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3 years ago

Which ordered pair is a solution of the system x + 2y < -2 and y <-3x + 4

Mathematics

1 answer:

kifflom [539]3 years ago

4 0

Where's the system? I can't answer your question without it.

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Find equation of the line passing through the given point in parallel to given equation. write your answer in slope intercept fo

denpristay [2]

Answer:

3) y = (7/2)x -12
4) y = 3x -5
7) y = (1/3)x +4/3
8) y = (-4/3)x +8/3

Step-by-step explanation:

In every case, you can ...

replace any constant in the equation by 0
for point (h, k), replace x with (x-h) and y with (y-k), then simplify
solve for y (add the opposite of the y-term; divide by the y-coefficient)

3) -7(x-4) +2(y-2) = 0 ⇒ -7x +2y +24 = 0

... y = (7/2)x -12

4) (y+2) = 3(x-1)

... y = 3x -5

7) -(x+4) +3(y-0) = 0 ⇒ -x +3y -4 = 0

... y = (1/3)x +4/3

8) 4(x-2) +3(y -0) = 0 ⇒ 4x +3y -8 = 0

... y = (-4/3)x +8/3

7 0

3 years ago

The recursive rule for a sequence is shown.an=an−1+9a1=21 what is the explicit rule for this sequence?

bixtya [17]

Answer:

Meaning of Explicit rule , is the general rule for a sequence.

The given sequence is defined as,

$a_{n}=a_{n-1}+9a_{1}-21$ ----(1)

Common Difference(d) of an airthmetic Sequence= N th term - (N-1) th term

$=a_{n}-a_{n-1}\\\\=a_{n-1}-a_{n-2}$

Equation 1 can be written as,

$a_{n}-a_{n-1}=9 a_{1}-21\\\\ d =9a_{1}-21$

General rule or explicit rule for this sequence is given as:

$a_{n}=a_{1} +(n-1)d\\\\a_{n}=a_{1}+(n-1)(9a_{1}-21)\\\\a_{n}=a_{1}+9na_{1}-21 n-9a_{1}+21\\\\a_{n}=-8a_{1}+21+n(9a_{1}-21)$

6 0

3 years ago

The image of F(-5,-9) after translating along <4, 6 > and then translating along < 3, 5> is? F’(?,?)

dusya [7]

<h3>Answer: (2, 2)</h3>

==============================================

Explanation:

The phrasing "translated along <4,6>" is another way of saying "shift 4 to the right, shift 6 up"

In general, "translated along <m,n>" is the same as writing $(x,y) \to (x+m, y+n)$ . If m is positive, then we shift m units to the right. If m is negative, then we shift to the left. The same story happens with the n, but we focus on the y coordinate.

-------------

With all that in mind, starting at F(-5,-9) and translating along <4,6> has us arrive at (-1, -3). Add 4 to the x coordinate and add 6 to the y coordinate.

We can say

$(x,y) \to (x+4,y+6)\\\\(-5,-9) \to (-5+4,-9+6)\\\\(-5,-9) \to (-1,-3)\\\\$

Showing that (-5,-9) moves to (-1,-3)

This is after the first translation, but there's a second translation.

We'll apply the same idea, but different numbers this time

$(x,y) \to (x+3,y+5)\\\\(-1,-3) \to (-1+3,-3+5)\\\\(-1,-3) \to (2,2)\\\\$

So (-1,-3) moves to (2,2)

Overall we have

(-5,-9) move to (-1,-3) after the first translation
(-1,-3) move to (2,2) after the second translation

Therefore, the original point ends up at (2,2) which is the final answer

--------------

Extra info:

A nice shortcut is that the vectors <4,6> and <3,5> can be added to get <4+3,6+5> = <7,11>. So overall, we're shifting 7 units to the right and 11 units up when we combine the two translation vectors.

5 0

3 years ago

Which of the following shows the division problem??

elena-14-01-66 [18.8K]

we are given

$\frac{3x^2-4x+9}{x-2}$