The line y = x + 3 has slope 1, so we look for points on the curve where the tangent line, whose slope is dy/dx, is equal to 1.
y² = x
Take the derivative of both sides with respect to x, assuming y = y(x) :
2y dy/dx = 1
dy/dx = 1/(2y)
Solve for y when dy/dx = 1 :
1 = 1/(2y)
2y = 1
y = 1/2
When y = 1/2, we have x = y² = (1/2)² = 1/4. However, for the given line, when y = 1/2, we have x = y - 3 = 1/2 - 3 = -5/2.
This means the line y = x + 3 is not a tangent to the curve y² = x. In fact, the line never even touches y² = x :
x = y² ⇒ y = y² + 3 ⇒ y² - y + 3 = 0
has no real solution for y.
Answer
• A. Equation: 25(5 + x) = 325
,
• B. Answer: 8 dogs
Explanation
Given
• Charge to wash a dog: $25.
• She washed 5 dogs on Saturday and then some more on Sunday.
• She made $325 for the weekend.
Procedure
She charges $25 per wash, she made $325 for the weekend, and we know that on Saturday she washed 5 dogs, but we don't know how many she washed on Sunday. Thus, we have to build an equation in which the number of dogs washed on Sunday is represented by x (as we do not know the real number).
Considering that the total money made has to be equal to the multiplication of the charge times the dogs washed, the equation is:

Then, we have to solve for x to know how many dogs did she wash on Sunday.
0. Multiplying the parenthesis

<em>2. Subtracting 125 from both sides of the equation</em>


<em>3. Dividing both sides of the equation against 25</em>

To represent the number of cans in each shelf you will divide the total number of cans by the number of shelves.
This is represented as
t/4 = n.
Average of 10 people = 65
65 × 10 = 650
average of 5 people = 35
35 × 5 = 175
650 + 175 = 825
825 ÷ 15 = 55
the average reading time for the entire book club each day is 55 minutes a day
Amount of money Aisha receive from selling all of the bracelets is $33.25.
<u>Step-by-step explanation:</u>
In this question, its given that Aisha made bracelets for a craft fair. She spent $29.75 on supplies to make the bracelets. Each bracelet cost her about $0.85 to make. Aisha sells each bracelet for $0.10 more than it cost her to make. Let's calculate Number of bracelets Aisha made as
.
Number = 
⇒ Number = 
⇒ Number = 
⇒ Number = 
Now , its given that Aisha sell these bracelets with $0.10 more then it cost her i.e. at $0.95 , Let's calculate selling price as :
Price = 
Price = $33.25
Therefore, amount of money Aisha receive from selling all of the bracelets is $33.25.