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3 years ago

Are the pair of lines parallel, perpendicular or neither? 8x-4y=12 and 4x-y=-15

Mathematics

1 answer:

Orlov [11]3 years ago

6 0

Answer:

neither, would technically be intersecting lines tho

Step-by-step explanation:

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Find the area. HELP PLEASE!!!!!!

kaheart [24]

Answer:

616

Step-by-step explanation:

The equation to find the area of a trapezoid is: A = ½ (b $^1$ +b²) h.

b1=43

b2=45

h=14

Plug the variables in and solve.

$A=\frac{1}{2} (43+45)14$

$A=\frac{1}{2} (88)14$

$A=\frac{1}{2} (1232)$

$A=616$

3 0

2 years ago

Read 2 more answers

How do I solve: 2 sin (2x) - 2 sin x + 2√3 cos x - √3 = 0

ziro4ka [17]

Answer:

$\displaystyle x = \frac{\pi}{3} +k\, \pi$ or $\displaystyle x =- \frac{\pi}{3} +2\,k\, \pi$ , where $k$ is an integer.

There are three such angles between $0$ and $2\pi$ : $\displaystyle \frac{\pi}{3}$ , $\displaystyle \frac{2\, \pi}{3}$ , and $\displaystyle \frac{4\,\pi}{3}$ .

Step-by-step explanation:

By the double angle identity of sines:

$\sin(2\, x) = 2\, \sin x \cdot \cos x$ .

Rewrite the original equation with this identity:

$2\, (2\, \sin x \cdot \cos x) - 2\, \sin x + 2\sqrt{3}\, \cos x - \sqrt{3} = 0$ .

Note, that $2\, (2\, \sin x \cdot \cos x)$ and $(-2\, \sin x)$ share the common factor $(2\, \sin x)$ . On the other hand, $2\sqrt{3}\, \cos x$ and $(-\sqrt{3})$ share the common factor $\sqrt[3}$ . Combine these terms pairwise using the two common factors:

$(2\, \sin x) \cdot (2\, \cos x - 1) + \left(\sqrt{3}\right)\, (2\, \cos x - 1) = 0$ .

Note the new common factor $(2\, \cos x - 1)$ . Therefore:

$\left(2\, \sin x + \sqrt{3}\right) \cdot (2\, \cos x - 1) = 0$ .

This equation holds as long as either $\left(2\, \sin x + \sqrt{3}\right)$ or $(2\, \cos x - 1)$ is zero. Let $k$ be an integer. Accordingly:

$\displaystyle \sin x = -\frac{\sqrt{3}}{2}$ , which corresponds to $\displaystyle x = -\frac{\pi}{3} + 2\, k\, \pi$ and $\displaystyle x = -\frac{2\, \pi}{3} + 2\, k\, \pi$ .
$\displaystyle \cos x = \frac{1}{2}$ , which corresponds to $\displaystyle x = \frac{\pi}{3} + 2\, k \, \pi$ and $\displaystyle x = -\frac{\pi}{3} + 2\, k \, \pi$ .

Any $x$ that fits into at least one of these patterns will satisfy the equation. These pattern can be further combined:

$\displaystyle x = \frac{\pi}{3} + k \, \pi$ (from $\displaystyle x = -\frac{2\,\pi}{3} + 2\, k\, \pi$ and $\displaystyle x = \frac{\pi}{3} + 2\, k \, \pi$ , combined,) as well as
$\displaystyle x =- \frac{\pi}{3} +2\,k\, \pi$ .

7 0

3 years ago

A travel agency books holiday tours to Italy, Greece, and other countries in Europe. A supervisor notes that the probability tha

lutik1710 [3]

P(Greece) =0.28 among tem P(G∩I) = 0.11. We also know tat
P(G ∪ I ) =1 [either Greece or Italy or both= all travelers)
The only data that is missing is te P(Italy)
P(G ∪ I ) = P(G) + P(I) - P(G∩ I)
1 =0.28 + P(I) so P(I) = 0.72
P(G) = 0.28 (including the 0 .11)
P(I) = 0.72 (including the 0.11)
P(G and I) =0.11

3 0

3 years ago

Read 2 more answers

A youth group is planning a trip to a theme park. The bus holds up to 40 people. The cost for bus parking is $60.00. Each person

Lilit [14]

Given equation is:

$T=36x+60$