Step-by-step explanation:
We have xy = 28, x² + y² = 65 and x³ + y³ = 407.
Since (x + y)(x² - xy + y²) = x³ + y³,
x + y = (x³ + y³)/(x² + y² - xy)
= (407) / [(65) - (28)]
= 407 / 37
= 11.
Hence the sum of the numbers is 11.
His mistake is that he used the differences of 6, 10 and 14 instead of the differences of 7, 17 and 31.
i.e. for a linear function, the y values should have a constant rate of change and not the differences.
Step-by-step explanation:
factor 4 out of the variable terms, as this helps.
but my approach is simply to define the target and then calculate "backwards".
we want to find
(ax + b)² = a²x² + 2abx + b²
and now we compare with the original equation :
a²x² = 4x²
a² = 4
a = 2
2abx = 16x
2×2×bx = 16x
4b = 16
b = 4
b² = 16, but we have only 3, so we need to subtract 16-3 = 13 from the completed square.
so, our equation is
(2x + 4)² - 13 = 0
(2x + 4)² = 13
2x + 4 = sqrt(13)
2x = sqrt(13) - 4
x = sqrt(13)/2 - 2
>; < - dot line
≥; ≤ - solid line
>; ≥ - shading above the line
<; ≤ - shading below the line
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y = 2x + 3 - it's a linear function. We only need two points to plot the graph. Select two any x values and calculate the y values:
for x = 0 → y = 2(0) + 3 = 0 + 3 = 3 → (0, 3)
for x = -2 → y = 2(-2) + 3 = -4 + 3 = -1 → (-2, -1)
y > 2x + 3
Dot line an shading above the line (look at the picture).
To do this you have to fill in the equation

, but you don't know the height, so we'll use

for height. Plugging in the numbers you gave me, the equation is:

. To solve this, we need to find

. To find height you do

. Doing this, we get

=
3.75 ft.Hope this helped!