Answer:
{(1,4) (2,8) (3,12) (4,16)}
Which equation can pair with 3x + 4y = 8 to create a consistent and independent system?
2 answers:
<span>The right answer is C)
<em>Consistent and independent system</em> of two linear equations is a system such that there is only one solution for the system, that is, the two straight lines cross at a point. So we can analyze each case and I have attached some graphs to provided you with examples. Those graphs aren't about the equations but it's about general cases:
<em>A) </em><u><em>Consistent and dependent</em></u><em>. </em>If we divide this given equation by 2 we get the same line. (See Figure 1)
<em>B) </em><u><em>Inconsistent</em></u><em>.</em><em> </em>No solutions. (See Figure 2)
C) <em><u>Consistent and Independent</u>.</em> (See Figure 3)
D) <u><em>Consistent and dependent</em></u>. If we multiply this equation by -1 we get the same line. (See Figure 1)</span>
<em>Consistent and independent system</em> of two linear equations is a system such that there is only one solution for the system, that is, the two straight lines cross at a point. So we can analyze each case and I have attached some graphs to provided you with examples. Those graphs aren't about the equations but it's about general cases:
<em>A) </em><u><em>Consistent and dependent</em></u><em>. </em>If we divide this given equation by 2 we get the same line. (See Figure 1)
<em>B) </em><u><em>Inconsistent</em></u><em>.</em><em> </em>No solutions. (See Figure 2)
C) <em><u>Consistent and Independent</u>.</em> (See Figure 3)
D) <u><em>Consistent and dependent</em></u>. If we multiply this equation by -1 we get the same line. (See Figure 1)</span>
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D. 192in^2
This would be a simple area problem with a triangle. REMEMBER THIS EQUATION: a=bh*1/2 (b for base and h for height, these are multiplied together then that answer is halved out.)
So we just need to plug in our values into the equation, so the equation would look like a= (16)*(24)*1/2. 16 times 24 would then give you 384, you could either divide by 2 or multiply by 0.5 to get the next answer, as long as your HALVING the answer.
So we have our bh value so now we can multiply by 1/2 which will give us 384*1/2 which leaves us with 192.
I have also attached a photo of doing a longer(ish) way than this, that also proves that this equation works. Either one will provide you an answer.
This would be a simple area problem with a triangle. REMEMBER THIS EQUATION: a=bh*1/2 (b for base and h for height, these are multiplied together then that answer is halved out.)
So we just need to plug in our values into the equation, so the equation would look like a= (16)*(24)*1/2. 16 times 24 would then give you 384, you could either divide by 2 or multiply by 0.5 to get the next answer, as long as your HALVING the answer.
So we have our bh value so now we can multiply by 1/2 which will give us 384*1/2 which leaves us with 192.
I have also attached a photo of doing a longer(ish) way than this, that also proves that this equation works. Either one will provide you an answer.
Answer:
John received 10% of the overall votes.
Step-by-step explanation:
Let us assume that the number of votes John got = m
So, the number of votes Vivienne received = 3 times (John's share )
= 3 times m = 3 m
Also, The number of Votes Nassim received = 2 times ( Vivienne's share)
2 x (3 m) = 6 m
Total Votes in the grade 6
= Votes received by { John + Vivienne + Nassim}
= m + (3 m) + (6 m) = 10 m
Hence, the total number of students who voted in grade 6 = 10 m
=
or, The percentage of John's Votes = 10%
Hence, John received 10% of the overall votes.
For this case we have to represent the following expression algebraically:
"10 less than x is -45"
So:
10 less than x is represented as:
Then, the complete expression is represented as:
Adding 10 to both sides of the equation:
Thus, the value of the variable is
Answer: