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3 years ago

HELP PLEASE ANSWER FULL QUESTION

Mathematics

1 answer:

nekit [7.7K]3 years ago

7 0

Answer:

the constant of proportionality is the ratio between two directly proportional quantities.

b. k=y/x or y = k*1/x

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-5 (1-5x) +5 (-8x-2)=-4x-8x need a worked out answer for x plz help me

xz_007 [3.2K]

The work inside parentheses cannot be carried out as shown, so the next approach to consider is multiplying the expressions inside the parentheses by -5 and 5 respectively:

-5 + 25x - 40x - 10 = -4x - 8x (Are you sure it's really "-4x - 8x"?)

Combining the x-terms:

-5 - 15x - 10 = -12x

Combining all like terms: -15 = 3x, so that x = -5 (answer)

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3 years ago

Jamilia was moving to a new city. she researched the rates

Sauron [17]

And? Where is the continuing?

4 0

3 years ago

A number is four times larger than the square of the number

svp [43]

Answer:

4x^2

Step-by-step explanation:

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4 years ago

X= <br> (-6x+125) (11x + 6)

artcher [175]

9514 1404 393

Answer:

x = 7

Step-by-step explanation:

The base angles of an isosceles triangle are congruent, so ...

11x +6 = -6x +125

17x = 119 . . . . . . . . . add 6x-6 to both sides

x = 7 . . . . . . . . divide by 17

7 0

3 years ago

A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t) = -16t2 + 6

galina1969 [7]

<h2>Hello!</h2>

The answers are:

a) The height of the ball after 3 seconds is 49 feet.

b) The maximum height of the ball is 66 feet.

c) That the ball hit the ground after 4 seconds.

d) The domain would be only the positive real numbers, from 0 to 4, since we found that the ball hit the ground at t equal to 4 seconds. However, if we were talking about a quadratic function with no time involved, the domain would be all the real numbers.

Since we are working with a quadratic function which describes the ball's motion in function of the time, we need to remember the following:

- The general equation of the parabola is:

$y=ax^{2} +bx+c$

- We can calculate the coordinates of the vertex of the parabola using the following formula:

$x_{vertex}=\frac{-b}{2a}$

- Evaluating a function means replacing the variable with the given value to evaluate.

The given function is:

$h(t)=-16x^{2}+63t+4$

Where,

$a=-16\\b=63\\c=4$

Now, calculating we have:

a) What is the height of the ball after 3 seconds?

We need to evaluate the time of 3 seconds into the function, so:

$h(3)=-16(3)^{2} +63(3)+4=49feet$

So, the height of the ball after 3 seconds is 49 feet.

b) What is the maximum height of the ball?

Since the function is describing the motion of a ball thrown into the air, we can find the maximum height by finding the y-coordinate of the vertex. If the parabola opens downward or upward, the vertex will be always the highest or the lowest point of the parabola.

So, calculating the vertex we have:

$x_{vertex}=\frac{-b}{2a}=\frac{-63}{2*-16}\\\\x_{vertex}=\frac{-63}{2*-16}=\frac{-63}{-32}=1.97$

Then, replacing "x" into the equation of the parabola, we find the y-coordinate of the vertex:

$y=-16(1.97)^{2}+63(1.97)+4=-16*3.88+63*1.97+4\\y=-16*3.88+63*1.97+4=-62.08+124.11+4=66.03$

So, if the y-coordinate is 66.03, the maximum height of the ball is 66.03 feet, or 66 feet (rounded to the nearest foot).

c) When will the ball hit the ground?

We can find the time when the ball hit the ground by making equal to 0 the function and finding the roots (zeroes)

Since it's a quadratic function, we can find the zeroes using the quadratic equation:

$\frac{-b+-\sqrt{b^{2}-4ac } }{2a}$

Substituting a, b and c, we have:

$\frac{-b+-\sqrt{b^{2}-4ac } }{2a}=\frac{-63+-\sqrt{63^{2}-4*(-16)*(4)} }{2*(-16)}\\\\\frac{-63+-\sqrt{63^{2}-4*(-16)*(4)} }{2*(-16)}=\frac{-63+-\sqrt{3969+256} }{-32}\\\\\frac{-63+-\sqrt{3969+256} }{-32}=\frac{-63+-\sqrt{4225} }{-32}=\frac{-63+-(65)}{-32}\\\\t1=\frac{-63-(65)}{-32}=4\\\\t1=\frac{-63+(65)}{-32}=-0.06$

Now, since negative time does not exists, we can conclude that the ball hit the ground after 4 seconds.

d) what domain makes sense for the function?

Since the function represents the motion of the thrown ball at "t" time, the domain would be only the positive real numbers, from 0 to 4, since we found that the ball hit the ground at t equal to 4 seconds. However, if we were talking about a quadratic function with no time involved, the domain would be all the real numbers,

Note: I've attached the graph of the function.

Have a nice day!

5 0

3 years ago