14. Marian wants to buy a double scoop of ice cream. The ice cream shop has 23 flavours, which can be served in a regular cone,

Response:

Move 2 units to the left

Reflect the graph across the y-axis

Expand horizontally by a factor of 2

Lift vertically by 2 units

Detailed explanation:

Provided:

Basic function:

Transformed function:

Extract -2 from the transformation function f(x)

Now, we can observe the step-by-step transformations

Move 2 units to the left ( x → x+2 )

Reflect the graph across the y-axis ( (x+2) → - (x+2) )

Expand horizontally by a factor of 2 [ -x(x+2) → -2(x+2) ]

Lift vertically by 2 units [ f(x) → f(x) + 2 ]

Simplifying the function:

Thus, applying four transformation steps results in the new function

Answer:

What is the variation for each successive input?

✔ 1

What is the variation for each successive output?

✔ 0.35

What is the rate of variation for the correlation?

✔ 0.35

Step-by-step explanation:

The change per input is 1 since the inputs are 10,11,12,13.

The change for each successive output is 0.35 because we must subtract 4.1 from 3.75.

Thus, the rate of variation for the correlation is likewise 0.35.

Answer:

F(t) = 10 + 5(t)

Step-by-step explanation:

The complete question is as follows;

Anumeha is mowing lawns for a summer job. For each lawn she mows, she charges a $10 starting fee plus an hourly rate. For example, her fee for a 5-hour job is $35. Let f(t) denote Anumeha's fee for a job f (in dollars) based on how many hours (t) were needed to finish it. Write the formula for this function.

Solution

We aim to establish the formula F(t) representing the fee Anumeha charges per job.

Key to formulating this function is understanding the constant charge she applies per job.

We know she earns $35 for mowing for 5 hours.

Therefore, the constant fee can be deduced as follows;

Since it’s a $10 starting fee along with an hourly rate;

35 = 10 + 5(x)

where x refers to the hourly rate

35 = 10 + 5x

5x = 35-10

5x = 25

x = 25/5

x = $5

This indicates that she charges a constant fee of $5 per hour

Thus, we can now write the equation.

F(t) = 10 + 5(t)

where t represents the number of hours spent on each job

Answer:

(a) What will his age be after 5 years?

"5 + y" years old

(b) What was his age 6 years ago?

"y - 6" years old

(c) If his grandfather’s age is five times his, how old is his grandfather?

"5y" years old

(d) His father is 6 years older than three times his age. How old is his father?

"6 + 3y" years old

Note: Disregard the quotation marks, ""

Answer:

1. x=±4

2. t=±9

3. r=±10

4. x=±12

5. s=±5

Step-by-step explanation:

1. x^2 = 16

By extracting the square root on both sides

x=±4

2. t^2=81

Again, take the square root of each side

t=±9

3. r^2-100=0

r=±10

4. x²-144=0

We rewrite as x²=144

Applying square roots

x=±12

5. 2s²=50

s=±5 ..