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Composite Functions: f(g(x)) and g(f(x)) | MathHelp.com
By MathHelp.com
In this problem, we’re asked to add the given polynomials, then we’re asked to subtract the second polynomial from the first. In part a, to add the given polynomials, we simply add parentheses t^2 + 6t – 9 + parentheses t^2 + 7t - 3. Notice that I used parentheses around the polynomials. This is a good habit to get into, even though the parentheses will not affect the addition. Next, we simply add the like terms, t^2 + t^2 is 2t^2, 6t + 7t is 13t, and -9 - 3 is -12. So we have 2t^2 + 13t – 12. In part b, we’re asked to subtract the second polynomial from the first, so we have parentheses t^2 + 6t – 9 minus parentheses t^2 + 7t - 3. Notice that the second polynomial is subtracted from the first. And again, notice that we use parentheses around each polynomial. Now, it’s important to understand that the minus sign outside the second set of parentheses can be thought of as a negative 1, so we need to distribute the -1 through each of the terms in the second set of parentheses. So, after rewriting our first polynomial, t^2 + 6t – 9, we have -1 times t^2, or –t^2, -1 times positive 7t, which is -7t, and -1 times -3, which is positive 3. Now, we combine like terms. t^2 – t^2 cancels out, positive 6t minus 7t is -1t, or –t, and -9 + 3 is -6. So we have –t – 6. Makes sure to distribute the negative 1 through the parentheses when subtracting the second polynomial from the first.
Adding and Subtracting Polynomials | MathHelp.com
By MathHelp.com
In this example, notice that each of our variables, x, y, and z, appears in all three equations. To solve this system, we use the addition method. In other words, let’s start with our first two equations, x + y + z = 4, and x – y + z = 2. Notice that if we add these equations together, the +y and –y will cancel out, and we have 2x + 2z = 6. So, in our new equation, 2x + 2z = 6, we’ve eliminated the variable y. Unfortunately, we still haven’t solved for any of our variables. However, if we can create another equation with just x and z in it, then we’ll have a system of equations in two variables, which we can use to solve for x and z. To create another equation with just x and z in it, we need to eliminate y. We can’t add the first and second equations together, because we’ve already done that. However, notice that if we add the first and third equations together, the first equation has a +y and the third equation has a –y, so we’ll be able to eliminate the y. So we have our first equation, x + y + z = 4, and our third equation, x – y – z = 0, and adding them together, notice that the +y – y cancels out, and, as a bonus, the +z – z also cancels out, so we have 2x = 4, and dividing both sides by 2, x = 2. Now, since we know that x = 2, notice that if we plug a 2 in for x in the equation that we created earlier, we can solve for z. And we have 2(2) + 2z = 6, or 4 + 2z = 6, and subtracting 4 from both sides, we have 2z = 2, and dividing both sides by 2, z = 1. So x = 2 and z = 1, and to find the value of y, we simply plug our values of x and z into any of the equations in the original system. Let’s use the first equation, x + y + z = 4. Since x = 2 and z = 1, we plug a 2 in for x and a 1 in for z, and we have 2 + y + 1 = 4, or 3 + y = 4, and subtracting 3 from both sides, y = 1. So x = 2, y = 1, and z = 1, and finally, we write our answer as the ordered triple, x, y, z, or (2, 1, 1).
14 - Solve Quadratic Systems of Equations by Addition - Part 1 (Simultaneous Equations)
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
OST 2020-21 Blueprint and Best Practices | 10 Min. webinar organized by EdShorts
By Lumos Learning
This Free 10 Min power-packed webinar organized by EdShorts on Jan 27th provides all the information available about 2021 OST Assessments - such as testing guidelines, blueprint changes, testing windows, and more! Join the EdShorts Facebook community today: https://www.facebook.com/groups/60370... for more bite-sized power-packed webinars every week!
Subordinating conjunctions | The parts of speech | Grammar | Khan Academy
By Khan Academy
This video shows that subordinating conjunctions join two parts of complex sentences––independent clauses to dependent clauses.
MAAP 2020-21 Blueprint and Best Practices | 10 Min. webinar organized by EdShorts
By Lumos Learning
This Free 10 Min power-packed webinar organized by EdShorts on Jan 28th provides all the information available about 2021 LEAP Assessments - such as testing guidelines, blueprint changes, testing windows, and more! Join the EdShorts Facebook community today: https://www.facebook.com/groups/60370... for more bite-sized power-packed webinars every week!
