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erma4kov [3.2K]
3 years ago
11

A line that passes through the point (1,-2) is parallel to the line y=-4x+1

Mathematics
1 answer:
aniked [119]3 years ago
6 0

y
−
6
=
1
4
(
x
−
4
)

Expanding the right hand side:
y
−
6
=
1
4
x
−
1

Add
6
to both sides:
y
=
1
4
x
−
1
+
6

So the answer is
y
=
1
4
x
+
5
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Solve the polynomial inequality x^2-3x-10>0
djverab [1.8K]

As x² - 3x - 10 factors, we can use the zero product property and pull it apart into factors. It factors because 2 and 5 have a difference of 3 and product of 10

x² - 3x - 10 > 0

(x - 5)(x + 2) > 0

To find where the inequality is true, we use a sign test. When x-5 > 0, it means x >5, and 5 is one of our sign test values. Similarly, -2 is the other. We can then make three intervals - A (less than -2), B (between -2 and 5), and C (more than 5).

<--------------- -2 ------------------ 5 -------------------------->

A B C

To do a sign test, we choose values to see what happens. First, test x = -5.

(-5 - 5)(-5 + 2) = (-10)(-3) = 30. Because 30 > 0, the inequality is true for x < -2. So interval A is true.

Next, test x = 0.

(0 - 5) (0 + 2) = (-5)(2) = -10. Because -10 < 0 is false, the inequality is false for x > -2 and x < 5. So interval B is false.

Last, test x = 10

(10 - 5) (10 + 2) = (5) (8) = 40. Because 40 > 0 is true, the inequality is true for x > 5. So interval C is true.

We put the true intervals together.

(-∞, -2) ∪ (5, ∞) is where this inequality is true,

{x : x < -2 or x > 5} is also how it's said in set notation.

7 0
3 years ago
A 64-ounce container of sports juice costs $6.50. A 48-ounce container of the same juice costs $4.25. Which juice container is t
larisa86 [58]

Answer:

The juice container that is a better buy is the 48 ounce container because the price per ounce is lower.

Step-by-step explanation:

In order to determine the juice container that is the better buy, you have to find the one that has a lower cost per ounce by dividing the price of each juice container by the number of ounces it has:

64-ounce container: 6.50/64=0.10

48-ounce container: 4.25/48=0.08

According to this, the answer is that the juice container that is a better buy is the 48 ounce container because the price per ounce is lower.

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10 gallons equals how many liters
DiKsa [7]

37.8541

roll another one

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3 years ago
What is the squair root of 9/49
adelina 88 [10]

Answer:

3/7

Step-by-step explanation:

To find the square root of a fraction, find the square root of the numerator and denominator individually

So, √9 = 3

√49 = 7

Put them back as a fraction = 3/7

Hope this helps

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Step-by-step explanation:

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