A pair of linear equations is shown below: y = −2x + 3 y = −4x − 1 Which of the following statements best explains the steps to solve the pair of equations graphically? Graph the first equation, which has slope = 3 and y-intercept = −2, graph the second equation, which has slope = −1 and y-intercept = −4, and find the point of intersection of the two lines. Graph the first equation, which has slope = −3 and y-intercept = 2, graph the second equation, which has slope = 1 and y-intercept = 4, and find the point of intersection of the two lines. Graph the first equation, which has slope = −2 and y-intercept = 3, graph the second equation, which has slope = −4 and y-intercept = −1, and find the point of intersection of the two lines. Graph the first equation, which has slope = 2 and y-intercept = −3, graph the second equation, which has slope = 4 and y-intercept = 1, and find the point of intersection of the two lines.
Answers
The answer is A) On a graph, find the point of intersection of two lines; the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1.
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The number of pens in each bag if Adams puts 3/4 of a bag of pens in 3 boxes is of a bag.
Given that:
Adams puts a fraction of of a bag of pens in 3 boxes.
It is required to find the number of pens in each box.
Total number of a fraction of pens available = of a bag
These pens are equally distributed among 3 boxes.
So, each box will have an equal number of pens.
So, the number of pens in each box is:
Take the reciprocal of the second number and the operation becomes multiplication.
Hence, the number of pens in each box is of a bag.
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Answers
The calculated product of the numbers without calculator is 9
How to calculate the product of the numbers
From the question, we have the following parameters that can be used in our computation:
1/4 of 36 without calculator
When represented as an equation, we have
1/4 of 36 = 1/4 * 36
Multiply 1 by 36
So, we have the following result
1/4 of 36 = 36/4
Divide 36 by 4
1/4 of 36 = 9
Using the above as a guide, we have the following:
the result is 9
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Answers
"a number" = x
"decreased by 5" = -5
"is less than 32" = <32
x - 5 < 32
That is the equation.
If you solve it...
x < 32+ 5
x < 37
x can be any number less than 37 to keep the equation true.
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The next would be the principle that states that all powers not under the Federal government would be under the power of the State.
Answer: The three branches of government
Step-by-step explanation:Legislative, Judicial, and executive
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Factor this by their GCF which is 6ab
6ab(4ab-3)
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Perfume A (a) costs $11 per ounce and perfume B (b) costs $19 per ounce. So, the expressions, 11a and 19b represent the cost of each perfume in the 5-ounce bottle. Because the perfume maker wants the bottle to cost $71, add the expressions 11a and 19b and set the sum equal to 71:
11a + 19b = 71
You would first make a table to help sort out the info. The table will have 3 rows and those rows will be PerfA, PerfB, and mix. The table will have 3 columns and those will be, from left to right, # oz, cost, total (which is the product of the first 2 columns). In the first row first column we will put an x, since we don't know how many ounces of perfume A we have. The cost of perfume A is 11, so that number goes in the first row second column. The total for the first row is x * 11 which is 11x. Now we move to row 2. We put a y in the second row first column since we don't know how much of perfume B we have. We do know that it costs 19 per ounce, so 19 goes in row 2 column 2. The product of those 2 is 19y. In row 3 first column we put a 5 since the maker wants the mix of A and B to be 5 ounces. In row 3 column 2 we put 71, since the maker wants the mix to cost 71. The product of those 2 numbers is 355. If you go straight down the first column, you have that the number of ounces of A (x) + the number of ounces of B (y) = 5, or x + y = 5. That equation relates the number of ounces to each other that is in the mix. We are looking for the money equation, which is going straight down the 3 column. This column relates the cost of A and B to each other that is in the mix. Standard form for an equation is Ax + By = C, so for us that will be 11x + 19y = 355. There you go!