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3 years ago

Write the following equation in slope-intercept form and identify the slope and y-intercept.

Mathematics

1 answer:

Sophie [7]3 years ago

5 0

Answer:

Your answer is

slope is -1

y intercept is 12

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The expression LaTeX: -5t^2+40t

dlinn [17]

Answer:

8 seconds

Step-by-step explanation:

Given

h = - 5t² + 40t

When the object hits the ground then h = 0

Substitute h = 0 into the function and solve for t

- 5t² + 40t = 0 ← factor out - 5t from each term

- 5t(t - 8) = 0

Equate each factor to zero and solve for t

- 5t = 0 ⇒ t = 0

t - 8 = 0 ⇒ t = 8

t= 0 denotes the time of launch

t = 8 denotes the time it hits the ground

7 0

3 years ago

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 31 ft/s. (a) A

Afina-wow [57]

Answer:

13.86 ft/sec

Step-by-step explanation:

If we let x = distance batter has run at time t and D = distance from second base to the batter at time t, then we know $\frac{dx}{dt}=31 ft/s$ and we want $\frac{dD}{dt}$ when he is halfway (at x = 45).

Using Pythagoras theorem

$D^2=90^2+(90-x)^2\\\text{Differentiating with respect to t}\\2D\frac{dD}{dt}=0+2(90-x)(-1)\frac{dx}{dt}\\2D\frac{dD}{dt}=-2(90-x)\frac{dx}{dt}$

When x=45

$D^2=90^2+(90-x)^2\\D^2=90^2+(90-45)^2\\D^2=10125\\D=\sqrt{10125}$

$2D\frac{dD}{dt}=-2(90-x)\frac{dx}{dt}\\2\sqrt{10125}\frac{dD}{dt}=-2(90-45)(31)\\\frac{dD}{dt}=\frac{-2(45)(31)}{2\sqrt{10125}} =-13.86ft/s$

Thus, when the batter is halfway to first base, the distance between second base and the batter is decreasing at the rate of about 13.86 ft/sec.

4 0

3 years ago

What are the possible values of x in 8x2 + 4x = -1?

Westkost [7]

Answer:

The possible values of x are:

x= $\frac{-1+\sqrt{3}}{4} \,\,or\,\, x= 0.18$

and

x= $\frac{-1-\sqrt{3}}{4} \,\, or \,\, x= -0.68$

Step-by-step explanation:

$8x^2+4x+1=0$

Using Quadratic formula to solve this equation:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\a = 8 \,\, b = 4\,\, c = -1\\Putting \,\, values \,\, in \,\, the\,\, equation\\x= \frac{-4\pm\sqrt{(4)^2-4(8)(-1)}}{2(8)}\\x= \frac{-4\pm\sqrt{16+32}}{16}\\x= \frac{-4\pm\sqrt{48}}{16}\\x= \frac{-4+ \sqrt{48}}{16} \,\, and \,\, x= \frac{-4- \sqrt{48}}{16}\\x= \frac{-1+ \sqrt{3}}{4} \,\, and \,\, x= \frac{-1- \sqrt{3}}{4}$

The possible values of x are:

x= $\frac{-1+\sqrt{3}}{4} \,\,or\,\, x= 0.18$

and

x= $\frac{-1-\sqrt{3}}{4} \,\, or \,\, x= -0.68$

4 0

3 years ago

Can someone help me with this please???

DIA [1.3K]

Answer:

148

Step-by-step explanation:

148

7 0

3 years ago

List 3 observations from your data.<br> 1. <br> 2. <br> 3.

Nina [5.8K]

Answer:

Step-by-step explanation:

hearing, taste, touch,

5 0

3 years ago