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Firlakuza [10]
3 years ago
15

I'd really appreciate some help on these questions, I'm really struggling

Mathematics
1 answer:
nikklg [1K]3 years ago
6 0
We can use linear combinations of the equations to eliminate variables.

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

To eliminate y we'll make the linear combination of 3 times the first equation minus four times the second. 

9x - 12y = 3
-8x + 12y = 4

Adding,
x = 7

We could solve for y directly but let's use another linear combination, twice the first plus three times the second:

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

y = 5

Check: 3(7)-4(5)=1 good.   -2(7)+3(5)=1 good.

Q18 Answer: (7,5)

y = -3x + 5
5x - 4y = -3

4y +1(5x - 4y) = 4(-3x + 5) + 1(-3)

5x = -12x + 20 -3

17 x = 17

x = 1
y = -3(1) + 5 = 2
Check: 5(1) - 4(2) = -3 good

Q19 Answer (1,2)

6x + 5y = 25
x = 2y + 24
6x = 12y + 144
5y = 25 - 12y - 144
17y = -119
y = -119/17= -7
x = 2y+24= 10
Check: 6(10)+5(-7)=25 good   2y+24=2(-7)+24=10=x good

Q20 Answer (10,-7)


3x + y = 18
-7x + 3y = -10
9x  + 3y = 54
9x - -7x = 54 - -10
16x = 64
x=4
y = 18 -3x = 18-12=6

Check: 3(4)+6=18 good,  -7(4)+3(6)=-10 good

Q21 Answer: (4,6)

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Which shows the pre-image of triangle X'Y'Z' before the figure was rotated 90° about the origin?
Oksanka [162]

Answer:

pre-image XYZ is X (2, 2), Y (6, 0), Z (1, -1)

The above is the second option in your question.

Step-by-step explanation:

a triangle has points X' (-2, 2), Y' (0, 6), Z' (1, 1)

To rotate the above triangle -90° about the origin you invert the x & y values and change the sign on the new y value.

pre-image XYZ is X (2, 2), Y (6, 0), Z (1, -1)

6 0
2 years ago
Read 2 more answers
Factor completely:<br><br> <img src="https://tex.z-dn.net/?f=3x%5E3%2B21x%5E2%2B36x" id="TexFormula1" title="3x^3+21x^2+36x" alt
guajiro [1.7K]
To factor, you can first treat it like a single bracket and find the common factor. In this case, the common factor is 3x, so you get
3x(x² + 7x + 12)
Now you can factor the bracket normally, by finding factors of 12 that add up to make 7. The factors would be 3 and 4, so the bracket becomes (x + 3)(x + 4).
This leaves your final answer as
3x(x + 3)(x + 4)

I hope this helps!
5 0
3 years ago
What is the value of x? Leave your answer in simplest radical form.
OleMash [197]

Step-by-step explanation:

By using Pythagoras theoram,

x²= (6)²+(4)²

{x}^{2}  = 36 + 16

{x}^{2}  = 52

x =  \sqrt{52}

x = 2 \sqrt{13}

optionD

5 0
3 years ago
Read 2 more answers
PLEASE HELP I GIVE BRAINLIEST
Galina-37 [17]
I Think it would either be D or C

(I’m not sure, let me know if I’m wrong)
4 0
3 years ago
William wants to keep his debt-to-income ratio at the recommended 15% orlower William's house payment is
3241004551 [841]

9514 1404 393

Answer:

  about $171,400

Step-by-step explanation:

William's total monthly debt is ...

  $1012.84 +579.13 +250 +300 = 2141.97

On an annual basis, this is ...

  12 × $2141.97 = $25,703.64

This will be 15% of (25703.64/0.15) = $171,357.60.

William's new annual salary should be about $171,400 to keep his debt ratio at the recommended 15%.

_____

<em>Additional comment</em>

A debt ratio of 15% is a pretty aggressive target. Most mortgage lenders like to see the "front end" ratio (housing expense) less than 28%, and the "back end" ratio (all debt) less than 36%.

4 0
3 years ago
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