefore, the final price of the riding mower is given by :-

[tex]\text{Final Price}=\$2746-\$88.95=\$2657.1[/tex]

Answer:

Luis, because his sample is taken from the population of all seventh graders. However, Samanthan has the advantage of having a bigger sample, and that makes it more representative.

Step-by-step explanation:

Taking the sample of the library as Samantha did, is biased, because most of the students there is checking a book, and the aim of the study is not only the ones that use the library, but in general the seventh grade students.

Answer: Graph D will be correct graph for the given function.

Explanation:

Given function [tex]f(x) = x^4-2x^3-3x^2+4x+1[/tex]

Since it is a bi-quadratic equation thus it must have 4 roots and (0,1) is one of its point.

Moreover, the degree of the function is even thus the end behavior of the function is[tex]f(x)\to+\infty[/tex], as [tex]x\to-\infty[/tex] and [tex]f(x)\to+\infty[/tex] as [tex]x\to+\infty[/tex]

In graph A, function has four root but it does not have the end behavior same as function f(x).( because in this graph [tex]f(x)\to-\infty[/tex], as [tex]x\to-\infty[/tex] and [tex]f(x)\to-\infty[/tex], as [tex]x\to+\infty[/tex].) so, it can not be the graph of given function.

In graph B,  neither  it has four root nor it has the end behavior same as function f(x).(because in this graph [tex]f(x)\to+\infty[/tex] as  [tex]x\to-\infty[/tex] and [tex]f(x)\to-\infty[/tex] as [tex]x\to+\infty[/tex].) so, it can not be the graph of given function.

In graph C, neither  it has four root nor it has the same end behavior as function f(x).(because in this graph [tex]f(x)\to-\infty[/tex] as  [tex]x\to-\infty[/tex] and [tex]f(x)\to+\infty[/tex] as[tex]x\to\infty[/tex].) so, it also can not be the graph of given function.

In graph D it has four root as well as it has the same end behavior as the given function. Also it passes through the point (0,1).

Thus, graph D is the graph of given function.

The idea is to find a linear combination a_1(5, -6) + a_2(-2, -2) = (-6, 2) It boils down to a system of equations: Take the augmented matrix:

Answer:  The required vector x is

[tex]x=\begin{bmatrix}-\dfrac{8}{11}\\ \dfrac{13}{11}\end{bmatrix}[/tex].

Step-by-step explanation:  Given that a basis B of R² consists of vectors (5, -6) and (-2, -2).

We are to find the vector x in R² whose co-ordinate vector relative to the basis B is [tex]\begin{bmatrix}-6\\ 2\end{bmatrix}[/tex].

Let us consider that a, b are scalars such that

[tex]a(5,-6)+b(-2,-2)=(-6,2)\\\\\Rightarrow (5a-2b,-6a-2b)=(-6,2)\\\\\Rightarrow 5a-2b=-6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-6a-2b=2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Subtracting equation (ii) from equation (i), we get

[tex](5a-2b)-(-6a-2b)=-6-2\\\\\Rightarrow 11a=-8\\\\\Rightarrow a=-\dfrac{8}{11}[/tex]

and from equation (i), we get

[tex]5\times\left(-\dfrac{8}{11}\right)-2b=-6\\\\\\\Rightarrow 2b=-\dfrac{40}{11}+6\\\\\\\Rightarrow 2b=\dfrac{26}{11}\\\\\\\Rightarrow b=\dfrac{13}{11}.[/tex]

Thus, the required vector x is

[tex]x=\begin{bmatrix}-\dfrac{8}{11}\\ \dfrac{13}{11}\end{bmatrix}[/tex].

The ordered pairs (0,0), (1,4), (2,16), (3,36), and (4,64) can be represented by the function y = x^2.

The question involves a list of ordered pairs that represent a mathematical function. Here, the ordered pairs are (0,0), (1,4), (2,16), (3,36), (4,64). Through these pairs, we can see a relationship between the x-values (first number in each ordered pair) and their respective y-values (second number in each pair). Specifically, each y-value appears to be the square of its respective x-value. By noticing this pattern, we can write a rule that represents this function: y = x^2. This means that for any given x-value, you just need to square it to get its corresponding y-value.

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Answer:

563

Step-by-step explanation:

Plato

Answer: The missing number would be 28.

Step-by-step explanation:

Use the rule

4

to find the missing number on the table.

x      y

0 0

2 8

5 20

7 28

10 40

7*4=28.

Answer:

8.99

Step-by-step explanation:

Final answer:

To solve the problem, an equation is set where the area of the square (a²) is equal to eight times its perimeter (8(4a)). Solving for a, we find the side length of the square to be 32 inches.

Explanation:

The student is presented with a problem where the area of a square is stated to be eight times its perimeter. Let the side length of the square be a inches. The area of a square is given by a², and the perimeter of a square is given by 4a. According to the problem, we have a² = 8(4a).

Firstly, we set up the equation based on the given information:

a² = 8(4a)

Solving for a:

a² = 32a

a² - 32a = 0

a(a - 32) = 0

Therefore, the side length a can be 0 or 32. Since the side length cannot be 0, the length of a side of the square is 32 inches.

To find variable values and angle measures, identify knowns, use appropriate equations for unknowns, calculate vector components, use trigonometric functions and the Pythagorean theorem for the resultant vector, and ensure angles are in radians.

To find the values of the variables and the measures of the angles, you need to follow a systematic approach. Start by making a list of known variables and inferences from the problem. Once you've identified what is given, you can solve for the unknowns using the appropriate equations. If the problem involves vectors, you would identify the x- and y-axes before finding the vector components Ax = A cos and Ay = A sin, where A is the magnitude of the vector and cos and sin are the trigonometric functions corresponding to the angles the vectors make with the x-axis. After computing these, you can use the Pythagorean theorem to find the resultant vector length.

To verify your solutions, including the measures of the angles in radians, it's important to assess whether the answers are reasonable. This may involve checking the magnitude and direction of the resultant vector and ensuring that the angles are within the possible range (0 to 2π radians for a full circle).

Answer:

The x-intercept is (6, 0); the y-intercept is (0, –9).

Step-by-step explanation:

Step [tex]1[/tex]

Convert mixed numbers to improper fractions

we know that

[tex]4\frac{1}{4}=\frac{4*4+1}{4}=\frac{17}{4}[/tex]

[tex]2\frac{3}{4}=\frac{2*4+3}{4}=\frac{11}{4}[/tex]

Step [tex]2[/tex]

Find the difference of the numbers

[tex]\frac{17}{4}-\frac{11}{4}=\frac{6}{4}=\frac{3}{2}[/tex]

Step [tex]3[/tex]

Convert improper fraction to mixed number

[tex]\frac{3}{2}=1.5=1+0.5=1+\frac{1}{2} =1\frac{1}{2}[/tex]

therefore

the answer is the option B

[tex]1\frac{1}{2}[/tex]

The square root of 81 is 9. Hence, it falls under the categories of Whole number, Integer, and Rational number since it can be a positive whole number without any fractional part and can be written as a ratio.

The square root of 81 is 9. Now, considering the types of numbers, 9 is a Whole number, because it is not a fraction, and it does not have a decimal point. It is also an Integer, which are numbers that can be written without a fractional component, including both positive and negative whole numbers plus zero. Lastly, 9 is a Rational number, a number that can be written as a fraction. So, the square root of 81 is all three: Whole number, Integer, and Rational number. It is not an Irrational number, which is a number that cannot be expressed as a ratio of two integers.

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Final answer:

The square root of 81 is 9, which makes it a whole number, an integer, and a rational number. It is not an irrational number.

Explanation:

The type of number the square root of 81 is can be determined simply by calculating the square root. The square root of 81 is 9, since 9 multiplied by 9 equals 81. Now, let's classify this number:

Whole number: Yes, because whole numbers include all the non-negative numbers (0, 1, 2, 3...), and 9 falls into this category.

Integer: Yes, because integers are all whole numbers, both positive and negative, including zero (-3, -2, -1, 0, 1, 2, 3...), so 9 is also an integer.

Rational number: Yes, because rational numbers are ratios of integers (like 2/1 or -3/4), and 9 can be expressed as 9/1.

Irrational number: No, because irrational numbers cannot be expressed as ratios of integers. Examples of irrational numbers include √2 or π.

Therefore, the square root of 81 is a whole number, an integer, and a rational number, but it is not irrational.

To find the depth of the gutter that will maximize its cross sectional area, we can use optimization. We need to set up the area equation, differentiate it, find critical points, and determine the maximum area.

To find the depth of the gutter that will maximize its cross sectional area, we need to use the concept of optimization. Let's assume the depth of the gutter is x inches. The width of the gutter would be 20 - 2x inches, as the edges are turned up to form right angles.

The cross-sectional area of the gutter would be x(20 - 2x) = 20x - 2x^2 square inches. To maximize this area, we can find the derivative of the area function with respect to x, set it equal to 0, and solve for x.

After finding the critical points, we can analyze which value of x gives the maximum area. Lastly, we can plug this value back into the area function to find the maximum area.

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Answer:

The correct option is:

C. 5,418.54 feet above sea level

Step-by-step explanation:

Nadia started at 19.26 feet below sea level.

She then changed her altitude by climbing a total of 5,437.8 feet up from her initial position.

Her new position would be 5437.8-19.26 feet above the sea level

i.e.  5,418.54 feet above sea level

Hence, the correct option is:

C. 5,418.54 feet above sea level

Answer:

5,418.54

Step-by-step explanation:

I guess there should be an options to choose. But I'm pretty sure that the answer is: To set up long division of polynomials, you should make sure that each polynomial is written in descending order and has no missing terms.