Podcast
Questions and Answers
When subtracting fractions with like denominators, which step is crucial after finding a common denominator?
When subtracting fractions with like denominators, which step is crucial after finding a common denominator?
- Divide the denominators.
- Subtract the numerators. (correct)
- Add the denominators.
- Multiply the numerators.
What is the simplified form of $p^{-1}q^2$?
What is the simplified form of $p^{-1}q^2$?
- $\frac{p}{q^2}$
- $\frac{1}{pq^2}$
- $pq^2$
- $\frac{q^2}{p}$ (correct)
Given the expression $\frac{7p}{pq^{-2}} - \frac{2}{q}$, what is the first step to simplify it?
Given the expression $\frac{7p}{pq^{-2}} - \frac{2}{q}$, what is the first step to simplify it?
- Eliminate the variable $p$.
- Factor out common terms.
- Combine the denominators.
- Write the expression with only positive exponents. (correct)
After rewriting $\frac{7p}{pq^{-2}} - \frac{2}{q}$ with positive exponents, what is the resulting expression before simplification?
After rewriting $\frac{7p}{pq^{-2}} - \frac{2}{q}$ with positive exponents, what is the resulting expression before simplification?
What is the simplified form of $\frac{7pq^2}{q} - \frac{2}{q}$?
What is the simplified form of $\frac{7pq^2}{q} - \frac{2}{q}$?
A rectangular field has a length of $\frac{6a}{3a+4}$ km and a width of $\frac{8}{3a+4}$ km. What expression represents the perimeter of the field?
A rectangular field has a length of $\frac{6a}{3a+4}$ km and a width of $\frac{8}{3a+4}$ km. What expression represents the perimeter of the field?
If the perimeter of a rectangular field is given by $2(\frac{6a}{3a+4} + \frac{8}{3a+4})$, what is the simplified expression for the perimeter?
If the perimeter of a rectangular field is given by $2(\frac{6a}{3a+4} + \frac{8}{3a+4})$, what is the simplified expression for the perimeter?
Given the expression $\frac{12a + 16}{3a+4}$, what is the completely simplified form of this expression?
Given the expression $\frac{12a + 16}{3a+4}$, what is the completely simplified form of this expression?
The area of a store's sign cannot exceed 900 square decimeters, according to a city bylaw. Which inequality represents the possible areas, $A$, of the sign?
The area of a store's sign cannot exceed 900 square decimeters, according to a city bylaw. Which inequality represents the possible areas, $A$, of the sign?
Given the numbers 176, 134, 208, 170, 149, 153, 136, 200, 168, 150, 157, 141, 211, 176, 145, 155, 128, 199, 182, 148, what is the median of this data set?
Given the numbers 176, 134, 208, 170, 149, 153, 136, 200, 168, 150, 157, 141, 211, 176, 145, 155, 128, 199, 182, 148, what is the median of this data set?
Rewrite the equation $5x + 3y = 9$ in slope-intercept form.
Rewrite the equation $5x + 3y = 9$ in slope-intercept form.
Which equation has a slope of $-\frac{1}{2}$ and a y-intercept of -3?
Which equation has a slope of $-\frac{1}{2}$ and a y-intercept of -3?
Which values from the set ${-1, 0, 1, 2}$ are solutions to the inequality $x - 1 \geq 4$?
Which values from the set ${-1, 0, 1, 2}$ are solutions to the inequality $x - 1 \geq 4$?
The graph shows the temperature is now at least the temperature it was this morning. How can the current temperature be expressed as a sentence given the inequality $x \ge -14$?
The graph shows the temperature is now at least the temperature it was this morning. How can the current temperature be expressed as a sentence given the inequality $x \ge -14$?
The specifications for a housing development include that each lot has to be at least $3\frac{1}{2}$ acres. Which inequality represents this situation, where $A$ is the size of a lot in acres?
The specifications for a housing development include that each lot has to be at least $3\frac{1}{2}$ acres. Which inequality represents this situation, where $A$ is the size of a lot in acres?
What is the first step in determining the equation of a line given two points?
What is the first step in determining the equation of a line given two points?
Given the simple interest formula I = prt, how would tripling the principal (p) and halving the time (t) affect the total interest (I) earned?
Given the simple interest formula I = prt, how would tripling the principal (p) and halving the time (t) affect the total interest (I) earned?
For what value(s) of x is the rational expression $\frac{x - 5}{15x^2 - 75x}$ undefined?
For what value(s) of x is the rational expression $\frac{x - 5}{15x^2 - 75x}$ undefined?
A line has a slope of 3 and passes through the points (-1, -2) and (4, y). What is the value of y?
A line has a slope of 3 and passes through the points (-1, -2) and (4, y). What is the value of y?
Which inequality correctly translates the sentence: "The difference of -4 and an unknown number is less than or equal to 0"?
Which inequality correctly translates the sentence: "The difference of -4 and an unknown number is less than or equal to 0"?
What is the value of $- \sqrt{x}$ when $x = \frac{25}{16}$?
What is the value of $- \sqrt{x}$ when $x = \frac{25}{16}$?
Arminda has a bag business. It costs her $1100 plus $18 per bag to produce them, and she sells the bags for $40 each. How many bags must she sell to gain a profit of at least $2200?
Arminda has a bag business. It costs her $1100 plus $18 per bag to produce them, and she sells the bags for $40 each. How many bags must she sell to gain a profit of at least $2200?
Given the dataset of newborns' weights: 5, 8, 6, 5, 7, 8, 10, 7, 8, 6. What are the mean, median, and mode, respectively?
Given the dataset of newborns' weights: 5, 8, 6, 5, 7, 8, 10, 7, 8, 6. What are the mean, median, and mode, respectively?
What is the slope of the line that passes through the points (-1, 2) and (3, 2)?
What is the slope of the line that passes through the points (-1, 2) and (3, 2)?
Rachel crochets 24 inches of a 72-inch blanket, and Michelle finishes it. If Michelle crochets at 8 inches per day, which equation represents the blanket's length, $y$, after Michelle crochets for $x$ days?
Rachel crochets 24 inches of a 72-inch blanket, and Michelle finishes it. If Michelle crochets at 8 inches per day, which equation represents the blanket's length, $y$, after Michelle crochets for $x$ days?
John is 500 miles from home and traveling towards it at a constant rate of 65 miles per hour. The equation $d = 500 - 65t$ gives his distance $d$ from home after $t$ hours. How far away from home is John after 4 hours?
John is 500 miles from home and traveling towards it at a constant rate of 65 miles per hour. The equation $d = 500 - 65t$ gives his distance $d$ from home after $t$ hours. How far away from home is John after 4 hours?
Which of the following expressions is a monomial?
Which of the following expressions is a monomial?
Determine the degree of the monomial: $7a^3b^2c$
Determine the degree of the monomial: $7a^3b^2c$
Which expression represents the total length Michelle needs to crochet to complete the blanket?
Which expression represents the total length Michelle needs to crochet to complete the blanket?
Consider John's trip home. If he travels for 5 hours, what does the value of $d$ represent in the equation $d = 500 - 65t$?
Consider John's trip home. If he travels for 5 hours, what does the value of $d$ represent in the equation $d = 500 - 65t$?
A monomial has a degree of 5 and contains the variables $x$ and $y$. Which of the following could represent this monomial?
A monomial has a degree of 5 and contains the variables $x$ and $y$. Which of the following could represent this monomial?
A company approximates its national advertising spending with the polynomial $59x^2 - 262x + 3888$ and local advertising with the polynomial $-33x^3 + 611x^2 - 1433x + 28060$, where $x$ represents years since the campaign began. What polynomial represents the total advertising spending?
A company approximates its national advertising spending with the polynomial $59x^2 - 262x + 3888$ and local advertising with the polynomial $-33x^3 + 611x^2 - 1433x + 28060$, where $x$ represents years since the campaign began. What polynomial represents the total advertising spending?
Given the points (4, 5) and (6, 4) lie on a line, what is the equation of this line in slope-intercept form?
Given the points (4, 5) and (6, 4) lie on a line, what is the equation of this line in slope-intercept form?
Which expression is not a polynomial?
Which expression is not a polynomial?
What is the degree of the polynomial $-a^2b^2c^3 + 5x^5$?
What is the degree of the polynomial $-a^2b^2c^3 + 5x^5$?
What polynomial, when subtracted from $3x^2 + 7x - 6$, results in $-6$?
What polynomial, when subtracted from $3x^2 + 7x - 6$, results in $-6$?
What is the equation of the line in point-slope form that passes through the point (3, 1) and has a slope of -1?
What is the equation of the line in point-slope form that passes through the point (3, 1) and has a slope of -1?
If a line passes through the point (6, -3) and has slope of -2, which of the following points also lies on this line?
If a line passes through the point (6, -3) and has slope of -2, which of the following points also lies on this line?
Is the statement $4 = 4x^0$ true or false, and why?
Is the statement $4 = 4x^0$ true or false, and why?
Given the distances of planets from the sun (in millions of miles): 36, 67, 93, 142, 484, 887, 1765, and 2791, which of the following values would be considered an outlier when constructing a box-and-whisker plot?
Given the distances of planets from the sun (in millions of miles): 36, 67, 93, 142, 484, 887, 1765, and 2791, which of the following values would be considered an outlier when constructing a box-and-whisker plot?
A product's price increased from $2175.00 to $2392.50. What is the approximate percentage increase in the price?
A product's price increased from $2175.00 to $2392.50. What is the approximate percentage increase in the price?
For the quiz scores: 86, 92, 88, 100, 86, 94, 92, 78, 90, 96, 94, 84, which measure of central tendency would be most appropriate to represent the data, considering potential outliers and distribution?
For the quiz scores: 86, 92, 88, 100, 86, 94, 92, 78, 90, 96, 94, 84, which measure of central tendency would be most appropriate to represent the data, considering potential outliers and distribution?
A skateboard factory has 467 skateboards in stock and produces 115 skateboards per hour. Assuming no shipments are made, which linear equation in slope-intercept form represents the number of skateboards in inventory after $x$ hours?
A skateboard factory has 467 skateboards in stock and produces 115 skateboards per hour. Assuming no shipments are made, which linear equation in slope-intercept form represents the number of skateboards in inventory after $x$ hours?
A tire's tread depth decreases as mileage increases. Given the data points (10000 miles, 20 mm), (20000 miles, 16 mm), (30000 miles, 12 mm), and (40000 miles, 8 mm), what is the average rate of wear for this tire brand, in mm per 10,000 miles?
A tire's tread depth decreases as mileage increases. Given the data points (10000 miles, 20 mm), (20000 miles, 16 mm), (30000 miles, 12 mm), and (40000 miles, 8 mm), what is the average rate of wear for this tire brand, in mm per 10,000 miles?
Consider the statements: (1) If a vehicle is a truck, then the vehicle is automatic. (2) All trucks are motor vehicles. Which of the following is true?
Consider the statements: (1) If a vehicle is a truck, then the vehicle is automatic. (2) All trucks are motor vehicles. Which of the following is true?
What is the key difference between $\sqrt{-1}$ and $\sqrt{1}$?
What is the key difference between $\sqrt{-1}$ and $\sqrt{1}$?
Why cannot the expression $\frac{2g}{2g + 6}$ be simplified to $\frac{1}{6}$?
Why cannot the expression $\frac{2g}{2g + 6}$ be simplified to $\frac{1}{6}$?
Flashcards
Subtracting Rational Expressions
Subtracting Rational Expressions
To subtract rational expressions, they must have a common denominator. Then, subtract the numerators and keep the denominator.
Inequality
Inequality
A mathematical statement that compares two expressions using inequality symbols.
Graph of an Inequality
Graph of an Inequality
A visual representation of all solutions to an inequality on a number line.
Positive Exponents
Positive Exponents
Signup and view all the flashcards
X-intercept
X-intercept
Signup and view all the flashcards
Greatest Common Factor (GCF)
Greatest Common Factor (GCF)
Signup and view all the flashcards
Perimeter
Perimeter
Signup and view all the flashcards
Y-intercept
Y-intercept
Signup and view all the flashcards
Proportion
Proportion
Signup and view all the flashcards
Rectangle
Rectangle
Signup and view all the flashcards
Slope
Slope
Signup and view all the flashcards
Perimeter of a Rectangle Formula
Perimeter of a Rectangle Formula
Signup and view all the flashcards
Slope-intercept form
Slope-intercept form
Signup and view all the flashcards
Substitution
Substitution
Signup and view all the flashcards
Median
Median
Signup and view all the flashcards
Simplification
Simplification
Signup and view all the flashcards
Zero Slope
Zero Slope
Signup and view all the flashcards
What is a Monomial?
What is a Monomial?
Signup and view all the flashcards
Degree of a Monomial
Degree of a Monomial
Signup and view all the flashcards
Like Terms
Like Terms
Signup and view all the flashcards
Adding Polynomials
Adding Polynomials
Signup and view all the flashcards
Subtracting Polynomials
Subtracting Polynomials
Signup and view all the flashcards
Term (in an Expression)
Term (in an Expression)
Signup and view all the flashcards
Simple Interest
Simple Interest
Signup and view all the flashcards
Undefined Rational Expression
Undefined Rational Expression
Signup and view all the flashcards
Mode
Mode
Signup and view all the flashcards
Radical Index
Radical Index
Signup and view all the flashcards
Point-Slope Form
Point-Slope Form
Signup and view all the flashcards
Polynomial
Polynomial
Signup and view all the flashcards
Degree of a Polynomial
Degree of a Polynomial
Signup and view all the flashcards
Zero Exponent Rule
Zero Exponent Rule
Signup and view all the flashcards
Box-and-Whisker Plot
Box-and-Whisker Plot
Signup and view all the flashcards
Ordering Data
Ordering Data
Signup and view all the flashcards
Percent Increase/Decrease
Percent Increase/Decrease
Signup and view all the flashcards
Measure of Central Tendency
Measure of Central Tendency
Signup and view all the flashcards
Average Rate of Wear
Average Rate of Wear
Signup and view all the flashcards
Counterexample
Counterexample
Signup and view all the flashcards
√-1 vs √1
√-1 vs √1
Signup and view all the flashcards
Study Notes
- Rational expressions include variables in the denominator.
- All values that would make the denominator equal to zero are excluded.
Identifying Excluded Values
- To identify excluded values set the Denominator = 0, and solve for variables
Simplifying Rational Expressions
- Factor out the greatest common factor (GCF).
- Divide out common factors.
- If there is more than one term in the numerator or denominator, begin by factoring
Simplifying Expressions with Integer Exponents
- Write the expression with only positive exponents.
- The expressions must have like denominators in order to subtract the numerators.
- Factor the numerator, and the GCF is 2. Simplify after factorisation
Application: Fencing a Field
- Use the formula for finding the perimeter of a rectangle: P = 2 (l + w)
- Substitute the length and width.
- If like denominators exist, add the numerators.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.