🧮 algebra

1. The problem states that the original price of the necklace was £54 and it is reduced by 8.5% in the sale. 2. To find the sale price, we first calculate the amount of discount us

1. We start with the given equation: $$(8^3 \times 8^4)^5 = 8^w$$ 2. Use the property of exponents for multiplication: $$a^m \times a^n = a^{m+n}$$ to combine $8^3$ and $8^4$. So,

1. The problem asks which two expressions are equivalent to $4^{-3}$. 2. Recall that negative exponents mean the reciprocal: $4^{-3} = \frac{1}{4^3}$.

1. **State the problem:** Solve the equation $$\left(\frac{3}{4}\right)^{2x-1} \cdot \left(\frac{4}{3}\right)^{x+2} = \frac{9}{16}.$$\n\n2. **Rewrite the bases to facilitate simpli

1. The problem is to evaluate the expression $1000^{-\frac{3}{2}}$. 2. Recall that a negative exponent means we take the reciprocal:

1. The problem asks to find the value of $$1000^{\left(-\frac{2}{3}\right)}$$. 2. Start by rewriting the base number 1000 as a power of 10: $$1000 = 10^3$$.

1. State the problem: Solve for $d$ in the equation $$(17^3)^d = 17^{12}$$. 2. Use the power of a power rule: When raising an exponential expression to another power, multiply the

1. **State the problem:** We need to find the difference between the sale prices of two houses. Each house has an original price and a percentage discount offer. We will calculate

1. The problem is to match the equation $y=2^x$ with its correct graph. 2. The equation $y=2^x$ represents an exponential function with base 2.

1. The problem asks to match the equation $y=5x$ with its corresponding graph. 2. The equation $y=5x$ is a linear equation representing a straight line passing through the origin.

1. We are asked to simplify or analyze the function $$y=\frac{2x^4 \tan x}{e^{2x} \sin x}$$. 2. Recall that $$\tan x = \frac{\sin x}{\cos x}$$, so substitute this in to rewrite the

1. We are given the function $$y = x(x - 1)$$ and the domain $$\{-2, -1, 0, 1, 2\}$$. 2. To find the range, substitute each value from the domain into the function and calculate th

1. We are asked to find the value of $h$ in the equation $$(19^3)^{-8} = 19^h.$$ 2. Recall the exponent rule: $$(a^m)^n = a^{m \cdot n}.$$

1. **State the problem:** We need to find the value of $f$ in the equation $$15^4 - 7 = 15^f.$$\n\n2. **Evaluate the left side expression:** Calculate $15^4$.\n$$15^4 = 15 \times 1

1. The problem asks to find the value of the function $f(x)$ at $x = -2.3$ given the function $f(x) = 12$. 2. Since $f(x) = 12$ is a constant function, it means that for every inpu

1. **State the problem:** Solve for $f$ in the equation $$154 - 7 = 15f.$$\n\n2. **Simplify the left side:** Calculate $154 - 7$.\n$$154 - 7 = 147.$$\n\n3. **Rewrite the equation:*

1. We are asked to find the value of $10,000^{\frac{3}{4}}$. 2. First, express $10,000$ in terms of powers of 10: $10,000 = 10^4$.

1. The problem is to analyze the function $y = x^4$ and understand its properties. 2. This function is a polynomial of degree 4. It is even because $y(-x) = (-x)^4 = x^4 = y(x)$.

1. Stating the problems: We have two separate problems to solve:

1. The problem gives us the expression $$\frac{6R - 18}{3(1 + R)} \div (k - 3).$$ 2. First, simplify the fraction $$\frac{6R - 18}{3(1 + R)}.$$ Factor the numerator: $$6R - 18 = 6

1. Mari kita tulis ulang persamaan yang diberikan: $$x^2 y^2 x - y = \frac{1}{2} 642 y^8.$$\n2. Sederhanakan bagian kiri persamaan: $$x^2 \cdot y^2 \cdot x = x^3 y^2,$$ jadi persam