Ratio of large box
96:6
Thus 96/6 = 16
Small box
2*16 = 32
There are 32 candles in the small box.
Answer:
x < 3
Step-by-step explanation:
When you multipy an inequality by a negative, remember to switch the inequality sign!
-x > -3
(-x)(-1) > (-3)(-1)
x < 3
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Answer:
Horizontal shift of 4 units to the left.
Vertical translation of 8 units downward.
Step-by-step explanation:
Given the quadratic function, y = (x + 4)² - 8, which represents the horizontal and vertical translations of the parent graph, y = x²:
The vertex form of the quadratic function is y = a(x - h)² + k
Where:
The vertex is (h , k), which is either the <u>minimum</u> (upward facing graph) or <u>maximum</u> (downward-facing graph).
The axis of symmetry occurs at <em>x = h</em>.
<em>a</em> = determines whether the graph opens up or down, and makes the graph wider or narrower.
<em>h</em> = determines how far left or right the parent function is translated.
<em>k</em> = determines how far up or down the parent function is translated.
Going back to your quadratic function,
y = (x + 4)² - 8
- The vertex occrs at (-4, -8)
- a is assumed to have a value of 1.
- Given the value of <em>h</em> = -4, then it means that the graph shifted horizontally by <u>4 units to the left</u>.
- Since k = -8, then it implies that the graph translated vertically at <u>8 units downward</u>.
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Answer:
x=5
Step-by-step explanation:
change to x=12-7
subtract
x=5
First lets work out the length of the top side which joins the points (-1,7) and (-5,5):-
this = sqrt ( (7-5)^2 + (-1 - (-5)^2 )
= sqrt (4 + 16)
= sqrt 20
Now find length of the longer side which is distance between the points (-1,7) and (4, -3)
this is sqrt ( (-1 - 4)^2 + (7 - -3)^2)
= sqrt 125
Area of the rectangle = sqrt 20 * sqrt 125
= sqrt 2500
= 50 units^2 Answer
