Answer:
(C) 10 units
Step-by-step explanation:
It is given that EFGH is a rhombus and EG = 16 and FH = 12.
We know that the diagonals of the rhombus are the perpendicular bisectors, therefore OF=6, OH=6, OE=8 and OG=8.
Now, using the Pythagoras theorem in ΔOFG, we have
Thus, the value of the side of the rhombus will be 10 units.
Hence, option C is correct.
Answer:
The minimum sample size required to ensure that the estimate has an error of at most 0.14 at the 95% level of confidence is n=567.
Step-by-step explanation:
We have to calculate the minimum sample size n needed to have a margin of error below 0.14.
The critical value of z for a 95% confidence interval is z=1.96.
To do that, we use the margin of error formula in function of n:
The minimum sample size to have this margin of error is n = 567.
Answer:
D)
Step-by-step explanation:
First we have to subtract 5 from both sides
Now, square both sides
x - 6 = 49
Now, add 6 to both sides
x - 6 +6 = 49 + 6
x = 55
Answer: or
Step-by-step explanation:
The complete exercise is: "A chicken salad recipe calls for pound of chicken per serving . How many pounds of chicken are needed to make
serving".
You can convert the Mixed number to a Decimal number. Divide the numerator 1 by the denominator 2 and then add the quotient to the Whole number. Then, you get:
Now divide the numerator 1 by the denominator 8 to write the fraction to a Decimal number. Then:
Let be "x" the amount of pounds are needed to make serving.
Then, you can set up the following proportion:
Solving for "x", you get:
or
The question is incomplete below you will find the missing part.
Step 1 : Choose ONE of the following triangles complete the table below:
1. Obtuse Scalene Triangle Translation to prove SSS Congruence
or
2. Isosceles Right Triangle Reflection to prove ASA Congruence
or
3. Equilateral Equiangular Triangle Rotation to prove SAS Congruence
Original Coordinate Point
Transformation Rule
Image Coordinate Points
A (1, 4) (x,y) -> (x+ ,y -) A’ ( , )
B ( 7,4) (x,y) -> (x+ ,y - ) B’ ( , )
C (8,9) (x,y) -> (x+ ,y -) C’ ( , )
The appropriate table is also shown below.
The triangles ABC and A'B'C' are congruent by SSS through Obtuse Scalene Triangle Translation because the corresponding sides are congruent
Two triangles are congruent if their size and shape are the same.
Now we have to transform the triangle,
The coordinates of the triangle ΔABC are given as:
A = (1, 4)
B = (7,4)
C = (8,9)
so the lengths of the sides of the triangle are given by
AB= √(7-1)²+(4-4)²= √6²= 6
BC= √(8-7)²+(9-4)²= √1²+5²= √1+25= √26
CA= √(8-1)²+(9-4)²= √7²+5²= √49+25= √74
In order to prove the SSS congruence, we have to transform the triangles under the following translation rule:
(x,y) -> (x -3, y +6)
in the above translation,
The triangle will be translated 3 units left
And then translated 6 units up.
So, we have the new coordination of the points of the translated triangle ΔA'B'C'
A' = (1-3, 4+6)
A' = (-2, 10)
B' = (7-3, 4+6)
B' = (4, 10)
C' = (8-3, 9+6)
C' = (5, 15)
Now
so the lengths of the sides of the triangle are given by
A'B'= √(4-(-2))²+(10-10)²= √6²= 6
B'C'= √(5-4)²+(15-10)²= √1²+5²= √1+25= √26
C'A'= √(-2-5)²+(10-15)²= √(-7)²+(-5)²= √49+25= √74
By comparing two triangles ΔABC and ΔA'B'C'
AB ≅ A'B'
BC ≅ B'C'
CA ≅ C'A'
Hence ΔABC ≅ A'B'C' (By S-S-S rule)
By the above transformation, the triangles ABC and A'B'C' are congruent by SSS because the corresponding sides are congruent as all the points are gone through the same transformation.
Learn more about the transformation
here: brainly.com/question/4289712
#SPJ10
