Answer:
(6, - 4 )
Step-by-step explanation:
Given the 2 equations
- 
y = 3 → (1)
x - 
= 12 → (2)
Multiply (1) by 8 and (2) by 6 to clear the fractions
2x - 3y = 24 → (3)
10x - 3y = 72 → (4)
Rearrange (3) expressing - 3y in terms of x by subtracting 2x from both sides
- 3y = 24 - 2x
Substitute 3y = 24 - 2x into (4)
10x + 24 - 2x = 72, that is
8x + 24 = 72 ( subtract 24 from both sides )
8x = 48 ( divide both sides by 8 )
x = 6
Substitute x = 6 in either (3) or (4) and solve for y
Substituting in (3)
2(6) - 3y = 24
12 - 3y = 24 ( subtract 12 from both sides )
- 3y = 12 ( divide both sides by - 3 )
y = - 4
Solution is (6, - 4 )
Answer:
8x^2 + 5y + 1
Step-by-step explanation:
1 + x^2 - 3 + 2y + 7x^2 + 3 + 3y
group like terms
= x^2 + 7x^2 + 2y + 3y + 1 - 3 + 3
add similar items
= 8x^2 + 2y + 3y + 1 - 3 + 3
add similar items
= 8x^2 + 5y + 1 - 3 + 3
= 8x^2 + 5y + 1
To solve this, it is helpful to set up an equation that reductions and additions of the games. The equation would be:
27 = 1/2v + 3
In this equation, v = the original number of video games. The 1/2 signifies Casey selling his games, and the + 3 shows Casey buying three more.
If we subtract 3 from both sides, we see that 1/2v = 24. Finally, we can multiply each side by 2 to isolate the variable, v, and we get v = 48.
Therefore our final answer is 48 video games.
Hope this is helpful!
∠5 ≅ ∠8 (vertically opposite angles)
Hence, ∠1 ≅ ∠8 by the transitive property.
<h3>How to find angles when parallel lines are cut by a transversal?</h3>
When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.
Therefore, line e and f are parallel lines cut by the the transversal g.
∠1 ≅ ∠4(vertically opposite angles)
Hence,
∠4 ≅ ∠8(corresponding angles)
Since, ∠1 ≅ ∠4
Then, by substitution,
∠1 ≅ ∠8 (transitive property)
∠5 ≅ ∠8 (vertically opposite angles)
Therefore, ∠1 ≅ ∠8 by the transitive property.
learn more on parallel lines here: brainly.com/question/13774044
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Answer: 
Step-by-step explanation:
In order to find the entire area of the rectangle, you have to first find the values of each quadrant, then you add the values together to find the answer. The top left quadrant is x times x, which is 
. The top right value is x times 7, which is 7x. the bottom left value is x times 5, which is 5x, and the bottom right value is 7 times 5, which is 35. Put all the answers together and you get 
, which simplifies to
