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\(a b c d = c_0 = -4\\ bcd+acd+abd+abc = -(c_1) = -7\\ \dfrac 1 a + \dfrac 1 b+\dfrac 1 c+\dfrac 1 d = \\\dfrac{bcd+acd+abd+abc}{a b c d } = \dfrac{-7}{-4}=\dfrac 7 4\)

3)

m∠FGE  =  m∠CGD  because they are vertical angles.

\(\frac{\overline{\text{GF}}}{\overline{\text{GE}}}\ \stackrel{?}{=}\ \frac{\overline{\text{GC}}}{\overline{\text{GD}}} \\~\\ \frac{540}{513}\ \stackrel{?}{=}\ \frac{220}{209}\\~\\ \frac{20}{19}\ \stackrel{?}{=}\ \frac{20}{19}\\~\\ \frac{20}{19}\ =\ \frac{20}{19}\)

And   \(\frac{\overline{\text{GF}}}{\overline{\text{GE}}}\ =\ \frac{\overline{\text{GC}}}{\overline{\text{GD}}}\)

So by SAS similarity,  △GFE  is similar to  △GCD

4 + 2y = 3y - 5    subtract 2 y from both sides of the equation

4 = y - 5              add 5 to both sides

9 = y       or    y=9

1 and 2)

m∠KJL  =  m∠DJC  because they are vertical angles

m∠JKL  =  m∠JDC  because they are alternate interior angles

So by AA similarity, △JKL is similar to △JDC

The option you have selected is correct

WOW thanks I'll try that thanks alot for that for the tip have a great day!

We can also solve for  x  like this:

\(\frac12\)( 2x - 14 )  =  4

                                Multiply both sides of the equation by  2

2x - 14  =  8

                                Add  14  to both sides.

2x  =  22

                                Divide both sides by  2

x  =  11

This way we avoid disributing the  \(\frac12\) . In this particular case it was shorter to do it the way CoolStuffYT said, but in many other cases it is easier to work it the other way. For example:

\(\frac12\)( x - 14 )  =  4

In this example, it is easier to first multiply both sides by  2  rather than distribute  \(\frac12\) .

Try it both ways and you can see why

The area of the two-dimensional cross section that is parallel to face ABC.that is Area of Δ DEF = 84 ft²

Step-by-step explanation: 

Given : A triangular prism with some side measurement.

We have  to find the area of the two-dimensional cross section that is parallel to face ABC.

Since, the cross section that is parallel to face ABC.

Since, face parallel to ABC is DEF .

And DEF is a triangle with ∠ E = 90°

So, Area of right angled triangle is 1/2 times base times height.

Base = 24 ft 

and height is 7 ft 

So, Area of Δ DEF = 1/2 times 24 times 7

Simplify , we have, 

Area of Δ DEF = 84 ft²

Thus, The area of the two-dimensional cross section that is parallel to face ABC.that is Area of Δ DEF = 84 ft²

Good! :D

Thanks Cphill 

Your a guest how did you earn points??????? 

Probally forgot to log in...........

Do you know how to distribute?

1/2 times 2x = x.

1/2 times -14 = -7.

Now we get x-7=4.

Can you solve it from here?

You are very welcome!

:P

Points aren't as important as helping other people with math or learning from the problems you posted.

I earned my points by helping others with math or posting questions that I learn I have trouble on. Try to be interactive with the question answerers and try to work with them to solve your problem

Since 1 US dollar is 108 yen, simply do 200 yen divided by 108 yen.

That roughly equals 1.85 US dollars. 

😏😏

Construct a circle of any radius and let chords AB and CD be parallel

Join AD, BC  and let E be the intersection of these chords

Now....because AB and CD are parallel and AD and BC are transversals, then angle BAE = angle CDE 

And angle ABE = angle DCE  for the same reason

And angle ABE = angle CDE  because they intercept the same arc

And angle BAE = angle DCE for the same reason

Therefore....angle CDE = angle DCE...so....in triangle CED.....CE = DE

And....angle BAE = angle ABE....so..in triangle AED.....AE = BE

Therefore....AE + DE  = CE + BE

And....AE + DE = AD

And CE + BE  = BC

So....AD = BC

The outlier is 23

So.....the rest of the data set is

2, 9, 1, 3, 7, 10, 2, 10, 9, 7

The mean =  6

The mean absolute deviation ≈ 3.6 

The second answer is correct

Mean =  [ 6(1)  + 3(2) + 2(3) + 1(4)  + 1(10)  ] / 13  ≈  2.46

Sorting the data in ascending order

1,1,1,1,1,1,2,2,2,3,3,4,10

Median  =  2

It appears that the median is a better measure because the data is skewed to the left and there is an outlier

Nickolas....list the data in ascending order....so we have

0, 0, 1,1, 2, 2, 2, 14

Mean  = add the values and divide by the number of values = 

 [ 0 + 0 + 1 + 1 + 2 + 2 + 2 + 14 ]  / 8  =   22 / 8  = 2.75

Median....add the two middle values and divide by 2 =   [ 1 + 2 ] / 2 =  3  / 2   = 1.5

So....the first answer is correct

Vieta's Formula
The equations  \(x^3 + 5x^2 + px + q = 0\) and \(x^3 + 7x^2 + px + r = 0\) have two roots in common.
If the third root of each equation is represented by \(x_1\) and \(x_2\) respectively,
compute the ordered pair \((x_1,x_2)\).

\(\begin{array}{|rcll|} \hline x^3 + 5x^2 + px + q &=& 0,\ \text{ the roots are }~ x_1,x_3,x_4. \\ x^3 + 7x^2 + px + r &=& 0,\ \text{ the roots are }~ x_2,x_3,x_4. \\ \hline \end{array} \)

\(\begin{array}{|rcll|} \hline \mathbf{5} &=& \mathbf{-(x_1+x_3+x_4)} \\ 5+x_1 &=& -(x_3+x_4) \\\\ \mathbf{7} &=& \mathbf{-(x_2+x_3+x_4)} \\ 7+x_2 &=& -(x_3+x_4) \\\\ 5+x_1 &=& 7+x_2 \\ \mathbf{x_1-x_2} &=& \mathbf{2} \\ \hline \end{array} \)

\(\begin{array}{|rcll|} \hline x_1x_3+x_1x_4+x_3x_4 = p &=& x_2x_3+x_2x_4+x_3x_4 \\ x_1x_3+x_1x_4 &=& x_2x_3+x_2x_4 \\ x_1(x_3+x_4)-x_2(x_3+x_4) &=& 0 \\ (x_3+x_4)(x_1-x_2) &=& 0 \quad | \quad \mathbf{x_1-x_2 = 2} \\ (x_3+x_4)*2 &=& 0 \quad | \quad : 2 \\ x_3+x_4 &=& 0 \\ \mathbf{x_3} &=& \mathbf{-x_4} \\ \hline \end{array} \)

\(\begin{array}{|rcll|} \hline \mathbf{5} &=& \mathbf{-(x_1+x_3+x_4)} \quad | \quad \mathbf{x_3 = -x_4} \\ 5 &=& -(x_1-x_4+x_4) \\ 5 &=& -x_1 \\ \mathbf{x_1} &=& \mathbf{-5} \\\\ \mathbf{7} &=& \mathbf{-(x_2+x_3+x_4)} \quad | \quad \mathbf{x_3 = -x_4} \\ 7 &=& -(x_2-x_4+x_4) \\ 7 &=& -x_2 \\ \mathbf{x_2} &=& \mathbf{-7} \\ \hline \end{array}\)

\((x_1,~x_2) = (-5,~-7)\)

"What is the probability of rolling six standard, six-sided dice and getting six distinct numbers?"

Doesn't matter what the first one is: probability = 1

There are 5 possibilities for the second one:  probability = 5/6

There are 4 possibilities for the third one:  probability = 4/6

There are 3 possibilities for the fourth one:  probability = 3/6

There are 2 possibilities for the fifth one:  probability = 2/6

There is 1 possibility for the sixth one:  probability = 1/6

Overall probability is obtained by multiplying all the above together (then reduce to lowest terms).