Answer:
1) -1/4
2) -1/2
3) 1/3
Step-by-step explanation:
perpendicular lines' slopes are opposite reciprocals so you flip it and change the positive or negative sign
parallel lines have the same slope
If we draw a perpendicular line from one of the vertices of the triangle we get 2 right angled triangles each with altitude 9 ins and vertex angle = 30 degrees. So:-
cos 30 = 9 /h where h = one of the sides of the equilateral triangle
h = 9 / cos 30 = 10.392 inches
Therefore the perimeter of the triangle = 3 * 10.392 = 31.1769 ins
Answer is 31.18 inches to the nearest hundredth.
Think of debt to GDP as a fraction. Debt / GDP
<span>So the two ways the ratio can decrease is if the nominator decreases (for example 2/3 goes to 1/3), or the denominator increases (1/3 goes to 1/4).
Dose this help?</span>
d) You have a <u>difference of squares</u>:
49y² - 9 = (7y)² - 3²
Recall the identity,
a² - b² = (a - b) (a + b)
So,
49y² - 9 = (7y - 3) (7y + 3)
e) Pull out the common factor 3 from each term:
3x² - 3x - 90 = 3 (x² - x - 30)
Now use the <u>sum-product method</u>. Notice that we can write 30 = 5 • 6, and 5 - 6 = 1, so
3x² - 3x - 90 = 3 (x + 5) (x - 6)
f) Same as in (e), use the <u>sum-product method</u>. Notice that 42 = 7 • 6, and -7 - 6 = -13, so
x² - 13x + 42 = (x - 7) (x - 6)
