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3 years ago

Use the subtraction property of equality to complete the following statement:

1 answer:

3 0

10x + 6 = 21
first subtract 6 from both sides of the equation
10x=15
so I believe the answer you are looking for is 10x=15

If you take this one step further and solve for x then you divide both sides of the equation by 10 so then the solution is x=1.5

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PLEASE LOOK AT THE IMAGE. I’m despite. It’s probably easy.

Sloan [31]

Answer:

Correct answer: (x - 10)² + y² = 441 / 4

Step-by-step explanation:

Given:

(a, b) = (10, 0) the coordinates of the center of the circle

(10, 21/2) circle passing through this point

The standard form of the circle equation is:

(x - a)² + (y - b)² = r² where r is radius of the circle

We will replace the given coordinates of the center of the circle and the point it passes through to get the radius of the circle:

(10 - 10)² + (21/2)² = r² ⇒ r² = (21/2)² = 441 / 4

r² = 441 / 4

(x - 10)² + y² = 441 / 4

God is with you!!!

6 0

3 years ago

Frankie wants to build a path from one corner of his hard to the opposite corner his yard measures 20ft x 32ft what will be the

Papessa [141]

Answer:

37.7 feet

Step-by-step explanation:

Given that:

Measurements of Frankie's yard = 20ft x 32ft

He wants to build a path from one corner to another.

To find:

The length of path = ?

Solution:

Let us consider a rectangle $ABCD$ as shown in the attached image in the answer area.

We are given the two adjacent sides of a rectangle and we have to find diagonal of the rectangle.

To find the diagonal, we can use the Pythagorean Theorem.

We are given the base and perpendicular of the right angled triangle and we have to find the hypotenuse.

According to Pythagorean theorem:

$\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}$

$Diagonal = 20^2 + 32^2\\\Rightarrow Diagonal = 400 + 1024\\\Rightarrow Diagonal = \bold{37.7\ ft}$

4 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

Hey! Could I get a lil bit of help? (10 points)

GrogVix [38]

Answer:

Neither A nor B

Step-by-step explanation:

Neither set of order pairs represent a function, because none of the points have a correlating function throughout them.

4 0

2 years ago

Read 2 more answers

Tính : a) (a+b+c)^2 b) (a-b-c)^2 c) (a+b-c)^2 d) (a-b+c)^2

LiRa [457]

Answer:

a.) a² + b² + c ² + 2ab + 2ac + 2bc

b.) a² + b² + c² - 2ab - 2 ac + 2bc

c ) a² + b² + c² + 2ab - 2ac - 2bc

d.) a² + b² + c² - 2ab + 2ac - 2bc

Step-by-step explanation:

Use ( a + b + c )² = a² + b² + c² + 2 × ab + 2 × ac + 2 × bc to expand all these expression

a) ( a + b + c )²

= a² + b² + c² + 2 × ab + 2 × ac + 2 × bc

= a² + b² + c ² + 2ab + 2ac + 2bc

b.) ( a - b - c )

= a² + ( - b )² + ( - c)² + 2a ( -b ) + 2a(-c) + 2(-b)(-c)

= a² + b² + c² - 2ab - 2 ac + 2bc

c.) ( a + b - c )²

= a² + b² + ( -c)² + 2ab + 2a ( - c) + 2 b( -c)

= a² + b² + c² + 2ab - 2ac - 2bc

d.) (a - b + c ) ²

= a² + ( -b)² + c² + 2a(-b) + 2ac + 2c( -b)

= a² + b² + c² - 2ab + 2ac - 2bc

3 0

2 years ago