Question

solvingstatement. if the statementne measurement from thees if you know5364ow the age of the242for the statement.he output is eleven more than the inputthe output is six times the input30. you be the teacher your friend graphsthe function represented by the input-output table.is your friend correct? explain your reasoning.| input, $x$ | $-4$ | $-2$ | $0$ | $2$ || ---- | ---- | ---- | ---- | ---- || output, $y$ | $-1$ | $1$ | $3$ | $5$ |a. $y=\frac{x}{3}$b. $y=x+1$c. $y=-2x+6$31. modeling real life a dolphin eats 30 poundsof fish per day.a. write and graph a function that relates the number $p$of pounds of fish that a dolphin eats in $d$ days.b. how many total pounds of fish does a dolphin eatin 30 days?32. modeling real life you fill a fish tank with 55 gallons of water onsaturday. the water evaporates at a rate of 1.5 gallons per day. you planto add water when the tank reaches 49 gallons. when will you add water?justify your answer.using an equation find the value of $x$ for the given value of $y$.33. $y=5x-7$; $y=-22$34. $y=9-7x$; $y=37$35. $y=\frac{x}{4}-7$; $y=2$

Explanation:

Problem 30

1. First, identify the linear function from the table. Use the slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ with two points, e.g., $(0,3)$ and $(2,5)$: $m=\frac{5-3}{2-0}=1$. The y-intercept $b$ is 3 (when $x=0$, $y=3$), so the function is $y=x+3$.
2. Now check the options:

• Option A ($y=\frac{x}{3}$): Does not match $y=x+3$.
• Option B ($y=x+1$): Does not match $y=x+3$.
• Option C ($y=-2x+6$): Does not match $y=x+3$.

The friend's graph is incorrect because none of the provided functions match the linear relationship derived from the input-output table.

Step1: Define the function

Let $p$ = total pounds of fish, $d$ = days. The dolphin eats 30 pounds per day, so:
$p=30d$

Step2: Calculate for 30 days

Substitute $d=30$ into the function:
$p=30\times30=900$

Step1: Define variables & equation

Let $d$ = days since Saturday. Starting volume = 55 gallons, target volume = 49 gallons, evaporation rate = 1.5 gallons/day. The equation for remaining water is:
$55 - 1.5d = 49$

Step2: Solve for $d$

Rearrange to isolate $d$:
$1.5d = 55 - 49$
$1.5d = 6$
$d=\frac{6}{1.5}=4$

Answer:

The friend is not correct. The input-output table represents the function $y=x+3$, which does not match any of the graphed options (A. $y=\frac{x}{3}$, B. $y=x+1$, C. $y=-2x+6$).

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Problem 31