A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.


y = -x^2 + 99x - 932

Answer:

[tex]g(x) = 4(x - 2)^2 -9[/tex]

Step-by-step explanation:

Given

[tex]g(x) = 4x^2 - 16x + 7[/tex]

Required

Complete the square

Rewrite so that [tex]x^2[/tex] has 1 coefficient

[tex]g(x) = 4(x^2 - 4x) + 7[/tex]

Take half of the coefficient of x

[tex]\frac{4}{2} = 2[/tex]

Square the result

[tex](\frac{4}{2})^2 = 2^2[/tex]

[tex](\frac{4}{2})^2 = 4[/tex]

Add and subtract the result in the bracket

[tex]g(x) = 4(x^2 - 4x + 4 - 4) + 7[/tex]

Expand the bracket to remove -4

[tex]g(x) = 4(x^2 - 4x + 4) - 16 + 7[/tex]

[tex]g(x) = 4(x^2 - 4x + 4) -9[/tex]

Expand the bracket

[tex]g(x) = 4(x^2 - 2x -2x+ 4) -9[/tex]

Factorize

[tex]g(x) = 4(x(x - 2) -2(x-2)) -9[/tex]

Factor out x - 2

[tex]g(x) = 4((x - 2)(x-2)) -9[/tex]

Express as square

[tex]g(x) = 4(x - 2)^2 -9[/tex]

Answer:

Graph B

Step-by-step explanation:

[tex]y = x^2[/tex] is a quadradic function. It graphs as a parabola.  It has a vertex point of (0,0) and it opens upwards.

See the graph attached.

Hope this helps.

Answer:

12

Step-by-step explanation:

This is because 2, 3, and 4 can all go into the number and it is the smallest of the ones listed.

Answer: 24

Step-by-step explanation:

1/2 x 12 = 12/24

2/3 x 8 = 16/24

3/4 x 6 = 18/24

Each number can be multiplied by "x" to get a denominator of 24.

Answer:

..y d tu ideograma idiosincrasias

Answer:

let

hypotenuse[h]=60ft

base[b]=36ft

perpendicular [p]=48ft

by using Pythagoras law

p²+b²=h²

48²+36²=60²

2896≠3600

since p²+b²≠ h²[so the stage is not in a right angled triangle]but it is scalene triangle

Answer:

104

Step-by-step explanation:

you have to find the least common multiple lcm between the bottom numbers. and since there is none before you just multiply the two together to get the same bottom number.

Answer:

8

Step-by-step explanation:

To do this, multiply the top and bottom of the first fraction by the second fraction's denominator, then multiply the top and bottom of the second fraction by the first fraction's denominator. This is how I answered on a test AND got it correct.

Answer:the answer is o.7.7

Step-by-step explanation:

Answer: the correct answer is 16.8°C.

Step-by-step explanation:

Answer:

-16.8

the number is in the negatives because the temperature is dropping

I hope this helps

Answer:

Using Sine Rule

w= 19.8

Answer:

5 toppings

Step-by-step explanation:

$20 - $9 = $11 dollars left for toppings

$11 ÷ 2 = 5.5

So, you can get 5 toppings with 50 cents left.

Have a great day!

Answer: [tex]\dfrac{43}{4}\ \text{Gallons}[/tex]

Step-by-step explanation:

Given

The first one has 4 gallons and 2 quarts of juice

The second one has 1 [tex]\frac{3}{4}[/tex] gallons more than the first

First has

[tex]\Rightarrow 4+\dfrac{2}{4}\\\\\Rightarrow \dfrac{9}{2}\ \text{Gallons}[/tex]

second has

[tex]\Rightarrow 1\dfrac{3}{4}+\dfrac{9}{2}\\\\\Rightarrow \dfrac{7}{4}+\dfrac{18}{4}\\\\\Rightarrow \dfrac{25}{4}\ \text{Gallons}[/tex]

together it is

[tex]\Rightarrow \dfrac{25}{4}+\dfrac{18}{4}\\\Rightarrow \dfrac{25+18}{4}\\\Rightarrow \dfrac{43}{4}\ \text{Gallons}[/tex]

Answer:

Step-by-step explanation:

Answer:

---

Step-by-step explanation:

Convert the fraction to a decimal(40% = 40/100 = 0.4). Multiply it by 120.

0.4x120=a

---

hope it helps

The equation 40 ÷ 100 × 120 = a shows

the relationship 40% of 120 is a

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side).

'An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.'

For example, 3x + 5 = 15.

Given,

Relation, 40% of 120 is a

⇒ 40% × 120 = a

Above relation can be written in equation as

40 ÷ 100 × 120 = a

Hence, 40 ÷ 100 × 120 = a is the equation

for relation such that  40% of 120 is a.

Learn more about equation here:

https://brainly.com/question/29657983

#SPJ2

Answer: 0 is y intercept and 6 is x intercept.

Step-by-step explanation:

Answer:

51.3 degrees

Step-by-step explanation:

Use Trig Ratio to solve for theta aka the angle formed between the ;adder and the ground.

So we have the hypotenuse = 24ft and the adjacent = 15ft so I am going to use the cos ratio.

cos ∅ = a/h

rearrange for theta

∅ = cos -1 ( a/h)

now sub in the information

∅ = 51.3178

now round to the nearest tenth

∅ = 51.3 degrees

write your therefore statement

therefore, the angle between the ladder and the ground is 51.3 degrees.

Answer:

Step-by-step explanation:

[tex]440.4 + 5\cdot(\frac12\cdot16\cdot20)=440.4+800=1240.4\ mm^2[/tex]

Answer:

[tex]\sqrt{3}[/tex] = m

Step-by-step explanation:

So we can say;

Tan(30) = m/3

=> Tan(30) * 3 = m

=> [tex]\sqrt{3}[/tex] = m

Hope this helps!

Answer:

(3 x 1) + (3(5) x 1) = a

Step-by-step explanation:

Answer:

[tex]\frac{dy}{dx}[/tex] = - [tex]\frac{3}{2x^{\frac{3}{2} } }[/tex]

Step-by-step explanation:

Differentiate using the power rule

[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]

Given

y = [tex]\frac{3}{\sqrt{x} }[/tex] = 3[tex]x^{-\frac{1}{2} }[/tex] , then

[tex]\frac{dy}{dx}[/tex] = - [tex]\frac{3}{2}[/tex] [tex]x^{-\frac{3}{2} }[/tex] = - [tex]\frac{3}{2x^{\frac{3}{2} } }[/tex]

Answer:

20x +80y -60 hope this helped:)

Step-by-step explanation:

Answer:

smaller number = 3 5/24

larger number =  6 13/24

Step-by-step explanation:

let the larger number = x

smaller number = y

x - y = 3 1/3 equation 1

2(x +y) = 191/2 equation 2

divide equation 2 through by 2

x + y = 9 3/4  equation 3

subtract equation 1 from 3

2y = 6 5/12

y = 77/12 x 1/2 = 3 5/24

substitute for y in equation 1

x - 3 5/24 = 31/3

x = 3 1/3 + 3 5/24

x = 6 13/24

Answer:

3 and 5/24

Step-by-step explanation:

trust me bro

i wish u luck

also

hi

i just realized that the other person got it right

ignore this lol

Answer:

50.24 is the circumfrence

If we were to use actual pi the answer would be -

50.26548246

Answer:

25.12

Step-by-step explanation:

2pi4=2*3.14*4=25.12

conviince me for my question (brainliest plzz)

Answer:

2√5

Step-by-step explanation:

d = √(x2 - x1)² + (y2 - y1)²

= √[1 - (-1)]² + [3 - (-1)]

= √(2)² + (4)²

= √(4) + (16)

= √20

= 2√5

Answer:

d. 30

A = a+b /2 h

A = 6+9/2 × 4

A = 30

Answer:

D, but I am not too sure.

Good luck

Answer:

5(3+7)are equal to15+35

Step-by-step explanation:

5(3+7) five multiply the bracket

15+35

it help you

Answer:

C5(3+7)

Step-by-step explanation:

So, lets ingore the answers, and jsut try to break down 15+35

What can we take from both 15 and 35?

Well, 5 is the only one I can see in this.

So lets take 5 from this:

5(3 + 7)

We got 3 since 5x3 is 15, and we got 7 since 5x7 is 35.

So lets look at our answers and see if 5(3 + 7) is one of them

Well, looking at C, that is exactly 5(3 +7)

So c is our answer.

Hope this helps!

Answer: bag 1 40%

bag 2 25%

i think hope it helped

Step-by-step explanation:

Answer:A

Step-by-step explanation: A is 8d+d, and since d=1, 8d,+1d is equal to 9d