Answer:
<em>x² - 28x√x + 294x - 1372√x + 2404 </em>
Step-by-step explanation:
f(x) = + 3
g(x) = x - 7
h(x) = √x
f(g(h(x))) - ?
g(h(x)) = √x - 7
f(g(h(x))) = + 3 = ( √x - 7 )² × ( √x - 7 )² + 3 =
= (x - 14√x + 49)(x - 14√x + 49) + 3 =
= x² - 14x√x + 49x - 14x√x + 196x - 686√x + 49x - 686√x + 2401 + 3 =
= <em>x² - 28x√x + 294x - 1372√x + 2404</em>
Answer:
Step-by-step explanation:
Given : Expression
To find : Factor the expression ?
Solution :
The given expression is a quadratic function the solution is
On comparing with general form,
a=16, b=0, c=49
Substitute in the formula,
Factors are
Therefore,
9514 1404 393
Answer:
(2.27, 0.96)
Step-by-step explanation:
The orthocenter is the point of intersection of altitudes of the triangle. The equation for an altitude is the equation of a line through a vertex that is perpendicular to the opposite side.
For example, the line perpendicular to side AC can be found as ...
(∆x, ∆y) = C-A = (3, -1) -(-4, 2) = (7, -3)
∆x(x -h) +∆y(y -k) = 0 . . . . perpendicular through point (h, k)
For side AC, we want the point to be B(4, 5), so the equation is ...
7(x -4) -3(y -5) = 0
7x -3y -13 = 0
Similarly, the altitude to side AB can be written as ...
(∆x, ∆y) = B -A = (4, 5) -(-4, 2) = (8, 3)
8(x -3) +3(y +1) = 0
8x +3y -21 = 0
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By the "cross multiplication method", the solution to these equations is ...
x = (-3(-21) -(3(-13))/(7(3) -8(-3)) = (63+39)/(21+24) = 102/45 = 2 4/15 ≈ 2.27
y = (-13(8) -(-21)(7))/45 = 43/45 ≈ 0.96
The orthocenter is near (2.27, 0.96).
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A graphing application confirms this result.
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<em>Additional information about the cross multiplication method</em>
For the general form equations ...
The "cross multiplication method" has you write the array ...
and form the "cross products" in groups of four coefficients:
D = ae -db, X = bg -ec, Y = cd -ga
Then the solution to the set of equations is ...
1/D = x/X = y/Y ⇒ x = X/D, y = Y/D
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<em>Additional note</em>
Videos of this method show you writing the array as bcab/egde and using the final equation x/X=y/Y=1/D. The above gets the same result in a more straightforward manner.
