Find the measure of an interior angle of a regular polygon with 18 sides

F(x)=20-x^2+8x<br> what are the minimum and maximum points and the axis of symmetry?

-Dominant- [34]

Vertex aka max or min point is found by -b/2a in form
f(x)=ax^2+bx+c
f(x)=-1x^2+8x+20
vertex x value is -8/(2)(-1)=-8/-2=4
input back to find y value
f(4)=-(4^2)+8*4+20
f(4)=-16+32+20
f(4)=36
max (since the graph opens down) is (4,36)
axis of symmetry is the x coordinate

max is (4,36)
axis of symmetrry is x=4

5 0

2 years ago

How do I complete these questions a bit confused . (extra credit work )

otez555 [7]

Answer:

(1)

$a = \frac{3\sqrt 3}{2}$

$b = \frac{3}{2}$

(2)

$a = \sqrt 6$

$b = \sqrt 2$

Step-by-step explanation:

Solving (1):

Considering

$\theta = 60^o$

We have:

$\sin(\theta) = \frac{Opposite}{Hypotenuse}$

This gives:

$\sin(60^o) = \frac{a}{3}$

Solve for a

$a = 3 * \sin(60^o)$

$\sin(60^o) = \frac{\sqrt 3}{2}$

So:

$a = 3 * \frac{\sqrt 3}{2}$

$a = \frac{3\sqrt 3}{2}$

To solve for b, we make use of Pythagoras theorem

$3^2 = a^2 + b^2$

This gives

$3^2 = (\frac{3\sqrt 3}{2})^2 + b^2$

$9 = \frac{9*3}{4} + b^2$

$9 = \frac{27}{4} + b^2$

Collect like terms

$b^2 = 9 - \frac{27}{4}$

Take LCM and solve

$b^2 = \frac{36 - 27}{4}$

$b^2 = \frac{9}{4}$

Take square roots

$b = \frac{3}{2}$

Solving (2):

Considering

$\theta = 60^o$

We have:

$\sin(\theta) = \frac{Opposite}{Hypotenuse}$

This gives:

$\sin(60^o) = \frac{a}{2\sqrt 2}$

Solve for a

$a = 2\sqrt 2 * \sin(60^o)$

$\sin(60^o) = \frac{\sqrt 3}{2}$

So:

$a = 2\sqrt 2 * \frac{\sqrt 3}{2}$

$a = \sqrt 2 * \sqrt 3$

$a = \sqrt 6$

To solve for b, we make use of Pythagoras theorem

$(2\sqrt 2)^2 = a^2 + b^2$

This gives

$(2\sqrt 2)^2 = (\sqrt 6)^2 + b^2$

$8 = 6 + b^2$

Collect like terms

$b^2 = 8 - 6$

$b^2 = 2$

Take square roots

$b = \sqrt 2$

3 0

2 years ago

I need help with these math questions :/

makkiz [27]

1. H (-4,-4) I (-2,-2) J (-5,-2)
2.B
3.J (-4,-1) K (-1,0) L (-2,-4)
4.B (0,-2) C (3,-3) D (4,1)
5.R (4,-3) S (3,-1) T (-1,1) U (0,4)

8 0

2 years ago

Read 2 more answers

Logx + log(3x-13) = 1

Tom [10]

X = 5
Condense the left side.
log x(3x-13)=1
Put a base 10 on each side to clear the log.
x(3x-13)=10
3x^2-13x-10=0
Factoring you get x=5 and x=-2/3. The domain for log is x>0 so the -2/3 is an extraneous solution.

8 0

2 years ago

Question 1. What will Amanda pay if she rents a truck and drives 45 miles and splits the total cost with two friends? Explain wi

BabaBlast [244]

Answer:

A) Amanda will pay $47.5

B) 0.5

C) $120

Step-by-step explanation:

A) From the graph given, at 45 miles, the total cost of rentage = $142.50

She now splits this cost with 2 of her friends. Thus each of them will pay;

Amount = 142.5/3 = $47.5

So,Amanda will pay $47.5

B) To find the slope, we will pick two points on the graph and use their respective coordinates to find the slope.

Coordinates we pick are;

(0, 120) and (50, 145)

Thus, slope; m = (y2 - y1)/(x2 - x1)

m = (145 - 120)/(50 - 0)

m = 25/50

m = 0.5

C) The equation for the graph will now be; y = mx + c

Where m is slope and c is y - intercept.

Thus;

y = 0.5x + 120

Coincidentally, c = 120 will be the fixed price of the truck while 0.5x will be the variable cost depending on how many miles are driven.

Thus renting for a day is simply the fixed cost of $120

5 0

2 years ago