Step-by-step explanation:
Square root of 25 can be +5 or -5
Square root of 16 can be +4 or -4.
As -5 can be square root of 25 and +4 can be a root of 16 , -5 < +4 . That's why square root of 25 could be less than square root of 16.
Looking at the first system of equations,
16x - 10y = 10
-8x - 6y = 6
If we multiply both sides of the second equation by 2, the coefficient of x is exactly the negative of the coefficient of x in the first equation.
-8x - 6y = 6
⇒ 2 (-8x - 6y) = 2 (6)
⇒ -16x - 12y = 12
By combining this new equation with the first one, we can eliminate x and solve for y :
(16x - 10y) + (-16x - 12y) = 10 + 12
⇒ -22y = 22
⇒ y = -1
Then we just solve for x by replacing y in either equation.
16x - 10y = 10
⇒ 16x - 10 (-1) = 10
⇒ 16x + 10 = 10
⇒ 16x = 0
⇒ x = 0
The main idea behind elimination is combining the given equations in just the right amount so that one of the variables disappears. The "right amount" involves using the LCM of the coefficients of a given variable. In this example, the x-coefficients had LCM(8, 16) = 16, so we only had to scale one of the equations (the one with -8x) to cancel all the x terms.
If we wanted to eliminate y first instead, we first note that LCM(6, 10) = 30. To get 30 as a coefficient on y, in the first equation we would have multiplied by 3:
16x - 10y = 10
⇒ 3 (16x - 10y) = 3 (10)
⇒ 48x - 30y = 30
And in the second equation, we would have multiplied by -5 (negative so that upon combining the equations, we end up with -30y + 30y = 0):
-8x - 6y = 6
⇒ -5 (-8x - 6y) = -5 (6)
⇒ 40x + 30y = -30
Now combining the two scaled equations gives
(48x - 30y) + (40x + 30y) = 30 + (-30)
⇒ 88x = 0
⇒ x = 0
We then solve for y :
16x - 10y = 10
⇒ -10y = 10
⇒ y = -1
so we end up with the same solution as before.
Answer:
12
Step-by-step explanation:
The angle equals 90 degrees so (8*12-6) would equal 90
Y intercept is where the line meets the Y axis
So the points shd be in (0,y) form.
So (0,0) (0,-7) (0,-0.25) are the y-intercepts in the following.
Answer:
9.6 cm
Step-by-step explanation:
Since the shapes are similar, we can write a proportion. Let x be the length of MN.
9/12 = 7.2/x Write a proportion.
9x = 12(7.2) Use cross products.
9x = 86.4 Multiply.
x = 9.6 Divide both sides by 9.
Side MN is 9.6 cm.
