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Lady_Fox [76]
3 years ago
10

Solve the following linear equation and please explain how you did it 6y+8=6(y+4)−16

Mathematics
2 answers:
Tasya [4]3 years ago
6 0

Answer:

infinite solutions, true for all y

Step-by-step explanation:

6y+8=6(y+4)−16

Distribute

6y+8 = 6y+ 24 - 16

Combine like terms

6y+8 = 6y+8

Subtract 6y from each side

8=8

Since this is always true, the equation is true for all real y

solniwko [45]3 years ago
5 0

Answer:

True of all values of 'y'.

Step-by-step explanation:

6y+8=6(y+4)-16\\\\6y+8=6y+24-16\\\\6y+8=6y+8\\\\6y+8-8=6y+8-8\\\\6y=6y\\\\6y-6y=6y-6y\\\\\boxed{0=0}

Hope this helps.

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What is the value of 4x2 + 5x when x= 1?
Darina [25.2K]

Answer:

13

Explanation:

Insert 1 for 'x'

(4)(1)(2) + 5(1)

(4)(1)(2) = 8

5(1) = 5

8 + 5 = 13

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Brian usually brushes his teeth in the morning, but 10% of the time he forgets. What is the probability that he will forget to b
Katena32 [7]

Using it's concept, it is found that there is a 0.001 = 0.1% probability that he will forget to brush his teeth three days in a row.

<h3>What is a probability?</h3>

A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>.

In this problem, for each day, there is a 0.1 probability that he forgers to brush his teeth, and days are independent, hence for 3 consecutive days the probability is given by:

p = (0.1)³ = 0.001.

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5 0
2 years ago
How to know if a function is periodic without graphing it ?
zhenek [66]
A function f(t) is periodic if there is some constant k such that f(t+k)=f(k) for all t in the domain of f(t). Then k is the "period" of f(t).

Example:

If f(x)=\sin x, then we have \sin(x+2\pi)=\sin x\cos2\pi+\cos x\sin2\pi=\sin x, and so \sin x is periodic with period 2\pi.

It gets a bit more complicated for a function like yours. We're looking for k such that

\pi\sin\left(\dfrac\pi2(t+k)\right)+1.8\cos\left(\dfrac{7\pi}5(t+k)\right)=\pi\sin\dfrac{\pi t}2+1.8\cos\dfrac{7\pi t}5

Expanding on the left, you have

\pi\sin\dfrac{\pi t}2\cos\dfrac{k\pi}2+\pi\cos\dfrac{\pi t}2\sin\dfrac{k\pi}2

and

1.8\cos\dfrac{7\pi t}5\cos\dfrac{7k\pi}5-1.8\sin\dfrac{7\pi t}5\sin\dfrac{7k\pi}5

It follows that the following must be satisfied:

\begin{cases}\cos\dfrac{k\pi}2=1\\\\\sin\dfrac{k\pi}2=0\\\\\cos\dfrac{7k\pi}5=1\\\\\sin\dfrac{7k\pi}5=0\end{cases}

The first two equations are satisfied whenever k\in\{0,\pm4,\pm8,\ldots\}, or more generally, when k=4n and n\in\mathbb Z (i.e. any multiple of 4).

The second two are satisfied whenever k\in\left\{0,\pm\dfrac{10}7,\pm\dfrac{20}7,\ldots\right\}, and more generally when k=\dfrac{10n}7 with n\in\mathbb Z (any multiple of 10/7).

It then follows that all four equations will be satisfied whenever the two sets above intersect. This happens when k is any common multiple of 4 and 10/7. The least positive one would be 20, which means the period for your function is 20.

Let's verify:

\sin\left(\dfrac\pi2(t+20)\right)=\sin\dfrac{\pi t}2\underbrace{\cos10\pi}_1+\cos\dfrac{\pi t}2\underbrace{\sin10\pi}_0=\sin\dfrac{\pi t}2

\cos\left(\dfrac{7\pi}5(t+20)\right)=\cos\dfrac{7\pi t}5\underbrace{\cos28\pi}_1-\sin\dfrac{7\pi t}5\underbrace{\sin28\pi}_0=\cos\dfrac{7\pi t}5

More generally, it can be shown that

f(t)=\displaystyle\sum_{i=1}^n(a_i\sin(b_it)+c_i\cos(d_it))

is periodic with period \mbox{lcm}(b_1,\ldots,b_n,d_1,\ldots,d_n).
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3 years ago
Consider the equation x/3+7=13.
Darya [45]

Answer:

Step-by-step explanation:x/3+7=13

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