🧮 algebra

1. The problem is to identify the asymptote of the given exponential decay function graphed. 2. An exponential decay function generally has the form $$y = ab^x$$ where $$0 < b < 1$

1. **State the problem:** We are given points from a graph showing bacteria growth over time and need to write an exponential function in the form $f(x) = a b^x$ that fits the data

1. **State the problem:** We are given an exponential function modeling bacteria population growth: $$f(x) = 575(1 + 0.40)^x$$ where $x$ is time in hours and $f(x)$ is population i

1. The problem asks to find the value of $x$ based on a figure that is not visible here. 2. Since no figure or equation is provided, we cannot apply any formulas or solve for $x$.

1. The problem is to understand how to simplify an expression or equation. 2. Simplification often involves reducing fractions, combining like terms, or factoring expressions.

1. Problem: Simplify $ (a^5 b^9)(a^{11} b) $. 2. Use the product of powers rule: $ x^m \cdot x^n = x^{m+n} $.

1. **State the problem:** Simplify or evaluate the expression $4c - 2a$ given no specific values for $a$ and $c$. 2. **Understand the expression:** The expression $4c - 2a$ is a li

1. The problem is to factor the expression $35x^3 + 14x$ using the greatest common factor (GCF). 2. The formula for factoring by GCF is: $$a b + a c = a(b + c)$$ where $a$ is the G

1. The problem asks for help with part d of question 2. Since the exact question is not provided, I will explain how to approach a typical part d in algebra or math problems, often

1. The problem asks to explain what each part of the equation represents in the situation where Marta was 10 when her little brother was born, and the equation relates their ages.

1. **State the problem:** A grocery store sells canned corn at 5 cans for 2.19. Jonathan wants to buy 40 cans. We need to find the price $x$ for 40 cans using a proportion.

1. **State the problem:** Find three consecutive even integers such that 50 times the smallest is 88 less than 46 times the largest. 2. **Define variables:** Let the smallest even

1. **State the problem:** Find a number such that one-fifth of the sum of the number and -3 is twice the number. 2. **Set up the equation:** Let the number be $x$. The sum of the n

1. Problem: If 18% of the goats crossed and that number is 45, find the total number of goats. Formula: Percentage crossed = $\frac{\text{number crossed}}{\text{total goats}} \time

1. **Problem:** If 18% of the goats crossed the bridge and that number is 45, how many goats were there in total? **Step 1:** Let the total number of goats be $x$.

1. **State the problem:** Find the zeros (roots) of the polynomial function given by the numerator of the rational expression: $$Q(x) = 6x^3 + 5x^2 - 30x + 11$$

1. **State the problem:** Find the roots of the polynomial $$p(x) = x^3 - 4x^2 - 5x + 14$$ using the Rational Root Theorem and synthetic division. 2. **Rational Root Theorem:** Pos

1. The problem asks to find the slope of the line passing through the points given in the table: (0, 21), (-4, 16), (-8, 11), and (-32, -19). 2. The formula for the slope $m$ betwe

1. The problem asks to find the slope of the line passing through the points given in the table: (-4, -18), (0, 2), (1, 7), and (3, 17). 2. The formula for the slope $m$ between tw

1. **State the problem:** We need to find the shortest distance from their home to the theater such that both Mark and Jodi use a whole number of gallons of gas. 2. **Given:**

1. **State the problem:** Find a number such that doubling the difference of the number and 4 is 6 more than the number. 2. **Define the variable:** Let the number be $x$.