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9966 [12]
3 years ago
12

Hi. Please i need help with this . No jokes .​

Mathematics
1 answer:
skad [1K]3 years ago
4 0

Answer:

I) The roots are:

First Case:

x=-2\text{ or } x=-6

Second Case:

x=2\text{ or } x=6

II) Possible values of p are:

First Case:

p=-12

Second Case:

p=4

Step-by-step explanation:

We have the equation:

x^2-(4+p)x+12=0

We know that one of the roots is three times the other.

And we want to find the roots of the equation and the possible values for p.

To find our solutions, we can use the process of factoring.

If we have an equation in the form:

x^2+bx+c=0

We want to find two numbers, say, k and j, such that:

\displaystytle kj=c\text{ and } k+j=b

After finding them, we can factor as such:

(x+k)(x+j)

So, -k and -j will be our zeros.

Therefore, for our equation, we will find two numbers k and j such that:

\displaystyle kj=12\text{ and } k+j=-(4+p)

Notice that for the first criterion, we can simply list all the factors of 12.

So, according to the first equation, possible values of k and j are:

1 and 12; 2 and 6; or 3 and 4.

Then, our roots will be -1 and -12; -2 and -6; or -3 and -4, respectively.

However, remember that one of our roots is three times the other.

Therefore, the only candidates that work will be the second option.

Hence, k and j are 2 and 6.

Therefore:

k=2\text{ and } j=6

With this information, we can now determine p. Since:

k+j=-(4+p)

Then it follows that:

\begin{aligned}(2)+(6)&=-(4+p)\\8&=-(4+p)\\-8&=4+p\\p&=-12\end{aligned}

Hence, our equation is:

x^2-(4+-12)x+12=0

Or, factored:

x^2+8x+12=0 \text{ or } (x+6)(x+2)=0

So, our roots are x=-6 and x=-2 when p=-12.

However, we also need to consider the negative factors of 12.

Factors of 12 also include -2 and -6.

Hence, our k and j can also be k=-2 and j=-6.

Then, in this case, our p is :

\begin{aligned} (-2)+(-6)&=-(4+p)\\-8&=-(4+p)\\8&=4+p\\p&=4\end{aligned}

Therefore, for our second case, k=-2 and j=-6. Then p=4. So, our equation is:

x^2-(4+4)x+12=0

Or, factored:

x^2-8x+12\text{ or } (x-2)(x-6)=0

Hence, when p=4, our roots are x=2 and x=6.

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Answer:

Hello,

Step-by-step explanation:

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Billy is hiking in Colorado. He walks eastward four miles, then turns $60$ degrees northward and walks six miles. How far is he
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Suppose Billy starts at point A, turns at point B, and ends at point D, as shown below.

If Billy turns 60◦ northward and walks six miles, then we can draw a 30 − 60 − 90 triangle whose hypotenuse is 6 miles

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By the Pythagorean Theorem, the distance from his starting point is q:

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Graph the image of the given triangle after the transformation that has the rule (x, y)→(x−5, y+6)
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Ashad is rewriting the expression 28 a + 36 a b as a product. Which statements about the expression are accurate and relevant to
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Answer:

(B)The GCF of the numbers(28 and 36) in each term in the expression is 4.

(C)The GCF of the variables(a and ab) in each term in the expression is a.

(E)The factored form of the expression is 4a(7+9b)

Step-by-step explanation:

Given the expression: 28a+36ab

If we write it as a product, we obtain:

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We can see the following

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The correct options are B, C, and E.

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Answer:

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Step-by-step explanation:

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