Given f(x) = 2x2 + 4x - 3 and g(x) = 5x – 2, find f(x) · g(x).
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Answer: The ball will hit the ground 6 seconds after it has ben thrown, at t = 6s.

Step-by-step explanation:

The equation for the height of the ball should be:

s(t) = (-16ft/s^2)*t^2 + 96ft/s*t

When s(t) = 0ft, means that the ball is in the ground

This represents the height of the ball as a function of t, the time in seconds.

We can see that at t = 0s:

s(0s) = (-16ft/s^2)*(0s)^2 + 96ft/s*(0s) = 0ft

Then at the time 0 seconds, the ball is in the ground, so we must look at the other root of the equation

(-16ft/s^2)*t^2 + 96ft/s*t = 0ft

To find it, we can use the Bhaskara equation, in this case is:

[tex]t = \frac{-96ft/s +- \sqrt{(96ft/s)^2 - 4*(-16ft/s^2)*0} }{-2*16ft/s^2} = \frac{-96ft/s^2 +-96ft/s^2}{-32ft/s^2}[/tex]

Then we have the two solutions:

t = (-96ft/s + 96ft/s)/(-32 ft/s^2) = 0s  (the one that we already found)

And the other one is:

t = (-96ft/s - 96ft/s)/(-32ft/s^2) = 6s

Then:

s(6s) = 0ft

This means that the ball will hit the ground at t = 6 seconds.

The time required to hit the ground is required.

The time taken by the ball to reach the ground is 2.45 seconds.

The equation is

[tex]s(t)=-16t^2+96[/tex]

At the ground [tex]t=0[/tex]

so,

[tex]0=-16t^2+96\\\Rightarrow 16t^2=96\\\Rightarrow t=\sqrt{\dfrac{96}{16}}\\\Rightarrow t=2.45\ \text{s}[/tex]

The time taken by the ball to reach the ground is 2.45 seconds.

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Answer:

2) 9/4

Step-by-step explanation:

12/5 in decimal form is 2.4. As a mixed number, 12/5 is 2 2/5. And, 12/5 is just a reduced form of 36/15. So, the only answer it can be is answer 2: 9/4

Answer:

u want step by step?

Step-by-step explanation:

Answer:

Plug in the values 1, 2, 3, 4, 5, one at a time into the function (replacing x with the number). Then calculate the result for each. Sum the results and divide it by the number of values (5).

Answer:

Step-by-step explanation:

If 41 students is in the roll (total), then

[tex]\frac{3}{41}[/tex] = [tex]\frac{x}{100}[/tex] ⇒ x = [tex]\frac{3*100}{41}[/tex] ≈ 7.3 %

Answer:

Option (C)  [0.2574 , 0.2626]

Step-by-step explanation:

Of 250 convicts, there are 65 cases of recidivism.

- Construct a 99% confidence interval for the proportion of cases of recidivism.

This calls for first finding the proportion of cases of recidivism. This will be 65/250  = 0.26

You are 100% confident that the proportion of cases of recidivism is 0.26

You will be 99% confident that the recidivism cases are between:

99% of 0.26  = 0.2574

1% of 0.26  = 0.0026

[0.26 - 0.0026] , [0.26 + 0.0026]  = [0.2574 , 0.2626]

This should be OPTION C, as that option is missing in the list of options.

Answer:

a=(2,8) b=(8,8)

c=(8,2) d=(2,2)

Step-by-step explanation:

Answer:

this quadrilateral would be a square because all of the sides are equal.

Answer:

I believe it is A.

Let me know if this helps!

Answer:

1.25 miles

Step-by-step explanation:

Lisa takes a night walk after dinner every night.

She walks 1/4 mile in 2 minutes.

Distance = 1/4 mile

Time, t = 2 minutes

For covering 1 mile,

1/4 mile = 2 minutes

In 1 minute she will cover [tex]\dfrac{1}{8}\ \text{mile}[/tex]

For 10 minutes, she will cover [tex]\dfrac{10}{8}\ \text{mile}\ or\ 1.25\ \text{miles}[/tex]

So, she will cover 1.25 miles.

Answer:

slope = 2

y-intercept= -4

Step-by-step explanation:

slope = y2- y1/ x2-x1

slope = 4-(-4) / 4-0

slope = 2

using (4,4) for (x,y)

y= mx+b

4= 2(4)+b

b= -4

Answer:

2

Step-by-step explanation:

g (x) = -x + 3

g(1) = -(1) + 3

= 2

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Answer:

A) 7 and 8

Step-by-step explanation:

root of 7 is 2.64575..... then when u multiply by 3

3*2.64575=7.93725

Answer: The bag of candy corn will take 5 seconds to land on the floor and it will hit it with velocity of 49m/s.

Step-by-step explanation: A free falling object has only Gravitational Force acting on it, so acceleration will be due to gravity, which has magnitude

g = 9.8m/s².

As Professor Sosa drops the bag, its initial velocity and time are 0.

The building has a height of 400ft, so adjusting units: y = 121.92 m and [tex]y_{0}[/tex] = 0.

For this problem, going down will be the positive reference.

Then:

[tex]y=y_{0}+v_{0}t+\frac{g}{2}t^{2}[/tex]

[tex]\Delta y=v_{0}t+\frac{g}{2}t^{2}[/tex]

[tex]121.92=\frac{9.8}{2}t^{2}[/tex]

[tex]t=\sqrt{\frac{121.92*2}{9.8} }[/tex]

t ≈ 5

It will take 5s for the candy corn bag to land on the ground.

Acceleration is the change in velocity per change in time, so:

[tex]g=\frac{\Delta v}{\Delta t}[/tex]

As initial velocity and time are 0 and rearraging it:

v = g.t

v = 9.8*5

v = 49

The bag will hit the ground with velocity of magnitude 49 m/s.

Answer:

The correct equation for the graph is B.) y = x- 3

Answer:

B

Step-by-step explanation:

the right answer us B is that right

Answer:

D) The domain of the function is all real numbers

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

in answer D, the values would equal "6" and "18" which is not equivalent to the given equation

Answer:

xxtentacion for life

Step-by-step explanation:

Answer:

7/6

Step-by-step explanation:

1/3+1/4

4/12+3/12=7/12

7/12 divided by 1/2

7/12 times 2 as when dividing fraction, multiply by reciprocal.

14/12

7/6

Answer:

4%

Step-by-step explanation:

2/50 is 4....I believe.

Answer:

The slope seems to be 4.

Step-by-step explanation:

The line seems to be starting at (3,0) and if you use the rule rise/run, it goes up (rises) 4 units and moves over (runs) 1 unit. You then rewrite this as 4/1 and you get 4 as the slope!

Answer:

The slope is 4

My logic:

Slope is delta y over delta x so if you take any 2 points on that graph and get the x and y of each point and find the change of the two x and the two y and put the change in y over the change in x. you get slope. like so= 16/4 or 4

Answer:

2,3,5,7,11,and 13

Step-by-step explanation:

Hope this helped :))

The sum of the numbers in the 15th row of pascals triangle are  2,3,5,7,11,and 13

Pascal triangles contains coefficient of 's expanded form's terms.

Thus, 1 is the value in the first row of Pascal triangle.

The variable x has coefficient 1, and that 1 itself, so second row of Pascal triangle has 1 , 1 as values.

For nth row, and its rth term(all counted from 0-indexing(that means, counting of index starts from 0), then that term in Pascal triangle is

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

........

The sum of row n is 2^n, thus the row number with a particular sum;

 2^n = sum

 n·log(2) = log(sum)

 n = log(sum)/log(2)

The sum of the numbers in the 15th row of pascals triangle

 2,3,5,7,11,and 13

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Answer:

A bottle of juice that says it holds 2 cups actually only holds 1 cup 5 ounces. The bottle of juice holds  

3 ounces less than it should. This represents a  18.75  percent error.

Step-by-step explanation:

answer = 5

Step-by-step explanation:

A cold water pipe can fill a swimming pool in 4 hours

And a hot water pipe in 6 hours.

If cold water pipe is turned on and hot water pipe is turned on 3 hours later

6-4 = 2

2+3 = 5

5 answer

Answer:

0.6 of an hour

Step-by-step explanation:

A cold pipe takes 4h hours so we can assume ¼ of our job is done in one hour.

After 3 hours go by with the cold pipe on, we have ¼ of the job left.

Now we have our hot pipe, which takes 6 hours for the entire pool, so we can assume that it has a rate of ⅙ per hour. Now since these two pipes are working together we can add them.

⅙ + ¼ = ⁵/₁₂

Now we divide.

Since at the start 3 hours had gone by with the cold pipe that would have been ¾ of our time so, 1 - ¾ = ¼

¼ ÷ ⁵/₁₂ = ⅗ or 0.6 of an hour

Answer:

17 with the remainder of 25

Step-by-step explanation:

Answer:

50 days?

Step-by-step explanation:

Answer:

i think it is 2 because

10 divide by 5 = 2

1 x 2 = 2

2 days

Answer:

a. Yes

Step-by-step explanation:

The answer fam is.......... 22

Answer:

The coordinates of point X that divides the line in 1:4 are: (3,8/5)

Step-by-step explanation:

When a point divides a line with coordinates (x1,y1) and (x2,y2) in ratio m:n,

the coordinates of point are given by:

[tex](x,y) = (\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n})[/tex]

Given points are:

(x1,y1) = (5,1)

(x2,y2) = (-5,4)

Putting the values in the formula

[tex]X(x,y) = (\frac{(1)(-5)+(4)(5)}{1+4} , \frac{(1)(4)+(4)(1)}{1+4})\\= (\frac{-5+20}{5}, \frac{4+4}{5})\\=(\frac{15}{5}, \frac{8}{5})\\=(3,\frac{8}{5})[/tex]

Hence,

The coordinates of point X that divides the line in 1:4 are: (3,8/5)