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postnew [5]
2 years ago
13

Solve the following equation using the substitution method 2x - y = -2 y = 8

Mathematics
1 answer:
anyanavicka [17]2 years ago
3 0
X will equal 3 bc 2x-8=-2 2x=6 x=3
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Which of the following is an extraneous solution of (45-3x)^1/2=x-9?
Iteru [2.4K]

Answer:

C. x =3

Step-by-step explanation:

Extraneous solution is that root of a transformed equation that doesn't satisfy the equation in it's original form because it was excluded from the domain of the original equation.

Let's solve the equation first

\sqrt{45-3x} = x-9\\Taking\ square\ on\ both\ sides\\{(\sqrt{45-3x})}^2 = {(x-9)}^2\\45-3x = x^2-18x+81\\0 = x^2-18x+81-45+3x\\x^2-15x+36 = 0\\x^2-12x-3x+36 = 0\\x(x-12)-3(x-12) = 0\\(x-3)(x-12)\\x-3 = 0\\=> x =3\\x-12 = 0\\x = 12\\We\ will\ check\ the\ solutions\ one\ by\ one\\So,\\for\ x=3\\\sqrt{45-3(3)} = 3-9\\\sqrt{45-9} = -6\\\sqrt{36}= -6\\6\neq -6\\For x=12\\\sqrt{45-3(12)} = 12-9\\\sqrt{45-36} = 6\\\sqrt{36}= 6\\6=6

Hence, we can conclude that x=3 is an extraneous solution of the equation ..

3 0
3 years ago
How many total terms are there in the following sequence. 7,10,13,...,391,394
nlexa [21]

Answer: n = 130

Step-by-step explanation:

The sequence is an Arithmetic progression ( AP )

The last term of the sequence is (L) is 394 with the formula

L  = a + ( n- 1 )d . From the sequence, a = 7, d ( common difference ) = 3 and L ( last term ) = 394, and n = ?

Put those values in the formula above and solve for n.

  a + ( n - 1 )d =  L

  7 + ( n - 1 ) x 3  = 394

         7 + 3n - 3   = 394

             4 + 3n     = 394

                    3n     = 394 - 4

                     3n     = 390

                        n     = 130      

4 0
3 years ago
Read 2 more answers
what is the difference between the commutative distributive and associative properties when multiplying?
Fantom [35]
<span>The associative rule is a rule about when it's safe to move parentheses around. You can remember that because the parentheses determine which expressions you have to do first--which numbers can associate with each other. It looks like this:

For addition: (a + b) + c = a + (b + c)
For multiplication: (ab)c = a(bc)

The commutative property is about which operations you can do backward and forward. You can remember this by thinking of people commuting to work: they go to work every morning, then they repeat the same operation backward when they commute home. It looks like this:

For addition: a + b = b + a
For multiplication: ab = ba

Finally, the distributive property tells you what happens when you distribute one operation against another kind in parentheses. It looks like this:

a * (b + c) = ab + ac

In other words, the a is "distributed" over the b and c.

Of course, you can make these work together:

a * (b + (c + d))
= a * ((b + c) + d) (by the associative property)
= a * (d + (b + c)) (by the commutative property)
= ad + a (b + c) (by the distributive property)
= ad + ab + ac (by the distributive property again).

Hope this helps. </span>
6 0
2 years ago
Read 2 more answers
4 x 105 in standard notation
Paul [167]

Answer:

Lol its 420

Step-by-step explanation:

6 0
3 years ago
Read the passage about Ötzi the Iceman.
Nataliya [291]
A Historian because they are describing what they see years later
6 0
2 years ago
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