Answer:
Refer to the Attachment
Step-by-step explanation:
Rewriting the fractions in decimal and whole number, we have the following:


Thus, 42/3 is on 14 and 25/3 is on 8 and then add 1/3 from 8 going to 9.
Therefore, the points must be plotted as follows:
The blue point indicates the 42/3 while the red point indicates the 25/3.
Answer:
Surface area is found:
Surface Area = 1700 cm²
Step-by-step explanation:
(The cereal box is shown in the ATTACHMENT)
The surface area of a rectangular prism can be found by added the areas of all 6 sides of the rectangular prism.
L = length = 20 cm
H = height = 30 cm
W = Width = 5 cm
<h3 /><h3>Side 1:</h3>
A(1) = L×H
A(1) = 20×30
A(1) = 600 cm²
<h3>Side 2:</h3>
As the measurements of the side at the back of side 1 has the same measurement of side 1. then:
A(2) = 600 cm²
<h3>Side 3:</h3>
A(3) = L×W
A(3) = 20×5
A(3) = 100 cm²
<h3>Side 4:</h3>
As the measurements of the side at the back of side 4 has the same measurement of side 4. then:
A(4) = 100 cm²
<h3>Side 5:</h3>
A(5) = H×W
A(5) = 30×5
A(5) = 150 cm²
<h3>Side 6:</h3>
As the measurements of the side at the back of side 5 has the same measurement of side 5. then:
A(6) = 150 cm²
<h3>Surface Area:</h3>
Adding areas of all the sides
A(1) + A(2) + A(3) +A(4) + A(5) + A(6) = 600 + 600 + 100 +100 + 150 +150
Surface Area = 1700 cm²
Step-by-step explanation:
Left hand side:
4 [sin⁶ θ + cos⁶ θ]
Rearrange:
4 [(sin² θ)³ + (cos² θ)³]
Factor the sum of cubes:
4 [(sin² θ + cos² θ) (sin⁴ θ − sin² θ cos² θ + cos⁴ θ)]
Pythagorean identity:
4 [sin⁴ θ − sin² θ cos² θ + cos⁴ θ]
Complete the square:
4 [sin⁴ θ + 2 sin² θ cos² θ + cos⁴ θ − 3 sin² θ cos² θ]
4 [(sin² θ + cos² θ)² − 3 sin² θ cos² θ]
Pythagorean identity:
4 [1 − 3 sin² θ cos² θ]
Rearrange:
4 − 12 sin² θ cos² θ
4 − 3 (2 sin θ cos θ)²
Double angle formula:
4 − 3 (sin (2θ))²
4 − 3 sin² (2θ)
Finally, apply Pythagorean identity and simplify:
4 − 3 (1 − cos² (2θ))
4 − 3 + 3 cos² (2θ)
1 + 3 cos² (2θ)
Answer:
x > -3.2
Step-by-step explanation:
Answer:
<h2>C. F(x) = (x - 3)⁴</h2>
Step-by-step explanation:
f(x) + n - shift the graph of f(x) n units up
f(x) - n - shift the graph of f(x) n units down
f(x - n) - shift the graph of f(x) n units to the right
f(x + n) - shift the graph of f(x) n units to the left
===================================
The graph og G(x) = x⁴ shifted 3 units to the right.
Therefore F(x) = G(x - 3) = (x - 3)⁴