🧮 algebra

1. **State the problem:** We need to determine which values of $c$ satisfy the inequality $$6c + 4 < 75.$$\n\n2. **Write the inequality and solve for $c$: **\n$$6c + 4 < 75$$\nSubt

1. **Stating the problem:** Find the first 4 terms of the arithmetic sequence where the first term is $f(1) = 5$ and the common difference is $d = -\frac{1}{2}$.

1. The problem is to order the given numbers from least to greatest: $\frac{5}{10}$, $\sqrt{2}$, $2!$, $\log_4(20)$, $\sum_{i=1}^2 i$, $\frac{6\pi}{4}$, $\int_2^5 x\, dx$, $e^5$, a

1. **State the problem:** We need to select all the squares in order from least to greatest based on the numerical values of the expressions inside them. 2. **Evaluate each express

1. **State the problem:** We want to predict the day's high temperature $x$ when Malika sold 57 hot cocoas, based on the line of best fit from the scatter plot. 2. **Understand the

1. **State the problem:** We want to find how many times a cricket will chirp per minute if the temperature outside is 57°F, based on the line of best fit from the given data. 2. *

1. **State the problem:** We have a polynomial $P(x)$ with the following properties:

1. **State the problem:** We analyze polynomial $P(x)$ with given properties: constant 4th finite differences equal to 48, three distinct x-intercepts at $x=-3$, $x=-1$, and $x=2$,

1. **Problem Statement:** Analyze the polynomial function's graph and verify which statements about its characteristics are true. 2. **Key Observations from the Graph:**

1. **Problem Statement:** Analyze the function $$y = 8 \cdot \left(\frac{1}{4}\right)^x$$ to determine its domain, range, y-intercept, and asymptote. 2. **Formula and Rules:** This

1. The problem asks to write an inequality representing the shaded region on the graph. 2. The graph shows a line passing through points $(-2,-1)$ and $(2,1)$.

1. The problem is to write an inequality representing the graph described. 2. The graph shows a dashed line passing through points (0,4) and (2,0).

1. The problem asks whether the function $f(x) = 6.7 \times 0.85^x$ represents exponential growth or decay. 2. The general form of an exponential function is $f(x) = a \times b^x$,

1. **State the problem:** We are given the exponential function $$k(x) = 6.7 (0.85)^{-x}$$ and asked to analyze its graph, including the y-intercept and horizontal asymptote. 2. **

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