Answer:
Step-by-step explanation:
h(g(x))
g(x)= 3x + 1
h(3x + 1) = 4(3x + 1) = 12x + 4
Answer:
Step-by-step explanation:
From table 1,
f(x) = bˣ
For x = -1,
f(-1) = 0.5
0.5 = (b)⁻¹
b = 
b = 2
For x = 1.585,
f(1.585) = 3
3 = 
3 = 
For x = 2.585,
f(2.585) = 
= 
= 4 × 1.5 [Since, ]
= 6
From table 2,
g(x) = 
For x = 0.5,
g(0.5) = -1
-1 = 
b⁻¹ = 0.5
b = 2
For x = 2,
g(2) = 1
1 = 
For x = 6,
g(6) = 2.585
2.585 = 
2.585 = 
2.585 = 
2.858 - 1 = 
For x = 3,
g(3) =
g(3) = 1.585
In order to figure out whether Luis or Isabella skates farther to get to school, we have to create a common denominator between the two fractions that represent the distance that each person walks.
The least common denominator of 3 and 4 is 12. This means that we have to change both fractions into equal fractions with denominators of 12.
To figure this out, we must set up a proportion.
2/3 = x/12
To solve this proportion, we must cross-multiply the fractions. We get:
24 = 3x
If we divide both sides by the coefficient of x which is 3, to get the variable x alone, we get:
x = 8
Therefore, 2/3 = 8/12, so Luis skates 8/12 mile from his home to school.
If we do the same process for the 2/4 mile to get to school for Isabella, we get 6/12, because both fractions are equal to 1/2.
Therefore, we know that Luis skates 8/12 mile to school and Isabella skates 6/12 mile to get to school. Because they have the same denominator, we can just compare the numerators. We know that 8 is greater than 6, thus Luis skates farther to get to school.
The exact cost is $23.75 for the show, and the exact change they should get is $1.25.
An adult ticket to the show costs $5.50
A student ticket to the show costs $4.25.
A family buys two adult tickets and three student tickets. This would imply that the total cost of two adult tickets would be
⇒ 2 × 5.5 = $11
It also implies that the total cost of three student tickets is
3 × 4.25 = $12.75
The total cost of two adult tickets and three student tickets is
⇒ 11 + 12.75 = $23.75
If the family pays $25, the exact change they should get is
⇒ 25 - 23.75 = $1.25
Thus, the exact cost is $23.75 for the show, and the exact change they should get is $1.25.
Learn more about Arithmetic operations here:
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145 blue paint are needed to make 28 pints of green paint
