PLEASE ANSWER Add. 51.342 + 36.530

Answers

Answer 1

Answer: Use the calculator :v nvm the answer is 87.872

Answer 2

Answer: 87.872 is the answer

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Solve, check and show your work plz

Answers

Answer:

1. 3=x 2. no solution 3. infinate

Step-by-step explanation:

1. x=-5x+18

+5x +5x

6x=18

18/6=3

3=x

2. 3x-5=7+3x

-3x -3x

-5=7 No solution

3. 1/4(8x-12)=2x-3

2x-3=2x-3

-2x -2x

-3=-3

infinate

Rewrite the function by completing the square.
f(x) = x^2 – 10x—96

Answers

Answer:

$f(x) = (x - 5)^(2) - 121$ .

Step-by-step explanation:

The goal is to rewrite $f(x)$ in the vertex form $a\, (x - h)^(2) + k$ by completing the square (where $a$ , $h$ , and $k$ are constants.)

Expand the vertex form expression:

$\begin{aligned}& a\, (x - h)^(2) + k\n &= a\, (x - h)\, (x - h) + k \n &= a\, \left(x^2 - h\, x - h\, x + h^2\right) + k \n &= a\, \left(x^2 - 2\, h\, x + h^2\right) + k\n &= a\, x^2 - 2\, a\, h\, x + \left(a\, h^2 + k\right) \end{aligned}$ .

Compare this expression to $f(x) = x^2 - 10\, x - 96$ and solve for the constants $a$ , $h$ , and $k$ . Make sure that the coefficient of each term matches:

Coefficient for the $x^2$ term: $a$ in the expanded expression and $1$ in the expression for $f(x)$ . Hence, $a = 1$ .

Coefficient for the $x$ term: $(-2\, a\, h)$ in the expanded expression and $(-10)$ in the expression for $f(x)$ . Hence, $-2\, a\, h = -10$ .

Coefficient for the constant term: $\left(a\, h^2 + k\right)$ in the expanded expression and $(-96)$ in the expression for $f(x)$ . Hence, $a\, h^(2) + k = -96$ .

Substitute $a = 1$ into the second equation, $-2\, a\, h = -10$ , and solve for $h$ .

$-2 \, h = -10$ .

$h = 5$ .

Substitute both $a = 1$ and $h = 5$ into the third equation, $a\, h^(2) + k = -96$ , and solve for $k$ .

$5^2 + k = -96$ .

$k = -121$ .

Therefore, $a\, (x - h)^(2) + k$ becomes $(x - 5)^2 + (-121)$ .

Hence, the vertex form of the parabola $f(x)$ would be:

$f(x) = (x - 5)^(2) - 121$ .

Answer:

(x - 5)² -121 = 0

Step-by-step explanation:

if you need to find the roots you can take the square root of each side:

(x-5)² = 121

square root of (x-5)² is x-5

square root of 121 is ±11

first root: x-5 = 11

x = 16

second root: x-5 = -11

x = -6

Mrs. Smith is giving a homework pass to a student whose expression is equivalent to - i. Which expression will win the homework pass?A. i^36
B. i^37
C. i^38
D. i^39
Help pleaseee

Answers

Answer:

D. i^39

Step-by-step explanation:

If you simplify i^39, you get i^35, i^31, i^27, i^23, i^19, i^15, i^11, i^7, to i^3, which is equal to -i.

Can someone please help me :)

Answers

Answer:

90 degree

Step-by-step explanation:

Three points A, B, and C are added and shown in attached picture.

As the property of inscribed angle in circle:

angle BAC = (1/2) x 88 = 44 deg

As the property of complement angle:

angle ABC = 180 - 89 = 91 deg

As the property of sum of three angles in a triangle:

angle ACB + angle ABC + angle BAC = 180 deg

=> angle ACB = 180 - angle ABC - angle BAC = 180 - 44 - 91 = 45 deg

One more time, we use the property of inscribed angle in circle:

x = 2 x angle ACB = 2 x 45 = 90 deg

Hope this helps!

Rewrite 3/11 amd 1/4 so they have a common denominator

Answers

Hello!

Answer:

$\Large \boxed{\sf (12)/(44) ~~ and~~ (11)/(44) }$

Step-by-step explanation:

We want that the fractions 3/11 and 1/4 have a common denominator.

Let's find the LCM (least common multiple) of 4 and 11:

$\text{\sf Multiples of 4:}~~ \sf 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, \boxed{\sf 44}, 48\n\n\text{\sf Multiples of 11:} ~~ \sf 11, 22, 33, \boxed{\sf 44}, 55, 66, 77, 88, 99, 110$

So the LCM of 4 and 11 is 44.

Convert fractions over 44:

$\sf (3)/(11) = (3 * 4 )/(11 * 4) = \boxed{\sf (12)/(44)}$

$\sf (1)/(4) = (1 * 11 )/(4 * 11) = \boxed{\sf (11)/(44)}$

A rectangular box without a lid is to be made from 48 m2 of cardboard. Find the maximum volume of such a box. SOLUTION We let x, y, and z to be the length, width, and height, respectively, of the box in meters. Then we wish to maximize V

Answers

Answer:

The maximum volume of such box is 32m^3

V = x×y×z = 32 m^3

Step-by-step explanation:

Given;

Total surface area S = 48m^2

Volume of a rectangular box V = length×width×height

V = xyz ......1

Total surface area of a rectangular box without a lid is

S = xy + 2xz + 2yz = 48 .....2

To be able to maximize the volume, we need to reduce the number of variables.

Let assume the rectangular box has a square base,that means; length = width

x = y

Substituting y with x in equation 1 and 2;

V = x^2(z) ....3

x^2 + 4xz = 48 .....4

Making z the subject of formula in equation 4

4xz = 48 - x^2

z = (48 - x^2)/4x .......5

To be able to maximize V, we need to reduce the number of variables to 1, by substituting equation 5 into equation 3

V = x^2 × (48 - x^2)/4x

V = (48x - x^3)/4

differentiating V with respect to x;

V' = (48 - 3x^2)/4

At the maximum point V' = 0

V' = (48 - 3x^2)/4 = 0

Solving for x;

3x^2 = 48

x = √(48/3)

x = √(16)

x = 4

Since x = y

y = 4

From equation 5;

z = (48 - x^2)/4x

z = (48 - 4^2)/4(4)

z = 32/16

z = 2

The maximum volume can be derived by substituting x,y,z into equation 1;

V = xyz = 4×4×2 = 32 m^3

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