Answer:
The solution to the system of equation would be the two order pairs (2,10) and (-1,16)
Explanation:
The solution means the value of x that satisfies both equations.
Therefore, we will equate the two equations given and solve for x.
The first is: y = x^2 - 3x + 12
The second is : y = -2x + 14
Equate both and solve for x as follows:
x^2 - 3x + 12 = -2x + 14
x^2 - 3x + 2x + 12 - 14 = 0
x^2 - x - 2 = 0
(x-2)(x+1) = 0
either x = 2 and y = (2)^2 - 3(2) + 12 = -2(2) + 14 = 10
or x = -1 and y = (-1)^2 - 3(-1) + 12 = -2(-1) + 14 = 16
Therefore, the solution to the system of equation would be the two order pairs (2,10) and (-1,16)
Hope this helps :)
Answer:
For Triangle 1
a. Hypothenus = 4
b. Adjacent = 2√3
For Triangle 2:
a. Hypothenus = 2√2
b. Adjacent = 2
Step-by-step explanation:
For Triangle 1
NOTE: We shall be using angle 30°.
a. Determination of the Hypothenus.
Opposite = 2
Angle (θ) = 30°
Hypothenus =?
Sine θ = Opposite /Hypothenus
Sine 30 = 2 / Hypo
0.5 = 2 / Hypo
Cross multiply
0.5 × Hypo = 2
Divide both side by 0.5
Hypo = 2 / 0.5
Hypothenus = 4
b. Determination of the Adjacent
NOTE: We shall be using angle 30°.
Opposite = 2
Angle (θ) = 30°
Adjacent =?
Tan θ = Opposite / Adjacent
Tan 30 = 2 / Adj
1 / √3 = 2 / Adj
Cross multiply
1 × Adj = 2 × √3
Adjacent = 2√3
For Triangle 2:
a. Determination of the Hypothenus.
Opposite = 2
Angle (θ) = 45°
Hypothenus =?
Sine θ = Opposite /Hypothenus
Sine 45 = 2 / Hypo
1 / √2 = 2 / Hypo
Cross multiply
1 × Hypo = 2 × √2
Hypothenus = 2√2
b. Determination of the Adjacent
Opposite = 2
Angle (θ) = 45°
Adjacent =?
Tan θ = Opposite / Adjacent
Tan 45 = 2 / Adj
1 = 2 / Adj
Cross multiply
1 × Adj = 2
Adjacent = 2
Theo got an 80% on the quiz because you multiply to get a equivalent fraction since a hundred is a whole of a percent. So basically, the percent is 80% and the decimal is 0.80.
Hope it helps!
Hoi!
Here's how you would write this.
z - 34.7 = 68.2
"Less than" indicates subtraction, but from what? "Less than z", so we're subtracting something from z. If you look at the equation, how would we calculate 34.7 less than z? To do this, we would subtract 34.7 from z. Since we're given our answer to the equation, just slap that into the equation after an "equals" symbol, and you're finished!
