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Questions in mathematics

📝 Answered - Homework Progress 52%% 61 / 95 Marks By rounding to one significant figure, estimate the answers to these questions: a) $98 \div 11$ b) $\frac{764}{19}$ c) $\frac{798}{8 \times 41}$

📝 Answered - Find the sum. $1+1.13+1.13^2+1.13^3+\cdots+1.13^{12}$ The sum is $\square$ . (Round to four decimal places as needed.)

📝 Answered - Suppose a triangle has sides [tex]$a, b$[/tex], and [tex]$c$[/tex], and that [tex]$a^2+b^2\ \textless \ c^2$[/tex]. Let [tex]$\theta$[/tex] be the measure of the angle opposite the side of length [tex]$c$[/tex]. Which of the following must be true? Check all that apply. A. [tex]$\cos \theta\ \textgreater \ 0$[/tex] B. [tex]$a^2+b^2-c^2=2 a b \cos \theta$[/tex] C. [tex]$\cos \theta\ \textless \ 0$[/tex] D. The triangle is not a right triangle.

📝 Answered - Consider w = 2(cos(210°) + i sin(210°)) and z = 2(cos(330°) + i sin(330°)). What is w – z expressed in rectangular form?

📝 Answered - Add or subtract the following monomials: 1. 4x² + 7x² 2. -5a - 2a 3. 9y - 4y 4. -11xy + 7xy 5. -10ab - 15ab 6. -12c²d² + 8c²d² 7. -10b³c + (-9b³c) + b³c 8. 3x² + 4x + 2x² - 7x - 5

📝 Answered - Convert the following fractions into percentages. i. \(\frac{22}{100}\) ii. \(\frac{3}{4}\) iii. \(\frac{28}{24}\)

📝 Answered - 2. Prove the second distributive law: [tex]m(\overline{A} + \overline{B}) = m\overline{A} + m\overline{B}[/tex] 3. Define the modulus of a vector.

📝 Answered - Find the constant of variation [tex]$k$[/tex] for the inverse variation. Then write an equation for the inverse variation. [tex]$y=5 \text { when } x=7.5$[/tex]

📝 Answered - Which exponential function is represented by the table? A. [tex]f(x)=0.2(0.5^x)[/tex] B. [tex]f(x)=0.5(5^x)[/tex] C. [tex]f(x)=0.5(0.2^x)[/tex] D. [tex]f(x)=0.2(0.2^x)[/tex]

📝 Answered - If [tex]f(x)=\frac{x}{3}-2[/tex] and [tex]g(x)=3 x^2+2 x-6[/tex], find [tex](f+g)(x)[/tex] A. [tex]3 x^2+\frac{7}{3} x-8[/tex] B. [tex]3 x^2+\frac{5}{3} x+4[/tex] C. [tex]x^2+12[/tex] D. [tex]3 x^2+\frac{2}{3} x-8[/tex]