As follows:
My statement above that "There are only four possibilities ..." assumes that we are dealing with integers only.
I like this answer guest.
Heureka has elaborated on it below.... for anyone who doesn't already understand.
It is very nice to see you back again Heureka
Use the calculator
3 divided by 8.8 =
Suppose a, b, c, and d are real numbers which satisfy the system of equations a + 2b + 3c + 4d = 10 4a + b + 2c + 3d = 4 3a + 4b + c + 2d = 10 2a + 3b + 4c + d = −4. Find a + b + c + d.
\(\begin{array}{|lrcll|} \hline (1) & a + 2b + 3c + 4d &=& 10 \\ (2) & 4a + b + 2c + 3d &=& 4 \\ (3) & 3a + 4b + c + 2d &=& 10 \\ (4) &2a + 3b + 4c + d &=& −4 \\ \hline \hline \text{sum} & 10a+10b+10c+10d &=& 10 + 4 + 10 - 4 \\ & 10(a+b+c+d) &=& 20 \quad | \quad : 10 \\ & a+b+c+d &=& \dfrac{20}{10} \\ & \mathbf{a+b+c+d} &=& \mathbf{2} \\ \hline \end{array} \)
Add the four equations together and we get
10a + 10b + 10c + 10d = 20,
so
a + b + c + d = 2.
Find an ordered triple (x,y,z) of real numbers satisfying x<= y<= z and the system of equations sqrtx + sqrty +sqrtz = 10 x+y+z=42 (sqrtxyz) = 20
Hello Guest!
\(\sqrt{x}+\sqrt{y}+\sqrt{z}=10\)
\(x+y+z=42\)
\(\sqrt{xyz}=20\)
\(xyz=400\)
\(z=\frac{400}{xy}=42-x-y\)
\(z= (10-\sqrt{x}-\sqrt{y})^2\)
\(I.\ \frac{400}{xy}=42-x-y\)
\(II.\ \frac{400}{xy}=(10-\sqrt{x}-\sqrt{y})^2 \)
\( y\in\{-3,3\}\\ x\in \{-2,2\}\)
\(z\in \{5,9,11,15\}\)
\(z=3\)
\(x+y+3=42\\ x+y=39\)
Error! To be continued.
!
If c is a constant such that 9x^2 + 12x + c is equal to the square of a binomial, then what is c?
\(9x^2 + 12x + c\)
\((u+v)^2=u^2+2uv+v^2\) first binom
\((3x+2 )^2=9x^2+12x+4\)
\( c=4\)
On the graph of y = (x + 4)^2 - 100, how many points are there whose coordinates are both negative integers?
\(y = (x + 4)^2 - 100\)
Two points are there whose coordinates are both negative integers:
P1 (-9, -75)
P2 (-4, -100)
Thanks for answering Helpbot,
I am sorry to say that you have not solved it.
You see you have a y on both sides.
You have to have y on one side and en expression with m on the other side.
Think of m just as a constant. I mean treat it like it is a number that stays the same all the time.
\(y^2-my+(2m-1)=0\\ \text{This is a quadatic equation}\\ \text{It is of the form}\\ ay^2+by+c=0\\ \)
NOW to solve this you use the quadratic formula.
\(y = {-b \pm \sqrt{b^2-4ac} \over 2a} \)
So now you solve yours.
Hint: a=1 b=-m c=(2m-1)
Your answer will be will have an m in it.
--------------
AFTER you have done this, think about how many answers there can be for y.
How can you make this happen?
(2, 4, 6, 10, 12, 14, 18, 20, 22, 26, 28, 30, 34, 36, 38, 42, 44, 46, 50, 52, 54, 58, 60, 62, 66, 68, 70, 74, 76, 78, 82, 84, 86, 90, 92, 94, 98, 100) >>Total = 38 such numbers.
The probability is = 38 / 100 =19 / 50
A short computer code shows that the 1000th number whose digits add up to 10 =100,036.
Largest number you CANNOT make = 53
(1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 21, 22, 25, 26, 29, 30, 33, 34, 37, 41, 45, 49, 53) >Numbers you CANNOT make = 27.
ALL numbers above 53 you can make. Numbers that you can make are ALL multiples of 19 and 4 or combinations thereof. All numbers that you cannot make fall outside of those multiple combinations.
Wait actually I obtain the answer of 4.
I solved for y and got
y^2=my-2m+1
y=sqrt(my-2m+1)
Hmmm how do u remove the y from my?
link.....https://web2.0calc.com/questions/what-is-line-bx
The length of XY = sqrt [402 - (31 - 7)2]
When the length of a rectangle is increased by 20% and the width increased by 12%, by what percent is the area increased?
the area is increased by 23.2%
A, B, C, D, and E are points on a circle of radius 2 in counterclockwise order. We know AB=BC=CD=DE=2. Find the area of pentagon ABCDE.
area = 5√3
By Hamilton's Theorem, the solutions are z = 4^{1/4}*e^(pi*i/4), 4^{1/4}*e^(pi*i/4 + pi/4), 4^{1/4}*e^(pi*i/4 + 2*pi/4), and 4^{1/4}*e^(pi*i/4 + 3*pi/4). Since 4^{1/4} = sqrt(2) and e^(pi*i/4) = (1 + i)/sqrt(2), the first solution is 1 + i. Then the other roots work out as
4^{1/4}*e^(pi*i/4 + pi/4) = 1 - i,
4^{1/4}*e^(pi*i/4 + 2*pi/4) = -1 - i, and
4^{1/4}*e^(pi*i/4 + 3*pi/4) = -1 + i.
Thanks!!
Common ratio r = 1/16
converging series because r <1
sum = a1 /(1-r) = 2.1333...
That makes sense. Thanks a lot!
!
