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4 years ago

What is the solution set for this linear-quadratic system of equations?

2 answers:

6 0

For this type of solution set, it is easiest to substitute one equation into another before we factor the resulting equation out...

y = x² - x - 12 (using this, we already know what y is equal to)
y - x - 3 = 0 (substitute the first value of y into this equation and simplify)

(x² - x - 12) - x - 3 = 0 (drop the parentheses)
x² - x - 12 - x - 3 = 0 (combine like terms)
x² - 2x - 15 = 0 (now we can factor -15)
(x - 5) (x + 3) = 0 (set each to equal 0)

x - 5 = 0 x + 3 = 0
x = 5 x = -3 (now we have the solution to the system)

Lostsunrise [7]4 years ago

3 0

Y - x - 3 = 0
y = x + 3

y = x^2 - x - 12
x + 3 = x^2 - x - 12
x^2 - x - 12 - x - 3 = 0
x^2 - 2x - 15 = 0
(x - 5)(x + 3) = 0

x - 5 = 0 y = x + 3
x = 5 y = 5 + 3
y = 8

x + 3 = 0 y = x + 3
x = -3 y = -3 + 3
y = 0

so ur solutions are : (5,8) and (-3,0)

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Prove by mathematical induction that 1+2+3+...+n= n(n+1)/2 please can someone help me with this ASAP. Thanks

Iteru [2.4K]

Let

$P(n):\ 1+2+\ldots+n = \dfrac{n(n+1)}{2}$

In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:

$P(1):\ 1 = \dfrac{1\cdot 2}{2}=1$

So, the base case is ok. Now, we need to assume $P(n)$ and prove $P(n+1)$ .

$P(n+1)$ states that

$P(n+1):\ 1+2+\ldots+n+(n+1) = \dfrac{(n+1)(n+2)}{2}=\dfrac{n^2+3n+2}{2}$

Since we're assuming $P(n)$ , we can substitute the sum of the first n terms with their expression:

$\underbrace{1+2+\ldots+n}_{P(n)}+n+1 = \dfrac{n(n+1)}{2}+n+1=\dfrac{n(n+1)+2n+2}{2}=\dfrac{n^2+3n+2}{2}$

Which terminates the proof, since we showed that

$P(n+1):\ 1+2+\ldots+n+(n+1) =\dfrac{n^2+3n+2}{2}$

as required

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3 years ago

Solve systems substitution. y=4x-13 3x-3y=12

Maru [420]

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List the markup and retail price of each item. Round to two decimal place when necessary.

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3 years ago

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inn [45]

It should be noted that a good that has a high demand elasticity for an economic variable implies that consumer demand for that good is more responsive to changes in the variable.

<h3>How to explain the demand?</h3>

It should be noted that an elastic demand is one werr the change in quantity demanded due to a change in price is large.

Also, an inelastic demand is one in which the change in quantity demanded due to a change in price is small. When the formula creates an absolute value greater than 1, the demand is elastic.

Here, a good that has a high demand elasticity for an economic variable implies that consumer demand for that good is more responsive to changes in the variable.

Learn more about demand on:

brainly.com/question/1245771

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1 year ago

Please help me <br><br> 6th grade math

Marta_Voda [28]

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Late response, sorry. It is 750 meters.

Step-by-step explanation:

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3 years ago