1) In △XYZ , XZ=7 , YZ=7 , and XY=6
What is the area of the triangle?
Enter your answer, in simplified radical form, in the box.

2) The arc length of an arc subtended by an angle measuring 13π18 radians is 18.4 inches.
What is the radius of the arc?
A) approximately 6.5 inches
B) approximately 7.3 inches
C) approximately 8.1 inches
D) approximately 12.6 inches

3) The radius of a circle measures 7 inches. A central angle of the circle measuring 4π15 radians cuts off a sector.
What is the area of the sector?
Enter your answer, as a simplified fraction, in the box.

Question 1.

The sketch of △XYZ is shown in the attachment .

Area of triangle XYZ

The base is |XY|=6.

We use the Pythagoras Theorem to find the height, h as follows:

The area then becomes:

The area of the triangle is 6√10 square units.

Question 2

We want to find the radius of an arc that subtends an angle of

radians and arc length is 18.4 inches.

We substitute these values into the following relation and solve for r.

This implies that:

C) approximately 8.1 inches

Question 3.

The area of a sector in radians is given by:

From the question the radius is r=7 inches and

We substitute into the formula to get:

square inches

answer: the two figures are congruent.

step-by-step explanation: they're congruent because figure efgh is reflected across the x and y axis but it was also rotated.

hope it !

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.