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1 year ago

In each of the following equations, what is

Mathematics

1 answer:

timama [110]1 year ago

8 0

The graph will cross at the coordinates (-2, 9)

<h3>How to solve equations?</h3>

y = 3x + 15

y = 3 - 3x

y = 3x + 15

Hence,

when x = 2

y = 3(2) + 15 = 21

when x = 0

y = 3(0) + 15 = 15

y = 3 - 3x

when x = 2

y = 3 - 3(2)

y = 3 - 6

y = -3

when x = 0

y = 3 - 3(0)

y = 3

Therefore, let's check if the equation will cross.

y = 3x + 15

y = 3 - 3x

using substitution,

3 - 3x = 3x + 15

3 - 15 = 3x + 3x

- 12 = 6x

x = -12 / 6

x = -2

y = 3 - 3(-2)

y = 3 + 6

y = 9

Therefore, the graph will cross at the coordinates (-2, 9)

learn more on equations here: brainly.com/question/19297665

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1 year ago

Read 2 more answers

2. When Joey dives off a diving board, the equation of his pathway can be modeled by h = -16- + 15 + 12.

Sergeu [11.5K]

Answer:

a) The maximum height is approx 15.5 unit.

b) The time it will take for Joey to reach the water is 1.45 hour.

Step-by-step explanation:

Given : When Joey dives off a diving board, the equation of his pathway can be modeled by $h(t)= -16t^2+15t + 12$

To find : a) Find Joey's maximum height.

b) Find the time it will take for Joey to reach the water.

Solution :

Modeled $h(t)= -16t^2+15t + 12$ ....(1)

a) To find maximum height

Derivate (1) w.r.t. t,

$h'= -32t+15$

For critical point put h'=0,

$-32t+15=0$

$t=\frac{15}{32}$

$t=0.46875$

Derivate again w.r.t. t,

$h''= -32$

It is maximum at t=0.46875.

Substitute t in equation (1),

$h(0.46875)= -16(0.46875)^2+15(0.46875)+12$

$h(0.46875)= -3.515625+7.03125+12$

$h(0.46875)= 15.515625$

The maximum height is approx 15.5 unit.

b) To find the time it will take for Joey to reach the water.

Put h=0 in equation (1),

$-16t^2+15t + 12=0$

Apply quadratic formula, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here, a=-16 , b=15, c=12

$t=\frac{-15\pm\sqrt{(15)^2-4(-16)(12)}}{2(-16)}$

$t=\frac{-15\pm\sqrt{225+768}}{-32}$

$t=\frac{-15\pm\sqrt{993}}{-32}$

$t=\frac{-15+\sqrt{993}}{-32},\frac{-15-\sqrt{993}}{-32}$

$t=−0.515,1.453$

Reject negative value.

The time is t=1.45.

The time it will take for Joey to reach the water is 1.45 hour.

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3 years ago