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3 years ago

What is the vertex form of f(x)=x^2+24x+138

Mathematics

2 answers:

Gre4nikov [31]3 years ago

8 0

F(x) = x^2 + 24x + 138
f(x) = x^2 + 24x + (24/2)^2 + 138 - (24/2)^2
f(x) = (x+12)^2 - 6

Veronika [31]3 years ago

6 0

Answer:

(x +12)^2 - 6

Step-by-step explanation:

d/dx x^2 + 24x + 138 = 2x + 24

when 2x + 24 = 0, the gradient = 0

x = -12

f(-12) = -6

therefore we have (x +12)^2 - 6.

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There are 4 students and 1/2 sh butcher paper how much paper will each student get

inna [77]

Answer:

Step-by-step explanation:

what is sh? sheets? if so try dividing 4 by 1/2

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3 years ago

A line containing the points (9, 1) and (5, 5) intersects the x -axis at what point?

Troyanec [42]

Answer:

It intersects the x-axis at x = 10

Step-by-step explanation:

Step 1: Find slope m

m = (5 - 1)/(5 - 9)

m = 4/-4

m = -1

y = -x + b

Step 2: Find b

5 = -5 + b

b = 10

Step 3: Rewrite equation

y = -x + 10

Step 4: Find x when y = 0

0 = -x + 10

-10 = -x

x = 10

So the graph crosses the x-axis at 10.

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3 years ago

The profit for a car company can be represented by the function P=−0.5 x² +4 x+ 12,

luda_lava [24]

Answer:

3x+12

Step-by-step explanation:

-0.5x*2+4x+12

Multiply 0.5x*2=x

= -x+4x+12

Add similar elements -x+4x+12

= 3x+12

4 0

3 years ago

4)In order to set rates, an insurance company is trying to estimate the number of sick daysthat full time workers at an auto rep

bagirrra123 [75]

Answer:

A sample of 18 is required.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.92}{2} = 0.04$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.04 = 0.96$ , so Z = 1.88.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

A previous study indicated that the standard deviation was 2.2 days.

This means that $\sigma = 2.2$

How large a sample must be selected if the company wants to be 92% confident that the true mean differs from the sample mean by no more than 1 day?

This is n for which M = 1. So

$M = z\frac{\sigma}{\sqrt{n}}$

$1 = 1.88\frac{2.2}{\sqrt{n}}$

$\sqrt{n} = 1.88*2.2$

$(\sqrt{n})^2 = (1.88*2.2)^2$

$n = 17.1$

Rounding up:

A sample of 18 is required.

3 0

3 years ago

A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the numb

ArbitrLikvidat [17]

Answer:

$9327

Step-by-step explanation:

Apparently, the cost function is supposed to be ...

C(x) = 0.4x^2 -112x +17167

This can be rewritten to vertex form as ...

C(x) = 0.4(x^2 -280) +17167

C(x) = 0.4(x -140)^2 +17167 -0.4(19600)

C(x) = 0.4(x -140)^2 +9327

The vertex of the cost function is ...

(x, C(x)) = (140, 9327)

The minimum unit cost is $9327.

_____

Comment on the question

You found the number of units that result in minimum cost (140 units), but you have to evaluate C(140) to find the minimum unit cost.

8 0

2 years ago