Answer:
Taylor's age = x = 35 years
Marty's age = y = 50 years
Step-by-step explanation:
Let
Taylor's age = x
Marty's age = y
Taylor is 15 years younger than Marty.
x = y - 15
Twice Marty’s age added to three times Taylors age totals 205.
205 = 2y + 3x...... Equation 1
Therefore, we substitute y - 15 for x in
205 = 2y + 3x...... Equation 1
205 = 2y + 3(y - 15)
205 = 2y + 3y - 45
Collect like terms
205 + 45 = 5y
250 = 5y
y = 250/5
y = 50 years
x = y - 15
x = 50 - 15
x = 35 years
Solving for x
Therefore:
Taylor's age = x = 35 years
Marty's age = y = 50 years
Using translation concepts, the graph of g(x) = 3x² + 1 is given at the end of the answer.
<h3>What is a translation?</h3>
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, we have that the parent function is:
f(x) = x².
The shifted function is:
g(x) = 3x² + 1.
The transformations are given as follows:
- It was vertically compressed by a factor of 3, due to the multiplication by 3.
- It was shifted up 1 unit, due to the addition of 1.
In the graph at the end of the answer, both functions are shown, with <u>f(x) in red and g(x) in blue</u>.
More can be learned about translation concepts at brainly.com/question/28393734
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Answer:
9000
Step-by-step explanation:
The first digit can't be 0, so there are 9 numbers that can be used for the first digit. The fifth digit must be 0, so there's only 1 number that can be used. The other three digits can be any of 10 numbers.
So the number of zipcodes is:
9 × 10 × 10 × 10 × 1 = 9000
D=r×t, plug in the numbers,
150=30×t.
then divide each side by 30.
150÷30=5
5=t
therefore, it will take him 5 hours.
Answer:
D, but careful on conventions
Step-by-step explanation:
Honestly, it's a matter of conventions. Either C or D, then it's a matter on what whoever wrote the book likes and how he got taught. For example, for me,
, please note the capital L, and
, in order to avoid any confusion - if someone has a terrible handwriting and their capital and small Ls look too similar.