<h3>
Answer: Choice D. </h3>
The red angle markers show those two angles are congruent. That's one "A" of "ASA". The S refers to a congruent pair of sides. We don't have any tickmarks to indicate congruent pairs; however, we do know that QR = QR is a shared side that overlaps (reflexive theorem). So this is the "S" in "ASA".
The thing missing is the angle Q of the top triangle, and also of the bottom triangle as well. If we know those two angles are congruent, then we have enough info to use ASA. More specifically, if we know that , then we can use ASA.
One thing to notice is that the other answer choices involve side lengths and not angles. This implies that if A, B or C were one of the answers, then we would have something like SAS or SSS. But instead we want ASA. So we can immediately rule choices A,B, and C out.
Answer:
The 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2 is (-8.04, 0.84).
Step-by-step explanation:
The (1 - <em>α</em>)% confidence interval for the difference between population means is:
The information provided is as follows:
The critical value of <em>z</em> for 98% confidence level is,
Compute the 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2 as follows:
Thus, the 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2 is (-8.04, 0.84).
1 /5 = 0 . 2
45 * . 2 = 9
Hope this helped :)
Answer:
a = 11.71 ; b = 15.56
Step-by-step explanation:
For this problem, we need two things. The law of sines, and the sum of the interior angles of a triangle.
The law of sines is simply:
sin(A)/a = sin(B)/b = sin(C)/c
And the sum of interior angles of a triangle is 180.
45 + 110 + <C = 180
<C = 25
We can find the sides by simply applying the law of sines.
length b
7/sin(25) = b/sin(110)
b = 7sin(110)/sin(25)
b = 15.56
length a
7/sin(25) = a/sin(45)
a = 7sin(45)/sin(25)
a = 11.71
<h3>Given</h3>
trapezoid PSTK with ∠P=90°, KS = 13, KP = 12, ST = 8
<h3>Find</h3>
the area of PSTK
<h3>Solution</h3>
It helps to draw a diagram.
∆ KPS is a right triangle with hypotenuse 13 and leg 12. Then the other leg (PS) is given by the Pythagorean theorem as
... KS² = PS² + KP²
... 13² = PS² + 12²
... PS = √(169 -144) = 5
This is the height of the trapezoid, which has bases 12 and 8. Then the area of the trapezoid is
... A = (1/2)(b1 +b2)h
... A = (1/2)(12 +8)·5
... A = 50
The area of trapezoid PSTK is 50 square units.