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Komok [63]
3 years ago
7

Explain how horizontal and vertical translations each affect the coordinates of the points of a figure?

Mathematics
1 answer:
Neporo4naja [7]3 years ago
6 0
Translations of geometric figures in the coordinate plane can be determined by translating the x- and y-coordinates of points. Horizontal and vertical translations are the easiest. ... Solution: A horizontal translation just changes the x-coordinates of all points, so the rule is (x, y) à (x + 3, y).
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Please explain with working!!! Find the set of values of x that satisfy the inequality 9x^2-15x<6
Oksi-84 [34.3K]

Answer:

-1/3

Step-by-step explanation:

When solving a quadratic inequality, first solve it normally like you would for a normal quadratic equation. We have:

9x^2-15x

Ignore the less than sign and replace it with an equal sign and solve the quadratic for its zeros:

9x^2-15x=6

Subtract 6 from both sides:

9x^2-15x-6=0

Divide everything by 3:

3x^2-5x-2=0

Factor. Find two numbers that equal (3)(-2)=-6 that add up to -5.

-6 and 1 works. Thus:

3x^2-6x+x-2=0\\3x(x-2)+1(x-2)=0\\(3x+1)(x-2)=0

Find the x using the Zero Product Property:

3x+1=0 \text{ or }x-2=0\\x=-1/3\text{ or }x=2

Now, we need to replace the equal signs with symbols again. To do so, we need to test which symbol to place. Let's do the first zero first.

So, the first zero is:

x=-1/3

Assume that the correct symbol is >. Thus,

x>-1/3

Now, pick any number that is greater than -1/3. I'll pick 0 since it's the easiest. Now, plug 0 back into the very original inequality. If it works, then the sign is correct, if it doesn't, then simply use the opposite one. Therefore:

9x^2-15x

0 is indeed less than six, so our first correct solution is:

x>-1/3

For the second one, do the same thing. We have:

x=2

Assume that the correct symbol is <. Thus:

x

Again, pick any number less than 2. I'm going to use 0. Plug 0 back into the original equation

9x^2-15x

Again, this is correct. Therefore, x<2 is also the correct inequality.

So together, we have:

x>-1/3 \text{ and } x

Together, we can write them as:

-1/3

(Note that we don't need to worry about the "or equal to" part since the original inequality didn't have it.)

6 0
3 years ago
While completing a multiplication problem I need to know how to do it by associative
Vera_Pavlovna [14]

Associative property Says that you can add or multiply regardless of how the numbers are group

3 0
3 years ago
Number of Bars
Montano1993 [528]

Answer: Disagree. 1 in 8 bars are cinnamon.

Step-by-step explanation:

There are a total of 8 bars in the pack. Cinnamon is 1 of the 8. Therefore, for every 8 bars, one is cinnamon.

7 0
3 years ago
What is the name of the formula to use when adding multiple cells together?
mr Goodwill [35]
C ) sum 

hope it helped...

sum is summation

 

6 0
3 years ago
Read 2 more answers
Mark bought 18 pounds of apples for $6. Use the ratio table to find the cost of 3 pounds of apples.
emmasim [6.3K]

Answer:

$1

Step-by-step explanation:

To set this ratio up, you would put $6 over 18lbs is equal to x over 3lbs.

Next, multiply $6 and 3lbs to give you 18.

Finally, divide 18 by 18 to give you a final answer of $1. Hope this helps!

6 0
3 years ago
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