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3 years ago

Which expression is equivalent to 9s + 3 x 5 -2s?

2 answers:

6 0

The answer is A. When you take the 9s and the -2s, you get 7s. Then you add the 3x5 and end up with 15. Giving you the answer 7s+15

VARVARA [1.3K]3 years ago

3 0

Answer is A hope this helps

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Please teach me on how to answer this question. (addmath question)

arsen [322]

We know that $\overline{x}=8$ so:

$\overline{x}=8\\\\\\\dfrac{\sum\limits_{k=1}^7\,x_k}{7}=8\qquad|\cdot7\\\\\\ \boxed{\sum\limits_{k=1}^7\,x_k=56}$

We want to calculate:

$\sum\limits_{k=1}^7\,\big(2x_k-3\big)^2=\sum\limits_{k=1}^7\,\big(4x_k^2-12x_k+9\big)=\\\\\\=\sum\limits_{k=1}^7\,4x_k^2-\sum\limits_{k=1}^7\,\big12x_k+\sum\limits_{k=1}^7\,9=4\sum\limits_{k=1}^7\,x_k^2-12\sum\limits_{k=1}^7\,x_k+\sum\limits_{k=1}^7\,9=\\\\\\=4\cdot672-12\cdot56+7\cdot9=2688-672+63=\boxed{2079}$

5 0

3 years ago

Find the distance between points P(9,8) and Q(7,6) to the nearest tenth.

sergey [27]

Answer:

2.8 units

Step-by-step explanation:

Think of this distance as the hypotenuse of a right triangle that has a vertical leg and a horizontal one as well.

Going from P to Q, the change in x is 2 and the change in y is also 2.

Thus, by the Pythagorean Theorem, this desired distance is:

d = √(2^2 + 2^2) = 2√2 units, or 2.8 units

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:

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

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

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

What is the least possible degree of a polynomial that has roots -5, 1 + 4i, and -4i?

just olya [345]

Hello,

Answer D:

the roots are -5,1+4i,1-4i,-4i,4i.

7 0

3 years ago

Read 2 more answers

Write down the bearing of: (a) Henly from Dinder (b) Dinder from Weare (c) Weare from Dinder (d) Weare from Henly (e) Dinder fro

Neko [114]

The bearing of the individuals from each other are as indicated below;

S45°E
N25°E
S65°E
S15°E
N45°E
N75°E

<h3>What is bearing of Henley from Dinder?</h3>

It follows from the task content that the bearing of the individuals from each other are expected to be determined.

a) For Henley from Dinder; it follows from observation that Henley is; S45°E of Dinder's position.

b) For Dinder from Weare; it follows from observation that Dinder is; N25°E of Weare's position.

c) For Weare from Dinder; it follows from observation that Weare is; S65°E of Dinder's position.

d) For Weare from Henly; it follows from observation that Weare is; S15°E of Dinder's position.

e) For Dinder from Henly; it follows from observation that Dinder is; N45°E of Henly's position.

f) For Henly from Weare; it follows from observation that Henly is; N75°E of Weare's position.