What is the diameter of a 15 ft circle?

A graph is shown with x- and y-axes labeled from 0 to 6 at increments of 1. A straight line labeled A joins the ordered pair 2,

Oksanka [162]

Answer:

A. one B. (3, 4)

Step-by-step explanation:

1. A good graph can answer both parts (see attached image).

2. Write equations for the two lines and find a simultaneous solution.

Line A: Slope from (2, 6) to (5, 0) is $m=\frac{6-0}{2-5}=\frac{6}{-3}=-2$

Using point-slope form $y-y_1=m(x-x_1)$

$y-6=-2(x-2)\\y-6=-2x+4\\y=-2x+10$

Line B: Slopt from (6, 6) to (0, 2) is $m=\frac{6-2}{6-0}=\frac{2}{3}$

Using point-slope form, the equation for Line B is

$y-2=\frac{2}{3}(x-0)\\y=\frac{2}{3}x+2$

To find the simultaneous solution, set the y's equal.

$-2x+10=\frac{2}{3}x+2\\-6x+30=2x+6\\-8x=-24\\x=3$

Find y using either equation to get y = 4.

3 0

3 years ago

Fill in the table using this function rule.

Elodia [21]

Answer:

1) 16
2) 12
4) 4
5) 0

Step-by-step explanation:

Plug in the value for x in the equation above and solve for y for all 5.

3 0

2 years ago

Extra Credit #4

Hunter-Best [27]

Answer:

The next two numbers following:

431

141311

1114111321

311431131211

are:

132114132113111221

AND

11131221141113122113312211

Step-by-step explanation:

I shall explain the pattern below:

431 (just the digits 4, 3, and 1)

141311 (one 4 becomes 14, one 3 becomes 13, one 1 becomes 11 -> looking at each digit of the previous number, 431)

1114111321 (one 1 becomes 11, one 4 becomes 14, one 1 becomes 11, one three becomes 13, two consecutive 1s becomes 21 -> looking at each digit of the previous number, 141311)

311431131211 (three consecutive 1s becomes 31, one 4 becomes 14, 3 more consecutive 1s becomes 31, one 3 becomes 13, one 2 becomes 12, and one 1 becomes 11 -> looking at each digit of the previous number, 1114111321)

NEXT TWO NUMBERS:

one 3 (13), two consecutive 1s (21), one 4 (14), one 3 (13), two consecutive 1s (21), one 3 (13), one 1 (11), one 2 (12), two consecutive 1s (21)

that makes: 132114132113111221

one 1 (11), one 3 (13), one 2 (12), two consecutive 1s (21), one 4 (14), one 1 (11), one 3 (13), one 2 (12), two consecutive 1s (21), one 3 (13), three consecutive 1s (31), two consecutive 2s (22), one 1 (11)

that makes: 11131221141113122113312211

The rule is that the next number is essentially the previous number with the number of times each digit appears consecutively before each digit of the previous number. I know that sounds convoluted. Hopefully it makes enough sense. Let me know if I should explain more fully.

8 0

3 years ago

In Lesson 3.05 we discussed comparing the key features of two functions given in different forms. Given the functions below:

vladimir1956 [14]

Answer:

Step-by-step explanation:

a) Compare the y-intercepts of f(x) and g(x). Use complete sentences.

The functions f(x) and g(x) are different, the y-intercepts for each function is y-intercepts (0,-1/3) for f(x)= 1/x-3 and y-intercepts (0,0) for g(x) as shown on the graph.

b) Compare the vertical asymptotes of f(x) and g(x). Use complete sentences.

The functions f(x) and g(x) have different Vertical Asymptotes, f(x)= 1/x-3 Vertical Asymptotes is x = 3 while g(x) as shown on the graph Vertical Asymptotes is x = 4. Both functions do have Horizontal Asymptotes that are the same y = 0

8 0

4 years ago

Which is the best first step to write this in standard form?

goldenfox [79]

Answer:

Set the function equal to 0

Step-by-step explanation:

Standard Form of the Quadratic Equation

The form

$ax^2+bx+c=0$

is called the standard form of a quadratic equation. It can be clearly identified the terms of a second-degree polynomial equated to 0.

The equation is given in the form:

$2(x-4)^2-3=8$

And we need to operate the expression to make it look like a standard form. The first logical step should be to set the function equal to 0 and then start to operate the resulting expression. It can be done by subtracting 8 on both sides of the equation:

$2(x-4)^2-3-8=0$

Answer: Set the function equal to 0

4 0

3 years ago