Solve each system of linear equations by substitutions.1. 3x-2y=9 y=2x-7
2. Y=x-4 2x+y=5
3. X+4y=6 y=-x+3

Answers

Answer 1

Answer: 1.
$3x-2y=9 \n y=2x-7 \n \n \hbox{substitute 2x-7 for y in the 1st equation:} \n 3x-2(2x-7)=9 \n 3x-4x+14=9 \n -x=9-14 \n -x=-5 \n x=5 \n \n y=2x-7=2 * 5-7=10-7=3 \n \n \boxed{(x,y)=(5,3)}$

2.
$y=x-4 \n 2x+y=5 \n \n \hbox{substitute x-4 for y in the 2nd equation:} \n 2x+x-4=5 \n 3x=5+4 \n 3x=9 \n x=3 \n \n y=x-4=3-4=-1 \n \n \boxed{(x,y)=(3,-1)}$

3.
$x+4y=6 \n y=-x+3 \n \n \hbox{substitute -x+3 for y in the 1st equation:} \n x+4(-x+3)=6 \n x-4x+12=6 \n -3x=6-12 \n -3x=-6 \n x=2 \n \n y=-x+3=-2+3=1 \n \n \boxed{(x,y)=(2,1)}$

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Write three different improper fractions that equal 4 1/2

Answers

To find the first improper fraction, multiply the denominator by the whole number and add the numerator, In the new fraction, the denominator remains the same:

2 x 4 = 8
8 + 1 = 9

9/2 is the first improper fraction.

To find two more fractions equivalent to this one, simply multiply both the numerator and the denominator by the same number:

9 x 2 = 18
2 x 2 = 4

18/4 is another improper fraction.

9 x 3 = 27
2 x 3 = 6

And 27/6 is a third improper fraction.

The three different improper fractions of 4 1/2 are 9/2, 18/4, and 36/8.

To express the mixed number 4 1/2 as three different improper fractions, we need to convert it to an improper fraction first. A mixed number consists of a whole number part and a fraction part.

Converting 4 1/2 to an improper fraction:

We multiply the whole number (4) by the denominator of the fraction (2) and add the numerator (1) to get the new numerator. The denominator remains the same.

Improper fraction: (4 x 2 + 1) / 2 = 9/2

Now, we can represent 4 1/2 as three different improper fractions:

9/2 - The original improper fraction we calculated.

18/4 - We multiplied both the numerator and denominator by 2 to get an equivalent fraction.

36/8 - We further multiplied both the numerator and denominator by 2 again to get another equivalent fraction.

All three improper fractions are different representations of the mixed number 4 1/2. They have the same value but are written with different numerators and denominators.

To learn more about the improper fraction;

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Write the expression 7x^10 + 6x^5 + 5 in quadratic form.a 7x P) + 6x +5
7x10 + 6(x+0 x
6. 7(x)* +6x? +5
7720 + 6(220)2 = 5

Answers

For this case we have the following expression:

$7x^(10) + 6x ^ 5 + 5$

We must rewrite it quadratically:

By definition, a quadratic equation is of the form:

$ax ^ 2 + bx + c = 0$

Now, suppose $u = x ^ 5$

Rewriting the given expression with the change of variable we have:

$7u ^ 2 + 6u + 5$

So, we have a quadratic expression.

Returning the change we have:

$7 (x ^ 5) ^ 2 + 6 (x ^ 5) +5$

ANswer:

Option B

Misty has 36 pairs of shoes arranged on a number of shelves

Answers

it would be 6 shelves because she has 36 pairs of shoes and if she put 6 pairs on it row it would be 6 shelves

the editor of the school newspaper must reduce the size of a graph to fit in one column. The original graph is 2 inches by 2 inches, and the scale factor from the original to the reduced graph is 8:3. Find the dimensions of the graph as it will appear in one column in the newspaper