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tankabanditka [31]
3 years ago
12

If the sum of four times a number and four less than three times a number is seventeen

Mathematics
1 answer:
NARA [144]3 years ago
8 0

Answer:

13divided by 7

Step-by-step explanation:

4x + 3x - 4 = 17 \\ 7x - 4 = 17 \\ 7x = 17 - 4 \\ 7x = 13 \\  \frac{7x}{7}  =  \frac{13}{7 }  \\ x =  \frac{13}{7} or1 \times \frac{6}{7}

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Determine the x- and y- intercepts for the graph defined by the given equation.
777dan777 [17]

Answer:

y-intercept is (0,8)

c. x-intercept is (-8, 0)

Step-by-step explanation:

y=x+8

x=0

y+0=8

y=8

y=0

y=x+8

0=x+8

x=-8

7 0
3 years ago
Read 2 more answers
-4t=15=-1 what is t
Alexandra [31]

Answer:

-4

Step-by-step explanation:

-4t+15=-1

Subtract 15 on both sides:

-4t=-16

Divide -4 on both sides:

t=-4

3 0
3 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).
4 0
3 years ago
Diving simply the following: 3 power 12÷3 power 7​
navik [9.2K]

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

{3}^{12}  \div  {3}^{7}  =

{3}^{12}  \times  {3}^{ - 7}  =

{3}^{12 - 7}  =  {3}^{5}

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

8 0
3 years ago
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Wionna needs to average 5.8 from 14 judges. The mean score from 13 judges is 5.9. What is the lowest score she can receive from
kirill115 [55]
(5.9*13+s)/(13+1)\geq5.8

(76.7+s)/14\geq5.8

76.7+s\geq81.2

s\geq4.5
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3 years ago
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