Write a rule in words and as an algebraic expression to model the relationship.
15. The cost of beverages in a vending machine is shown.
Beverages cost
1. $1.25
2. $2.50
3. $3.75

Answer:

41. is c.

42. is d.

Step-by-step explanation:

Answer:

(11,6)

Step-by-step explanation:

Answer:

three hundred thousand plus ten thousand plus six thousand plus twenty plus nine

Step-by-step explanation:

300,000 → three hundred thousand

10,000 → ten thousand

6,000 → six thousand

20 → twenty

9 → nine

+ → plus

Now put everything together.

Best of Luck!

Using the method of Lagrange multipliers: the Lagrangian is

[tex]L(x,y,z,\lambda) = (x-4)^2+(y-5)^2+(z-6)^2 - \lambda (z-4x^2-4y^2)[/tex]

Fix λ > 0.

That is, we are minimizing the squared distance of a point (x, y, z) on the paraboloid to the point (4, 5, 6). We can use the squared distance in place of the proper Euclidean distance because both f(x) and √f(x) have critical points at the same point x ; plus the math works out much more easily.

Find the critical points of the Lagrangian:

[tex]\dfrac{\partial L}{\partial x} = 2(x-4) + 8\lambda x = 0 \\\\ \dfrac{\partial L}{\partial y} = 2(y-5) + 8\lambda y = 0 \\\\ \dfrac{\partial L}{\partial z} = 2(z-6) - \lambda = 0 \\\\ \dfrac{\partial L}{\partial\lambda} = -z+4x^2+4y^2 = 0[/tex]

Solving for λ in terms of x, y, or z gives

[tex]\displaystyle \lambda = \frac1x-\frac14 = \frac5{4y} - \frac14 = 2z-12[/tex]

so right away, we get

[tex]\dfrac5{4y} - \dfrac14 = \dfrac1x - \dfrac14 \implies y=\dfrac{5x}4 \\\\ 2z-12 = \dfrac1x-\dfrac14 \implies z = \dfrac1{2x} + \dfrac{47}8[/tex]

Substitute these into the constraint and solve for x, then for y and z :

[tex]\dfrac1{2x} + \dfrac{47}8 = 4x^2 +4\left(\dfrac{5x}4\right)^2 \implies 82x^3 - 47x - 4 = 0[/tex]

This has 3 roots, but we take the lone positive solution for x because otherwise λ would be negative. This root is x ≈ 0.7965.

Then it follows that the closest point on the paraboloid to (4, 5, 6) is the critical point (0.7965, 0.9956, 6.5028).

Answer:

Choice C. [tex](f-g)(x)=-x^2+17x+7[/tex]

Step-by-step explanation:

Recall that [tex]f-g[/tex] is defined by

[tex](f-g)(x)=f(x)-g(x)[/tex]

Therefore we compute

[tex](f-g)(x)=f(x)-g(x)=10x+7-x^2+7x=-x^2+17x+7[/tex]

Answer:

X = 7

Step-by-step explanation:

5x-9=2x+12

5x-2x=12+9

3x=21

X=21/3

X=7

Answer:

15

Step-by-step explanation:

x*x = 9*9 + 12*12

--> x = 15

Answer:

sorry  cause pic is small and cant enlarge

Step-by-step explanation:

Answer:

C is the answer to your question

It's A and C.

A because if you multiply the numbers inside square roots , you will get exactly same ans.

C because √75 is 5√3 and if you multiply it with 2 you get 10√3. √50 is 5√2 and if you multiply it with 3 then you get 15√2.

5−33−32+39+3

Not sure?

Answer:

Step-by-step explanation:

[tex](-1)^{2} + 2^{3} -0^{4}[/tex]

[tex] = 1 + 8 - 0[/tex]

= 9 (Ans)

Answer:

Points A and B are represented on the number line.

А

B

-ht

-2

-1

0

1

2

Determine whether each inequality is true or false. Choose "True" or "False" for each inequality.

Statement True or False?

IAI > IBI

False

IAI > 0

False

A>B

true

Line 1-Line 2-Associative property .

Line 2-Line 3- Distributive property

[tex]\\ \rm\longmapsto (9+x)x[/tex]

[tex]\\ \rm\longmapsto x(x+9)[/tex]

[tex]\\ \rm\longmapsto x(9+x)[/tex]

[tex]\\ \rm\longmapsto x^2+9[/tex]

Answer:

-22

Step-by-step explanation:

f(x) = 3x^2 - 5

let x= 3

f(3) = 3*(3)^2 -5 = 3(9) -5 =27-5 =22

g(x) = -2x+5

Let x = 3

g(3) = -2(3) +5 = -6+5 = -1

f(3) *g(3) = 22(-1) = -22

Answer:

it's closer to 2

Step-by-step explanation:

In order to get to 1 from that number, you have to subtract 3/4.  In order to get to 2 from that number, you only have to add 1/4.  Clearly, the jump in adding is  smaller than the jump to subtracting, which means it's closer to 2.

The number is closer to 2

A fraction shows part of a whole. This whole can be a region or a collection. The word fraction is derived from the Latin word "fractio" which means 'to break'. The Egyptians, being the earliest civilization to study fractions, used fractions to resolve their mathematical problems, which included the division of food, supplies, and the absence of a bullion currency.

All fractions consist of a numerator and a denominator and they are separated by a horizontal bar known as the fractional bar.

Given number:

1 3/4 = 7/4

On dividing

7/4 = 1.75

Hence, the number is closer to 2.

Learn more about fraction here:

https://brainly.com/question/10354322

#SPJ2

Answer:

ok

Step-by-step explanation:

Answer:

300

Step-by-step explanation:

I hope it will help you.

Answer:

[tex]f(x) = 15 \csc(x) + 5[/tex] (first option)

Step-by-step explanation:

[tex]f(x) = a \: \csc(x) + b[/tex]

[tex]a + b = 20[/tex]

[tex] - a + b = - 10[/tex]

••••

[tex]2b = 10[/tex]

[tex]b = 5[/tex]

[tex]a = 20 - 6 = 15[/tex]

[tex] = f(x) = 15 \csc(x) + 5[/tex]

Answer:

12.566

Step-by-step explanation:

A = ∫1/2(r)^2dtheta from a - b = 0 to 2π

∫1/2(sin^2theta-4sintheta+4)dtheta

[9/4theta+2costheta-1/8sin2theta] from 0 to 2π…

when you solve this you get 14.137 without taking out the cos(2theta+3)

Answer:

x= 1/2 or x= -2/3

Step-by-step explanation:

-6x²-x+2=0

-6x²-4x+3x+2=0

-2x(3x+2) + 1(3x+2)=0

(-2x+1) (3x+2)=0

-2x+1=0 or 3x+2=0

x= -1/-2 or x= -2/3

so therefore

x=1/2 0r -2/3

using FOIL method

FIRST: (-2x)(3x)= -6x²

OUTER: (-2x)(2)= -4x

INNER: (1)(3x)= 3x

LAST: (1)(2) =2

-6x²-4x+3x+2

Answer:

x=-2.2180

Step-by-step explanation:

steps are in picture

Answer:

4t^2 - 8tna + nat - 2 n^2 a^2

Step-by-step explanation:

Dudjdkdjejdnkdhdbd

9514 1404 393

Answer:

Step-by-step explanation:

a) The original point is in quadrant 2. Reflection into quadrant 3 is a reflection over the x-axis.

__

b) Reflection over the x-axis changes the sign of the y-coordinate. The new point is (-2, -5).

Answer:

I'm pretty sure it's the first and last one

Answer:

answer i dont know please

Answer:

2x+1=0.

2x=0-1.

2x=-1.

2x/2=-1/2.

x=-2.

3x+4=0

3x=0-4

3x=-4

3x/3=-4/3

[tex]x = 1 \frac{1 }{3} [/tex]

The bolded line represents a line segment rather than a line or a plane.

A line refers to an infinite figure that extends to the sides. For example, the railway track is composed of two lines.

This differs from a line because it is not infinite, instead, it is a section of a line with two endpoints. This concept applies to the bolded section of the tile because the section shows only a section of a line between two corners rather than a complete line.

Learn more about lines in: https://brainly.com/question/2696693

Answer:

The answer is B

Step-by-step explanation: