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kondaur [170]
3 years ago
12

You Have Tiangle XYZ with X(-7,-9), Y(-10,-3), and Z(-1,-9) After a 90 Degree Counterclockwise rotation, what is the new coordin

ate of Z'?
Mathematics
1 answer:
Marrrta [24]3 years ago
3 0

Answer:

Z'(9, - 1)

Step-by-step explanation:

For a 90 degree counterclockwise rotation about the origin,

The original coordinates of point P (x,y) will now be positioned as P' (-y,x).

Hence, given :

Triangle XYZ with X(-7,-9), Y(-10,-3), and Z(-1,-9)

The new position of Z denoted as Z' will be :

Z(-1, - 9) ; X = - 1 ; y = - 9

-y = - - 9 = 9

x = - 1 will remain as - 1

Z(-1, - 9) - - - > Z'(9, - 1)

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Express the function graphed on the axes below as a piecewise function.
adoni [48]

Answer:

  f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}

Step-by-step explanation:

To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.

__

<h3>Left Piece</h3>

The domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.

The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.

The first piece can be written ...

  f(x) = x-3 for x ≤ -1

__

<h3>Right Piece</h3>

The domain is shown as 5 to ∞, with 5<em> not included</em>.

The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...

  y -(-1) = -3(x -5)

  y = -3x +15 -1 = -3x +14

The second piece can be written ...

  f(x) = -3x +14 for x > 5

__

<h3>Whole function</h3>

Putting these pieces together, we have ...

  \boxed{f(x)=\begin{cases}x-3&\text{for }x\le-1\\-3x+14&\text{for }5 < x\end{cases}}

_____

<em>Additional comment</em>

Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, <em>x > 5</em>.

3 0
3 years ago
13. 5/6+9/11
Juli2301 [7.4K]

Explanation:

Addition of fractions can be accomplished using the formula ...

a/b + c/d = (ad +bc)/(bd)

Usually, you are asked to find the common denominator and rewrite the fractions using that denominator. It is not necessary, but it can save a step in the reduction of the final result. Here, we'll use the formula, then reduce the result to lowest terms.

___

13. 5/6 +9/11 = (5·11 +6·9)/(6·11) = 109/66 = 1 43/66

___

14. 7/20 -5/8 = (7·8 -20·5)/(20·8) = -44/160 = -11/40

___

15. 1/5 -1/12 = (1·12 -5·1)/(5·12) = 7/60

___

Dividing fractions can be accomplished different ways. I was taught to multiply by the inverse of the divisor. ("Invert and multiply.") Here, that means the problem (2/7) / (1/13) can be rewritten as ...

(2/7) × (13/1) . . . . . where 13/1 is the inverse of 1/13.

You can also express the fractions over a common denominator. In that case, the quotient is the ratio of the numerators. Perhaps a little less obvious is that you can express the fractions using a common numerator. Then the quotient is the inverse of the ratio of the denominators: (2/7) / (2/26) = 26/7. (You can see how this works if you "invert and multiply" the fractions with common numerators. Those numerators cancel.)

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16. (2/7)/(1/13) = 2/7·13/1 = 26/7 = 3 5/7

8 0
4 years ago
I really need help! Please, please, PLEASE do not give me a link.
MArishka [77]

Answer:

7 fiction and 23 non- fiction

Step-by-step explanation:

The number of non-fiction read was 5 less than 4 times the number of fiction books.

Assume fiction books are x.

An equation representing this would be:

x + (4x - 5) = 30

5x - 5 = 30

5x = 30 + 5

x = 35 / 5

x = 7 fiction books

Non-fiction books:

= 4x - 5

= 4 * 7 - 5

= 23 non - fiction books

3 0
2 years ago
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Figure J is similar to Figure M.
marusya05 [52]

Answer:

what are the equations?

Step-by-step explanation:

6 0
3 years ago
Write as a numeral in simplest form:(6x1000)+(4x100)+(6x1)
Anni [7]
Answer:
6401
step-by-step explanation:
6 x 1000
6000
4 x 100
400
6 x 1
6
6401
4 0
3 years ago
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