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3 years ago

I WILL GIVE 30 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOO SCAMS HFGK - ZMWR. Complete the statement below.

Mathematics

2 answers:

DENIUS [597]3 years ago

5 0

Answer:

∠F=∠M

Step-by-step explanation:

They are corresponding angles.

Hope this helps!

Bezzdna [24]3 years ago

4 0

Answer:

angle f ≈ angle m

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Let f(x)=5x3−60x+5 input the interval(s) on which f is increasing. (-inf,-2)u(2,inf) input the interval(s) on which f is decreas

o-na [289]

Answers:

(a) f is increasing at $(-\infty,-2) \cup (2,\infty)$ .

(b) f is decreasing at $(-2,2)$ .

(c) f is concave up at $(2, \infty)$

(d) f is concave down at $(-\infty, 2)$

Explanations:

(a) f is increasing when the derivative is positive. So, we find values of x such that the derivative is positive. Note that

$f'(x) = 15x^2 - 60
$

So,

$
f'(x) \ \textgreater \ 0
\\
\\ \Leftrightarrow 15x^2 - 60 \ \textgreater \ 0
\\
\\ \Leftrightarrow 15(x - 2)(x + 2) \ \textgreater \ 0
\\
\\ \Leftrightarrow \boxed{(x - 2)(x + 2) \ \textgreater \ 0} \text{ (1)}$

The zeroes of (x - 2)(x + 2) are 2 and -2. So we can obtain sign of (x - 2)(x + 2) by considering the following possible values of x:

-->> x < -2
-->> -2 < x < 2
--->> x > 2

If x < -2, then (x - 2) and (x + 2) are both negative. Thus, (x - 2)(x + 2) > 0.

If -2 < x < 2, then x + 2 is positive but x - 2 is negative. So, (x - 2)(x + 2) < 0.
If x > 2, then (x - 2) and (x + 2) are both positive. Thus, (x - 2)(x + 2) > 0.

So, (x - 2)(x + 2) is positive when x < -2 or x > 2. Since

$f'(x) \ \textgreater \ 0 \Leftrightarrow (x - 2)(x + 2) \ \textgreater \ 0$

Thus, f'(x) > 0 only when x < -2 or x > 2. Hence f is increasing at $(-\infty,-2) \cup (2,\infty)$ .

(b) f is decreasing only when the derivative of f is negative. Since

$f'(x) = 15x^2 - 60$

Using the similar computation in (a),

$f'(x) \ \textless \ \ 0 \\ \\ \Leftrightarrow 15x^2 - 60 \ \textless \ 0 \\ \\ \Leftrightarrow 15(x - 2)(x + 2) \ \ \textless \ 0 \\ \\ \Leftrightarrow \boxed{(x - 2)(x + 2) \ \textless \ 0} \text{ (2)}$

Based on the computation in (a), (x - 2)(x + 2) < 0 only when -2 < x < 2.

Thus, f'(x) < 0 if and only if -2 < x < 2. Hence f is decreasing at (-2, 2)

(c) f is concave up if and only if the second derivative of f is positive. Note that

$f''(x) = 30x - 60$

Since,

$f''(x) \ \textgreater \ 0
\\
\\ \Leftrightarrow 30x - 60 \ \textgreater \ 0
\\
\\ \Leftrightarrow 30(x - 2) \ \textgreater \ 0
\\
\\ \Leftrightarrow x - 2 \ \textgreater \ 0
\\
\\ \Leftrightarrow \boxed{x \ \textgreater \ 2}$

Therefore, f is concave up at $(2, \infty)$ .

(d) Note that f is concave down if and only if the second derivative of f is negative. Since,

$f''(x) = 30x - 60$

Using the similar computation in (c),

$f''(x) \ \textless \ 0 
\\ \\ \Leftrightarrow 30x - 60 \ \textless \ 0 
\\ \\ \Leftrightarrow 30(x - 2) \ \textless \ 0 
\\ \\ \Leftrightarrow x - 2 \ \textless \ 0 
\\ \\ \Leftrightarrow \boxed{x \ \textless \ 2}$

Therefore, f is concave down at $(-\infty, 2)$ .

3 0

3 years ago

Is 3(5x - 4) = 15x - 12 a one solution , no solution or infinite solutions

vaieri [72.5K]

Answer:

Infinite Solutions

Step-by-step explanation:

3(5x - 4) needs to be simplified

So we multiply 5x by 3

So 3 x 5x = 15x

Then we multiply -4 by 3

3 x -4 = - 12

Put those together we get 15x - 12

The same equation as the one on the right side

So since 15x - 12 = 15x - 12, the x variable can be any number

Also a little tip:

With Forms quizzes, you can hit control + U and find the answers in the code

6 0

3 years ago

The rule in this pattern is add 3. Write the next 4 terms of the pattern. What do you observe about the terms in the pattern? Ex

Afina-wow [57]

If the rule for this pattern is add 3, you would take term 1 which had 5 dots then add 3, that makes term 2 have 8 dots, than add 3 that means term 3 has 11 dots, term four would have 14, and each term after that would have 3 more

8 0

3 years ago

A cab driver is paid $6 plus $0.45 per mile driven. Which expression shows the amount of money the cab driver earns in m miles?

Lunna [17]

No expressions are showing to choose from, but it should look like:

A= amount of money earned
m= # of miles driven

Amount earned equals $6 plus ($0.45 times the # of miles driven.)

EQUATION:
A= $6 + $0.45m

Hope this helps! :)

4 0

3 years ago

Can some one help me plz !!!!!!!!!,!<br> 25points

allsm [11]

You would multiply 6 × 5 and you would get 30.

better explanation : solution would be A = B H = 6 × 5 which would give you 30ft²

8 0

3 years ago