Answer:
3x +8y = -17
Step-by-step explanation:
The point-slope equation is a good place to start.
y -k = m(x -h) . . . . . equation through (h, k) with slope m
Filling in your numbers gives ...
y +4 = -3/8(x -5)
Multiplying by 8, we get
8y + 32 = -3x + 15
Adding 3x-32 puts this in standard form.
3x + 8y = -17
_____
Standard form is ...
ax +by = c
where a, b, c are mutually-prime integers and the leading coefficient is positive. (If a=0, the leading coefficient is b.)
yuhhdhisjehe yup yup yup yup yup yup
So this is considered a "special triangle." The 30-60-90 triangle states that if the short leg is x, then the hypotenuse is 2x and the long leg is x√3.
Since we have the short leg, to find the hypotenuse, or y in this case, multiply the short leg by 2:
17 × 2 = 34
Next, to find the long leg, or x in this case, multiply the short leg by √3:
17 × √3 = 17√3
<u>In short, x = 17√3 and y = 34. The correct option is the last option.</u>
Answer: 200 adult tickets and 400 student tickets were sold.
Step-by-step explanation:
Let x represent the number of adult tickets that were sold.
Let y represent the number of student tickets that were sold.
Adult tickets to a play cost $1.75 each and student tickets cost $1.25 each. If the income from the play was $850, the expression would be
1.75x + 1.25y = 850- - - - - - - - - -1
Suppose there are twice as many student tickets sold as adult tickets. This is expressed as
y = 2x
Substituting y = 2x into equation 1, it becomes
1.75x + 1.25 × 2x = 850
1.75x + 2.5x = 850
4.25x = 850
x = 850/4.25
x = 200
y = 2x = 2 × 200
y = 400
Answer: b. The adjacent angles formed by two intersecting lines are supplementary.
Step-by-step explanation:
In the given picture , we can see that there are intersecting lines with adjacent angles which have shown.
If we add the adjacent angles for each pair of intersecting lines we get,
Therefore,b is the right option "The adjacent angles formed by two intersecting lines are supplementary."
- Two Angles are supplementary when their sum is 180 degrees.
- Two Angles are complementary when their sum is 90 degrees.
- Vertical angles are always equal.
