Visualize the problem. We will have to use the distance formula:
d = √(x₂ - x₁)² + (y₂ - y₁)²
Let the unknown point be (x,y). The solution is as follows:
Distance between A and the point.
3 = √(4 - x₁)² + (8 - y₁)²
9 = 16 - 8x₁ + x₁² + 64 - 16y₁ + y₁² --> eqn 1
Distance between point and B
1 = √(14 - x₁)² + (10 - y₁)²
1 = 196 - 28x₁ + x₁² + 100 - 20y₁ + y₁² --> eqn 2
Subtract eqn 2 from eqn 1:
8 = -180 + 20x₁ - 36 + 4y₁
8 = -216 + 20x₁ + 4y₁
224 = 20x₁ + 4y₁
56 = 5x₁ + y₁ --> eqn 3
The last equation would be the linear equation using points A and B.
m = (10-8)/(14-4) = 1/5 = (8 - y₁)/(4 - x₁)
4 - x₁ = 5(8 - y₁)
4 - x₁ = 40 - 5y₁
-36 = x₁ - 5y₁ --> eqn 4
Solve equations 3 and 4 simultaneously:
x₁ = 9.38
y₁ = 9.08
<em>Therefore, the closest answer is letter B.</em>
Answer:
<h2>
Hence a = -1, b = 10</h2>
Step-by-step explanation:
Given h(x) = (x - 1)³ + 10, f(x) = x + a and g(x) = x³ + b so that h(x) = (gof)(x)
To get the value of a and b that will make the composite function true, we will first need to get the composite function (gof)(x).
(gof)(x) = g[f(x)]
g[f(x)] = g[ x + a]
To get g(x+a), we will replace the variable x in the function g(x) = x+b with x+a as shown;
g[x + a] = (x+a)³+b
Hence (gof)(x) = (x+a)+b
Equating h(x) = (gof)(x)
(x - 1)³ + 10 = (x+a)³+b
On comparing both sides of the equation;
(x - 1)³ = (x+a)³ and 10 = b
For (x - 1)³ = (x+a)³
Take cube root of both sides
∛ (x - 1)³ = ∛(x+a)³
x-1 = x+a
collect like terms
a = x-x-1
a = -1
Hence a = -1, b = 10
Answer:
59.25 < hb ≤ 86.25 (also = 59.3 < 1dp ≤ 86.2 to 1dp)
Step-by-step explanation:
60- 0.75 = human height therefore 59.25 < h ≤ ? then to find greatest height we subtract again 87 - 0.75 = 86.25 and fill in 59.25 < h ≤ ? = 59.25 < h ≤ 86.25 and should we show inhes to 1 dp we keep lowest rounded up 59.3 < 1dp ≤ 86.2 as lowest bound is 59.15 < lb ≤ 86.15 = 59.25 < hb ≤ 86.25
Answer:
what's the problem
Step-by-step explanation:
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