Find the next three numbers in this sequence. 20, 15, 10, . . .

The graph shows the distance Arlene ran on Saturday preparing for a marathon. What is the rate of change and what does it repres

andreev551 [17]

Answer:

Rate of change = 6 miles per hour

Step-by-step explanation:

Rate of change of the line is represented by the slope of the line.

Formula to get the rate of change is,

m = $\frac{\triangle y}{\triangle x}$

From the graph attached,

Given straight line is passing through two points (2, 12) and (4, 24).

Rate of change = $\frac{y_2-y_2}{x_2-x_1}$

= $\frac{24-12}{4-2}$

= 6

Rate of change of the line = 6 miles per hour

Therefore, rate of change of the graph will define the speed of Arlene.

3 0

3 years ago

A golf player is trying to make a hole-in-one on the miniature golf green shown.

Flauer [41]

The path of the ball is an illustration of absolute equation.

The equation of the path is: $y =- \frac{12}7|x- 4.8| + 6.4$

The given parameters are:

$(h,k) = (4.8,6.4)$ --- the vertex (i.e. the point where the ball hits the wall)

$(x_1,y_1) = (2,1.6)$

$(x_2,y_2) = (7.6,1.6)$

An absolute function is represented as:

$y = a |x - h| + k$

Substitute $(h,k) = (4.8,6.4)$

$y = a |x - 4.8| + 6.4$

Substitute $(x_1,y_1) = (2,1.6)$ for x and y

$1.6 = a|2 - 4.8| + 6.4$

$1.6 = a|- 2.8| + 6.4$

Remove absolute bracket

$1.6 = 2.8a + 6.4$

Collect like terms

$2.8a = -6.4+1.6$

$2.8a =- 4.8$

Solve for a

$a =-\frac{4.8}{2.8}$

Simplify

$a =-\frac{12}{7}$

Substitute $a =-\frac{12}{7}$ in $y = a |x - 4.8| + 6.4$

$y =- \frac{12}7|x- 4.8| + 6.4$

Hence, the equation of the path is: $y =- \frac{12}7|x- 4.8| + 6.4$

See attachment for graph that models the path

Read more about absolute equations at:

brainly.com/question/2166748

5 0

2 years ago

Factorise 9w² - 100

ohaa [14]

Answer:

$9\, w^{2} - 100 = (3\, w - 10) \, (3\, w + 10)$ .

Step-by-step explanation:

Fact:

$\begin{aligned} & (a - b)\, (a + b)\\ =\; & a^{2} + a\, b - a\, b - b^{2} \\ =\; & a^{2} - b^{2} \end{aligned}$ .

In other words, $(a^{2} - b^{2})$ , the difference of two squares in the form $a^{2}$ and $b^{2}$ , could be factorized into $(a - b)\, (a + b)$ .

In this question, the expression $(9\, w^{2} - 100)$ is the difference between two terms: $9\, w^{2}$ and $100$ .

$9\, w^{2}$ is the square of $3\, w$ . That is: $(3\, w)^{2} = 9\, w^{2}$ .
On the other hand, $10^{2} = 100$ .

Hence:

$9\, w^{2} - 100 = (3\, w)^{2} - (10)^{2}$ .

Apply the fact that $a^{2} - b^{2} = (a - b) \, (a + b)$ to factorize this expression. (In this case, $a = 3\, w$ whereas $b = 10$ .)

$\begin{aligned}& 9\, w^{2} - 100 \\ =\; & (3\, w)^{2} - (10)^{2} \\ = \; & (3\, w - 10)\, (3\, w + 10)\end{aligned}$ .

8 0

3 years ago

Which of these ordered pairs is a solution to the inequality

bezimeni [28]

Answer:

(1, -1)

Step-by-step explanation:

If you replace y and x with (1 and -1) you have -1 - 2^1 < -3

And that equals -3 if solved. The sign says equal to or less than, so you answer is (1, -1)

7 0

3 years ago

PLEASE SOLVE THE QESTIONS

jeka57 [31]

Answer:??????????????????

Step-by-step explanation:

3 0

2 years ago