Graph and equation both shows the proportional comparison between two quantities
for example, equation y = 4x, this means, the value of 'y' will always be 4 times the value of 'x'
More complex equation such as y = 3x + 5, means that the value of 'y' equals to 5 more triples of value of 'x'
Another example is the conversion graph attached below, it shows the relationship between kilometers and miles. For example, we want to find out how many miles are in 10 kilometers, we would draw a line from the point that shows 10 km towards the graph, then across from the graph to miles, and we'd get a reading of 12 miles.
9514 1404 393
Answer:
4. height: 5√3 cm; area: 25√3 cm²
5. 30√2 ft ≈ 42.43 ft
Step-by-step explanation:
4. The height of an equilateral triangle is (√3)/2 times the side length, so is ...
height = (√3)/2 × (10 cm) = 5√3 cm
The area is given by the formula ...
A = 1/2bh
A = 1/2(10 cm)(5√3 cm) = 25√3 cm²
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5. The diagonal of a square is √2 times the side length, so the distance from 3rd to 1st base is ...
(30 ft)√2 ≈ 42.43 ft
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The length of the diagonal of a square is something you should be familiar with. If you're not, you can figure the distance using the Pythagorean theorem.
d = √(30² +30²) = √1800 ≈ 42.43 . . . feet
4 pizzas because, 12 slices /3 per person =4 and 16 people /4 = 4 pizzas
Answer:
Value of the independent variable = 25
Step-by-step explanation:
y-intercept form of a straight line is represented by the equation,
y = mx + b
here y = dependent variable
m = slope
b = y intercept or vertical intercept
x = independent variable
In our question,
y-intercept 'b' = 150
slope of the line 'm' = 4
dependent variable y = 250
We will plug in these values in the equation of the line to get the value of the independent variable.
250 = 4x + 150
250 - 150 = 4x
x =
x = 25
Therefore, value of the independent variable is 25.
Answer:
vertex = (-4, 5)
Step-by-step explanation:
In general, the graph of the absolute value function f(x) = a|x - h| + k will have its lowest value when f(x) = k (or highest value for f(x) = -a|x - h| + k). The lowest/highest value is the vertex (turning point).
Therefore, from inspection of the equation we can say that the y-coordinate of the vertex is 5.
Set the equation to 5 and then solve for x:
⇒ 5 = 1/2 |-X – 4| + 5
⇒ 1/2 |-X – 4| = 0
⇒ |-X – 4| = 0
Therefore, (-X - 4) = 0 and -(-X - 4) = 0
⇒ X = -4 (for both)
So the vertex is (-4, 5)
<u>Translations</u>
Absolute value parent function: f(x) = | -x |
Horizontal translation left 4 units: f(x) = |-x - 4|
Horizontal stretch of sf 1/2: f(x) = 1/2 |-x - 4|
Vertical translation up 5 units: f(x) = 1/2 |-x - 4| + 5