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Use the law of cosines to calculate the angels.

a² = b² + c² −2bc * cos(A)

~~~~~~~~~~~~~~~~~~~~~~~~

Example:

Triangle ABC has sides: a=2, b=3, c=4

2² = 3² + 4² - 2*3*4*cos(A)

cos(A) = 3² + 4² - 2²/ 2*3*4 = 0.875

Angle  A = 28.955º

Did you try:  (5 + 3)^2 mod 5      =

                        (5 + 3)^3 mod 5   =

                        (5 + 3) mod 5       =

Let the number of hours of 1st mechanic=F
Let the number of hours of 2nd mechanic=S

F + S = 25........................(1)
85F + 90S =2,200......  ....(2)

Now you have 2 simultaneous equations. Can you solve them?

No, but I think the clue helped! I still don't really understand what to do next though...

Thank you everyone! I really needed some help on the question, and you helped me so much. Thank you!

I tried it then realized that the median of a set of consecutive positive integers is equal to the mean of the set of integers so therefore it was:

\(\frac{3^7}{3^3}=81\)

thanks for helping me get the answer :D

The sum of 27 conescutive integers is 3^7 or 2187.

We write an equation x+(x+1)+(x+2)+...(x+26)=2187 and solve for x.

x+(x+1)+(x+2)+...(x+26)=2187

27x+351=2187

27x=1836

x=68.

The median is x+12, so the median is 68+12=80.

it is correct!

my explaintion is:

For each point on the unit circle with y-coordinate equal to -0.73, there is a corresponding angle whose sine is -0.73. There are two such points; these are the intersections of the unit circle and the line y=-0.73, shown in red above. Therefore, there are 2 values of x with \(0^\circ \le x < 360^\circ\) such that \(\sin x = -0.73\).

The slope intercept equation is in the form y=mx+b. We already know the slope so we have y=-2x+b. Then we plug in the point (-3, 10) to find b, the y-intercept.

y=-2x+b

10=-2(-3)+b

10=6+b

b=4

So the y intercept of line PQ is (0, 4).

There are 2 values,  x=226.88639405,313.11360594.

We can rephrase the question, and say: Out of 7 points, how many ways can we choose 3? The key word here is "choose". This tells us to use the choose formula.

What you should do is solve for 7 choose 3. 

-56 since 1/7*1/-8=1/(-56) and 1/(1/(-56))=(-56)/1=-56 so our final answer is -56

For a number to be divisible by 5, it has to end in a 0 or 5. Also, a 4 digit number can't start with 0. 

We could do casework. Case 1, where it ends in 0, Case 2, where it ends in 5.

Case 1:

3*2*1*1

That gives us 6. Divide by 2!, and we get 3.

Case 2:

2*2*1*1

Divide by 2!, and we get 2.

2+3 is 5. Therefore, there are 5 ways to arrange the numbers.

Thanks Heureka :)

The best estimate for the mean of a population is the mean of the sample. Find the mean of the sample.

The number of days for the test is 10.

p(0) represents the number of days that there were 0 successful tests divided by the number of days.

p(1) represents the number of days that there was 1 successful test divided by the number of days.

P(2) represents the number of days that there were 2 successful tests divided by the number of days.

etc.

As an example:  p(4)  =  2/10  =  0.0  because there were 2 days which had 4 successful test and the

total number of days is 10.

Hint: Try using angles and line measures (and some geometric intuition) to find the ratio of ET to TC

Extra hint: (congruent triangles/similar triangles?)

Even more extra hint: Look at triangles EST and TRC

Even even more extra hint: How do we find out what shape SDRQ is?

(If you still need help, just ask me!)

:)

help with geometry

\(\begin{array}{|rcll|} \hline \mathbf{ \overline{NM}*\overline{AM} } &=& \mathbf{ \overline{LM}*\overline{KM} } \\ (x-4)*(3+x-4) &=& (x-5)*(6+x-5) \\ (x-4)*(x-1) &=& (x-5)*(x+1) \\ x^2-x-4x+4 &=& x^2+x-5x-5 \\ -x-4x+4 &=& +x-5x-5 \\ -5x+4 &=& -4x-5 \\ -x &=& -9 \\ \mathbf{x} &=& \mathbf{9} \\ \hline \end{array}\)

\(\begin{array}{|rcll|} \hline \mathbf{\overline{KM}} &=& \mathbf{6+x-5} \\ \overline{KM} &=& x+1 \quad | \quad \mathbf{x=9} \\ \overline{KM} &=& 9+1 \\ \mathbf{\overline{KM}} &=& \mathbf{10} \\ \hline \end{array}\)

Thanks heureka!

 I suggest you first draw it: