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3 years ago

Solving x + 3y = 5 and -x - y = -3 by eliminationg.

Mathematics

1 answer:

Marina CMI [18]3 years ago

4 0

Answer:

(x, y) = (2, 1)

Step-by-step explanation:

The x-coefficients are opposites of each other, so the x variable will be eliminated if the two equations are added.

(x +3y) +(-x -y) = (5) +(-3)

2y = 2

y = 1

Substituting into the first equation gives ...

x +3(1) = 5

x = 2 . . . . . . . subtract 3

The solution is (x, y) = (2, 1).

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What is the image of the point (3,4) after a rotation of 90 degree counterclockwise about the origin

jeka57 [31]

Answer:

(- 4, 3 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x ) , then

(3, 4 ) → (- 4, 3 )

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2 years ago

Which expression gives the distance between the points (-3,4 and (6,-2)

krok68 [10]

Answer:

10.8

Step-by-step explanation:

We can find the distance using the distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

We then substitute (-3,4) as $(x_1,y_1)$ and (6,-2) as $(x_2,y_2)$ .

$d=\sqrt{(6--3)^2+(-2-4)^2} \\d=\sqrt{(9)^2+(-6)^2} \\d=\sqrt{81+36}\\d=\sqrt{117}=10.8$

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3 years ago

What is 8 - 7x = 1 find x

Natali5045456 [20]

Answer:

x=1

Step-by-step explanation:

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1 year ago

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2 years ago

Determine the solution set of x2 - 80 = 0. {± } {±4 } {±2 }

Ne4ueva [31]

Answer: $\Big\{\pm 4\sqrt{5} \Big\}$

This is the shorthand way of writing $\Big\{4\sqrt{5}, -4\sqrt{5} \Big\}$

=====================================================

Work Shown:

$x^2 - 80 = 0\\\\x^2 = 80\\\\x = \pm\sqrt{80}\\\\x = \pm\sqrt{16*5}\\\\x = \pm\sqrt{16}*\sqrt{5}\\\\x = \pm4\sqrt{5}\\\\x = 4\sqrt{5} \ \text{ or } \ x = -4\sqrt{5}\\\\$

The plus or minus is needed because squaring a negative leads to a positive. As another example, x^2 = 25 has x = 5 and x = -5 as the two solutions. Note that x^2 = (-5)^2 = (-5)*(-5) = 25.

Also, note that the 80 was broken up into 16*5. This was done to simplify the square root. We pull out the largest factor that's a perfect square.

So that's how we get to the solution set $\Big\{\pm 4\sqrt{5} \Big\}$ . The curly braces tell the reader that they are dealing with a set.

7 0

2 years ago