Since AED forms a straight line, all involved angles sum to 180°. Therefore AEB + BED = 180. Also, since EC bisects BED, BEC = CED, and BED = 2× CED. Now to substitute the first equation:
AEB + BED = 180
AEB + 2×CED = 180
11x-12 + 2(4x+1) = 180
11x-12+8x+2 = 180
19x-10 = 180
19x-10+10 = 180+10
19x = 190
x = 10
So what is m<AEC?? It is the sum of AEB + BEC, and since BEC = CED we can say that:
AEC = AEB + CED
AEC = 11x-12 + 4x+1 = 15x-11 = 15(10)-11 = 150-11
m<AEC = 139°

3 0

4 years ago

There are 8 performers who will present their comedy acts this weekend at a comedy club. One of the performers insists on being

Korvikt [17]

This is a permutations problem. There are only 7 comics you can move into different time slots, the 8th one being fixed in that last position. So you can look at it this way:
For the 1st position, you can choose from all 7 people. Once you've picked that one, you have 6 people to choose from for the 2nd position, and similarly for the remaining ones . This gives you 7x6x5x4x3x2x1 = 5040 ways to arrange them. And the last comic stays in the same position all the time so does not change this number. Make sense? If you need to demonstrate it to yourself, use a smaller number of comics, like 3 or 4, and write out the combinations to see that it works.

7 0

3 years ago

If P'(-1,-3) is obtained by a 180ºccw rotation about the origin what are the coordinates of P?

Nuetrik [128]

-1,3 because your moving the quadrant counter clockwise into the 2nd quadrant

4 0

4 years ago

A welcome kit contains 3 grocery store and seven drugstore coupons. The coupons are worth $45. Another welcome kit contains thre

Kobotan [32]

Answer:

The value of each grocery store coupon is $6

Then the value of each drugstore coupon is $3.

Step-by-step explanation:

Let's define:

G = value of a grocery store coupon.

D = value of a drugstore coupon.

We know that:

"A welcome kit contains 3 grocery store and seven drugstore coupons. The coupons are worth $45"

We can write this as:

3*G + 7*D = $45

And we also know that:

"Another welcome kit contains three grocery store coupons and six drugstore coupons worth $42"

We can write this as:

3*G + 6*D = $42

Then we have the system of equations:

3*G + 7*D = $45

3*G + 6*D = $42

To solve this, we can isolate the term "3*G" in one of the equations (because it appears on both of them)

Let's isolate it on the second equation:

3*G = $42 - 6*D

Now let's replace this on the first equation:

($42 - 6*D) + 7*D = $45

$42 + D = $45

D = $45 - $42 = $3

Then the value of each drugstore coupon is $3.

And we also have the relation:

3*G = $42 - 6*D

We can just replace the value of D to get:

3*G = $42 - 6*$3 = $42 - $24 = $18

G = $18/3 = $6

The value of each grocery store coupon is $6

4 0

3 years ago