First box = 14 pounds
Second box = 2x = 28 pounds
Third Box = x+2= 16 pounds
Fourth box = x/2 = 7 pounds
<u>Step-by-step explanation:</u>
Here we have , Sixty-five pounds of candy was divided into four different boxes. The second box contained twice the amount of the first box. The third box contained two more pounds than the first box. The last box contained one-fourth the amount in the second box. We need to find How much candy was in each box. Let's find out:
We have a total of 65 pounds of candy ! Let in first box we have x pounds so , second box contained twice the amount of the first box i.e.
⇒
The third box contained two more pounds than the first box i.e.
⇒
The last box contained one-fourth the amount in the second box i.e.
⇒
Therefore , Sum of pounds of candy are :
⇒
⇒
⇒
⇒
⇒
Therefore , Candy in each box is :
First box = 14 pounds
Second box = 2x = 28 pounds
Third Box = x+2= 16 pounds
Fourth box = x/2 = 7 pounds
I'm going to assume you meant to write fractions (because if are all non-negative integers, the series would clearly diverge), so that
and so on.
a. If the pattern continues as above, we would have the general term
b. Note that we can write as
The series diverges by comparison to the divergent series
Answer:
The image coordinates are D'(8, 5), E'(12, 3) and F'(10,0)
Step-by-step explanation:
Given the vertices of △ DEF are D (2, 5), E (6, 3), and F (4, 0). We have to translate the triangle using the vector (6, 0)
Now, translation by vector (6, 0)
D (2, 5)=D'(2+6, 5+0)=D'(8, 5)
E (6, 3)=E'(6+6, 3+0)=E'(12, 3)
F (4, 0)=F'(4+6, 0+0)=F'(10,0)
Now, we have to label the coordinate of the triangle or to get image of triangle after translation.
Hence, The image coordinates are D'(8, 5), E'(12, 3) and F'(10,0)
Consider right triangle with vertices B - base of the hill, S - top of the statue and Y - you. In this triangle angle B is right and angle Y is 13.2°. If h is a height of the statue, then the legs YB and BS have lengths 77 ft and 16+h ft.
You have lengths of two legs and measure of one acute angle, then you can use tangent to find h:
ft.
Answer: the height of the statue is 2.0565 ft.
Given:
Vertices of ABCD are A(-4,4), (-2,2), C(-2,-1) and D(-4,1).
Vertices of A'B'C'D' are A'(3,-4), B'(5,-2), C'(5,1) and D'(3,-1).
To find:
The sequence of transformations that changes figure ABCD to figure A'B'C'D'.
Solution:
Part A:
The figure ABCD reflected across the x-axis, then
Using this rule, we get
Similarly, the other points are .
Then figure translated 7 units right to get A'B'C'D'.
Similarly, the other points are .
Therefore, the figure ABCD reflected across the x-axis and then translated 7 units right to get A'B'C'D'.
Part B:
Reflection and translation are rigid transformation, it means shape and size of figures remains same after reflection and translation.
Therefore, the two figures congruent.
