Emmanuel bought 28 lb of potting soil this week. This amount is 4 lb more than twice the amount of potting soil he bought last w
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
It is given that a box contains 2 dozen pairs of contact lenses ,of which 8 pairs are tinted.
1 dozen = 12 units
Total pairs of contact lenses
Tinted pairs of contact lenses = 8
Pairs of contact lenses not tinted = 24 - 8 = 16
If a pair of contact lenses is drawn at random from the box, then we need to find the probability that it is not tinted.
Therefore, the required probability is
Answer: x = 10
========================================================
Explanation:
Check out the attached image. I've basically redrawn your image and added point D. This point is the intersection of the angle bisector and segment BC. The red angle (DAC) and the green angle (DAB) are congruent.
The reason why I added point D is to help with the angle bisector theorem. This theorem states that if we have a triangle ABC, and angle A is bisected (as the diagram shows), then we can set up the following proportion
AB/BD = AC/CD
Note how AB and BD are on the left side of point D, and they form the ratio AB/BD. Similarly, AC and CD are to the right of point D so they form the ratio AC/CD. These two ratios are equal by the angle bisector theorem.
---------------------
Let's plug in the given info and then isolate x
AB/BD = AC/CD
8/(x+4) = 12/(2x+1)
8(2x+1) = 12(x+4) ... cross multiply
8(2x)+8(1) = 12(x)+12(4) ... distribute
16x+8 = 12x+48
16x+8-8 = 12x+48-8 ... subtract 8 from both sides
16x = 12x+40
16x-12x = 12x+40-12x ... subtract 12x from both sides
4x = 40
4x/4 = 40/4 ... divide both sides by 4
x = 10
---------------------
Check:
8/(x+4) = 12/(2x+1)
8/(10+4) = 12/(2*10+1) ... replace every x with 10
8/(10+4) = 12/(20+1)
8/14 = 12/21
4/7 = 4/7
Answer is confirmed
========================================================
Explanation:
Check out the attached image. I've basically redrawn your image and added point D. This point is the intersection of the angle bisector and segment BC. The red angle (DAC) and the green angle (DAB) are congruent.
The reason why I added point D is to help with the angle bisector theorem. This theorem states that if we have a triangle ABC, and angle A is bisected (as the diagram shows), then we can set up the following proportion
AB/BD = AC/CD
Note how AB and BD are on the left side of point D, and they form the ratio AB/BD. Similarly, AC and CD are to the right of point D so they form the ratio AC/CD. These two ratios are equal by the angle bisector theorem.
---------------------
Let's plug in the given info and then isolate x
AB/BD = AC/CD
8/(x+4) = 12/(2x+1)
8(2x+1) = 12(x+4) ... cross multiply
8(2x)+8(1) = 12(x)+12(4) ... distribute
16x+8 = 12x+48
16x+8-8 = 12x+48-8 ... subtract 8 from both sides
16x = 12x+40
16x-12x = 12x+40-12x ... subtract 12x from both sides
4x = 40
4x/4 = 40/4 ... divide both sides by 4
x = 10
---------------------
Check:
8/(x+4) = 12/(2x+1)
8/(10+4) = 12/(2*10+1) ... replace every x with 10
8/(10+4) = 12/(20+1)
8/14 = 12/21
4/7 = 4/7
Answer is confirmed