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The value of <em>b</em> so that 3 · x² + b · x - 24 has the same <em>x</em>-intercepts (only one <em>x</em>-intercept) is 12 √2.
<h3>How to determine a missing coefficient in a second order polynomial</h3>
<em>Second order</em> polynomials are represented graphically by parabolae and it may have two, one or no <em>x</em>-intercepts. The quantity of <em>x</em>-intercepts can be deducted from the discriminant of the quadratic formula, which is defined below:
For <em>a · x² + b · x + c = 0</em>, the discriminant is defined by:
<em>d = b² - 4 · a · c</em> (1)
There are three rules to determine the number of possible intercepts:
- If <em>d < 0</em>, then there are no <em>x</em>-intercepts.
- If <em>d = 0</em>, then there is only one <em>x</em>-intercept.
- If <em>d > 0</em>, then there are two <em>x</em>-intercepts.
Then, we have to find a value of <em>b</em> so that (1) has the following form:
<em>b² - 4 · 3 · (-24) = 0</em>
<em>b² - 288 = 0</em>
<em>b = 12√ 2</em>
The value of <em>b</em> so that 3 · x² + b · x - 24 has the same <em>x</em>-intercepts (only one <em>x</em>-intercept) is 12 √2.
The answer choices do not correspond with the given statement, the phrase "same x-intercepts" may lead to confusion and possible graph cannot be found. A possible corrected statement is shown below:
<em>The graph of g(x) = 3 · x² + b · x - 24 has only one x-intercept. What is the value of </em><em>b</em><em>?</em>
To learn more on parabolae, we kindly invite to check this verified question: brainly.com/question/10572747
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Answer:
The vertex of the parabola is (-2,0)
Step-by-step explanation:
The given function is:
Now, in order to find the vertex for the parabola, that is v(h,k), comparing the above equation with the standard form of equation that is , we get
a=-3, b=-6 and c=0
We know, and
, therefore
and
Thus, the vertex is given as:(h,k)=(-2,0).
Answer:
Refer to the explanation.
Step-by-step explanation:
Let's take each one at a time.
1.
To solve for the complement, we simply subtract our markup rate by 100%.
100% - 30% = 70%
Now to solve for the selling price, we use the formula
Selling Price = $123.91
2.
We do the same process with the first number.
100% - 40% = 60%
SellingPrice = $366.67
3.
The same as the first two.
100% - 20% = 80%
SellingPrice = $111.88
4.
Now to solve for the markup rate, we use the formula:
In this case we first need to find the markup. The markup is the difference between the selling price and the cost.
Selling Price = $235.28
Cost = $199.99
Markup = $235.28 - $199.99
Markup = $35.29
Now the we know our markup, we can then solve for the markup rate using the formula.
MarkupRate = 0.1499 x 100 = 14.99% or 15%
5.
Now for the last one, we need to find for the cost. Let's use the selling price formula to find for the cost.
Selling Price = $30.77
Complement = 65% or 0.65
This will then give us.
We multiple both sides of the equation by 0.65 to leave our cost alone.
30.77 x 0.65 = Cost
Cost = $20
The factored form of the equation 9x⁴y - 6x³y² + 3x²y³ is 3x²y(3x²-2xy+y²).
<h3>What is factored form?</h3>The product of a constant and two linear expressions in factored form. The roots of the function are the parameters and the x-intercepts of the graph. Often Factoring is referred to as the process of converting a quadratic function to factored form.
We need to write the given expression in the factored form, therefore, we will take the common terms out of the given expression,
1. Taking 3 as the common term, we will get,
2. Taking x² as the common term
3. Taking y as the common term,
Hence, the factored form of the equation 9x⁴y - 6x³y² + 3x²y³ is 3x²y(3x²-2xy+y²).
Learn more about Factored Form: