Answer:
Given the statement: Kite QRST has a short diagonal of QS and a long diagonal of RT. The diagonals intersect at point P.
Properties of Kite:
- The diagonals are perpendicular
- Two disjoint pairs of consecutive sides are congruent by definition of kite
- One diagonal is the perpendicular bisector to the other diagonal.
It is given that: Side QR = 5m and diagonal QS = 6m.
Then, by properties of kite:
Substitute the value of QS we get QP;
= 3 m
Now, in right angle 
Using Pythagoras theorem:
Substitute the given values we get;
or
Subtract 9 from both sides we get;
Simplify:
Therefore, the length of segment RP is, 4m
Answer:
MO = 17
Step-by-step explanation:
First, you need to define what if the unknown x.
segment MN and NO are equal to MO.
thus, your equation for the combination is x +8
Now set the values equal to each other
x + 8 = 3x - 10 (subtract x from both sides)
8 = 2x - 10 ( get your x value alone, add 10 to both sides)
18 = 2x (simplfy)
x = 9
Now plug x value into MO
3 (9) - 10 = 17
Check with opposing equation:
9 + 8 = 17 √
Answer: altitude at starting point is -11ft or 11ft below sea level
Step-by-step explanation:
Equation for this situation will be
A = Ag - 11
A = actual altitude
Ag = altitude gained.
At starting point, altitude gained is zero, therefore;
A = 0 - 11
A = -11ft
Basically, you have two circles. You are asked to take circle 1 and "move it" so that it is on top of circle 2. This process of moving is called a translation and can be thought of as sliding. You do this by ensuring that the two have the same center. So, starting at (-4,5) how do you have to move to end up at (2,1)?
To do this we need to move right 6 as the x-coordinate goes from -4 to 2. We also need to move down 4 as the y-coordinate goes from 5 to 1. So we add 6 to the x-coordinate and subtract 4 from the y-coordinate. The transformation rule is (x+6, y-4).
Once you do this the circles have the same center. Next you wish to dilate circle 1 so it ends up being the same size at circle 2. That means you stretch it out in such a way that it keeps its shape. Circle 1 has a radius of 2 centimeters and circle 2 has a radius of 6 centimeters. That is 3x bigger. So we dilate by a factor of 3.
Translations and dilations (along with reflections and rotations) belong to a group known as transformations.
Answer:
95% Confidence interval = (23.4,26.2)
Step-by-step explanation:
In this problem we have to develop a 95% CI for the mean.
The sample size is n=49, the mean of the sample is M=24.8 and the standard deviation of the population is σ=5.
We know that for a 95% CI, the z-value is 1.96.
The CI is
