Question 6 ( 2 points)
Two numbers have a difference of 18 .
a) If represents the larger number, state an equation you would use to solve this
question. (write your equation in Blank #1)
b) State the minimum product of the two numbers. (write your answer in Blank #2)
Blank # 1 A
Blank #

Ask by Beck Gardner. in Canada

Mar 26,2025

Question

Question 6 ( 2 points)
Two numbers have a difference of 18 .
a) If represents the larger number, state an equation you would use to solve this
question. (write your equation in Blank #1)
b) State the minimum product of the two numbers. (write your answer in Blank #2)
Blank # 1 A
Blank #

Ask by Beck Gardner. in Canada

Mar 26,2025

UpStudy AI · Accepted Answer

Let's break down the problem step by step.

### Part a
We are given that the difference between two numbers is 18. If we let $$ x $$ represent the larger number, we can denote the smaller number as $$ y $$. The relationship between the two numbers can be expressed as:

$$
x - y = 18
$$

This is the equation we would use to solve the problem.

**Blank #1:** $$ x - y = 18 $$

### Part b
To find the minimum product of the two numbers, we can express the product $$ P $$ of the two numbers as:

$$
P = x \cdot y
$$

From the equation $$ x - y = 18 $$, we can express $$ y $$ in terms of $$ x $$:

$$
y = x - 18
$$

Now, substituting this expression for $$ y $$ into the product equation gives us:

$$
P = x \cdot (x - 18) = x^2 - 18x
$$

To find the minimum product, we can analyze the quadratic function $$ P = x^2 - 18x $$. The vertex of a parabola given by $$ ax^2 + bx + c $$ occurs at $$ x = -\frac{b}{2a} $$. Here, $$ a = 1 $$ and $$ b = -18 $$:

$$
x = -\frac{-18}{2 \cdot 1} = \frac{18}{2} = 9
$$

Now, substituting $$ x = 9 $$ back into the equation for $$ y $$:

$$
y = 9 - 18 = -9
$$

Now we can calculate the product:

$$
P = 9 \cdot (-9) = -81
$$

**Blank #2:** $$-81$$

### Summary
- **Blank #1:** $$ x - y = 18 $$
- **Blank #2:** $$-81$$
**Blank #1:** $$ x - y = 18 $$ **Blank #2:** $$-81$$

Question 6 ( 2 points)
Two numbers have a difference of 18 .
a) If represents the larger number, state an equation you would use to solve this
question. (write your equation in Blank #1)
b) State the minimum product of the two numbers. (write your answer in Blank #2)
Blank # 1 A
Blank #

Upstudy AI Solution

Answer

Solution

Part a

Part b

Summary

The Deep Dive

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Question 6 ( 2 points) Two numbers have a difference of 18 . a) If represents the larger number, state an equation you would use to solve this question. (write your equation in Blank #1) b) State the minimum product of the two numbers. (write your answer in Blank #2) Blank # 1 A Blank #

Upstudy AI Solution

Answer

Solution

Part a

Part b

Summary

The Deep Dive

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Question 6 ( 2 points)
Two numbers have a difference of 18 .
a) If represents the larger number, state an equation you would use to solve this
question. (write your equation in Blank #1)
b) State the minimum product of the two numbers. (write your answer in Blank #2)
Blank # 1 A
Blank #