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2 years ago

Please solve this Screenshot/attachment that is included below, thanks!

Mathematics

1 answer:

amm18122 years ago

6 0

Answer:

1) A=5

Step-by-step explanation:

1) W should be greater than 1, so the only option that satisfies this is A which is 5.

(For the number line please look at the attachment)

I'm sorry, I don't know how to solve the second problem. I hope the first question helps. Sorry and Hope its clear.

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Give a geometric description of the following system of equations.a. 2x−4y=12 −3x+6y=−15.b. 2x−4y=12 −5x+3y=10.a. 2x−4y=12 −3x+6

Reptile [31]

Answer:

a. No solution, parallel lines.

b. One solution.

Step-by-step explanation:

Given the system of equations:

a. $2x-4y=12$

$-3x+6y=-15$

b. $2x-4y=12$

$-5x+3y=10$

To give a geometric description of the given system of equations.

The geometric description of a system of equations in 2 variables mean the system of equations will represent the number of lines equal to the number of equations in the system given.

i.e.

Number of planes = Number of variables

Number of lines = Number of equations in the system.

Here, we are given 2 variables and 2 equation in each system.

So, they can be represented in the xy-coordinates plane.

And the number of solutions to the system depends on the following condition.

Let the system of equations be:

$A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0$

1. One solution:

There will be one solution to the system of equations, If we have:

$\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}$

2. Infinitely Many Solutions: (Identical lines in the system)

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}= \dfrac{C_1}{C_2}$

3. No Solution:(Parallel lines)

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}$

Now, let us discuss the system of equations one by one:

a. $2x-4y=12$ OR $2x-4y-12=0$

$-3x+6y=-15$ OR $-3x+6y+15=0$

$A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -3, B_2 = 6, C_2= 15$

Here, the ratio:

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2} = -\dfrac{2}{3}\\\dfrac{C_1}{C_2} = -\dfrac{4}{5}$

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}$

Therefore, no solution i.e. parallel lines.

b. $2x-4y=12$ OR $2x-4y-12=0$

$-5x+3y=10$ OR $-5x+3y-10=0$

$A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -5, B_2 = 3, C_2 = -10$

$\dfrac{A_1}{A_2}= -\dfrac{2}{5}\\\dfrac{B_1}{B_2} = -\dfrac{4}{3}\\\dfrac{C_1}{C_2} = -\dfrac{6}{5}$

$\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}$

So, one solution.

Kindly refer to the images attached for the graphical representation of the given system of equations.

6 0

3 years ago

13. Find the vertex of f(x)=x2 -6x +8 .

Mekhanik [1.2K]

9514 1404 393

Answer:

a (3,-1)

Step-by-step explanation:

The number that "completes the square" is the square of half the x-coefficient, (-6/2)^2 = 9. Rearranging the given function to include the square trinomial, we have ...

f(x) = x^2 -6x +9 -1 . . . . . . . here, we have 8 = 9 - 1

f(x) = (x -3)^2 -1 . . . . . . . . . . vertex form

Comparing this to the generic vertex form ...

f(x) = (x -h)^2 +k . . . . . . . vertex at (h, k)

we see that h=3 and k=-1.

The vertex is (h, k) = (3, -1).

6 0

2 years ago

IF THE RATIO IN A VALENTINE'S

GalinKa [24]

Answer:

12 dark chocolates

Step-by-step explanation:

Let there are 2x milk chocolates and 3x dark chocolates.

Total no of milk chocolates = 8

ATQ,

2x = 8

x = 4

Dark chocolates = 3x

= 3(4)

= 12

Hence, there are 12 dark chocolates.

3 0

2 years ago

Whoever answer's will give branliest

Rudik [331]

Answer:

i cant even see properly

Step-by-step explanation:

6 0

3 years ago

PLEASE HELP !! ILL GIVE BRAINLIEST !

fomenos

Answer:

20 + 0i

Step-by-step explanation:

(10 + 5i) + (10 - 5i) = 20 + 0i

7 0

3 years ago