4-5a+b=87a +9b = -32I need to use substitution for this one. Help?

Mathematics

1 answer:

Sauron [17]3 years ago

8 0

Answer:

Step-by-step explanation:

$\left\{\begin{array}{ccc}-5a+b=8&\text{add}\ 5a\ \text{to both sides}\\7a+9b=-32\end{array}\right\\\\\left\{\begin{array}{ccc}b=5a+8&(1)\\7a+9b=-32&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\7a+9(5a+8)=-32\qquad\text{use the distributive property}\\\\7a+(9)(5a)+(9)(8)=-32\\\\7a+45a+72=-32\qquad\text{subtract 72 from both sides}\\\\52a=-104\qquad\text{divide both sides by 52}\\\\\boxed{a=-2}\\\\\text{Put the value of}\ a\ \text{to (1):}\\\\b=5(-2)+8\\\\b=-10+8\\\\\boxed{b=-2}$

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What is the slope of the line that passes through points A ( -2, -3) and B ( 5,3 )

xxMikexx [17]

Answer: 6/7

Step-by-step explanation:

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6 0

3 years ago

The height (feet) of an object moving vertically is given by s= (-16t^2)+(208t)+(156), where t is in seconds.

OverLord2011 [107]

Answer:

The object's velocity at t = 7 is -16 ft/s

The maximum height is 832 ft and it occurs when $t=\frac{13}{2}$

Step-by-step explanation:

From the information given, the equation of motion of the object is

$s(t)= -16t^2+208t+156$

For any equation of motion s(t), the instantaneous velocity at time t is given by

$v(t)=\frac{ds}{dt}$

(a) To find the object's velocity at t = 7, you must:

$v(t)=\frac{d}{dt}(-16t^2+208t+156)\\\\v(t)=-\frac{d}{dt}\left(16t^2\right)+\frac{d}{dt}\left(208t\right)+\frac{d}{dt}\left(156\right)\\\\v(t)=-32t+208+0\\\\v(t)=-32t+208$

Next, we evaluate when t = 7

$v(7)=-32(7)+208=-224+208\\\\v(7)=-16$

The object's velocity at t = 7 is -16 ft/s

(b) <em>To find the maximum of a function we always use the derivative of the function and we set it equal zero to find the</em><em> critical points.</em>

To find the maximum height and when it occurs, we set the velocity function equal to 0 and solve for t.

$-32t+208=0\\\\-32t+208-208=0-208\\\\-32t=-208\\\\\frac{-32t}{-32}=\frac{-208}{-32}\\\\t=\frac{13}{2}$