Evaluate the expression 2x-(4y-3)+5xz, when x=-3,y=2, and z=-1

An Olympic athlete of mass 80kg competes in a 100m race. What is the best estimate of his mean kinetic energy during the race?

kipiarov [429]

For this question, you need to know that the average velocity of a 100m Olympic athlete is 10 m/s before you start solving the equation. The equation is K (energy in Jules) = 1/2 mv^2 (where m is the mass in kg and v the speed in meters per second).
The correct answer is 4000J. To see how I got it, take a look at the attachment.

3 0

2 years ago

Solve the system of linear equations using multiplication.

Anna71 [15]

Answer:

$(8,-1)$

Step-by-step explanation:

The given system is:

$3x+3y=21$

$6x+12y=36$

Since I prefer to use smaller numbers I'm going to divide both sides of the first equation by 3 and both sides of the equation equation by 6.

This gives me the system:

$x+y=7$

$x+2y=6$

We could solve the first equation for $x$ and replace the second $x$ with that.

Let's do that.

$x+y=7$

Subtract $y$ on both sides:

$x=7-y$

So we are replacing the second $x$ in the second equation with $(7-y)$ which gives us:

$(7-y)+2y=6$

$7-y+2y=6$

$7+y=6$

$y=6-7$

$y=-1$

Now recall the first equation we arranged so that $x$ was the subject. I'm referring to $x=7-y$ .

We can now find $x$ given that $y=-1$ using the equation $x=7-y$ .

Let's do that.

$x=7-y$ with $y=-1$ :

$x=7-(-1)$

$x=7+1$

$x=8$

So the solution is (8,-1).

We can check this point by plugging it into both equations.

If both equations render true for that point, then we have verify the solution.

Let's try it.

$3x+3y=21$ with $(x,y)=(8,-1)$ :

$3(8)+3(-1)=21$

$24+(-3)=21$

$21=21$ is a true equation so the "solution" looks promising still.

$6x+12y=36$ with $(x,y)=(8,-1)$ :

$6(8)+12(-1)=36$

$48+(-12)=36$

$36=36$ is also true so the solution has been verified since both equations render true for that point.

5 0

2 years ago

Read 2 more answers

Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure.

ZanzabumX [31]

Answer:

a) 22.94 psi

b) $5.93\times10^{-5}$

Step-by-step explanation:

a)The pressure at which will trigger a warning is

31 - 31*0.26 = 22.94 psi

b) The probability that that the TPMS will trigger warning at 22.94 psi, given that tire pressure has a normal distribution with average of 31 psi and standard deviation of 2 psi

$f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}$

where x = 22.94, $\mu = 31, \sigma = 2$

$f(22.94)={\frac {1}{2 {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {22.94-31}{2 }}\right)^{2}}$

$f(22.94)=0.2e^{-8.12} = 5.93\times10^{-5}$

6 0

2 years ago

A regular decagon has sides that are 8 cm long. What is the area of the figure? Round to the nearest whole number.

blsea [12.9K]

<u>Given</u>:

Given that the regular decagon has sides that are 8 cm long.

We need to determine the area of the regular decagon.

<u>Area of the regular decagon:</u>

The area of the regular decagon can be determined using the formula,

$A=\frac{s^{2} n}{4 \tan \left(\frac{180}{n}\right)}$

where s is the length of the side and n is the number of sides.

Substituting s = 8 and n = 10, we get;

$A=\frac{8^{2} \times 10}{4 \tan \left(\frac{180}{10}\right)}$

Simplifying, we get;

$A=\frac{64 \times 10}{4 (\tan \ 18)}$

$A=\frac{640}{4 (0.325)}$

$A=\frac{640}{1.3}$

$A=642.3$

Rounding off to the nearest whole number, we get;

$A=642 \ cm^2$

Thus, the area of the regular decagon is 642 cm²

Hence, Option B is the correct answer.

5 0

2 years ago

The local skating rink pays marry a fixed rate per pupil plus a base amount to work as a skating instructor. she earns $90 for i

Ganezh [65]

You have to make a system of equations: lets make a equal the amount marry makes per student and b be her base amount.
90=15a+b (you have to subtract the top equation by the bottom equation)
62=8a+b (90-62=28, 15a-8a=7a, and b-b=0)
Since b canceled out, you are left with 7a=28 which means a=4. you can than plug a into the equation 62=8a+b to find that b=30.

since Lisa makes half of the base amount marry, her base amount is 15. However, she also make twice the amount per kid so she makes 8 per kid.
using the found values found you can make the equations (m=the amount Marry makes, l=the amount Lisa makes, and c is the number of children)
m=4c+30
l=8c+15
set c=20 and you should get m=110 and l=175. Based off of that information, we can say that Lisa makes more money instructing a class of 20 students.
I hope this helps.

8 0

2 years ago