🧮 algebra

1. The problem is to find the value of $\log( (0.35)^2 )$.\n\n2. Recall the logarithm power rule: $\log(a^b) = b \log(a)$.\n\n3. Apply the power rule: $\log((0.35)^2) = 2 \log(0.35

1. The user has provided a series of fractions representing daily percentages as $\frac{numerator}{33}$. 2. To convert each fraction to a percentage, multiply by 100: $$\text{Perce

1. The problem is to simplify and understand the given fractions: 33/33, 33/33, 33/33, 31/33, 37/33, 34/33, 35/33, 33/33, 35/33, 34/33, 33/33, 35/33, 31/33, 33/33, 32/33, 34/33, 33

1. The problem states that Uche and Chidi shared a sum of money in the ratio $m:n$. 2. Chidi's share corresponds to the part $n$ in the ratio, and it is given as 4200.

1. **State the problem:** We are given the function $f(x) = -x^2 + 2x + 3$ and need to find: b. x- and y-intercepts

1. **State the problem:** Simplify the expression $$\frac{(5m^4k^{-1})^{-4}}{2m^{-3}k^{-9}}$$. 2. **Apply the negative exponent rule:** For any expression $a^n$, $(a^n)^{-m} = a^{-

1. The problem is to express the fraction \frac{3}{7} as a decimal or simplified form. 2. Since \frac{3}{7} is already in simplest form (3 and 7 have no common factors other than 1

1. **State the problem:** Simplify the expression $$\frac{5(t^{-4} x^{-5})^{-1}}{3 t^{4} x^{-1}}$$. 2. **Apply the negative exponent rule:** For any expression $a^m$, $(a^m)^{-1} =

1. **State the problem:** Solve the equation $$p^{\frac{2}{3}} - 2p^{\frac{1}{3}} = 8$$ for $p$. 2. **Substitute:** Let $x = p^{\frac{1}{3}}$. Then $p^{\frac{2}{3}} = (p^{\frac{1}{

1. The problem is to order and place the given rational numbers on the number lines approximately. 2. Convert all values to decimals for easier comparison:

1. **State the problem:** Simplify the expression $$\frac{(-3x^{5} m^{-3})^{5}}{12x^{-1} m^{2}}$$. 2. **Apply the power to each factor in the numerator:**

1. **State the problem:** Simplify the expression $$\frac{(-3x^{5}m^{-3})^{5}}{12x^{-1}m^{2}}$$. 2. **Apply the power of a product rule:** Raise each factor inside the parentheses

1. **State the problem:** Simplify the fraction $$\frac{-4(y^5)^3}{20y^{-6}}$$ and express the result using only positive exponents. 2. **Simplify the numerator:** Apply the power

1. The user asked to "do equestions," which is unclear but likely means "do equations." 2. Since no specific equation or problem was provided, I cannot solve a particular equation.

1. **State the problem:** We need to order the rational numbers and decimals on a number line from -1 to 1. 2. **Convert all values to decimals for easy comparison:**

1. The problem is to analyze and plot the quadratic function $$y = x^2 + 10x + 7$$ including its vertex, turning point, and intercepts. 2. First, find the vertex (turning point) of

1. The problem asks us to place the values $\frac{3}{5}$, $-\frac{3}{5}$, $0$, $-0.15$, $-\frac{9}{20}$, $-0.85$, and $-40\%$ on number lines ranging from $-1$ to $1$ and $-1$ to $

1. **Problem statement:** We need to find the missing values in three lists of rational numbers ordered from least to greatest. 2. **List A:** Given: $0.08$, $\frac{1}{8}$, ____, $

1. **State the problem:** We need to analyze the quadratic function $$y = x^2 + 10x + 7$$ by finding its vertex (turning point), and the x- and y-intercepts. 2. **Find the vertex:*

1. **State the problem:** We are given the quadratic function $f(x) = -x^2 + 2x + 3$ and need to find: b. x- and y-intercepts

1. **State the problem:** We know a pen costs 10 and a pencil costs 5. Two pens are bought, and the total cost is 45. We need to find how many pencils were bought. 2. **Define vari