Answer:
Solution: x = 2, y = -1 or (2, -1)
Step-by-step explanation:
Equation 1: 2x + y = 3
Equation 2: 5x - 2y = 12
Using the substitution method:
Transform the Equation 1 into its slope-intercept form:
2x + y = 3
2x - 2x + y = -2x + 3
y = 2x + 3
Substitute the value of y = -2x + 3 into Equation 2:
5x - 2y = 12
5x - 2(-2x + 3) = 12
5x + 4x - 6 = 12
9x - 6 = 12
9x - 6 + 6 = 12 + 6
9x = 18
9x/9 = 18/9
x = 2
Substitute the value of x = 2 into Equation 2 to solve for y:
5x - 2y = 12
5(2) - 2y = 12
10 - 2y = 12
10 - 10 - 2y = 12 - 10
-2y = 2
-2y/-2 = 2/-2
y = -1
Double-check whether the values for x and y will provide a true statement for both equations:
Equation 1: 2x + y = 3
2(2) + (-1) = 3
4 - 1 = 3
3 = 3 (True statement)
Equation 2: 5x - 2y = 12
5(2) - 2(-1) = 12
10 + 2 = 12
12 = 12 (True statement)
Therefore, the correct answers are: x = 2; y = -1 or (2, -1).
Answer:
The other leg is 6 and the Hypotenuse is 6√2
Step-by-step explanation:
because it's a 45 45 90 the legs equal and the Hypotenuse is square root 2 times leg
Answer: tan62 = 10/x
Step-by-step explanation: Let me know if you need an explanation.
By applying Pythagorean theorem, we have proven that the point (-1/2, -√3/2) lies on the unit circle.
<h3>How to prove this point lies on the unit circle?</h3>
In Trigonometry, an angle with a magnitude of -120° is found in the third quarter and as such, both x and y would be negative. Also, we would calculate the reference angle for θ in third quarter as follows:
Reference angle = 180 - θ
Reference angle = 180 - 120
Reference angle = 60°.
For the coordinates, we have:
sin(-120) = -sin(60) = -1/2.
cos(-120) = -cos(60) = -√3/2.
By applying Pythagorean theorem, we have:
z² = x² + y²
z = √((-1/2)² + (-√3/2)²)
z = √(1/4 + 3/4)
z = √1
z = 1.
Read more on unit circle here: brainly.com/question/9797740
#SPJ1
The answer is:
B. The cost for a group of friends to see a movie compared to the number of friends.
We can tell that this is most likely to have a constant rate of change because of what we already know about movie prices.
Movie prices are fixed, therefore, no matter how many friends you bring, the total price will always go up by the same amount.
For example:
Let's say a movie ticket costs $5 and you brought 3 friends with you. Since there are 4 people in total, you'd have to pay $20 for the tickets (5x4=20). Just as you're about to pay, Sally shows up. Now you have to pay for 5 people in total. How much do you need to pay now?
You will now need to pay $25 (5x5=25) for all of the tickets. Even though you now have 5 people in the group, you still only have to pay $5 for each ticket.
This is an example of a constant rate of change.
