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4 years ago

Which statement best describes a graph of paired points that form a proportional relationship?

2 answers:

7 0

It's B) A straight line can be drawn through all the points and the line passes through the point (0,0)

This is because in the problem it says that the points are paired and proportional. For example, say you're given the point (3,6). To make this a proportional relationship, you'd have another point in the third quadrant: (-3,-6). When you draw a line from one of these points to the other, it passes through the origin.

Marianna [84]4 years ago

4 0

I would also have to agree that the answer is B.

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In the accompanying diagram, lines a and b are parallel, and lines c and d are transversals. 5 a 6 3 4 7/8 be Which angle is con

OLga [1]

Answer:

Step-by-step explanation:

7 0

3 years ago

In how many ways can 4 people sit next to each other in a movie theater row? [?] question 4 options:

emmainna [20.7K]

Any of the 4 people can take the first seat
since it gets occupied by one person , the next seat can be occupied by any of the remaining 3
similarly, the next one has 2 possibilities and the last seat can only be occupied by the man who is left

so by the principal of multiplication, no. of ways equals 4! = 4×3×2×1 = 24 ways

3 0

3 years ago

Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinat

tensa zangetsu [6.8K]

Answer:

The volume of the largest rectangular box (V) = 81/4

Step-by-step explanation:

Step 1:-

Given volume of the largest rectangular box in the first octant

V = l b h

let (x ,y, z) be the one vertex in the given plane

V = f(x, y, z) = x y z

given plane. Ф (x, y, z) = x + 9y + 4z = 27 ........(1)

Step( ii):

By using Lagrange multipliers

Suppose it is required to find the extreme for the function f(x, y, z) subject to the condition Ф (x, y, z) =0

Form Lagrange function F(x, y, z) = f(x, y, z) + λ Ф (x, y, z) where λ is called the Lagrange multipliers

F(x, y, z) = x y z+ λ ( x + 9y + 4z - 27) ......(2)

Obtain the equations are δ F / δ x = 0

δ f / δ x +λ δ Ф / δ x =0

⇒ y z + λ ( 1) = 0

⇒ y z = - λ ......(a)

Obtain the equations are δ F / δ y = 0

δ f / δ x +λ δ Ф / δ x =0

⇒ x z + λ ( 9) = 0

⇒ $\frac{xz}{9}$ = - λ .......(b)

Obtain the equations are δ F / δ z = 0

δ f / δ x +λ δ Ф / δ z =0

x y + λ ( 4) = 0

⇒ $\frac{xy}{4}$ = - λ .......(c)

Step (iii):-

Equating (a) and (b) equations

we get $y z = \frac{xz}{9}$

cancel 'z' value we get x = 9y .......(d)

Equating (b) and (c) equations

we get $\frac{xy}{4} = \frac{xz}{9}$

cancel 'x' value on both sides , we get

4z =9y ......(e)

substitute (d) (e) values in equation (1) we get

x + 9y + 4z -27 = 0

9y + 9y + 9y -27 =0

27y -27 =0

y = 1

substitute y =1 in x = 9y

x = 9

substitute y =1 in 4z =9y

z = 9 /4

therefore the dimensions are x =9 , y=1 and z = 9 /4

Conclusion:-

The largest volume of the rectangular box V = x y z

substitute x =9 , y=1 and z = 9 /4

V = 9(1)(9/4) =81/4

The largest volume of the rectangular box (V) = 81/4

Verification :-

Given plane x + 9y + 4z = 27

substitute x =9 , y=1 and z = 9 /4

9 + 9 + 4(9/4) = 27

27 =27

so satisfied equation

3 0

3 years ago

2a^(2) – (4b + c); a = –3, b = –2, and c = 1

vfiekz [6]

Answer:

= 25

Step-by-step explanation:

2 (-3)^2 - (4(-2) + 1)

2 (9) - (-8 + 1)

18 - (-7)

3 0

3 years ago

A quiz has 5 true-false questions and 3 multiple choice questions with 4 options each. How many possible ways are there to answe

8_murik_8 [283]

This answer is d 2024

4 0

3 years ago

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