All categories

3 years ago

What is the axis of symmetry for f(x)=32+9x+15 ?

Mathematics

1 answer:

Alex787 [66]3 years ago

6 0

Answer:

The axis of symmetry is

$x=-\frac{3}{2}$

Step-by-step explanation:

The given function is $f(x)=3x^2+9x+15$ .

Compare to $f(x)=ax^2+bx+c$ ,

$a=3,b=9,c=15$

The axis of symmetry of the parabola is given by the formula;

$x=-\frac{b}{2a}$

We substitute into the formula to get;

$x=-\frac{9}{2(3)}$

The axis of symmetry is

$x=-\frac{3}{2}$

You might be interested in

Which shapes have rotational symmetry that occurs at 180°?

zmey [24]

- Regular Octagon
- Regular Hexagon
- Square

5 0

3 years ago

Read 2 more answers

Identify the middle line for the function.

Ierofanga [76]

The solution to the problem is as follows:

'(t) = 0 gives:

-24t + 60 = 0

t = 2.5

For this t, the second derivative s"(t) = -24 is negative.

And so, s(t) is maximum for t = 2.5.

Maximum height is:

S = -12(2.5)^2 + 60(2.5) +8 = 233ft

I hope my answer has come to your help. God bless and have a nice day ahead!

7 0

3 years ago

Read 2 more answers

What is the linear inequalitie of m=2 over 7

lord [1]

Answer:

Step-by-step explanation:

m=2ov(2.718282)r(7)

Answer:

m=38.055946orv

I think hope this is correct

5 0

3 years ago

The quantity demanded x each month of Russo Espresso Makers is 250 when the unit price p is $138. The quantity demanded each mon

Stells [14]

Answer:

(a) $D(q)=\frac{-1}{25} q+148$

(b) $S(q)=\frac{1}{50}q+58$

Step-by-step explanation:

(a) For the demand equation D(q) we have

P1: 138 Q1: 250

P2: 108 Q2: 1000

We can find m, which is the slope of the demand equation,

$m=\frac{p_{2} -p_{1} }{q_{2} -q_{1} }=\frac{108-38}{1000-250} =\frac{-30}{750}=\frac{-1}{25}$

and then we find b, which is the point where the curve intersects the y axis.

We can do it by plugging one point and the slope into the line equation form:

$y=mx+b\\\\D(q)=mq+b\\\\138=\frac{-1}{25}(250) +b\\\\138=-10+b\\\\138+10=b=148$

With b: 148 and m: -1/25 we can write our demand equation D(q)

$D(q)=\frac{-1}{25} q+148$

(b) to find the supply equation S(q) we have

P1: 102 Q1: 2200

P2: 102 Q2: 700

Similarly we find m, and b

$m=\frac{p_{2} -p_{1} }{q_{2} -q_{1} }=\frac{72-102}{700-2200} =\frac{-30}{-1500}=\frac{1}{50}$

$y=mx+b\\\\D(q)=mq+b\\\\72=\frac{1}{50}(700) +b\\\\72=14+b\\\\72-14=b=58\\$

And we can write our Supply equation S(q):

$S(q)=\frac{1}{50}q+58$

(c) Now we may find the equilibrium quantity q* and the equilibrium price p* by writing D(q)=S(q), which means the demand equals the supply in equilibrium:

$D(q)=S(q)\\\\\frac{-1}{25}q+148=\frac{1}{50}q+58\\\\$

$148-58=\frac{1q}{50} +\frac{1q}{25} \\\\90= \frac{1q}{50} +\frac{2q}{50}\\\\90=\frac{3q}{50}\\ \\q=1500\\\\$

We plug 1500 as q into any equation, in this case S(q) and we get:

$S(q)=\frac{1}{50}q+58\\\\S(1500)=\frac{1}{50}(1500)+58\\\\S(1500)=30+58\\\\S(1500)=88$

Which is the equilibrium price p*.

8 0

3 years ago

What is the area that she paints

Andre45 [30]

To determine this, we need to multiply 8 by 36 and 3 by 4 to get the total area.
8 x 36 = 288
3 x 4 = 12

Subtract the two to get the total area she is painting.
288-12 = 276
Your total area is 276 sq ft.
Your answer is D.)
I hope this helps!

6 0

3 years ago

Read 2 more answers