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mylen [45]
3 years ago
12

Which of the following equations is paralllel to the line y+3x+1 and passes through the point (6,-3)

Mathematics
1 answer:
RideAnS [48]3 years ago
7 0

Answer:

y=3x-21

Step-by-step explanation:

a line is parallel if the slopes of the lines are the same

so that means that out line should look something like this

y=3x+b

then, we use our point given to find b

-3=18+b

b=-21

the equation of out line is y=3x-21

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What we are looking for are points of discontinuity. Think of it as when you remove your pencil from the paper.

From left to right, the graph stops at x = -3. So anything less than -3 is in the domain. Next, the graph starts up again at x =-1 after an asymptote (the vertical dashed lines). This piece goes to x = 4. So our domain is from -1 to 4.

Lastly, there's a jump from 4 to 5 and the graph goes on again. After 5, we take all the stuff more than it. So x > 5 is in the domain.

So x < -3, - 1 < x < 4, and x > 5 appears to be our domain. However, end points needed to be checked to see if we include them or not. Again we go left to right.

At x = -3 there is a filled (or closed) circle and that means we include -3.

At x = -1 there is an asymptote. Asymptotes are things you get close to but don't get to. (Think of it as the "I'm Not Touching" game you play on car trips.) So we exclude -1.

At x = 4 there is an unfilled (or open) circle and that means we exclude 4.

At x = 5 there is a filled circle so we include 5.

Now we refine our domain for the endpoints.

x ≤ -3, -1 < x < 4, x ≥ 5 is our domain.

The problem gives us intervals, and we gave it in inequalities. When we include an endpoint we use brackets - [ and } and when we exclude and endpoint we use parentheses - ( and ). Let's go back to x ≤ -3. Anything less works, and -3 is included (closed circle). That interval is (-∞, -3]. Next is the piece between -1 and 4. Since both are excluded, (-1,4) is our interval. We include 5 to write x ≥5 as the interval [5,∞).

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Our domain is (-∞, -3] ∪(-1,4) ∪ [5,∞).

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3 years ago
Some steps to rewrite the expression x3 − 4x + x2 − 4 as a product of three factors are shown below:
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3 years ago
Write the equation for the area of a triangle with a height that is 5 more than twice its base using one variable. Please help m
zysi [14]

Answer:

A=b(b+\frac{5}{2} )

Step-by-step explanation:

hey there!!!

we know already that the area of a triangle is given as

A=\frac{1}{2}b *h

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and h= heigth

Given that the height is 5 times more than twice it base

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Now we substitute h=2b+5 in the area of the triangle

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3 years ago
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