#18. C. 1&3
This is be cause when you simplify to y=.. for 4y=3x and 8y=6x, they both turn out to be y=3/4x. The constant of proportionality is 3/4 because both equations simplify to have that as a constant.
#19. D
Kathy can add less than or equal to 7 books to her suitcase.
To cross off the first two choices(A&B), you input a number above 7 and then multiply it by 1 3/4 . Add it to 37 1/2 and it will be more than 50, meaning it will not fit since the suitcase can’t have more than 50 pounds in it.
To cross off C, you would multiply 1 3/4 by 7 and get 12.25. Add 12.25 to 37 1/2 and you will get 49.75 . This result would mean that you can have less than 7 books or just 7 books, leaving the answer to be D.
Answer:
60 miles
Step-by-step explanation:
Ashok and Brian are both walking east along the same path; Ashok walks at a faster constant speed than does Brian. If Brian starts 30 miles east of Ashok and both begin walking at the same time, how many miles will Brian walk before Ashok catches up with him?
Statement 1. Brian’s walking speed is twice the difference between Ashok’s walking speed and his own
Statement 2. If Ashok’s walking speed were five times as great, it would be three times the sum of his and Brian’s actual walking speeds
Solution
A. Brian’s walking speed is twice the difference between Ashok’s walking speed and his own.
Let Brian speed=b
Ashok speed=a
Brian's walking speed=2(a-b)
b=2(a-b)
Divide both sides by 2
b/2=a-b
Ashok catches up in (time)= distance /( relative rate
=30/(a-b)
=30/(b/2)
=30÷b/2
=30*2/b
=60/b.
By that time Brian will cover a distance of
distance=rate*time
=b*60/b
=2(a-b)*60/2(a-b)
=60 miles
(2) If Ashok’s walking speed were five times as great, it would be three times the sum of his and Brian’s actual walking speeds.
5a=3(a+b)
5a=3a+3b
5a-3a=3b
2a=3b
Answer:
or 
Step-by-step explanation:
we know that
The general equation of a horizontal parabola open to the left is equal to
where
(h,k) is the vertex of the parabola
p is the focal distance (distance from the vertex to the focus)
In this problem we have
The vertex is the point (2,-4)
so
The Focus is the point F(1,-4)
so
the focal distance p=2-1=1 ---> distance from the vertex to the focus
substitute in the formula
Step-by-step explanation:
the area of a parallelogram is
baseline × height
the height here is 4 cm.
the baseline is 12 - 2 = 10 cm
the area of the parallelogram is then
10 × 4 = 40 cm²
