Before sending track and field athletes to the Olympics, the U.S. holds a qualifying meet.

Select all the expressions that are equivalent to 2•2•2•2•2•2

aliina [53]

Answer:

2^6, 64

Step-by-step explanation: The simplified version is two to the fifth power and the answer is 64. Those are the two I know

8 0

3 years ago

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The sum of three consecutive even numbers is 552. What is the 1st number?

wariber [46]

Answer:

Let 2n = the first of three consecutive even numbers, where n is an integer.

Let 2n + 2 = the second of three consecutive even numbers, and

Let 2n + 4 = the third of three consecutive even numbers.

We're given that "sum of three consecutive even numbers is 552." We can translate this English sentence mathematically into the following equation to be solved for n:

2n + (2n + 2) + (2n + 4) = 552

Removing the parentheses, we have:

2n + 2n + 2 + 2n + 4 = 552

Now, by the Commutative Law of Addition, i.e., a + b = b + a, we have on the left side of the equation:

2n + 2n + 2n + 2 + 4 = 552

Now, collecting like-terms on the left, we get:

6n + 6 = 552

To solve for the variable n, We now begin isolating n on the left side by subtracting 6 from both sides as follows:

6n + 6 - 6 = 552 - 6

6n + 0 = 546

6n = 546

Now, divide both sides by 6 to finally solve for n:

(6n)/6 = 546/6

(6/6)n = 546/6

(1)n = 91

n = 91

Therefore, the first of three consecutive even numbers, 2n, is:

2n = 2(91)

= 182

The second of three consecutive even numbers is:

2n + 2 = 2(91) + 2

= 182 + 2

= 184

The third of three consecutive even numbers is:

2n + 4 = 2(91) + 4

= 182 + 4

= 186

CHECK:

2n + (2n + 2) + (2n + 4) = 552

182 + 184 + 186 = 552

552 = 552

Therefore, the desired and first of three consecutive even numbers is indeed 2n = 182.

7 0

3 years ago

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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:

$g(x)=x^3-9x \quad \textsf{when x is less than 3}$

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

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.

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).

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

Consider a parallelogram in which one side is 3 inches long, another side measures 4 inches, and the measurement of one angle is

goldenfox [79]

Answer:

Only one parallelogram can be drawn based on the given conditions.

Step-by-step explanation: just believe me

7 0

3 years ago

Find the slope of the line that passes through the points (-12,10) and (-18,14).

9966 [12]

Answer:

-2/3

Step-by-step explanation:

To find the slope we use the formula

m= ( y2-y1)/(x2-x1)

= ( 14-10)/(-18- -12)

= (14-10)/(-18+12)

= 4/-6

= -2/3

5 0

3 years ago