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dlinn [17]
3 years ago
6

Which of the following are ordered pairs for the equation y = -2x - 3?

Mathematics
1 answer:
Alexus [3.1K]3 years ago
5 0

Answer:

b. (0,-3) (1,-5) (-1,-1)

Step-by-step explanation:

we only have to replace the first part of the parenthesis by x and the second part by y, and see if equality is met

y = -2x - 3

a.

(0,-3) (-1,-4) (-1,-5)

y = -2x - 3

-3 = -2(0) -3

-3 = -3

-4 = -2(-1) - 3

-4 = 2 -3

-4 = -1

WRONG OPTION

b.

(0,-3) (1,-5) (-1,-1)

y = -2x - 3

-3 = -2(0) -3

-3 = -3

-5 = -2(1) - 3

-5 = -2 -3

-5 = -5

-1 = -2(-1) -3

-1 = 2 -3

-1 = -1

CORRECT OPTION

c.

(0,-3) (1,4) (-1,-5)

y = -2x - 3

-3 = -2(0) -3

-3 = -3

4 = -2(1) -3

4 = -2 -3

4 = -5

WRONG OPTION

d.

(0,-3) (1,-4) (-1,-5)

y = -2x - 3

-3 = -2(0) -3

-3 = -3

-4 = -2(1) -3

-4 = -2 -3

-4 = -2

WRONG OPTION

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3 years ago
(1/1+sintheta)=sec^2theta-secthetatantheta pls help me verify this
Xelga [282]

Answer:

See Below.

Step-by-step explanation:

We want to verify the equation:

\displaystyle \frac{1}{1+\sin\theta} = \sec^2\theta - \sec\theta \tan\theta

To start, we can multiply the fraction by (1 - sin(θ)). This yields:

\displaystyle \frac{1}{1+\sin\theta}\left(\frac{1-\sin\theta}{1-\sin\theta}\right) = \sec^2\theta - \sec\theta \tan\theta

Simplify. The denominator uses the difference of two squares pattern:

\displaystyle \frac{1-\sin\theta}{\underbrace{1-\sin^2\theta}_{(a+b)(a-b)=a^2-b^2}} = \sec^2\theta - \sec\theta \tan\theta

Recall that sin²(θ) + cos²(θ) = 1. Hence, cos²(θ) = 1 - sin²(θ). Substitute:

\displaystyle \displaystyle \frac{1-\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta \tan\theta

Split into two separate fractions:

\displaystyle \frac{1}{\cos^2\theta} -\frac{\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta\tan\theta

Rewrite the two fractions:

\displaystyle \left(\frac{1}{\cos\theta}\right)^2-\frac{\sin\theta}{\cos\theta}\cdot \frac{1}{\cos\theta}=\sec^2\theta - \sec\theta \tan\theta

By definition, 1 / cos(θ) = sec(θ) and sin(θ)/cos(θ) = tan(θ). Hence:

\displaystyle \sec^2\theta - \sec\theta\tan\theta \stackrel{\checkmark}{=}  \sec^2\theta - \sec\theta\tan\theta

Hence verified.

8 0
3 years ago
Make the indicated trigonometric substitution in the given algebraic expression and simplify(x-25)/x = Sin y0
Strike441 [17]

Answer:

x = 25 /(1 − sin(y )) and y ≠ π/2  +2πn

Step-by-step explanation:

Let's solve and simplify for x,

(x − 25 )/ x  = sin(y)

Let's multiply both sides by x

((x − 25 )/x) *x= sin(y)*x

Then,

x − 25 = sin(y) * x

Let's add 25 to both sides

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If simplify again,

x = sin(y) * x + 25

Then we need subtract sin y x from both sides

x − sin(y) * x = sin (y)* x + 25 − sin (y)* x

It will equal:

x − sin (y)* x = 25

Factor x−sin(y) x: x(1−sin(y) ), then we get:

x (1 − sin(y)) = 25

Finally we need divide both sides by 1 − sin(y) ; y ≠π /2 + 2πn

And it will give us this equation:

x = 25 /(1 − sin(y )) and y ≠ π/2  +2πn

3 0
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