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Hannah does push-ups in sets of three she did 10 sets of push-ups today then her coach asked her to do 15 more push-ups how many

scoray [572]

Answer:

30+ 15 =45

Step-by-step explanation:

(3×10)+15 =45

4 0

3 years ago

3x − 2y = 6 3x + 10y = −12 Find the common x and y.

Ganezh [65]

x = 1

y = -3/2

Solution: (1, -3/2)

//Hope it helps.

7 0

3 years ago

Read 2 more answers

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

Please help due today

sweet-ann [11.9K]

Answer:

It is a function

Step-by-step explanation:

This isn't really a step by step explanation but I'm going to explain this simply. An output can have as many inputs possible but an input can only have ONE OUTPUT(just putting emphasis on this one output, I'm not yelling). Example, the input "2" can be equal to the output of "4" depending on the equation the fuction, however, the input of "2" CAN NOT be equal to the outputs of "4" and "6" because as my Algebra teacher explained it "for every input, there is exactly one output". I hope this helps and I hope I didn't lose you in my explaination.

4 0

2 years ago

If a car can drive 62 miles on 3 gallons of gas, how many gallons of gas will it use to travel 231 miles?

aksik [14]

Answer:

11 gallons of gas is needed to travel 231 miles.

Step-by-step explanation:

We can set up a proportion for this problem.

For every 62 miles, you use 3 gallons of gas.

$\frac{62}{3}*\frac{231}{?}$