Solve for the variable <br><br> 3(x+5)=18

Write an equation with a variable x and solve it to find these unknown amounts. a. 18 more than double a number is divided by 5

Harlamova29_29 [7]

Answer:

x = 21

Step-by-step explanation:

1. Write the equation

(18 + 2x) ÷ 5 = 12

2. Multiply both sides by 5

18 + 2x = 60

3. Subtract 18 from both sides

2x = 42

4. Solve for x by dividing both sides by 2

x = 21

4 0

3 years ago

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Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 2 cos(t) + sin(2t),[0, π/2].

castortr0y [4]

Answer:

The absolute maximum is $\frac{3\sqrt 3}2$ and the absolute minimum value is $0.$

Step-by-step explanation:

Differentiate of $f$ both sides w.r.t. $t$ ,

$f(t)=2 \cos t+\sin 2t$

$\Rightarrow f'(t)=-2\sin t+2\cos 2t$

Now take $f'(t)=0$

$\Rightarrow -2\sin t+2\cos 2t=0$

$\Rightarrow 2\cos 2t=2\sin t$

$\Rightarrow \cos 2t=\sin t$

$\Rightarrow 1-2\sin ^2t =\sin t \quad \quad [\because \cos 2t = 1-2\sin ^2t]$

$\Rightarrow 2\sin ^2t+\sin t-1=0$

$\Rightarrow 2\sin ^2t+2\sin t-\sin t-1=0$

$\Rightarrow 2\sin t(\sin t+1)-1(\sin t+1)=0$

$\Rightarrow (\sin t+1)(2\sin t-1)=0$

$\Rightarrow \sin t+1=0 \;\text{and}\; 2\sin t-1=0$

$\Rightarrow \sin t =-1 \;\text{and}\; \sin t =\frac 12$

In the interval $0\leq t\leq \frac {\pi}2$ , the answer to this problem is $\frac {\pi}6$

Now find the second derivative of $f(t)$ w.r.t. $t$ ,

$f''(t)=-2\cos t-4\sin 2t$

$\Rightarrow \left[f''(t)\right]_{t=\frac {\pi}6}=-2\times \frac {\sqrt 3}2-4\times \frac{\sqrt 3}2=-3\sqrt 3$

Thus, $f(t)$ is maximum at $t=\frac {\pi}6$ and minimum at $t=0$

$\left[f(t)\right]_{t=\frac {\pi}6}=2\times \frac {\sqrt 3}2+\frac{\sqrt 3}2=\frac{3\sqrt 3}2\;\text{and}\;\left[f(t)\right]_{t=\frac{\pi}2}= 2\times 0+0=0$

Hence, the absolute maximum is $\frac{3\sqrt 3}2$ and the absolute minimum value is $0$ .

7 0

3 years ago

Show how you can use the distributive property to rewrite and find (32x6)+(32x4)

Nikitich [7]

32(6+4) =320 you need to find the common term and then place on ouside of the parentheses

8 0

3 years ago

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Alice wants to prove to her parents that listening to music while she does her homework will help her get better grades. She dec

Airida [17]

Answer:

She did not separate her friends into different groups, and she didn't apply a treatment.

Step-by-step explanation:

Alice decides to ask 25 of her friends if they listen to music while they do their homework and what their grades are.

She finds that her friends who have high grades also listen to music while they do their homework.

She tells her parents that she has proven that listening to music while doing homework will cause her grades to improve.

First of all it cannot be proven like this way.

Secondly, she did not use a random sample, and did not separated her friends into groups and applied treatment.

So, the answer is She did not separate her friends into different groups, and she didn't apply a treatment.

7 0

3 years ago

Lynn has 4 red candles and 8 blue candles . how many candles does she have?

schepotkina [342]

8+4=12. In total, she has 12 candles

6 0

4 years ago

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Solve for the variable 3(x+5)=18