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3 years ago

Please can someone help please?

Mathematics

1 answer:

sergejj [24]3 years ago

6 0

Answer: C

Step-by-step explanation:

Segments AC and CE are collinear, meaning they must have equal slopes.

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Which expression demonstrates the distributive property applied to the expression 4(3 + 7)

GREYUIT [131]

4(3 + 7)

= 4(3) + 4(7) //Demonstrating distributive property

= 12 + 28

= 40

7 0

3 years ago

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

1) a=b+√b²+√c² make c the subject of the formula

Nonamiya [84]

Answer:(A²-B²) = (A-B)² + 2AB

Step-by-step explanation:

5 0

3 years ago

288/32 in simplest form

inn [45]

288/32=144/16=72/8=9

Hope it helps you

5 0

3 years ago

Read 2 more answers

A circular piece of metal has a radius of 3.5 meters.

prisoha [69]

1) we calculate the area of the circular piece of metal.
area=πr²
area=π(3.5 m)²=12.25π m² ≈ 38.48 m²

2)we calculate the total cost of the circular piece of meta by the rule of three.

$3.25-------------------1 m²
x--------------------------38.48 m²

x=($3.25 * 38.48m²) / 1 m²=125.06$

Answer: 125.06$

We can also calcultate the total cost of the ciucular piece of metal by the ratius.
Ratius=$3.25/1m²

Total cost=ratius * area of the circular piece of metal.
total cost=($3.25/ m²)*(38.48 m²)=$125.06

Answer: $125.06

4 0

4 years ago

Please can someone help please?​

Please can someone help please?