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2 years ago

What is the slope-intercept form of the linear equation 4x + 2y = 24?

Mathematics

1 answer:

joja [24]2 years ago

6 0

Step-by-step explanation:

the slope-intercept form =x + (y/2) =6

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Which equation shows y=3/4x−52 in standard form? 4x−3y=10 4x−3y=−10 3x−4y=10 3x−4y=−10

snow_tiger [21]

Y = 3/4x - 5/2....subtract 3/4x from both sides
-3/4x + y = -5/2 ....multiply everything by common denominator of 4
-3x + 4y = -10

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2 years ago

The difference between 13 and a number k in algebraic expression?

viva [34]

13-k

Explanation: it’s just 13 minus the number k

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2 years ago

Write a compound interest function to model the following situation. Then, find the balance after the given number of years.

lakkis [162]

Y=17400(1+0.025)^8 is your equation and with that you get $21200.21

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2 years ago

Read 2 more answers

The middle one is the one I need help with

gulaghasi [49]

Answer:

it would be 3x1 or 1x3

Step-by-step explanation:

5 0

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

2 years ago