Triangle a b c is shown with an angle bisector and two congruent sides. side a b is congruent to side a c. segment a d is the bisector of angle a. point d is on side b c. angle b a d is labeled y degrees. angle b d a is labeled x degrees. angle a c d is labeled 47 degrees. find the values of x and y.

x=90 degrees, y=43 degrees

Step-by-step explanation:

The triangle ABC is an isosceles triangle with congruent sides AB and AC.  Therefore, the angles ABC and ACB are equal. Segment AD is the bisector of angle A (or BAC). The angle ACD is given as 47 degrees. So, angles ABC and ACB are 47 degrees each, since the point D is on side BC. The angle BAC is 180-2(47) degrees which is 86 degrees. Since AD is bisector of the angle BAC, BAD is 86/2=43 degrees . From the triangle BAD, angle of BDA is 180 - (the angle ABD + the angle BAD) = 180 -(47+43)=90 degrees. So x=90 and y=43 degrees.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

~