Answer:
Step-by-step explanation:
There are four axioms to prove the triangles are contruent.They are
SSS(side side side axiom)
SAS(side angle side axiom)
AAS(angle angle side axiom)
ASA(angle side angle axiom)
RHS (right angle hypotenuse side axiom)
here two triangles are congruent by RHS axiom
So it tells us that g(3) = -5 and g'(x) = x^2 + 7.
So g(3) = -5 is the point (3, -5)
Using linear approximation
g(2.99) is the point (2.99, g(3) + g'(3)*(2.99-3))
now we just need to simplify that
(2.99, -5 + (16)*(-.01)) which is (2.99, -5 + -.16) which is (2.99, -5.16)
So g(2.99) = -5.16
Doing the same thing for the other g(3.01)
(3.01, g(3) + g'(3)*(3.01-3))
(3.01, -5 + 16*.01) which is (3.01, -4.84)
So g(3.01) = -4.84
So we have our linear approximation for the two.
If you wanted to, you could check your answer by finding g(x). Since you know g'(x), take the antiderivative and we will get
g(x) = 1/3x^3 + 7x + C
Since we know g(3) = -5, we can use that to solve for C
1/3(3)^3 + 7(3) + C = -5 and we find that C = -35
so that means g(x) = (x^3)/3 + 7x - 35
So just to check our linear approximations use that to find g(2.99) and g(3.01)
g(2.99) = -5.1597
g(3.01) = -4.8397
So as you can see, using the linear approximation we got our answers as
g(2.99) = -5.16
g(3.01) = -4.84
which are both really close to the actual answer. Not a bad method if you ever need to use it.
Answer:
B
Step-by-step explanation:
The maximum amount Eric can spend on magazines is $25 less the cost of lunch, $15.
The appropriate inequality sign would be less than since he cannot spend more than $25.
Also, the amount he can spend on magazines would be what is left after paying for lunch.
So the correct inequality is 4m - 15 < 25
Answer:
855
Step-by-step explanation:
90x9.5=855
Yes! Let me help you!
Here is the original equation, lets solve this step-by-step
(x + 2)/4 = 5
Now, lets find out how.
We must apply the inverse operation.
4/2 is the reciprocal, so lets multiply that to both sides.
4/2 = 2
5*4 = 20
4x + 8 = 20
-8 -8 Subtract 8 from both sides. (Inverse operation)
4x = 12
4x/4 = 12/4 Divide 4 by both sides (Inverse)
x = 12/4
x = 3 Simplified
Answer: x = 3
