What are the coordinates of the vertex of the function below? Write your answer in the form (x,y).

The following binary numbers are 4-bit 2's complement binary numbers. Which of the following operations generate overflow? Justi

LuckyWell [14K]

Answer:Decide whether each statement is an example of direct characterization, an example of indirect characterization, or not characterization at all.

Toby’s next move in the game was clever and quick, just like his reputation.

Because the thunder and lightning came so close together, Julia knew that the storm was close by.

Every few minutes Angela glanced at the clock. Her eyes twinkled, and she couldn’t help but smile as she put the finishing touches on the decorations for the surprise party.

Step-by-step explanation:

8 0

3 years ago

Which quadratic function has Vertex (-1,4) and passes through (4,19) HELP

hichkok12 [17]

Answer:

$f(x)=\frac{3}{5}(x+1)^2+4$

Step-by-step explanation:

The equation of a quadratic function in vertex form is given by:

$f(x)=a(x-h)^2+k$

Where (h,k) is the vertex.

It was given in the question that the vertex of the parabola is (-1,4).

When we substitute the vertex into the formula we get:

$f(x)=a(x+1)^2+4$

The parabola also passes through (4,19) hence it must satisfy its equation.

$19=a(4+1)^2+4$

$19-4=a(5)^2$

$15=25a$

We divide both sides by 25 to get:

$a=\frac{15}{25}= \frac{3}{5}$

Hence the quadratic function is:

$f(x)=\frac{3}{5}(x+1)^2+4$

6 0

3 years ago

Ben and Josh went to the roof of their 40-foot tall high school to throw their math books offthe edge.The initial velocity of Be

Taya2010 [7]

Answer

Josh's textbook reached the ground first

Josh's textbook reached the ground first by a difference of $t=0.6482$

Step-by-step explanation:

Before we proceed let us re write correctly the height equation which in correct form reads:

$h(t)=-16t^2 +v_{o}t+s$ Eqn(1).

Where:

$h(t)$ : is the height range as a function of time

$v_{o}$ : is the initial velocity

$s$ : is the initial heightin feet and is given as 40 feet, thus Eqn(1). becomes:

$h(t)=-16t^2 + v_{o}t + 40$ Eqn(2).

Now let us use the given information and set up our equations for Ben and Josh.

Ben:

We know that $v_{o}=60ft/s$

Thus Eqn. (2) becomes:

$h(t)=-16t^2+60t+40$ Eqn.(3)

Josh:

We know that $v_{o}=48ft/s$

Thus Eqn. (2) becomes:

$h(t)=-16t^2+48t+40$ Eqn. (4).

Now since we want to find whose textbook reaches the ground first and by how many seconds we need to solve each equation (i.e. Eqns. (3) and (4)) at $h(t)=0$ . Now since both are quadratic equations we will solve one showing the full method which can be repeated for the other one.

Thus we have for Ben, Eqn. (3) gives:

$h(t)=0-16t^2+60t+40=0$

Using the quadratic expression to find the roots of the quadratic we have:

$t_{1,2}=\frac{-b+/-\sqrt{b^2-4ac} }{2a} \\t_{1,2}=\frac{-60+/-\sqrt{60^2-4(-16)(40)} }{2(-16)} \\t_{1,2}=\frac{-60+/-\sqrt{6160} }{-32} \\t_{1,2}=\frac{15+/-\sqrt{385} }{8}\\\\t_{1}=4.3276 sec\\t_{2}=-0.5776 sec$