Answer :
To determine when Olivia will have exactly 4 blooms on her rose bushes, we start by analyzing the given linear relationship modeled by the equation:
[tex]\[ y = 1.345x + 4 \][/tex]
where:
- [tex]\( y \)[/tex] represents the number of blooms,
- [tex]\( x \)[/tex] represents the amount of fertilizer (in ounces).
We are asked to find the value of [tex]\( x \)[/tex] that results in [tex]\( y \)[/tex] equaling 4 blooms. Therefore, we set [tex]\( y = 4 \)[/tex] in the equation and solve for [tex]\( x \)[/tex]:
[tex]\[ 4 = 1.345x + 4 \][/tex]
Next, we isolate the term involving [tex]\( x \)[/tex]. Start by subtracting 4 from both sides of the equation:
[tex]\[ 4 - 4 = 1.345x + 4 - 4 \][/tex]
This simplifies to:
[tex]\[ 0 = 1.345x \][/tex]
Next, solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 1.345:
[tex]\[ \frac{0}{1.345} = \frac{1.345x}{1.345} \][/tex]
This simplifies to:
[tex]\[ 0 = x \][/tex]
Thus, [tex]\( x = 0 \)[/tex].
The result shows that Olivia will have exactly 4 blooms when she adds no fertilizer (0 ounces). Hence, the correct answer is:
A) When she adds no fertilizer.
[tex]\[ y = 1.345x + 4 \][/tex]
where:
- [tex]\( y \)[/tex] represents the number of blooms,
- [tex]\( x \)[/tex] represents the amount of fertilizer (in ounces).
We are asked to find the value of [tex]\( x \)[/tex] that results in [tex]\( y \)[/tex] equaling 4 blooms. Therefore, we set [tex]\( y = 4 \)[/tex] in the equation and solve for [tex]\( x \)[/tex]:
[tex]\[ 4 = 1.345x + 4 \][/tex]
Next, we isolate the term involving [tex]\( x \)[/tex]. Start by subtracting 4 from both sides of the equation:
[tex]\[ 4 - 4 = 1.345x + 4 - 4 \][/tex]
This simplifies to:
[tex]\[ 0 = 1.345x \][/tex]
Next, solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 1.345:
[tex]\[ \frac{0}{1.345} = \frac{1.345x}{1.345} \][/tex]
This simplifies to:
[tex]\[ 0 = x \][/tex]
Thus, [tex]\( x = 0 \)[/tex].
The result shows that Olivia will have exactly 4 blooms when she adds no fertilizer (0 ounces). Hence, the correct answer is:
A) When she adds no fertilizer.