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3 years ago

How can I solve this equation 5x^2-2x-6=-2x^2+9x

1 answer:

wel3 years ago

3 0

Add 2x^2 to both sides
7x^2-2x-6=9x

Subtract 9x from both sides
7x^2-11x-6=0

Factor by using slip and slide
x^2-11x-42
(x-14)(x+3)
(x-14/7)(x+3/7)
(x-2)(7x+3)

Then use the Zero Product Property to find roots
x-2=0
x=2

7x+3=0
7x=-3
x=-3/7

Final answer: x=-3/7, x=2

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A juggler tosses a ball into the air . The balls height, h and time t seconds can be represented by the equation h(t)= -16t^2+40

malfutka [58]

PART A

The given equation is

$h(t) = - 16 {t}^{2} + 40t + 4$

In order to find the maximum height, we write the function in the vertex form.

We factor -16 out of the first two terms to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + 4$

We add and subtract

$- 16(- \frac{5}{4} )^{2}$

to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + - 16( - \frac{5}{4})^{2} - -16( - \frac{5}{4})^{2} + 4$

We again factor -16 out of the first two terms to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4})^{2} ) - -16( - \frac{5}{4})^{2} + 4$

This implies that,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4}) ^{2} ) + 16( \frac{25}{16}) + 4$

The quadratic trinomial above is a perfect square.

$h(t) = - 16 ( t- \frac{5}{4}) ^{2} +25+ 4$

This finally simplifies to,

$h(t) = - 16 ( t- \frac{5}{4}) ^{2} +29$

The vertex of this function is

$V( \frac{5}{4} ,29)$

The y-value of the vertex is the maximum value.

Therefore the maximum value is,

$29$

PART B

When the ball hits the ground,

$h(t) = 0$

This implies that,

$- 16 ( t- \frac{5}{4}) ^{2} +29 = 0$

We add -29 to both sides to get,

$- 16 ( t- \frac{5}{4}) ^{2} = - 29$

This implies that,

$( t- \frac{5}{4}) ^{2} = \frac{29}{16}$

$t- \frac{5}{4} = \pm \sqrt{ \frac{29}{16} }$

$t = \frac{5}{4} \pm \frac{ \sqrt{29} }{4}$

$t = \frac{ 5 + \sqrt{29} }{4} = 2.60$

or

$t = \frac{ 5 - \sqrt{29} }{4} = - 0.10$

Since time cannot be negative, we discard the negative value and pick,

$t = 2.60s$

8 0

3 years ago

Draw 8 lines that are between 1 inch and 3 inches long measure each line to the nearest fourth inch and make a line plot

Paraphin [41]

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3 years ago

Solve for x and y 9/x-4/y=8

borishaifa [10]

You can solve 9/x-4/y=8 for x or for y but NOT at the same time.

Solving for x: 9/x-4/y=8 Mult all 3 terms by xy to eliminate the fractions.

9(xy)/x - 4xy/y = 8xy => 9y - 4x = 8xy, or 9y = 4x + 8xy = 4x(1+2y)

then 9y = x [ 4(1+2y) ]
9y
therefore x = ------------
4(1+2y)

Solve for y using a similar approach.

7 0

3 years ago

I need help or my report card is gonna have a f its coming out tommorow

OverLord2011 [107]

Answer:

Step-by-step explanation:

hope this helps you

8 0

3 years ago

Find the slope of each line 5y = -2x + 15

Kipish [7]

The slope of the line is -2/5x

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2 years ago