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Vikentia [17]
3 years ago
7

John, Mark, and Michael completed a total of 25 laps during track practice on Thursday. If John completed a laps,mark completed

b laps, and Michael completed c laps, which equation BEST describes the number of laps Michael ran?​
Mathematics
1 answer:
Fantom [35]3 years ago
6 0

Answer:

25-a-b=c or also c=25-a-b

Step-by-step explanation:

We need to get "c" by itself.

The equation for the total amount of laps is a+b+c=25

To get c by itself, we subtract a and b from both sides

Thus, we get c=25-a-b

Hope this helped!

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2/8 and 5/8 in simplest form
8090 [49]

Answer:

2/8 is simplest form is 1/4 and 5/8 in simplest form is just 5/8

Step-by-step explanation:

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2 years ago
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Zx and Zy are supplementary angles. Zy measures 108°,
gulaghasi [49]

Answer:

72°

Step-by-step explanation:

Given

Zy = 108°

Zx = ?

We know

Zx + Zy = 180° {being supplementary angles }

Zx + 108° = 180°

Zx = 180° - 108°

Zx = 72°

Hope it will help :)

4 0
3 years ago
What expression is the simplest form of -(4x+y) +2(x-3y)?
jolli1 [7]

the answer would be d, very much appreciated if you would give me brainliest

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3 years ago
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Which is M=9pm solved for p
zaharov [31]
<h2>Answer:</h2>

<u>The value of </u><u>p :M/9m</u>

<h2>Explanation:</h2>

As we have been given value of M

Value of M=9pm

So we can find value of p from here by simple mathematics rule

M=9pm

divide both side with 9m so

M/9m=9pm/9m

we get value of p so M/9m=p.

we can write it as p=M/9m

6 0
3 years ago
PLEASE HELP 100 POINTS!!!!!!
horrorfan [7]

Answer:

A)  See attached for graph.

B)  (-3, 0)  (0, 0)  (18, 0)

C)   (-3, 0) ∪ [3, 18)

Step-by-step explanation:

Piecewise functions have <u>multiple pieces</u> of curves/lines where each piece corresponds to its definition over an <u>interval</u>.

Given piecewise function:

g(x)=\begin{cases}x^3-9x \quad \quad \quad \quad \quad \textsf{if }x < 3\\-\log_4(x-2)+2 \quad  \textsf{if }x\geq 3\end{cases}

Therefore, the function has two definitions:

  • g(x)=x^3-9x \quad \textsf{when x is less than 3}
  • g(x)=-\log_4(x-2)+2 \quad \textsf{when x is more than or equal to 3}

<h3><u>Part A</u></h3>

When <u>graphing</u> piecewise functions:

  • Use an open circle where the value of x is <u>not included</u> in the interval.
  • Use a closed circle where the value of x is <u>included</u> in the interval.
  • Use an arrow to show that the function <u>continues indefinitely</u>.

<u>First piece of function</u>

Substitute the endpoint of the interval into the corresponding function:

\implies g(3)=(3)^3-9(3)=0 \implies (3,0)

Place an open circle at point (3, 0).

Graph the cubic curve, adding an arrow at the other endpoint to show it continues indefinitely as x → -∞.

<u>Second piece of function</u>

Substitute the endpoint of the interval into the corresponding function:

\implies g(3)=-\log_4(3-2)+2=2 \implies (3,2)

Place an closed circle at point (3, 2).

Graph the curve, adding an arrow at the other endpoint to show it continues indefinitely as x → ∞.

See attached for graph.

<h3><u>Part B</u></h3>

The x-intercepts are where the curve crosses the x-axis, so when y = 0.

Set the <u>first piece</u> of the function to zero and solve for x:

\begin{aligned}g(x) & = 0\\\implies x^3-9x & = 0\\x(x^2-9) & = 0\\\\\implies x^2-9 & = 0 \quad \quad \quad \implies x=0\\x^2 & = 9\\\ x & = \pm 3\end{aligned}

Therefore, as x < 3, the x-intercepts are (-3, 0) and (0, 0) for the first piece.

Set the <u>second piece</u> to zero and solve for x:

\begin{aligned}\implies g(x) & =0\\-\log_4(x-2)+2 & =0\\\log_4(x-2) & =2\end{aligned}

\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b

\begin{aligned}\implies 4^2&=x-2\\x & = 16+2\\x & = 18 \end{aligned}

Therefore, the x-intercept for the second piece is (18, 0).

So the x-intercepts for the piecewise function are (-3, 0), (0, 0) and (18, 0).

<h3><u>Part C</u></h3>

From the graph from part A, and the calculated x-intercepts from part B, the function g(x) is positive between the intervals -3 < x < 0 and 3 ≤ x < 18.

Interval notation:  (-3, 0) ∪ [3, 18)

Learn more about piecewise functions here:

brainly.com/question/11562909

3 0
2 years ago
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