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Ivan
3 years ago
12

Help answering these math questions

Mathematics
2 answers:
Leto [7]3 years ago
5 0
I’m pretty sure the first one is c
Gwar [14]3 years ago
5 0

Answer:

Step-by-step explanation:

1. y = x^{2}  - 2x- 15 = x^{2}  - 5x +3x -15 = x(x-5) + 3(x-5) = (x-5)(x+3)

2.

4x^{2}  - 8x - 12 = 0\\x^{2} - 2x - 3 = 0\\x^{2} - 3x + x - 3 = 0\\ x(x-3) + 1 (x-3) = 0\\(x-3)(x+1) = 0

x= 3 and x = -1

3. x^{2}  - 36 = 0

  (x-6) (x+6) = 0

x = 6 and -6

You might be interested in
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:

<u>Step 1</u>:-

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)

<u>Step( ii):</u>

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)

<u>Step (iii):-</u>

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

<u> y = 1</u>

substitute y =1 in x = 9y

<u>x = 9</u>

substitute y =1 in 4z =9y

<u>z = 9 /4</u>

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

<u>Conclusion</u>:-

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
Q1: Gabbi purchased a 30 lb. bag of dog food. Gabbi has 3 dogs that each eat 20 ounces of dog food per day. How many days will t
olya-2409 [2.1K]

Answer:

x=8

Step-by-step explanation:

First multiply 30 and 16 to find out how many ounces are in the 30 lb. bag of dog food.

30 x 16=480

Since the 3 dogs eat 20 ounces of food, we can make a equation.

3(20x)=480

20 x 3=60

60x=480

x=8

<u>Final answer</u>

8 days

3 0
3 years ago
Check all that apply please
love history [14]

As, synthetic division by -4 gives remainder 0. Hence, Option B is correct. -4 is a root of 3x^{2} +7x-20

As, x+4=0 gives x=-4.

So, option C is correct,

(x+4) is factor of 3x^{2} +7x-20

Option E is correct

\frac{3x^{2} +7x-20 }{x+4}=3x-5

3 0
3 years ago
Name and degree for x+2
Ipatiy [6.2K]

Answer:

the answer is quadratic 2

Step-by-step explanation:

x2-x2+5

8 0
3 years ago
What is this i'm very confused
snow_tiger [21]

Answer:

That's the symbol for pi

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
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