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Sure!

To make a fraction, we want the denominator to be as small as possible and the numerator as large as possible. We need to make x the smallest value that satisifies the inequality. We will use 1 because we don't want our denominator to negative because then the decimal form will be negative. The largest value of y that satisfies the conditions is 4. 4 + 1/1 = ?

You do that yourself

Hats of to you!

\(\sqrt{4-2}\sqrt{3} \)

 = \(\sqrt{3}+1\)

\(\sqrt{7-4\sqrt{3}}=2-\sqrt{3}\)

We cancel out \(\sqrt{3}\) to get -1 + 2.

For humor, you do -1 + 2 yourself!

add the two equations to get    2x = sqrt31 + sqrt21      x = 1/2 ( sqrt31+sqrt21)

multiply second  equation by -1 to get    -x+y = -sqrt21    add to first equation to get

     2 y = sqrt31 - sqrt21

         y = 1/2 (sqrt31 - sqrt21)

               multiply the red equations together       31/4    -  21/4 = 10/4 = 2.5

Triangle ABC is isosceles with AB=BC.  If AC = 20 and [ABC] = 240, then find the perimeter of triangle ABC.

ABC area is 240 u²            AC = 20

Height    H = 240/ (20/2) = 24

AB = sqrt[( 10² + 24²) = 26            AB = BC

Parameter    P = AB + BC + AC = 72  

Solve the equation sqrt(5x - 1) = sqrt(x) + 1.        square both sides

5x-1 = x + 2 sqrtx  + 1

4x -2 = 2 sqrtx

16x^2 - 16x +4= 4x

16x^2- 20x+4 =0             Quadratic formula     shows   x = 1   or  1/4    (throw out 1/4)

the two numbers in    (7x  + a     )(x  + b  )      must multiply together to -11

ab = -11       then     a,b    =   -11,1     11,-1    -1,11   1,-11

if you put all of those into the red equation above you will find   n = -4     4      76    -76           I believe.......

20 in the collection     .4 (20 ) = cars = 8 cars

add x number of cars to the collection to make it 75% cars

(20 + x)(.75) = 8+x

15 + .75x = 8 + x        you can take it from here ! 

If 0 ⁰   is considered North then yes   214 ⁰    is south and west

No, it is not !! if you count all the digits from 1 to 100 inclusive, you get = 192 digits

Here is a lazy person's way of summing up your sequence. You could have done the same thing?

1+2-3-4+5+6-7-8+9+10-11-12+13+14-15-16+17+18-19-20+21+22-23-24+25+26-27-28+29+30-31-32+33+34-35-36+37+38-39-40+41+42-43-44+45+46-47-48+49+50-51-52+53+54-55-56+57+58-59-60+61+62-63-64+65+66-67-68+69+70-71-72+73+74-75-76+77+78-79-80+81+82-83-84+85+86-87-88+89+90-91-92+93+94-95-96+97+98-99-100 = - 100

If you plot the points (7, 4) and (6, 3), you can gather information about the slope of the line. From point (7, 4) you would go down two, and go to the left two to get (6, 3).

For the next point, you would do the same. From point (6, 3) you would go down two, and go the left two. You would then get (5, 2).

Because it asks for the x-intercept, you would use the slope to plot points on the line until you reach the x-axis.

The points on the line would then include:

(7, 4) 

(6, 3)

(5, 2)

(4, 1)

(3, 0)

(3, 0) is the point at which the x-intercept lies. Therefore, your answer is (3, 0).

There are 600 such numbers.

Sum them up as an arithmetic sequence:

sum_(n=1)^1009((2020 - 2 n)^2 - (2019 - 2 n)^2) = 2,037,171

1009/2 * [2*4035 +  ( - 4*1008)] = S, solve for S

S =2,037, 171

thanks melody! i got it right!!! :)

We can work out that the height of triangle ABC is 32.  So the perimeter of triangle ABC is 94.

Thank you so much! I see what I did wrong. I got the 37.5 part, but after that, I was beyond confused! I understand a lot better:)

So, would that mean the ship was 31 miles to the south and 21 miles to the west of where the ship left port? 
I graphed the point, and that's what my conclusion was, I just want to be sure! 
Thank you again xx 

simulatenus equation 

190 is the answer
Because 90 times 2 plus 10 = 190

where is the absolute value located on the calculator?