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gogolik [260]
2 years ago
9

Which expressions are equivalent to 5(1/3x+7)-3(1/2x-4)? Select three options. (There’s a picture)

Mathematics
1 answer:
Otrada [13]2 years ago
7 0

3rd option

Step-by-step explanation:

solve and simplify to find

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2x - 12 + 6 = 4x - 4

2x- 6 = 4x - 4

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x= -2/2

x = -1

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Rona mixes 2 pounds of meat with some chopped vegetables to make a mixture. She divides the mixture into 4 equal portions. Each
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Well if each portion is 3 pounds and there is 4 portions all together it would be 12 pounds. you already know know that the meat is 2 pounds so you subtract 2 from the whole and you are left with 10. The chopped vegetables are 10 pounds in total.
The answer is
4x3=12-2=10

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What is the equation of the line show In this graph? ASAP!! Please
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The equation is y= 1

Step-by-step explanation:


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3 years ago
Given that sec (x) = 2 and cosec (x) is negative,
weeeeeb [17]

Answer:

i) sin(2x) = -\frac{\sqrt{3}}{2}

ii) cot(x+360) = -\frac{\sqrt{3}}{3}

iii) sin(x-180) = \frac{\sqrt{3}}{2}

Step-by-step explanation:

sec(x) = 2

Since cos(x) is reciprocal of sec(x), this means:

cos(x) = \frac{1}{2}

cosec(x) is negative , this means sin(x) is also negative. The only quadrant where cos(x), sec(x) are positive and sin(x), cosec(x) are negative is the 4th quadrant. Hence the terminal arm of the angle x is in 4th quadrant.

Part i)

sin(2x) can be simplified as:

sin(2x) = 2 sin(x) cos(x)

First we need to find the value of sin(x). According to Pythagorean identity:

sin^{2}(x)=1-cos^{2}(x)\\\\ sin(x)=\pm \sqrt{1-cos^{2}(x)}

Since, angle is in 4th quadrant, sin(x) will be negative. So considering the negative value of sin(x) and substituting the value of cos(x), we get:

sin(x)=- \sqrt{1-cos^{2}(x)}\\\\ sin(x)=-\sqrt{1-(\frac{1}{2})^{2}}\\\\ sin(x)=-\frac{\sqrt{3}}{2}

So,

sin(2x)=2 \times -\frac{\sqrt{3} }{2} \times \frac{1}{2}\\\\ sin(2x)=-\frac{\sqrt{3}}{2}

Part ii)

We have to find cot(x + 360)

An addition of 360 degrees to the angle brings it back to the same terminal point. So the trigonometric ratios of the original angle and new angle after adding 360 or any multiple of 360 stay the same. i.e.

cot(x + 360) = cot(x)

cot(x) = \frac{cos(x)}{sin(x)}\\

Using the values, we get:

cot(x)=\frac{\frac{1}{2}}{-\frac{\sqrt{3}}{2} }\\\\ cot(x)=-\frac{\sqrt{3}}{3}

Part iii)

We need to find the value of sin(x - 180)

sin(x - 180) = - sin(x)

Addition or subtraction of 180 degrees changes the angle by 2 quadrants. The sign of sin(x) becomes opposite if the angle jumps by 2 quadrants. For example, sin(x) is positive in 1st quadrant and negative in 3rd quadrant.

So,

sin(x - 180) = -(-\frac{\sqrt{3}}{2}) = \frac{\sqrt{3}}{2}

6 0
3 years ago
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