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3 years ago

When factoring polynomials, why it is best to look for a greatest common monomial factor first?

Mathematics

1 answer:

Alex73 [517]3 years ago

8 0

Answer:

Step-by-step explanation:

Binomials and polynomials are much easier to factor when reduced by a greatest common monomial.

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What is the effect on the graph of the function f(x) = x2 when f(x) is changed to f(x − 6)?

suter [353]

Answer:

Horizontal translation in the $+x$ direction.

Step-by-step explanation:

A function of the form $f(x)$ experiments an horizontal translation when the following substitution is applied:

$x \to x + a$ , where $a \in \mathbb{R}$

If $a > 0$ , the function is translated in the $-x$ direction, whereas $a < 0$ is the case for the function being translated in the $+x$ direction.

The effect on the graph can be defined by a composition between two function:

$f(x) = x^{2}$ , $g (x) = x-6$

$f\,\circ\,g\,(x) = (x-6)^{2}$

The resulting expression represents a horizontal translation in the $+x$ direction.

Finally, we plot $f(x)$ (red) and $f\,\circ g\,(x)$ (blue) by a graphing tool and proved the certainty of this theory.

5 0

3 years ago

Raul and Ivan each make a number pattern, as described.

alina1380 [7]

Answer:

Option C. 23

Step-by-step explanation:

To know the correct answer to the question given above, let us determine the sequence of Raul and Ivan. This is illustrated below:

From the question given above,

Raul's pattern: start with 15, add 2

Ivan's pattern: start with 11, add 3

For Raul:

Raul's pattern: start with 15, add 2

1st term = 15

2nd term = 15 + 2 = 17

3rd term = 17 + 2 = 19

4th term = 19 + 2 = 21

5th term = 21 + 2 = 23

6th term = 23 + 2 = 25

For Ivan:

Ivan's pattern: start with 11, add 3

1st term = 11

2nd term = 11 + 3 = 14

3rd term = 14 + 3 = 17

4th term = 17 + 3 = 20

5th term = 20 + 3 = 23

6th term = 23 + 3 = 26

Summary

Term >>>>> Raul >>>>>> Ivan

1 >>>>>>>>> 15 >>>>>>>> 11

2 >>>>>>>>> 17 >>>>>>>> 14

3 >>>>>>>>> 19 >>>>>>>> 17

4 >>>>>>>>> 21 >>>>>>>> 20

5 >>>>>>>>> 23 >>>>>>>> 23

6 >>>>>>>>> 25 >>>>>>>> 26

From the calculations made above, we can see that in the 5th term, both Raul and Ivan has the same number as 23.

5 0

3 years ago

How do you solve systems of equations

Anna71 [15]

Where the two lines intersect is your solution.

3 0

4 years ago

Solve for y 2x-3y+6=0

Volgvan

2x - 3y + 6 = 0
 - 6 - 6
 2x - 3y = -6
2x - 2x - 3y = -6 - 2x
 -3y = -6 - 2x
 -3 -3
 y = 2 + ²/₃x

5 0

4 years ago

A waitress sold 17 ribeye steak dinners and 16 grilled salmon dinners, totaling $571.16 on a particular day. another day she s

avanturin [10]

Let x = ribeye steak cost, y = grilled salmon cost. With this we set up two equations:

17x + 16y = 571.16
21x + 8y = 583.22

We must now pick which dinner we could like to find the cost of first. I choose the ribeyes. To do so, I'm going to divide the first equation by - 2. I will explain why:

- 8.5x - 8y = - 285.58
21x + 8y = 571.16

Now we combine like terms. Notice that the y-variables cancel each other out. This why I divided by - 2. It causes this cancellation leaving us with only one variable to solve. This gives us:

12.5x = 297.64

Divide both sides by 12.5 to isolate variable x.

x = 23.8112 or x ≈ 23.81. I round two decimal points since we're dealing with money.

Now, we plug this cost into either of the two equations and solve for variable y. I'll use the first one.

17(23.81) + 16y = 571.16
404.77 + 16y = 571.16

Subtract 404.77 from both sides to isolate the variable and its coefficient.

16y = 166.37

Divide by 16 on both sides to get rid of the coefficient

y ≈ 10.3993 or y ≈ 10.40 since we're dealing with money.

Cost of ribeye steak -- $23.81
Cost of grilled salmon -- $10.40

5 0

3 years ago