The vertical shifts in graphs are caused by a constant added to the output (y - axis).
<h3>What is vertical shift in a graph?</h3>
Vertical shifts are outside changes that affect the output (y- axis) values and shift the function up or down (vertical direction).
Horizontal shifts are inside changes that affect the input (x-) axis values and shift the function left or right
<h3>The cause of vertical shift in a graph</h3>
The vertical shift results from a constant added to the output (y - axis). The graph will move up if the constant added is positive OR it will move down if the constant is negative.
Thus, the vertical shifts in graphs are caused by a constant added to the output (y - axis).
Learn more about vertical shifts in graph here: brainly.com/question/27653529
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Answer:
- <u>First choice, 984 cm²</u>
Explanation:
The plastic pencil case has form of a triangular prism.
This triangular prism has five faces:
- Top and bottom faces: two congruent triangles with a 10 cm base and 12 cm height.
- Lateral faces: two congruent rectangles with a 24 cm length and 13 cm widht, and one rectangle with 24 cm length and 10 cm widht.
<u>Surface area:</u>
- <u>Top and bottom triangles</u>:
area = (1/2) base × height
area of one triangle = 10 cm × 12 cm × (1/2) = 60 cm²
area of the two triangles = 2 × 60 cm² = 120 cm²
- <u>Lateral rectangles:</u>
area of a rectangle = length × width
area of the trhee triangles = 24 cm × 10 cm + 2 × 24 cm × 13 cm = 240 cm² + 624 cm² = 864 cm².
- <u>Total area: </u>120 cm² + 864 cm² = 984 cm²
Answer: first choice, 984 cm²
Answer:
Formula for area of triangle:
A = bh x 1/2
Formula for area of parallelogram:
A = bh
Now find the area of the figure above which is a triangle:
3(base) x 8(height) x 1/2 = <em>12</em>
Let's find the area of the parallelogram;
6(height) x 9(base) = <em>54</em>
Add the two areas together:
12 + 54 = 66 cm2
The exponential function that passes through (0,2) and (3,54) is a growth function
The exponetial function is y = 2 * 3^x
<h3>How to construct the exponential function?</h3>
The points are given as:
(x,y) = (0,2) and (3,54)
An exponential function is represented as:
y = ab^x
Substitute the points in the equation
2 = ab^0 and 54 = ab^3
Solve 2 = ab^0
a = 2
Substitute 2 for a in 54 = ab^3
54 = 2b^3
Divide by 2
27 = b^3
Take the cube roots of both sides
b = 3
So, we have:
y = ab^x
This becomes
y = 2 * 3^x
Hence, the exponetial function is y = 2 * 3^x
Read more about exponential functions at:
brainly.com/question/24077767
Mode = 11
Reason: 11 appeared twice, which is the most frequent number observed in this set of data.