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Marianna [84]
3 years ago
7

What is an equation of the line that passes through the point (-2 1) and is parallel to the line whose equation is 4x-2y=8 ?

Mathematics
1 answer:
monitta3 years ago
4 0
4x-2y=8 ==> y=2x-4 (to better show you what I mean) 

2 lines are parallel if they have the same slope (m the coefficient of x).

So y=mx + b // y =2x-4 means m=2 & y=mx + b, becomes y=2x + b.
Moreover they are telling us that this function passes by (-2,1), where -2 represents x & 1, represents y. To calculate b , replace x & y by their values:
y=2x+b ==> 1 = 2(- 2) + b==> 1 = -4 + b ==> b= 5. Finally the equation is
y=-2x+5
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The height of water shooting from a fountain is modeled by the function f(x) = −0.2x2 − 2.8x − 5.4 where x is the distance from
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Start by setting the function equal to 0 and then moving the -5.4 over to the other side of the equals sign.  -.2 x^{2} -2.8x=5.4.  The first rule for completing the square is that the leading coefficient be a +1.  Ours is a -.2.  So we need to factor it out. -.2( x^{2} +14x)=5.4.  Now we will take half the linear term, square it, and add it to both sides.  Our linear term is 14.  Half of 14 is 7, and 7 squared is 49.  So we add 49 in to the left side just fine, but we cannot forget about that -.2 hanging around out front as a multiplier.  What we have actually "added" in is -.2*49 which is -9.8.  Now here's what we have after all that: -.2( x^{2} +14x+49)=5.4-9.8.  In that process, we have created a perfect square binomial on the left.  Along with expressing that binomial we will do the math on the right: -.2(x+7) ^{2} =-4.4.  Now we will move the -4.4 back over by addition, and it will then be apparent as to what our vertex is.  The y coordinate of the vertex will give us the max height of the water.  -.2(x+7) +4.4=y.  As you can see, our work matches choice C from above.
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3 years ago
Please help a girl out:
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Mai is making personal pizzas. For 4 pizzas, she uses 10 ounces of cheese. How much cheese does she use for each pizza?
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Step-by-step explanation:

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A package of 4 red,white and blue hats costs $8. What is the unit rate
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Step-by-step explanation:

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2 years ago
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What must be added to both sides in 4x² + 24x + 8 = 32 in order to complete the square?
Sergeu [11.5K]

Answer:

16

Step-by-step explanation:

To solve a quadratic equation by using the completing the square method, the coefficient of the square term i.e x² must be one (1).

Therefore, we would have to first make the coefficient of x² to be equal to 1.

4x² + 24x + 8 = 32

We would simplify the equation;

4x² + 24x = 32 - 8

4x² + 24x = 24

Divide all through by 4;

x² + 8x = 24

The value to be added = (8/2)² = 4² = 16

x² + 8x + 16 = 8 + 16

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Taking the square root of both sides;

x + 4 = ± 4.9

x = -4 ± 4.9

x = -4 + 4.9 = 0.9

or

x = -4 - 4.9 = - 8.9

<em>Therefore, 16 must be added to solve the quadratic equation by completing the square method. </em>

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3 years ago
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