Determine the number of Solutions for the system of equations y = 2x + 3 and y = 2x +3

Sandra throws an object straight up into the air with initial velocity of 38 ft per square from platform that is 30 ft above the

expeople1 [14]

Answer:

3 seconds.

Step-by-step explanation:

We have been given that Sandra throws an object straight up into the air with initial velocity of 38 ft per second from platform that is 30 ft above the ground.

To find the time it will take for object to hit the ground, we will use formula:

$h(t)=-16t^2+v_0t+h_0$ , where, $v_0$ represents initial velocity and $h_0$ represents initial height.

Upon substituting our given initial velocity and initial height, we will get:

$h(t)=-16t^2+38t+30$

We know that object will hit the ground, when height will be 0, so we will equate object's height equal to 0 and solve for t as:

$-16t^2+38t+30=0$

Divide by 2:

$-8t^2+19t+15=0$

Upon using quadratic formula, we will get:

$t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-19\pm\sqrt{19^2-4(-8)(15)}}{2(-8)}$

$t=\frac{-19\pm\sqrt{361+480}}{-16}=\frac{-19\pm\sqrt{841}}{-16}$

$t=\frac{-19\pm29}{-16}$

$t=\frac{-19-29}{-16},t=\frac{-19+29}{-16}$

$t=\frac{-48}{-16},t=\frac{10}{-16}$

$t=3,t=-\frac{5}{8}$

Since time cannot be negative, therefore, it will take 3 seconds for object to hit the ground.

7 0

2 years ago

What is the sum of 9c+(8+3c)?

mixas84 [53]

9c+(8+3c)
9c+8+3c (collect like terms)

9c+3c+8
12c+8

12c+8 is the answer.
im not sure if your teacher also wants the answer to be in simplest form so im going to do that below as well:

12c+8 (4*3=12 and 4*2=8. you can take out a 4 from those 2 numbers)

4(3c+2) (this is the simplest form of 9c+(8+3c))

6 0

2 years ago

Given the lengths of two sides of a triangle, find the range for the length of the third side (between what two numbers should t

frozen [14]

Answer:

The length of the third side of given triangle lies between 6.5 and 19.9.

Step-by-step explanation:

The law of cosine is as follows

$c^{2} =a^{2}+b^{2}+2abcos\alpha$ ---------------1

⇒ a and b are the given sides of the triangle and c is the third side, and $\alpha$ is the angle between a and b .

In equation 1 , the maximum and minimum values of $cos\alpha$ are 1 and -1.

so the value of c lies in between

⇒ $\sqrt{a^{2}+b^{2}-2ab }$ and $\sqrt{a^{2}+b^{2}+2ab }$ = $|a-b| and |a+b|$

Given a=13.2 and b=6.7 so the the side lies in between |13.2-6.7| and |13.2+6.7|

so the third side lies between 6.5 and 19.9

3 0

2 years ago

Solve this equation ÷2(1+2)

nasty-shy [4]

The answer is 6 because you add the 1 and the 2 first and then multiple to get 6. I don’t know why you put the division sign in front of the 2 though.

6 0

3 years ago

Read 2 more answers

Each morning Rin rides 1.5 miles to school and then rides home in the afternoon. Later in the evening, she rides to the park and

brilliants [131]

Answer:

Last equation given in the list of possible answers:

5 ( 1.5 + 1.5 + x ) = 25

Step-by-step explanation:

We need to include in the total addition of miles ridden during the week:

a) 1.5 miles to the school

b) 1.5 miles from school back home

c) x miles for the evening ride

so for the miles ridden per day we have: "1.5 +1.5 + x"

Now, since per week she does 5 days like this, then we need to multiply the expression above by 5 in order to total the number of miles she rides weekly (25 miles)

5 ( 1.5 + 1.5 + x ) = 25

And we can use this equation to find the amount "x" that Rin rides in the evening.

7 0

3 years ago