Choose the equation of the vertical line passing through the point (−2, 3). (5 point)

Solve the inequality.

victus00 [196]

Answer: A. x ≤ -3

x/3 - x-1/2 ≥ 1 would make x ≤ -3

5 0

3 years ago

Read 2 more answers

What is 36 to 21 ratio in simplest form?

OLga [1]

36:21 in simplest form is 12:7, because 3 goes into both 36 and 21. Simplifying ratios is essentially the same thing as simplifying fractions. Once we have 12:7, we can't reduce any further, because 7 is prime.

Hope this helps!

7 0

3 years ago

Which of the following graphs shows the solution set for the inequality below? 3|x + 1| < 9

Bas_tet [7]

Step-by-step explanation:

The absolute value function is a well known piecewise function (a function defined by multiple subfunctions) that is described mathematically as

$f(x) \ = \ |x| \ = \ \left\{\left\begin{array}{ccc}x, \ \text{if} \ x \ \geq \ 0 \\ \\ -x, \ \text{if} \ x \ < \ 0\end{array}\right\}$ .

This definition of the absolute function can be explained geometrically to be similar to the straight line $\textbf{\textit{y}} \ = \ \textbf{\textit{x}}$ , however, when the value of x is negative, the range of the function remains positive. In other words, the segment of the line $\textbf{\textit{y}} \ = \ \textbf{\textit{x}}$ where $\textbf{\textit{x}} \ < \ 0$ (shown as the orange dotted line), the segment of the line is reflected across the x-axis.

First, we simplify the expression.

$3\left|x \ + \ 1 \right| \ < \ 9 \\ \\ \\\-\hspace{0.2cm} \left|x \ + \ 1 \right| \ < \ 3$ .

We, now, can simply visualise the straight line, $y \ = \ x \ + \ 1$ , as a line having its y-intercept at the point $(0, \ 1)$ and its x-intercept at the point $(-1, \ 0)$ . Then, imagine that the segment of the line where $x \ < \ 0$ to be reflected along the x-axis, and you get the graph of the absolute function $y \ = \ \left|x \ + \ 1 \right|$ .

Consider the inequality

$\left|x \ + \ 1 \right| \ < \ 3$ ,

this statement can actually be conceptualise as the question

$``\text{For what \textbf{values of \textit{x}} will the absolute function \textbf{be less than 3}}"$ .

Algebraically, we can solve this inequality by breaking the function into two different subfunctions (according to the definition above).

Case 1 (when $x \ \geq \ 0$ )

$x \ + \ 1 \ < \ 3 \\ \\ \\ \-\hspace{0.9cm} x \ < \ 3 \ - \ 1 \\ \\ \\ \-\hspace{0.9cm} x \ < \ 2$

Case 2 (when $x \ < \ 0$ )

$-(x \ + \ 1) \ < \ 3 \\ \\ \\ \-\hspace{0.15cm} -x \ - \ 1 \ < \ 3 \\ \\ \\ \-\hspace{1cm} -x \ < \ 3 \ + \ 1 \\ \\ \\ \-\hspace{1cm} -x \ < \ 4 \\ \\ \\ \-\hspace{1.5cm} x \ > \ -4$

*remember to flip the inequality sign when multiplying or dividing by

negative numbers on both sides of the statement.

Therefore, the values of x that satisfy this inequality lie within the interval

$-4 \ < \ x \ < \ 2$ .

Similarly, on the real number line, the interval is shown below.

The use of open circles (as in the graph) indicates that the interval highlighted on the number line does not include its boundary value (-4 and 2) since the inequality is expressed as "less than", but not "less than or equal to". Contrastingly, close circles (circles that are coloured) show the inclusivity of the boundary values of the inequality.

3 0

2 years ago

Look at picture y=_ the height of the baseball after 5 seconds is ___ feet

Wittaler [7]

Answer:

y = -2(x -3)² +24
16 feet

Step-by-step explanation:

We expect the equation for y to be quadratic. Since the table is obviously symmetrical about x=3, we can start with the vertex form ...

y = a(x -3)² +b

Filling in the values from the first two table points, we get

For (x, y) = (0, 6):

6 = a(0 -3)² + b ⇒ 9a +b = 6

For (x, y) = (2, 22):

22 = a(2-3)² +b ⇒ a +b = 22

Subtracting the second equation from the first gives ...

(9a +b) -(a +b) = (6) -(22)

8a = -16 . . . . . . collect terms

a = -2 . . . . . . . . divide by 8

The second equation above tells us ...

b = 22 -a = 22 -(-2) = 24

So, our equation for y is ...

y = -2(x -3)² +24

__

The value of y for x=5 is ...

y = -2(5 -3)² +24 = 16

The height of the ball after 5 seconds is 16 feet.

5 0

2 years ago

Mr flores opened an account with a deposit of 5,000

Galina-37 [17]

Answer:

+5000

when he opened the bank there would be an addition to his account

3 0

2 years ago