Answer:
A
Step-by-step explanation:
Rules:
odd x odd = odd
even x even = even
even x odd = even
even + even = even
odd + odd = even
odd + even = odd
We can determine whether 2a + 3b is odd if we have both statements because we know that a is odd and 2 is even, which means their product will be even. 3 is odd and b is odd, so their product will be odd. The sum of the even and odd will be odd.
If we have just the second statement we can determine the answer because anything multiplied by 2 is even.
So whether or not we know if a is odd, we know that 2a is even because 2 doubles everything which means it's divisible by 2 which means it's even.
However, statement 1 alone is not enough because if a is odd, then 2a is even. However, 3b can be even or odd depending on b. If b is odd, then 3b is odd. if b is even, 3b is even.
Therefore, if you have statement 2 you can answer the question but if you only have statement 1 then you also need statement 2
2. x + y = 82
x - y = 24
---------------add
2x = 106
x = 53
x + y = 82
53 + y = 82
y = 82 - 53
y = 29
solution is : (53,29)
=======================
3. y = 2x
y = 4x + 6
2x = 4x + 6
2x - 4x = 6
-2x = 6
x = -3
y = 2x
y = 2(-3)
y = -6
solution is (-3,-6)
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4. 5x + 8y = -29
7x - 2y = -67...multiply by 4
----------------
5x + 8y = -29
28x - 8y = - 268 ..result of multiplying by 4
-----------------add
33x = - 297
x = - 9
5x + 8y = -29
5(-9) + 8y = -29
-45 + 8y = -29
8y = -29 + 45
8y = 16
y = 2
solution is : (-9,2)
=======================
5. y = -4x + 6
y = -5x - 4
-4x + 6 = -5x - 4
-4x + 5x = -4 - 6
x = -10
y = -4x + 6
y = -4(-10) + 6
y = 40 + 6
y = 46
solution is (-10,46)
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6. H(m) = 2m + 12
H(m) = 3m + 10
=========================
7. -8x + 4y > -52
4y > 8x - 52
y > 2x - 13 <==
=========================
8. 3x - y = 28
3x + y = 14
---------------add
6x = 42
x = 7
3x - y = 28
3(7) - y = 28
21 - y = 28
-y = 28 - 21
-y = 7
y = -7
solution is (7,-7)
=====================
10. 5x - 5y > 70
-5y > -5x + 70
y < x - 14 <==
=====================
11. sorry...dont know
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12. y = 4x + 4
y = -3x - 3
4x + 4 = -3x - 3
4x + 3x = -3 - 4
7x = -7
x = -1
y = 4x + 4
y = 4(-1) + 4
y = 0
solution is (-1,0)
=======================
13. -12x - 2y > - 42
-2y > 12x - 42
y < -6x + 21 <==
=======================
14. -5x + 2y = 9
3x + 5y = 7
solution is (-1,2)
========================
15. 3x + 6y = -2
15x + 30y = -10....divide by 5 to reduce = 3x + 6y = -2
is the same line....infinite solutions
========================
1. (the graph).....y < = 3x - 4....3rd one
========================
9. (2nd graph)....y < = -3x + 4....last one
Answer: b = p - a -c
Step-by-step explanation:
p= a + b + c Solving for b means getting b on one side by itself.
p = a + b + c To solve for b first subtract a from both sides to get,
-b -b
p - a = b + c Now subtract c from both sides to get
-c -c
p - a - c = b
b = p - a -c
Answer:
B
Step-by-step explanation:
We are given the function:
And we want to determine the value of:
Let this value equal <em>a</em>. In other words:
Then by the definition of inverse functions:
Hence:
Solve for <em>a: </em>
By the Zero Product Property:
Hence:
Thus, f(9) = 225. Consequently, f⁻¹(225) = 9.
In conclusion, our answer is B.
