All categories

3 years ago

Which of the following sets of ordered pairs represents a function

Mathematics

1 answer:

IgorC [24]3 years ago

3 0

Answer:

D is the correct answer.

Step-by-step explanation:

When given points, one way to tell if it is a function is to see if the x-coordinate changes. If all the x-coordinates are different, then it is a function. If there is a group of x-coordinates that are the same, then you need to check the y-coordinate. If the y-coordinate is the same with the same x-coordinate, then it is still a function [Example: (12, 15), (12, 15) is a function, but (12, 15), (12, 18) is not)

You might be interested in

Y=|x−5|+|x+5|, if −5

KIM [24]

Answer: 10
Explaination: the two l looking lines around the 2 parts of the problem like arenthesis are a sign for absolute for which means there are no negatives so all negative number turn positive and in stead of subtracting you add

6 0

3 years ago

Read 2 more answers

5. GEOMETRY The volume of a rectangular pyramid is one third the product of the area of its base and its height. Find

tatuchka [14]

Answer:

x³ + 7x² + 15x + 9

Step-by-step explanation:

Given that the volume (V) of a rectangular pyramid is

V = $\frac{1}{3}$ A h ( A is the area of base and h the height ), then

V = $\frac{1}{3}$ (3x² + 12x + 9)(x + 3) ← factor out 3 from A

= $\frac{1}{3}$ × 3(x² + 4x + 3)(x + 3)

= (x² + 4x + 3)(x + 3)

Each term in the second factor is multiplied by each term in the first factor, that is

x² (x + 3) + 4x(x + 3) + 3(x + 3) ← distribute parenthesis

= x³ + 3x² + 4x² + 12x + 3x + 9 ← collect like terms

= x³ + 7x² + 15x + 9

Thus the expression for the volume is

V = x³ + 7x² + 15x + 9

4 0

3 years ago

Suppose the coefficient matrix of a linear system of four equations in four variables has a pivot in each column. Explain why th

Veseljchak [2.6K]

If the coefficient matrix has a pivot in each column, it means that it is shaped like this:

$A=\left[\begin{array}{cccc}a_{1,1}&a_{1,2}&a_{1,3}&a_{1,4}\\0&a_{2,2}&a_{2,3}&a_{2,4}\\0&0&a_{3,3}&a_{3,4}\\0&0&0&a_{4,4}\end{array}\right]$

So, the correspondant system

$Ax = b$

will look like this:

$\left[\begin{array}{cccc}a_{1,1}&a_{1,2}&a_{1,3}&a_{1,4}\\0&a_{2,2}&a_{2,3}&a_{2,4}\\0&0&a_{3,3}&a_{3,4}\\0&0&0&a_{4,4}\end{array}\right]\cdot \left[\begin{array}{c}x_1\\x_2\\x_3\\x_4\end{array}\right] = \left[\begin{array}{c}b_1\\b_2\\b_3\\b_4\end{array}\right]$

This turn into the following system of equations:

$\begin{cases}a_{1,1}x_1+a_{1,2}x_2+a_{1,3}x_3+a_{1,4}x_4=b_1\\a_{2,2}x_2+a_{2,3}x_3+a_{2,4}x_4=b_2\\a_{3,3}x_3+a_{3,4}x_4=b_3\\a_{4,4}x_4=b_4\end{cases}$

The last equation is solvable for $x_4$ : we easily have

$x_4=\dfrac{b_4}{a_{4,4}}$

Once the value for $x_4$ is known, we can solve the third equation for $x_3$ :

$x_3 = \dfrac{b_3-a_{3,4}x_4}{a_{3,3}}$

(recall that $x_4$ is now known)

The pattern should be clear: you can use the last equation to solve for $x_4$ . Once it is known, the third equation involves the only variable $x_3$ . Once

4 0

3 years ago

What is the vector sum of 7, 5 and 13, −5?

FrozenT [24]

The answer is (20,0). We can determine the sum of two vector points by adding x1 to x2 and y1 to y2. This is like adding integers, the only difference is the answer is in vector form. In here, we have (x,y). x = 7+13 and y = 5+(-5). that is why we have the (20,0) as the answer.

6 0

3 years ago

Read 2 more answers

A right triangle has two legs with measure of 12 inches and 15 inches. Find the length of the hypotenuse to the nearest tenth of

Len [333]

Answer:

19 inches

Step-by-step explanation:

12^2+15^2=c^2

c=19.2094

4 0

3 years ago