Answer:
x = -2
y = 5
Step-by-step explanation:
2x - 3y = -19 ---------------------------(I)
7x+ 7y = 21 -----------------------------(II)
Multiply equation (I) by 7 and equation (II) by 3.Then add and so y will be eliminated and you will get the value of x
(I)*7 14x - 21y = - 133
(II)* 3 <u> 21x + 21y = 63 </u> {Now add}
35x = -70
x = -70/35
x = - 2
Plug in x = - 2 in equation (I)
2*(-2) - 3y = -19
-4 - 3y = -19
-3y = -19 + 4
-3y = -15
y = -15/-3
y = 5
<h3>
Answer: 72%</h3>
Explanation:
The phrasing "given that he or she is a graduate" means we focus on the middle row only. We ignore everything else.
We see that A = 1879 graduates receive financial aid out of B = 2610 graduates total.
This means the probability we want is therefore A/B = 1879/2610 = 0.7199 approximately. This converts to 71.99% and that rounds to 72%
Answer:
x = 6, 9
Step 1:
To solve this equation, we need to subtract 3 from both sides like this:
Step 2:
We square both sides (multiply using FOIL) to get rid of the radical.
If you did not understand how these were done, here is an example:
(x + 1)(x + 2)
First terms: x * x = <u><em>x^2</em></u>
Outer terms: x * 2 = 2x
Inner terms: 1 * x = x
2x - x = <u><em>x</em></u>
Last terms: 1 * 2 =<em> </em><u><em>2</em></u>
x^2 + x + 2
Step 3:
Solve for x:
9x - 45 = x^2 - 6x + 9
x^2 - 6x + 9 (+45) = 9x - 45 (+45)
x^2 - 6x + 54 (-9x) = 9x (-9x)
x^2 - 15x + 54 = 0
Factor:
(x^2 - 6x) + (- 9x + 54)
x(x - 6) - 9(x - 6)
Factor out (x - 6):
(x - 6)(x - 9) = 0
x - 6 = 0; 6 - 6 = 0
x - 9 = 0; 9 - 9 = 0
Our anwer: x = 6, 9
As consecutive odd numbers differ by two (example: 3, 5, 7), the first odd number can be expressed as 2n + 1, the next can be found by adding two to the first to get 2n + 1 + 2 which simplifies to 2n + 3. Finally the expression for the third consecutive odd integer can be found by adding two to the previous, 2n + 3, to get 2n + 5. Adding these three together and setting them equal to your sum gets the equation
2n + 1 + 2n + 3 + 2n + 5 = 63
Combine like terms and solve For n.
Once you have n, you must substitute it back into your three expressions (2n + 1, 2n + 3, 2n + 5) to find the three odd integers.
Hope this helps :)
Answer:
right angle ( right )
Step-by-step explanation:
Pythagoras' theorem only works for right-angled triangles, so you can use it to test whether a triangle has a right angle or not. In the triangle above, if a 2 < b 2 + c 2 the angle is acute.
