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sergiy2304 [10]
3 years ago
6

using a number line, find both the intersection and the union of the following interval: (-∞, 7) and [-5, +∞)

Mathematics
1 answer:
Gwar [14]3 years ago
7 0

Step-by-step explanation:

the intersection of the interval: (-∞, 7) and [-5, +∞)

is [-5, 7)

and the union of the interval: (-∞, 7) and [-5, +∞)

is (-oo, +oo)

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which of the following represents the equation of the line with an x- intercept of 6 that passes through the point (4,4)?
luda_lava [24]

Answer:

y=-2x+12

Step-by-step explanation:

To write the equation of a line, find the slope between two points. Substitute two points into the slope formula. If the equation has an x-intercept of 6 then the line passes through the point (6,0). Use (6,0) and (4,4) in the formula.

m = \frac{y_2-y_1}{x_2-x_1} =\frac{4-0}{4-6} =\frac{4}{-2} =-2

Since m = -2, substitute its value and the point (6,0) into the point slope form. Then simplify.

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2 years ago
Use a number line to find the quotient <br> 3/5 divided by 3/10<br> (———————————)
frutty [35]

Answer:

2 ( plot the answer on 2)

Step-by-step explanation:

We do the reciprocal of 3/10 because we are dividing fraction. Which would be 10/3. Change the sign to multiplication because we are dividing fractions. And multiply regularly. SO it would be 3/5 times 10/3 = 2

5 0
3 years ago
HELP ME PLEASE!!!!!!
Deffense [45]

9514 1404 393

Answer:

  -2x +4

Step-by-step explanation:

We can write the polynomial p(x) in terms of the factors (x+2) and (x-3) as ...

  p(x) = (x+2)(x-3)q(x) +ax +b

Where ax+b is the remainder from division by x^2 -x -6 = (x+2)(x-3). The values of 'a' and 'b' can be found from ...

  p(-2) = 8 = -2a +b

  p(3) = -2 = 3a +b

Subtracting the first equation from the second gives ...

  (3a +b) -(-2a +b) = (-2) -(8)

  5a = -10

  a = -2

Then the first equation tells us ...

  8 = -2(-2) +b

  4 = b

So, the remainder from division by (x^2 -x -6) is (-2x +4).

5 0
2 years ago
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