Determine whether triangle TJD is congruent to triangle SEK given T (-4,-2), J (0,5), D (1,-1), S (-1,3), E (3,10), K (4,4) and
nataly862011 [7]
Yes, it is.
The three points of triangle SEK are the points of TJD shifted 3 units right and 5 units upward.
So they are the same triangle, just translated in the plane.
The Lagrangian for this function and the given constraints is

which has partial derivatives (set equal to 0) satisfying

This is a fairly standard linear system. Solving yields Lagrange multipliers of

and

, and at the same time we find only one critical point at

.
Check the Hessian for

, given by


is positive definite, since

for any vector

, which means

attains a minimum value of

at

. There is no maximum over the given constraints.
Answer:
d
Step-by-step explanation:
Hope this helps! Good luck!
Answer:
By using hypothesis test at α = 0.01, we cannot conclude that the proportion of high school teachers who were single greater than the proportion of elementary teachers who were single
Step-by-step explanation:
let p1 be the proportion of elementary teachers who were single
let p2 be the proportion of high school teachers who were single
Then, the null and alternative hypotheses are:
: p2=p1
: p2>p1
We need to calculate the test statistic of the sample proportion for elementary teachers who were single.
It can be calculated as follows:
where
- p(s) is the sample proportion of high school teachers who were single (
) - p is the proportion of elementary teachers who were single (
)
- N is the sample size (180)
Using the numbers, we get
≈ 1.88
Using z-table, corresponding P-Value is ≈0.03
Since 0.03>0.01 we fail to reject the null hypothesis. (The result is not significant at α = 0.01)
Answer:
Step-by-step explanation:
- find the area of the base (square)=900 sq. cm
- find area of triangles=1260 sq. cm
- total= 2160 sq. cm