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2 years ago

Whoch of the following statements are true? Select all that apply

Mathematics

1 answer:

sineoko [7]2 years ago

8 0

Answer:

C and D

atleast 20 characters to explain it well

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The height h of a projectile is a function of the time t it is in the air. the height in feet for t seconds is given by the func

alexgriva [62]

Domain means the values of independent variable(input) which will give defined output to the function.

Given:

The height h of a projectile is a function of the time t it is in the air. The height in feet for t seconds is given by the function

$h(t)=-16t^2 + 96t$

Solution:

To get defined output, the height h(t) need to be greater than or equal to zero. We need to set up an inequality and solve it to find the domain values.

$To \; find \; domain:\\\\h(t) \geq0\\\\-16t^2+96t \geq 0\\Factoring \; -16t \; in \; the \; left \; side \; of \; the \; inequality\\\\-16t(t-6) \geq 0\\Step \; 1: Find \; Boundary \; Points \; by \; setting \; up \; above \; inequality \; to \; zero.\\\\t(t-6)=0\\Use \; zero \; factor \; property \; to \; solve\\\\t=0 \; (or) \; t = 6\\\\Step \; 2: \; List \; the \; possible \; solution \; interval \; using \; boundary \; points\\(- \infty,0], \; [0, 6], \& [6, \infty)$

$Step \; 3:Pick \; test \; point \; from \; each \; interval \; to \; check \; whether \\\; makes \; the \; inequality \; TRUE \; or \; FALSE\\\\When \; t = -1\\-16(-1)(-1-6) \geq 0\\-112 \geq 0 \; FALSE\\(-\infty, 0] \; is \; not \; solution\\Also \; Logically \; time \; t \; cannot \; be \; negative\\\\When \; t = 1\\-16(1)(1-6) \geq 0\\80 \geq 0 \; TRUE\\ \; [0, 6] \; is \; a \; solution\\\\When \; t = 7\\-16(7)(7-6) \geq 0\\-112 \geq 0 \; FALSE\\ \; [6, -\infty) \; is \; not \; solution$

Conclusion:

The domain of the function is the time in between 0 to 6 seconds

$0 \leq t \leq 6$

The height will be positive in the above interval.

7 0

2 years ago

Read 2 more answers

Line L passes through the points (0, --3) and (6,9).<br> (a) Find the equation of line L.

valentina_108 [34]

Step-by-step explanation:

Given points are :

$(0,\:-3)=(x_1,\:y_1) \:\&\: (6,\:9)=(x_2 ,\:y_2)$

Equation of line in two point form is given as:

$\frac{y -y_1 }{y_1 -y_2 } = \frac{x -x_1 }{x_1 -x_2 } \\ \\ \therefore \frac{y -( - 3)}{ -3 -9 } = \frac{x -0 }{0 -6 } \\ \\ \therefore \frac{y + 3}{ -12} = \frac{x }{ -6 } \\ \\ \therefore \frac{y + 3}{ 2} = \frac{x }{1} \\ \\ \therefore \: y + 3 = 2x \\ \\ \huge \red{ \boxed{\therefore \: 2x - y - 3 = 0}} \\ is \: the \: required \: equation \: of \: line.$

5 0

3 years ago

The average price of a movie ticket in the United States from 1980 to 2000 can be modeled by the expression, 2.75+0.10x, where x

MissTica

Answer:

Step-by-step explanation:

step one:

Let the cost be y

to solve for the cost of a movie ticket, we need to solve the expression

y=2.75+0.10x

step two:

given that x is the number of years between 1980-2000

the number of years is 20years

put x= 20 in the expression for the cost we have

y=2.75+0.10(20)

y=2.7+2

y=$4.7

5 0

2 years ago

Plz help !!!!!!!!1

rosijanka [135]

Answer:

As outdoor temperatures increased, residents' electric bills increased.

Step-by-step explanation:

7 0

2 years ago

If y is 6 when x is 3 and y varies directly with x, find y when x is 8.<br> 04<br> 16<br> 11

Zarrin [17]

Answer

y = kx

from the info given k=2

hence when x=8 y=16:

4 0

2 years ago