What's the average of x-y and x+y

Linear Relationships Study Guide 1.) Select all the equations for which (-6, -1) is a solution. Show your work to prove that eac

TiliK225 [7]

we have point (-6, - 1)

Now we will put these points in each equation,

y = 4x +23

put x = -6 and y = -1

-1 = 4 (-6) +23

-1 = -24 + 23

-1 = -1

LHS = RHS, so this equation has (-6 , -1) as solution.

y = 6x

put x = -6 and y = -1

-1 = 6 (-6)

-1 not= -36

LHS is not equal RHS, so (-6 , -1) is not a solution for that equation,

y = 3x - 5

put x = -6 and y = -1

-1 = 3 (-6) - 5

-1 = -18 - 5

-1 not= -23

LHS is not equal RHS, so (-6 , -1) is not a solution for that equation,

y= 1/6 x

put x = -6 and y = -1

-1 = -6/6

-1 = -1

LHS = RHS, so (-6 , -1) is a solution for that equation,

6 0

1 year ago

WILL GIVE BRAINLIEST PLEASE ADD THE REASONING PART!!

nasty-shy [4]

Answer:

new price= $2.40

Step-by-step explanation:

20%= 20/100= 1/5

$3.00/5= 00.60

1/5 of the price is being subtracted from $3.00

$00.60 is 1/5

3.00-.60= 2.40

3 0

2 years ago

Read 2 more answers

Find out the number of combinations and the number of permutations for 8 objects taken 6 at a time. Express your answer in exact

umka2103 [35]

Solution:

The permutation formula is expressed as

$\begin{gathered} P^n_r=\frac{n!}{(n-r)!} \\ \end{gathered}$

The combination formula is expressed as

$\begin{gathered} C^n_r=\frac{n!}{(n-r)!r!} \\ \\ \end{gathered}$

where

$\begin{gathered} n\Rightarrow total\text{ number of objects} \\ r\Rightarrow number\text{ of object selected} \end{gathered}$

Given that 6 objects are taken at a time from 8, this implies that

$\begin{gathered} n=8 \\ r=6 \end{gathered}$

Thus,

Number of permuations:

$\begin{gathered} P^8_6=\frac{8!}{(8-6)!} \\ =\frac{8!}{2!}=\frac{8\times7\times6\times5\times4\times3\times2!}{2!} \\ 2!\text{ cancel out, thus we have} \\ \begin{equation*} 8\times7\times6\times5\times4\times3 \end{equation*} \\ \Rightarrow P_6^8=20160 \end{gathered}$

Number of combinations:

$\begin{gathered} C^8_6=\frac{8!}{(8-6)!6!} \\ =\frac{8!}{2!\times6!}=\frac{8\times7\times6!}{6!\times2\times1} \\ 6!\text{ cancel out, thus we have} \\ \frac{8\times7}{2} \\ \Rightarrow C_6^8=28 \end{gathered}$

Hence, there are 28 combinations and 20160 permutations.

7 0

1 year ago

Simplify 4( x - 6) ^2 / ( x - 6)

Leno4ka [110]

Answer:

4x - 24

Step-by-step explanation:

$\frac{4(x - 6 {)}^{2} }{(x - 6)}$

$4(x - 6) = 4x - 4 \times 6 = 4x - 24$

$4x - 24$

5 0

2 years ago

Read 2 more answers

A quadratic equation is shown below:

Valentin [98]

Part A)

The given equation is:

$25 x^{2} +10x+1=0$

The radicand or discriminant(d) of the equation will be:

$d=(10)^{2}-4(25)(1) \\ \\ 
d=100-100 \\ \\ 
d=0$

Since the discriminant is equal to 0, the given quadratic equation has only 1 root. In other words we can say the the given equation is a perfect square.

Part B)

The given equation is:

$4 x^{2} -4x+1=0$

We can solve this expression by factorization. Factors of middle term are to be made in such a way that their product equals the product of first and third term and sum is equal to the middle term i.e. product should be 4x² and sum should be -4x.
So the two such terms are -2x and -2x. Using the factors and simplifying the equation by taking common we get:

$4 x^{2} -2x-2x+1=0 \\ \\ 
2x(2x-1)-1(2x-1)=0 \\ \\ 
(2x-1)(2x-1)=0 \\ \\ 
(2x-1) ^{2}=0 \\ \\ 
2x-1=0 \\ \\ 
x= \frac{1}{2}$

4 0

3 years ago