Help me please I will mark 5 stars please it is urgent

Write the sentence as an absolute value inequality, then solve the inequality: A number “n” is more than 9 units from 3

Helga [31]

Answer:

absolute vlaue inequality: |x-3| > 9; solved: x<-6 and x>12

Step-by-step explanation:

I’m going to start this off by saying I learned all this right now by just searching up how to solve an absolute inequality equation and watching one video, so this might not be an accurate explanation. (I’m pretty sure the answer’s right though)

So an absolute value inequality must be written like this:

| x - a | *inequality* b

a is going to be the number that the inequality is centered around, in this case, 3. b will be how far you can deviate from that number, which in this case is 9.

Now, you will have this:

|x - 3| *inequality* 9

Now, to find the inequality, you need to understand the wording. If it says “more than” as it does here, then you would have the greater-than symbol (>). If you have “less than” then you’d have the less-than symbol (<). If the problem says “at least b away” then it would be greater-than-or-equal to (≥), and likewise, if it says “at most b away” then it would be less-than-or-equal-to (≤).

So now we're at:

|x - 3| > 9

To solve the equation, you just need to subtract 9(b) from 3(a) and add 9(a) to 3(b) to get -6 and 12. Since x must be more than 9 units away, you would get:

x<-6 and x>12

Hope this is helpful!

6 0

3 years ago

1. Slove the system of equations, first by graphing, and then algebraically. (8 points) y=x-2 and y=-2x+7

Anton [14]

The solution of the equation is $x=3$ and $y=1$

Explanation:

The equations are $y=x-2$ and $y=-2 x+7$

First we shall solve the equation graphically.

The image of the graph is attached below.

This contains the solution to the system of equations.

The equations $y=x-2$ and $y=-2 x+7$ are plotted on the graph.

The intersection of these two equations are the solutions of the system of equations.

Thus, the intersection of the two equations are $x=3$ and $y=1$

Now, we shall solve the equation algebraically.

Let us solve the equation using substitution method.

Let us substitute $y=x-2$ in $y=-2 x+7$ , we get,

$x-2=-2x+7$

Adding both sides by 2x, we have,

$3x-2=7$

Adding both sides by 2, we get,

$3x=9$

Dividing both sides by 3,

$x=3$

Thus, the value of x is 3.

Substituting $x=3$ in $y=x-2$ , we get,

$y=3-2\\y=1$

Thus, the value of y is 1.

Hence, The solution of the equation is $x=3$ and $y=1$

4 0

3 years ago

The table shows the results of two surveys that randomly sampled 100 kids about their favorite types of movies.

Soloha48 [4]

The only consistent right answer will be B.
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6 0

3 years ago

Read 2 more answers

If Acot theta + Bcot theta =4 and

geniusboy [140]

Answer is: B

Step-by-step explanation: correct answer is B

b

2

−a

2

Given, acotθ+bcscθ=p

bcotθ+acscθ=q

⇒p

2

−q

2

=(p−q)(p+q)

=[acotθ+bcscθ−bcotθ−acscθ][acotθ+bcscθ+bcotθ+acscθ]

=[cotθ(a−b)−cscθ(a−b)][cotθ(a+b)+cscθ(a+b)]

=(a−b)(cotθ−cscθ)(a+b)(cotθ+cscθ)

=(a

2

−b

2

)(cot

2

θ−csc

2

θ)

=(−1)(a

2

−b

2

)[∵csc

2

θ−cot

2

θ=1]

=(b

2

−a

2

)

7 0

3 years ago

1) 6=A/4+2 can someone help please

monitta

Answer:

A=16

Step-by-step explanation:

6=A/4+2

-2 -2

4=A/4

x4 x4

16=A

6 0

3 years ago