Questions in mathematics

Questions in mathematics

📝 Answered - When solving an equation, we use the properties of equality to isolate the variable on one side of the equation. Properties of Equality Let [tex]$a, b, c$[/tex] be real numbers. | Symmetric | If [tex]$a=b$[/tex], then [tex]$b=a$[/tex]. | When the values or expressions in an equation switch sides, they remain equal. | | Addition | If [tex]$a=b$[/tex], then [tex]$a+c=b+c$[/tex]. | When the same value is added on both sides of an equation, the sums are equal. | | Subtraction | If [tex]$a=b$[/tex], then [tex]$a-c=b-c$[/tex] | When the same value is subtracted from both sides of an equation, the differences are equal. | | Multiplication | If [tex]$a=b$[/tex], then [tex]$a c=b c$[/tex] . | When both sides of an equation are multiplied by the same value, the products are equal. | | Division | If [tex]$a=b$[/tex], then [tex]$\frac{a}{c}=\frac{b}{c}$[/tex]. | When both sides of an equation are divided by the same value, the quotients are equal. | | Distributive | [tex]$a(b+c)=a b+ac$[/tex] | The product of a value and a sum is equal to the sum of the products of the value and each addend. | | Zero Product | If [tex]$a c=0$[/tex], then [tex]$a=0$[/tex] or [tex]$c=0$[/tex]. | When a product is equal to zero, at least one of the factors must equal zero.

📝 Answered - Solve the equation. Express numbers as integers or simplified fractions. [tex]\frac{6 y-4}{6}=\frac{4 y-8}{9}+\frac{y}{3}[/tex]

📝 Answered - Consider the following: 1. [tex]$(\neg Z \vee \neg I) \leadsto \neg(H \wedge Q)$[/tex] 2. [tex]$(\neg Z)$[/tex] [tex]$\therefore(L \rightarrow N)$[/tex] Which of the following can be derived from the premises? a) [tex]$(L)$[/tex] b) [tex]$(-2 \vee -4)$[/tex] c) [tex]$(- H \vee C )$[/tex]

📝 Answered - Calculate $\frac{5}{8} \times \frac{4}{15}$. Give your answer in its simplest form.

📝 Answered - Fill in the gaps to factorise this expression. [tex]x^2+4 x-21=(x-\ldots)(x+\ldots)[/tex]

📝 Answered - Express [tex]\sqrt{\frac{19}{20}}[/tex] as a decimal.

📝 Answered - What is $1.63 \times 10^9$ written in standard form?

📝 Answered - Deposits and purchases: | Day | Debit ($) | Credit ($) | | --------- | --------- | ---------- | | Monday | 194.62 | 35.45 | | Tuesday | - | 11.20 | | Wednesday | 145.86 | 24.75 | | Thursday | 53.35 | 33.80 | | Friday | 31.60 | 45.77 | | Saturday | 12.90 | 61.63 | Anna gets an overdraft fee if her balance at the end of the day is negative. On which day or days does Anna get charged an overdraft fee? I. Wednesday II. Thursday III. Friday A. I only B. I and II C. II and III D. III only

📝 Answered - An upholsterer cuts a $1 \frac{6}{3}$ foot piece of cording from a piece that is $2 \frac{1}{4}$ feet long. How much cording is left? A. $\frac{7}{12}$ ft B. $1 \frac{5}{12}$ ft C. $1 \frac{7}{12}$ ft D. $3 \frac{11}{12}$ ft

📝 Answered - How to solve the equation -6x + 10 = 46