Answer: x ≥ 5
Step-by-step explanation:
7 is increased by the product of a number and 3: 7 + 3x
Is at least 22: ≥ 22
Your equation is: 7 + 3x ≥ 22
subtract 7 from both sides
3x ≥ 15
divide both sides by 3
x ≥ 5
Answer: option d. C (0,3), D (0,5).
Justification:
1) The x - coordinates of the vertices A and B are shown in the diagrama, They are both - 4, so the new vertices C and D must be in a line parallel to y = - 4.
2) The y-coordinates of the vertices A and B are also shown in the diagrama. They are equal to 3 and 5 respectively.
3) We can see that the new points C and D must be over a parallel line to y = - 4 and that their distance to the points A and B has to be the same distance of the point R and S to U and T.
That distance is 4, so the line may be y = - 7 or y = 0.
4) If the line is y = 7 the points C and D would have coordinates (-7,3) and (-7,5), but this points are not among the options.
5) If the line is y = 0 the points C and D would have coordinates (0, 3) and (0,5), which is precisely the points of the option d. That is the answer.
An arithmetic sequence takes the form
where
is the common difference between terms. You can solve for
in terms of any of the previous terms of the sequence:
for some integer
Continuing in this way, you know that the sequence can be defined explicitly in terms of the first term
Given that the 4th term is
and the 11th term is
, you have the following system of equations.
Solving this system for the two unknowns yields
and
.
So, the sequence is given explicitly by
If the triangles are similar, then the corresponding ratio of their sides have equal ratios. Through ratio and proportion, we would determine the answer.
5/6 = x/9, where x is the length for side PN
Transposing the equation so that x is on the left side:
x = (5/6)*9
x = 7.5
Step-by-step explanation:
and one of these day I must get straigh and drip all over you
