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3 years ago

Which line is parallel to 2x - y = -3 and goes through (5, 5)?

Mathematics

2 answers:

Sunny_sXe [5.5K]3 years ago

8 0

Answer:

G. y=2x-5

Step-by-step explanation:

First, find the slope from 2x-y=-3

-y=-2x-3

y=2x+3, which means that the slope is 2

Since it is parallel, the given equation and the line we are finding has the same slope.

let y=mx+b, where m=2, y=5, x=5

5=2(5)+b

5=10+b

-5=b

Thus, y=2x-5

irga5000 [103]3 years ago

6 0

Answer:

F Y=1x+5 G Y=2x-5 H Y =x-3 J Y=2x+5

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which of the functions have a range of real numbers greater than or equal to 1 or less than or equal to-1

lilavasa [31]

The question is incomplete. Here is the complete question:

Which of the functions have a range of all real numbers greater than or equal to 1 or less than or equal to -1? check all that apply.

A. $y=\sec x$

B. $y= \tan x$

C. $y= \cot x$

D. $y= \csc x$

Answer:

A. $y=\sec x$

D. $y=\csc x$

Step-by-step explanation:

Given:

The range is greater than or equal to 1 or less than or equal to -1.

The given choices are:

Choice A: $y=\sec x$

We know that, the $\sec x=\frac{1}{\cos x}$

The range of $\cos x$ is from -1 to 1 given as [-1, 1]. So,

$|\cos x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\cos x|}\geq 1\\|\sec x|\geq 1$

Therefore, on removing the absolute sign, we rewrite the secant function as:

$\sec x\leq -1\ or\ \sec x\geq 1\\$

Therefore, the range of $y=\sec x$ is all real numbers greater than or equal to 1 or less than or equal to-1.

Choice B: $y= \tan x$

We know that, the range of tangent function is all real numbers. So, choice B is incorrect.

Choice C: $y= \cot x$

We know that, the range of cotangent function is all real numbers. So, choice C is incorrect.

Choice D: $y=\csc x$

We know that, the $\csc x=\frac{1}{\sin x}$

The range of $\sin x$ is from -1 to 1 given as [-1, 1]. So,

$|\sin x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\sin x|}\geq 1\\|\csc x|\geq 1$

Therefore, on removing the absolute sign, we rewrite the cosecant function as:

$\csc x\leq -1\ or\ \csc x\geq 1\\$

Therefore, the range of $y=\csc x$ is all real numbers greater than or equal to 1 or less than or equal to-1.

6 0

3 years ago

Jonathan is rolling to dice and needs to roll and 11 to win the game he is playing what is the probability that Jonathan wins th

hjlf

Answer:

1 / 18

Step-by-step explanation:

In a roll of two dice :

Number of faces on a dice = 6

Total sample space for 2 6-sided dice = (number of faces)^Number of dice = 6^2 = 36

Total possible outcomes = 36

Required outcome = sum of 11

11 = {(5,6) ; (6, 5)}) = 2 possibilities

Probability = required outcome / Total possible outcomes

P(obtaining a sum of 11) = 2 / 36 = 1/18

5 0

3 years ago

What are the solutions of the equation x² = 49

olga55 [171]

To find x you do √49=x

5 0

3 years ago

Write the equation of the line that passes through the given points in slope intercept form

shepuryov [24]

Answer:

y=3x

Step-by-step explanation:

To put this in slope intercept form, let’s first find the slope

To find slope, use the equation Y2-Y1/X2-X1

When we do this, we get 0-6/0-2

This simplifies out into -6/-2 which is 3

So our slope is 3. Our equation becomes y=3x+b

Now, we find our b

We don’t have to do any solving for this, since we have the point 0,0 listed for us, it goes through the origin and that is our y-intercept or b

So our final equation is y=3x

Hope this helps and have a good day!

5 0

2 years ago

Read 2 more answers

What is the area of the base?

MAXImum [283]

Answer:

24 in²

Step-by-step explanation:

Hello there!

the figure shown is a triangular prism

The base is the triangle

So we need to find the area of the triangle using this formula

$A=\frac{bh}{2}$

where b = base and h = height

The base (triangle) has a base length of 8 inches and a height of 6 inches

Having found the information we needed, we plug it into the formula

$A=\frac{6*8}{2} \\6*8=48\\\frac{48}{2} =24\\A=24in^2$

So the area of the base is 24 in²

7 0

3 years ago

Which line is parallel to 2x - y = -3 and goes through (5, 5)?​

Which line is parallel to 2x - y = -3 and goes through (5, 5)?