Answer:
The tax is $1.88
Step-by-step explanation:
7.5% = 0.075 (divide by 100)
0.075 * $25 = 1.875 or $1.88
The factor outside the parentheses is -1. Distribute using that factor.
2 - (4 - <em>x</em>) = 7<em>x</em> - 5<em>x</em>
<em />
-1 * 4 = -4 and -1 * -<em>x</em> = <em>x</em>
<em />
2 - 4 + <em>x</em> = 7<em>x</em> - 5<em>x</em>
Simplify.
-2 + <em>x</em> = 2<em>x</em>
<em>x</em> = 2<em>x</em> + 2
-<em>x</em> = 2
<em>x</em> = -2
<h3>
Answer:</h3>
<em>x</em> = -2
3.) An extreme value refers to a point on the graph that is possibly a maximum or minimum. At these points, the instantaneous rate of change (slope) of the graph is 0 because the line tangent to the point is horizontal. We can find the rate of change by taking the derivative of the function.
y' = 2ax + b
Now that we where the derivative, we can set it equal to 0.
2ax + b = 0
We also know that at the extreme value, x = -1/2. We can plug that in as well.

The 2 and one-half cancel each other out.


Now we know that a and b are the same number, and that ax^2 + bx + 10 = 0 at x = -1/2. So let's plug -1/2 in for x in the original function, and solve for a/b.
a(-0.5)^2 + a(-0.5) + 10 = 0
0.25a - 0.5a + 10 = 0
-0.25a = -10
a = 40
b = 40
To determine if the extrema is a minima or maxima, we need to go back to the derivative and plug in a/b.
80x + 40
Our critical number is x = -1/2. We need to plug a number that is less than -1/2 and a number that is greater than -1/2 into the derivative.
LESS THAN:
80(-1) + 40 = -40
GREATER THAN:
80(0) + 40 = 40
The rate of change of the graph changes from negative to positive at x = -1/2, therefore the extreme value is a minimum.
4.) If the quadratic function is symmetrical about x = 3, that means that the minimum or maximum must be at x = 3.
y' = 2ax + 1
2a(3) + 1 = 0
6a = -1
a = -1/6
So now plug the a value and x=3 into the original function to find the extreme value.
(-1/6)(3)^2 + 3 + 3 = 4.5
The extreme value is 4.5
We know that
length of a sector=[∅]*r--------> when ∅ is in radians
so
∅=length of a sector/r
for r=7 ft
length of a sector=4 ft
∅=4/7-----> 0.57 radians
the answer part 1) is 0.57 radians
part 2)
area of a sector=(∅/2)*r²--------> when ∅<span> is in radians
</span>area of a sector=(4/7/2)*7²-----> (4/14)*49----> 14 ft²
the answer Part 2) is 14 ft²