Answer:
4x + 10y = 36 ≡ to 2x + 5y = 18
As you can see, the the coefficients on the first one are double those in the second.
12x - 9y = -60 ≡ to -4x + 3y = 20
In this case, the terms in the first one are all the same, but multiplied by -3
And by simple elimination we can say:
-24x - 8y = 40 ≡ -6x - 2y = 10
In this case, the terms of the first equation are equal to those of the latter, but all multiplied by 4.
Answer:
A.
Step-by-step explanation:
4 < 6t + 1 ≤ 43 (Given)
3 < 6t ≤ 42 (Subtracted 1 on both sides)
1/2 < t ≤ 7 (Divided 6 on both sides)
You are looking for an open dot on 1/2 and a shaded dot on 7 with a line between them. Therefore, the answer is A.
Answer:
C
Step-by-step explanation:
We have the equation:
![4x^2+5x=-10](https://tex.z-dn.net/?f=4x%5E2%2B5x%3D-10)
Add 10 to both sides to isolate the equation.
![4x^2+5x+10=0](https://tex.z-dn.net/?f=4x%5E2%2B5x%2B10%3D0)
This is not factorable*, so we can use the quadratic formula:
![\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
In this case, <em>a</em> = 4, <em>b</em> = 5, and <em>c</em> = 10.
Substitute:
![\displaystyle x=\frac{-(5)\pm\sqrt{(5)^2-4(4)(10)}}{2(4)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B-%285%29%5Cpm%5Csqrt%7B%285%29%5E2-4%284%29%2810%29%7D%7D%7B2%284%29%7D)
Simplify:
![\displaystyle x=\frac{-5\pm\sqrt{-135}}{8}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B-5%5Cpm%5Csqrt%7B-135%7D%7D%7B8%7D)
Since we cannot take the root of a negative, we have no real solutions.
Our answer is C.
*To factor something in the form of:
![ax^2+bx+c=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0)
We want two numbers <em>p</em> and <em>q</em> such that <em>pq</em> = <em>ac</em> and <em>p</em> + <em>q</em> = <em>b</em>.
Since <em>ac</em> = 4(10) = 40. We need to find two whole numbers that multiply to 40 and add to 5.
No such numbers exist, so the equation is not factorable.
Answer:
9/10 pounds
Step-by-step explanation:
3/5 × 1 1/2
= 9/10