Answer:
The value of the side PS is 26 approx.
Step-by-step explanation:
In this question we have two right triangles. Triangle PQR and Triangle PQS.
Where S is some point on the line segment QR.
Given:
PR = 20
SR = 11
QS = 5
We know that QR = QS + SR
QR = 11 + 5
QR = 16
Now triangle PQR has one unknown side PQ which in its base.
Finding PQ:
Using Pythagoras theorem for the right angled triangle PQR.
PR² = PQ² + QR²
PQ = √(PR² - QR²)
PQ = √(20²+16²)
PQ = √656
PQ = 4√41
Now for right angled triangle PQS, PS is unknown which is actually the hypotenuse of the right angled triangle.
Finding PS:
Using Pythagoras theorem, we have:
PS² = PQ² + QS²
PS² = 656 + 25
PS² = 681
PS = 26.09
PS = 26
The correct transformation is a rotation of 180° around the origin followed by a translation of 3 units up and 1 unit to the left.
<h3>
Which transformation is used to get A'B'C'?</h3>
To analyze this we can only follow one of the vertices of the triangle.
Let's follow A.
A starts at (3, 4). If we apply a rotation of 180° about the origin, we end up in the third quadrant in the coordinates:
(-3, -4)
Now if you look at A', you can see that the coordinates are:
A' = (-4, -1)
To go from (-3, -4) to (-4, -1), we move one unit to the left and 3 units up.
Then the complete transformation is:
A rotation of 180° around the origin, followed by a translation of 3 units up and 1 unit to the left.
If you want to learn more about transformations:
brainly.com/question/4289712
#SPJ1
Answer:
N(t) = 0.188t + 22.76
Step-by-step explanation:
Number of licensed drivers in 2004 = 22.76 million
Number of licensed drivers in 2009 = 23.7 million
Number of licensed drivers, N as a function of t since year 2004 ;
General form of a linear function :
y = mx + c
c = intercept ; m = slope
Intercept c = value of y ; when x = 0
Here, population after uerssmmx,
Hence,
In 2004 ;
22.76 = mx + c
x = 0
22.76 = c
Number in 2009
x = number of yesrs after 2004 ; x = 2000 - 2004 = 5years
We can find the slope :
y = m*5 + 22.76
y = 23.7 in 2009
23.7 = 5m + 22.76
23.7 - 22.76 = 5m
m = 0.94 / 5
m = 0.188
Hence, the linear function can be written as :
N(t) = 0.188t + 22.76
Answer:
A
Step-by-step explanation:
Given
4n² + 4(4m³ + 4n² ) ← distribute terms in parenthesis by 4
= 4n² + 16m³ + 16n² ← collect like terms
= (4n² + 16n²) + 16m³
= 20n² + 16m³
= 16m³ + 20n² ← in standard form → A
Step-by-step explanation:
The solution to this problem is very much similar to your previous ones, already answered by Sqdancefan.
Given:
mean, mu = 3550 lbs (hope I read the first five correctly, and it's not a six)
standard deviation, sigma = 870 lbs
weights are normally distributed, and assume large samples.
Probability to be estimated between W1=2800 and W2=4500 lbs.
Solution:
We calculate Z-scores for each of the limits in order to estimate probabilities from tables.
For W1 (lower limit),
Z1=(W1-mu)/sigma = (2800 - 3550)/870 = -.862069
From tables, P(Z<Z1) = 0.194325
For W2 (upper limit):
Z2=(W2-mu)/sigma = (4500-3550)/879 = 1.091954
From tables, P(Z<Z2) = 0.862573
Therefore probability that weight is between W1 and W2 is
P( W1 < W < W2 )
= P(Z1 < Z < Z2)
= P(Z<Z2) - P(Z<Z1)
= 0.862573 - 0.194325
= 0.668248
= 0.67 (to the hundredth)