Answer:
y = 2x - 25
Step-by-step explanation:
First find the gradient, we can see it goes through (30,35) and 35,45), and since gradient is found by 'change in y / change in x' we can do: (45-35) / (35-30) = 10/5 = 2
So we know we are looking for an equation with 2x in it.
We have two options: y = 2x - 25 and y = 2x - 75.
Plug in one of the points and see which of the equations works.
Replacing y with 35 and x with 30 in the first equation we have: 35 = 2(30) - 25 = 60 - 25 = 35, this is indeed true.
However if we did the same with the second equation: 35 = 2(30)-75 = 60 - 75 = -15, this is false since 35 does not equal -15, so it can't be the second equation.
In conclusion it must be y = 2x - 25
The value of a and b is 3 and - 8 respectively.
A continuous function is one in which a continuous change in the argument results in a continuous change in the function's value. This suggests that there are no abrupt changes in value or discontinuities.
We have,
f(x) = { 1, if x ≤ 3; ax + b, if 3 < x < 5; 7, if x ≥ 5}
Since f(x) is continuous at x = 3 and x = 5,
Therefore,
At x =3,
Left-hand limit = Right hand limit
lim( x → 3-) f(x) = lim( x → 3+ ) f(x)
lim( x → 3-) (1) = lim( x → 3+ ) ( ax + b )
1 = a × 3 + b
3a + b = 1 -------------(i)
So, At x = 5
Left-hand limit = Right-hand limit
lim( x → 5-) f(x) = lim( x → 5+ ) f(x)
lim( x → 3-) (7) = lim( x → 3+ ) ( ax + b)
5(a) + b = 7 --------------(ii)
Soling the two-equation,
We get,
a = 3 and b = - 8
Learn more about continuous function here:
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2 and 1/4 = 9/4
4 and 1/12 = 49/12
3 and 2/3 = 11/3
Perimeter = 9/4 + 49/12 + 11/3
= 27/12 + 49/12 + 44/3
= 120/12
= 10inches
Answer:
A = 50.29 units²
Step-by-step explanation:
See attached photo
I honestly believe its D but I'm not for sure. Sorry if i didn't help much