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Here is a labelled one:

a=17ft

b=8ft

c=16ft

\(\gamma=[?]^0\)

Hello Guest!

\(\color{blue}c^2=a^2+b^2-2ac\ cos\gamma\\ cos\ \gamma=\frac{a^2+b^2-c^2}{2ac}\\ coc\ \gamma=\frac{17^2+8^2-16^2}{2\cdot 17\cdot 16}\)

\(cos\ \gamma=0.1783\\ \gamma=arccos\ 0.1783\)

\(\gamma=79.7^0\)

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This is of low priority, but I need a response in the next 3ish hours.

Just plug into the Law of Cosines clue and solve for angle C

8² +17² -2(8)(17) cos c = 16²      Solve for angle C   (using arc cos)

The inverse of the funktion \(y=\sqrt{3x-5}\) is

Hello Guest!

\(x=\sqrt{3y-5}\\ x^2=3y-5\)

\(y=\frac{x^2+5}{3}\)   B)

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At a glance this problem seems really hard but it atually is no, replacing the red marble does not affect the overall answer. So, all we have to do is multiply this out:

Pulling a red marble out*Pulling a red marble out

=4/18*4/18

=2/9*2/9

=4/81 

And thus 4/81 is our final answer.

First lets denote x to be how much mph he runs and 2x to be how much mph he bikes. We construct the following equation:

20/2x+10/x=2.5

10/x+10/x=2.5

10/x=1.25

x=10/1.25

x=8miles per hour

So there for his biking speed will be 2x=2*8=16miles per hour and his running speed will be 8 miles per hour.

AC = BC + AB

2x + 7 = x + 5x - 9       solve for x

AB = 5x - 9 = ? 

Vertex   3 , -5   

Vertex from of parabola:

y = a(x-3)^2  - 5       point 1, -3

-3 = a(1-3)^2 - 5

a = 1/2

y = 1/2 (x-3)^2 - 5      expand to find  a  b  c     to complete the question.......

Alejandro rode his bike to work at an average rate of 15 miles per hour. To go home, he put his bike on the front rack of the bus and took the bus home along the same route, traveling at an average rate of 22.5 miles per hour. If Alejandro’s bike ride to work took 45 minutes, how many hours did the bus ride home take?

Hello Guest!

\(s=vt=\frac{15mls}{h}\cdot45min\cdot \frac{h}{60min}=\color{blue}11\frac{1}{4}mls\)

\(t=\frac{s}{v}=\frac{11.25mls\cdot h}{22.5mls}=\color{blue}\frac{1}{2}h\)

\(\frac{1}{2}\ hours\ did\ the\ bus\ ride\ home\ take.\)

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Some of us on Chromebooks and cell phones do not get that option. 

15/22.5 x 3/4 = ......   hr

AB  +   BC = AC

5x-9      +     x    =    2x+7

4x= 16

x = 4

AB = 5x-9

       = 5(4) - 9 = 11  units, Domenica......

I will not start a fight on the first part, however, you are jumping to conclusions on a different front ;). How did you deduce that I am offended?

oh wait i got it nevermind

oh it's supposed to say x*(3x+1) < c

This question makes no sense, are you sure it is correct?

area = [(10/2)² * 3.14] / 2 + (6 * 8) / 2

Example:       -25 / -5 = 5          -2.5 / -5 = 0.5           - 0.25 / - 5 = 0.05

- 0.37 / - 15 = 0.0246666666

I take this to mean calculate \(\int(-\sin x)e^{\cos x}dx\)

Well, since the derivative of cos x is - sin x, and that of e^x is just e^x, we can see from the chain rule that:

 \(\int(-\sin x)e^{\cos x}dx = e^{\cos x}\)  plus a constant of course.

Mach 2.4 is   2.4 times the speed of sound

                        2.4 x 344 m/sec   x   3600sec/hr   x  1 km / 1000m = ..........   km/hr

Arc AC is a quarter-circle with center B. The shaded region ABC is "rolled" along a straight board PQ until it reaches its original orientation for the first time with point B landing at point B'. If BC=2/pi cm, what is the length of the path that point B travels? Express your answer in the simplest form.

BC = 2/pi cm       (radius of the circle)

The length of the arc L is         L = [ 2( 2/pi )] * pi / 4       L = 1 cm

The length of the path that point B travel is  3L  or  3 cm

The 171st even integer is 171*2=342

The 219th odd integer is 219*2-1=437

437-342=95 And thus 95 is our answer.

We convert the equation x+3y=-12 into slope intercept for: y=-x/3-4.

So the slope of this equation is -1/3. We know that 2 parrelell lines have the same slope so we just have to look for the equation that has slope of -1/3.

And thus y=-1/3x-2 is our final answer.