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2 years ago

Solve by substitution 3x-4y=-4 y=2x-4

Mathematics

1 answer:

dybincka [34]2 years ago

7 0

Answer:

x=4 and y=4

Step-by-step explanation:

From first function we have:

$3x - 4y = - 4 \\ 4y = 3x + 4$

And from the second one:

$y = 2x - 4 \\ 4y = 8x - 16$

Substitute them:

$4y = 3x + 4 \\ 4y = 8x - 16 \\ \\ 0 = - 5x + 20 \\ x = 4 \\ y = 4$

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3 years ago

A fastball is hit straight up over home plate. The ball's height, h (in feet), from the ground is modeled by ℎ = −16푡 ଶ+103푡+5 w

Liono4ka [1.6K]

Question:

A fastball is hit straight up over home plate. The ball's height, h (in feet), from the ground is modeled by h(t)=-16t^2+80t+5, where t is measured in seconds. Write an equation to determine how long it will take for the ball to reach the ground.

Answer:

$t = 5.0625$

Step-by-step explanation:

Given

$h(t)=-16t^2+80t+5$

Required

Find t when the ball hits the ground

This implies that h(t) = 0

So, we have:

$0=-16t^2+80t+5$

Reorder

$-16t^2+80t+5 = 0$

Using quadratic formula, we have:

$t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}$

Where

$a = -16$ $b =80$ $c = 5$

So, we have:

$t = \frac{-80\±\sqrt{80^2 - 4*-16*5}}{2*-16}$

$t = \frac{-80\±\sqrt{6400 +320}}{-32}$

$t = \frac{-80\±\sqrt{6720}}{-32}$

$t = \frac{-80\±82.0}{-32}$

This gives:

$t = \frac{-80+82.0}{-32}$ or $t = \frac{-80-82.0}{-32}$

$t = \frac{2}{-32}$ or $t = \frac{-162}{-32}$

$t = -\frac{2}{32}$ or $t = \frac{162}{32}$

But time can not be negative.

So, we have:

$t = \frac{162}{32}$

$t = 5.0625$

<em>Hence, time to hit the ground is 5.0625 seconds</em>

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3 years ago

(18 + 4i) + (-11 + 23i) =<br> Express your answer in the form (a + bi).

Andru [333]

Answer:

7+27i

Step-by-step explanation:

(18+4i)+(-11+23i)

=18+4i-11+23i

=7+27i

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3 years ago

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abruzzese [7]

Answer:

Step-by-step explanation:

1) Lets rewrite the expression in expanded form to make is easier to understand:

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2) Simplify the interior of the parenthesis:

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3) Divide:

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3 years ago