Answer:
Any [a,b] that does NOT include the x-value 3 in it.
Either an [a,b] entirely to the left of 3, or
an [a,b] entirely to the right of 3
Step-by-step explanation:
The intermediate value theorem requires for the function for which the intermediate value is calculated, to be continuous in a closed interval [a,b]. Therefore, for the graph of the function shown in your problem, the intermediate value theorem will apply as long as the interval [a,b] does NOT contain "3", which is the x-value where the function shows a discontinuity.
Then any [a,b] entirely to the left of 3 (that is any [a,b] where b < 3; or on the other hand any [a,b] completely to the right of 3 (that is any [a,b} where a > 3, will be fine for the intermediate value theorem to apply.
Step 1: Simplify both sides of the equation.
Step 2: Subtract 6x from both sides.
- 65x²+390x+585−6x=6x−6x
- 65x²+384x+585=0
For this equation: a=65, b=384, c=585
Step 3: Use quadratic formula with a=65, b=384, c=585
- x=−b±√b2−4ac/2a
- x=−(384)±√(384)2−4(65)(585)/
- 2(65)
- x=−384±√−4644/130
Therefore, There are no real solutions.
Answer:
See explanation below
Step-by-step explanation:
Find the value of x in each of the following
1) x-1+5√x-1+3=0
5√x-1 = -x -2
Square both sides
25(x-1) = (-x-2)^2
25(x-1) = x^2+4x + 4
25x-25 = x^2+4x + 4
x^2 +4x + 4 - 25x + 25 = 0
x^2 - 21x + 29 = 0
x = 21±√21²-4(29)/2
x = 21±√441-116/2
x = 21±√325/2
x = 21±18.03/2
x = 21+18.03/2 and 21-18.03/2
x = 19.515 and 1.485
4) x^4-64=0
x^4 = 64
![x = \sqrt[4]{64}](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%5B4%5D%7B64%7D)
x = 2.83
Every even number is 2 away from the last.
0, 2, 4, 6, 8, 10, 12, 14...etc.
If we had an even number p, then the next three even numbers would be
p+2, p+4, and p+6.
<em>(If we had an odd number p, then the next three even numbers would be</em>
<em>p+1, p+3, and p+5. I'm not sure if p is even is implied in the question. Technically the answer would be p - p mod 2 + 2, where p is an interger...that gets into more technical function stuff, though.)</em>
Answer:
m∠A = 30°
m∠B = 80°
m∠C = 70°
Step-by-step explanation:
By applying cosine rule in the given triangle,
b² = a² + c² - 2ac[cos(∠B)]
From the given triangle,
a = 14 m
b = 28 m
c = 24 m
(28)² = (14)² + (24)² - 2(14)(24)cos(B)
784 = 196 + 576 - 672cos(∠B)
cos(∠B) = 0.1786
∠B = 
∠B = 79.71°
∠B = 80°
By applying sine rule in the given triangle,
sinA = 0.491958
A = 29.47°
A ≈ 30°
By applying triangle sum theorem,
m∠A + m∠B + m∠C = 180°
30° + 80° + m∠C = 180°
m∠C = 70°
