Express x^2 + 4x - 7 in the form (x + a)^3 - b where a and b are integers

Answer:

[tex](a)[/tex] [tex]C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2[/tex]

    [tex]p(x)=320-7.7p[/tex]

    [tex]R(x)=(320-7.7p)p=320p-7.7p^2[/tex]

[tex](b)[/tex] [tex]x=82 \text{planes}[/tex]

[tex](c)[/tex] [tex]p=\$30.91 M\;\; \text{per plane}[/tex]

[tex](d)[/tex] maximum profit [tex]=\$ 15.90M[/tex]

Step-by-step explanation:

Given that,

The company estimates that the initial cost of designing the aeroplane and setting up the factories in which to build it will be 500 million dollars.

The additional cost of manufacturing each plane can be modelled by the function.

[tex]m(x)=20x-5x^{\frac{3}{4}}+0.01x^2[/tex]

[tex](a)[/tex]  Find the cost, demand (or price), and revenue functions.

   [tex]C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2[/tex]

   [tex]p(x)=320-7.7p[/tex]

   [tex]R(x)=(320-7.7p)p=320p-7.7p^2[/tex]

[tex](b)[/tex]  Find the production level that maximizes profit.

    [tex]f=R(x)-C(x)[/tex]

 [tex]\Rightarrow f=320p-7.7p^2-(500+20x-5x^{\frac{3}{4}}+0.01x^2)[/tex]

[tex]\Rightarrow df=320dp-15.4pdp-20dx+5(\frac{3}{4} )x^{\frac{-1}{4} }dx-0.02xdx[/tex]

     [tex]x=320-7.7p[/tex]

     [tex]p=\frac{320-x}{7.7}[/tex]

    [tex]\frac{dp}{dx} = \frac{-1}{7.7}[/tex]

[tex]\frac{df}{dx}=\frac{320}{-7.7} -\frac{15.4(320-x) }{7.7(\frac{-1}{7.7} )}-20+5\frac{3}{4} x^{\frac{-1}{4}} -0.02x=0[/tex]

    [tex]\Rightarrow -41.5584+83.1169-0.2597x-20+3.75x^{\frac{-1}{4} }-0.02x=0[/tex]

   [tex]\Rightarrow 21.5585+3.75x^{\frac{-1}{4} }-0.279x=0[/tex]

   [tex]\Rightarrow x=82 \text{planes}[/tex]

[tex](c)[/tex]  Find the associated selling price of the aircraft that maximizes profit.

  [tex]p=\frac{320-82}{7.7}[/tex]

[tex]\Rightarrow p=\$30.91 M\;\; \text{per plane}[/tex]

[tex](d)[/tex]  Find the maximum profit.

Manufacturing cost of one plane is:

[tex]m(1)=20-5+0.01[/tex]

         [tex]=\$15.01 M[/tex]

maximum profit [tex]=\$(30.91-15.01)M[/tex]

                           [tex]=\$15.90M[/tex]

Note: this answer assumes that the equation of the line must be in slope-intercept form.

Answer:

[tex]y= -3x + 5[/tex]

Explanation:

When you need to write an equation and know its slope and a point it intersects, you can use the point slope formula [tex]y-y_1 = m (x-x_1)[/tex] first. In order to write an equation using this formula, the [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] must be substituted in for real values.

The [tex]m[/tex] represents the slope, so write the slope of this equation, -3, in its place. The [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects. We know that the line must intersect the point (2, -1). Write 2 in the place of

[tex]y-(-1) = -3(x-(2))[/tex]

[tex]y+1 = -3(x-2)[/tex]

Now, to put it in slope-intercept or [tex]y = mx + b[/tex] form, just expand the right side and isolate [tex]y[/tex]:

[tex]y+1 = -3(x-2)\\y + 1 = -3x + 6 \\y = -3x + 5[/tex]

Therefore, [tex]y= -3x + 5[/tex] is the answer.

Answer:

60

Step-by-step explanation:

Shoes= 10

Human= 5

Cone= 4

10+5= 15 x 4= 60

Answer: she has 15 dimes and 45 pennies.

Step-by-step explanation:

01p+1d=1.95

p=3d

01(3d)+.1d=1.95

p=3.15

03d+.1d=1.95

p=45

.13d=1.95

d=15

Answer:

i can't not understand sorry

Answer:

$43680

Step-by-step explanation:

Given data

Tuition was ​$. 42,000 last year

The tuition increased by​ 4%

Hence the current year tuition is given as

Current tuition= 42,000 + 4/100*42,000

Current tuition= 42,000 + 0.04*42,000

Current tuition= 42,000 +1680

Current tuition= $43680

Hence the current tuition is $43680

Answer:

R=√a/3

now put square on both side to remove square root

(√A/3)²=R²

A/3=R²

so we get

A=3(R²)

plz mark me brainest

Step-by-step explanation:

Ratio

= Difference between Prediction and Actual / Prediction

= (99 - 88)/99 = 11/99.

Percentage Error

= Difference between Prediction and Actual * 100%

= (99 - 88) * 100% = 11.1%. (1)

The ratio (a) & percent error (b) will be option A which is a=11/99 and b= 11.11% respectively

Approximate value = 99 frames

Exact value = 88 frames

∴ Ratio (a) = (99-88)/99

∴ a = 11/99

∴ Percent error (b) = (11/99) x 100

∴ b = 11.11%

So, the answer of ratio (a) & percent error (b) will be 11/99 and 11.11% respectively

Learn more about Ratio and percent error here:

https://brainly.com/question/5493941

#SPJ2

Answer:

Please check the explanation.

Step-by-step explanation:

Given the quadratic equation

5x²−2x−9 = 0

To factor the quadratic function 5x²−2x−9, we should solve the corresponding quadratic equation 5x²−2x−9 = 0.

Indeed, if x₁ and x₂ are the roots of the quadratic equation ax²+bx+c=0, then

ax²+bx+c = a(x-x₁)(x-x₂)

Now,

solving the quadratic function 5x²−2x−9 = 0

[tex]-5x^2+2x+9=0[/tex]

subtract 9 from both sides

[tex]-5x^2+2x+9-9=0-9[/tex]

Simplify

[tex]-5x^2+2x=-9[/tex]

Divide both sides by -5

[tex]\frac{-5x^2+2x}{-5}=\frac{-9}{-5}[/tex]

[tex]x^2-\frac{2x}{5}=\frac{9}{5}[/tex]

Add (-1/5)² to both sides

[tex]x^2-\frac{2x}{5}+\left(-\frac{1}{5}\right)^2=\frac{9}{5}+\left(-\frac{1}{5}\right)^2[/tex]

[tex]x^2-\frac{2x}{5}+\left(-\frac{1}{5}\right)^2=\frac{46}{25}[/tex]

[tex]\left(x-\frac{1}{5}\right)^2=\frac{46}{25} \\[/tex]

[tex]\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}[/tex]

so solving

[tex]x-\frac{1}{5}=\sqrt{\frac{46}{25}}[/tex]

[tex]x-\frac{1}{5}=\frac{\sqrt{46}}{\sqrt{25}}[/tex]

Add 1/5 to both sides

[tex]x-\frac{1}{5}+\frac{1}{5}=\frac{\sqrt{46}}{5}+\frac{1}{5}[/tex]

[tex]x=\frac{\sqrt{46}+1}{5}[/tex]

similarly solving

[tex]x-\frac{1}{5}=-\sqrt{\frac{46}{25}}[/tex]

[tex]x-\frac{1}{5}=-\frac{\sqrt{46}}{5}[/tex]

Add 1/5 to both sides

[tex]x-\frac{1}{5}+\frac{1}{5}=-\frac{\sqrt{46}}{5}+\frac{1}{5}[/tex]

[tex]x=\frac{-\sqrt{46}+1}{5}[/tex]

Thus, the roots are:

[tex]x_{1} =\frac{\sqrt{46}+1}{5},\:x_{2}=\frac{-\sqrt{46}+1}{5}[/tex]

Conclusion:

Since the roots are irrational, we do not factor further.

Therefore, we leave 5x²−2x−9 as it is.

Answer:

I am not sure but sold of the say 2,334

Answer:

58 child tickets

Step-by-step explanation:

5.7(x)+9.8(149-x)=1222.40

5.7x+1460.2-9.8x=1222.40

1460.2-4.1x=1222.40

-4.1x=-237.8

x=58

Answer:

okay so look

Step-by-step explanation:

you calculate the area of the whole square then the area of the triangle , then you subtract the area of the square with the area of the triangle so you'll get the area of the blue region

Answer:

13x+23.5

Step-by-step explanation: I dont know how to explain

Answer:

17》6

18》12

19》8

20》3

21》2

the bar with age 18 this is because as you minus from both sides the middle number will be in age 18

Solve for x and y :

x + y = 1   →   y = 1 - x

x ² + y ² = -1

x ² + (1 - x)² = -1

x ² + (1 - 2x + x ²) = -1

2x ² - 2x + 1 = -1

2x ² - 2x + 2 = 0

x ² - x + 1 = 0

x ² - x + 1/4 = -3/4

(x - 1/2)² = -3/4

x - 1/2 = ±√(-3/4)

x - 1/2 = ±√3/2 i

x = 1/2 ± √3/2 i   →   x = exp(± iπ/3)

y = 1 - (1/2 ± √3/2 i )   →   y = -1/2 ± √3/2 i   →   y = exp(± 2iπ/3)

Then

x ⁷ + y ¹³ = exp(± 7iπ/3) + exp(± 26iπ/3)

… = exp(± iπ/3) + exp(± 2iπ/3)

since 7π/3 is equivalent to π/3, and 26π/3 is equivalent to 2π/3 (both modulo 2π).

In either case, we get

x ⁷ + y ¹³ = x + y = 1

so the answer is (2) 1.

Answer:

She brew 4 lb of tea 6 days a week.

The first step is multiply 4 lb by the number of days that 4 lb are brewed.

The second step is to add 6.2 lb to the amount brewed the rest of the week.

The answer to the question will be: "She brews ______ lb each week."

Step-by-step explanation:

Answer:

-2 - 24i

Step-by-step explanation:

a + bi + (7 - 3i) + (5 + 9i) + 13i = 10 - 5i

a + bi + 7 + 5  - 3i + 9i + 13i = 10 - 5i

                a + bi  + 12  + 19i = 10 - 5i

                         a + bi          = 10 - 5i - 12 - 9i

                                 a + bi = 10 - 12 - 5i - 9i

                                 a + bi = -2 - 24i

Answer:

[tex]Mean = 7[/tex]

Step-by-step explanation:

Given

[tex]Data: 2, 4, 6, 12, 8, 10.[/tex]

Required

Determine the mean

The mean of a data is calculated as thus:

[tex]Mean = \frac{\sum x}{n}[/tex]

In this case:

[tex]n = 6[/tex]

So, the formula becomes:

[tex]Mean = \frac{2+4+6+12+8+10}{6}[/tex]

[tex]Mean = \frac{42}{6}[/tex]

[tex]Mean = 7[/tex]

Answer:

x= -2

Step-by-step explanation:

Answer:

x < - 2

Step-by-step explanation:

I hope this helps.

Answer:

x < -2

Step-by-step explanation:

1) 12x+8< -16 Rearrange the expression

2) 12x < -16+8 Separate the constants and variables

3) 12x< -24 Add the the number

4) 12x/12 < -24/12 Divide both sides by 12

5) x< -2 Answer

Hope that helps.

True.

Hope this helped!

Answer:

I would say true

Step-by-step explanation:

Answer:

Rewriting [tex]6^{-2}[/tex] without an exponent we get [tex]\mathbf{\frac{1}{36}}[/tex]

Step-by-step explanation:

We need to rewrite the following without an exponent. [tex]6^{-2}[/tex]

We need to solve the exponent to find the result.

We know the exponent rule: [tex]a^{-b}=\frac{1}{a^b}[/tex]

Now using this rule to solve the equation:

[tex]6^{-2}\\=\frac{1}{6^2}\\We \:know \:that\:6^2 = 6\times 6=36\\=\frac{1}{36}[/tex]

So, Rewriting [tex]6^{-2}[/tex] without an exponent we get [tex]\mathbf{\frac{1}{36}}[/tex]

Hey there!

I believe the answer to your question is 47.21 ml of oxygen are in the 55 ml sample of sea water.

To get this, you can do 0.8584 x 55 = 47.212, because you want to find 85.84% of 55, to know how much oxygen is in the sample. Then, you round it to the nearest hundreth.

Hope it helps! Have a great day! Do tell me if I'm mistaken.

Answer:

The first one

Step-by-step explanation:

You You need to make it 5 lb of crawfish so 6$ for 4 pounds is 12$

1 pound is 3$

4 pounds + 1 pound is 15$

Shop a and b is 15$

Answer:

$15.02

Step-by-step explanation:

Let's write out some equations.

Company A:

60.50+0.12x=A

Company b:

45.50+0.10x=B

Now let's compare. If x=1, Company A charges

60.50+0.12=60.62=A

On the other hand, Company B charges

45.50+0.10=45.60=B

A-B=60.62-45.60=15.02

Since these are linear we can safely assume that this is constant :)

Answer:

Assuming you combingin like terms

3x-6+3y