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3 years ago

How do you solve 2x=12+2y

Mathematics

1 answer:

Sonbull [250]3 years ago

7 0

2(x) - [12 + 2y) ➡ 0
2(x - y - 6)
2 ➡0 {It doesn't have any solution for the equation}
x - y - 6 ➡0
y ➡ 6 over -1 ; x ➡6 over 1
The slope = 1

Therefore your answer would have to be ➡
y= 6 over -1 ; x = 6 over 1 ; slope = 1

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A survey asked students whether they would like a drama club, a step team, both clubs, or neither club. The results are below:

Dmitry [639]

Hi, you've asked an incomplete question. Here are the remaining questions:

a) Describe what each region in the Venn diagram represents.

Region I: In drama club, not in step team.

Region II: In both clubs.

Region III: In step team not in drama.

Region IV: Not in either club.

b) How many students were in only one of the two clubs?

c) How many students were in the drama club or in the step team?

d) How many students were surveyed?

Attached is the Venn diagram depicting the regions.

Explanation:

b) By adding the number of students that like drama club and those that like step club we can derive the answer: 34 + 27 = 61.

c) By adding 34 + 27 + those that like both (14) = 75.

d) The total number of students surveyed is gotten by summing any number in attached the diagram: 34 + 27 + 14 + 13 = 88.

7 0

3 years ago

WHAT TWO EQAUL NUMBERS ADD TO THE EVEN NUMER 40

Mars2501 [29]

Answer:

Step-by-step explanation:

20+20=40

7 0

2 years ago

Write the sum of the numbers as the product of their gcf and another sum 32 and 20

pav-90 [236]

Ymm makes no sense but its pulsing so yea the answer is 52

7 0

3 years ago

A side of the triangle below has been extended to form an exterior angle of 164". Find

Arada [10]

Given:

Measure of exterior angle = 164°

The measure of opposite interior angles are x° and 53°.

To find:

The value of x.

Solution:

According to the Exterior Angle Theorem, in a triangle the measure of an exterior angles is always equal to the sum of measures of two opposite interior angles.

Using Exterior Angle Theorem, we get

$x^\circ+53^\circ=164^\circ$

$x^\circ=164^\circ-53^\circ$

$x^\circ=111^\circ$

$x=111$

Therefore, the value of x is 111.

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