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3 years ago

One of my factors is 9. The sum of my product of my two factors is 13. What inumber am I?

Mathematics

1 answer:

timofeeve [1]3 years ago

5 0

4 x+9=13 X=4 subtract 9 from the 9 and 13 and 13-9 =4 so x=4

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Find the polynomial of minimum degree, with real coefficients, zeros at

drek231 [11]

Answer:

$\huge\boxed{p(x)=4x^3-20x^2+4x+300}$

Step-by-step explanation:

$\text{If}\ x=4\pm3i\ \text{and}\ x=-3\ \text{are the zeros of a polynomial, then it has a form:}\\\\p(x)=\bigg(x-(4-3i)\bigg)\bigg(x-(4+3i)\bigg)\bigg(x-(-3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x-4+3i)(x-4-3i)(x+3)\bigg(r(x)\bigg)\\\\p(x)=\underbrace{\bigg((x-4)+3i\bigg)\bigg((x-4)-3i\bigg)}_{\text{use}\ (a+b)(a-b)=a^2-b^2}(x+3)\bigg(r(x)\bigg)\\\\p(x)=\bigg((x-4)^2-(3i)^2\bigg)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2$

$p(x)=(x^2-2(x)(4)+4^2-3^2i^2)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ i^2=-1\\\\p(x)=(x^2-8x+16-9(-1))(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+16+9)(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+25)(x+3)\bigg(r(x)\bigg)\qquad\text{use FOIL}:\ (a+b)(c+d)=ac+ad+bc+bd\\\\p(x)=\bigg((x^2)(x)+(x^2)(3)+(-8x)(x)+(-8x)(3)+(25)(x)+(25)(3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x^3+3x^2-8x^2-24x+25x+75)\bigg(r(x)\bigg)\qquad\text{combine like terms}\\\\p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)$

$\text{The y-intercept is at 300}.\\\\\text{For}\ w(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_1x+a_0\\\\\text{y-intercept is}\ a_0\\\\\text{Therefore for}\ p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)\\\\\text{y-intercet is}\ 75\bigg(r(x)\bigg)\\\\75\bigg(r(x)\bigg)=300\qquad\text{divide both sides by 75}\\\\r(x)=4\\\\\text{Finally:}\\\\p(x)=(x^3-5x^2+x+75)(4)\qquad\text{use the distributive property}\\\\p(x)=(x^3)(4)+(-5x^2)(4)+(x)(4)+(75)(4)\\\\p(x)=4x^3-20x^2+4x+300$

7 0

4 years ago

Find the equation of the line through ( - 10, - 8) that is perpendicular to the line through (10,6), (5,5).

Furkat [3]

Answer:

y=-5x-58

Step-by-step explanation:

The equation of a line in slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

Perpendicular lines have opposite reciprocal slopes.

Anyways we need to find the slope of the line going through (10,6) and (5,5).

To find the slope, we are going to line up the points vertically and subtract vertically, then put 2nd difference over 1st difference. Like so:

( 10 , 6)

- ( 5 , 5)

------------------

5 1

So the slope of the line through (10,6) and (5,5) is 1/5.

The slope of a line that is perpendicular will be the opposite reciprocal of 1/5.

The opposite reciprocal of 1/5 is -5.

The line we are looking for is y=-5x+b where we need to find the y-intercept b.

y=-5x+b goes through (-10,-8)

So we can use (x,y)=(-10,-8) to find b in y=-5x+b.

y=-5x+b with (x,y)=(-10,-8)

-8=-5(-10)+b

-8=50+b

Subtract 50 on both sides:

-8-50=b

-58=b

So the equation is y=-5x-58

4 0

4 years ago

Factor 64 - P.<br> (8 - x(8 - x)<br> (8 + x (8 - x)<br> (X + 8)(x-8)

muminat

Question:

Factor $64-x^2$

(8 - x)(8 - x)

(8 + x) (8 - x)

(X + 8)(x-8)

Answer:

Option B: $(8+x)(8-x)$ is the factor

Explanation:

Given that the expression is $64-x^2$

We need to find the factor of the given expression.

Let us rewrite the expression as $8^2-x^{2}$

Since the expression is of the form $a^2-b^2$ , let us use the identity $a^2-b^2=(a+b)(a-b)$

where a = 8 and b = x

Substituting the values in the identity, then the expression can be written as

$8^2-x^{2}=(8+x)(8-x)$

Thus, the factor of the expression is $(8+x)(8-x)$

Hence, Option B is the correct answer.

4 0

3 years ago

3 3/4 ÷ 4 1/2 = ????????????????

nata0808 [166]

Answer:

$\frac{5}{6}$

6 0

3 years ago

Read 2 more answers

A box of jerseys for a pick-up game of basketball contains 9 extra-large jerseys, 6 large jerseys, and 5 medium jerseys. If you

aleksley [76]

Answer:

1/114 or 0.008772

Step-by-step explanation:

I am not very sure, my answer seems unlikely, but here's what I think:

There are 20 jerseys in the box to begin with, and 5 medium jerseys that you can have.

Therefore, the probability of you randomly grabbing a medium sized jersey is 5/20 or 1/4.

After taking out one medium sized jersey, there are 19 jerseys in the box and 4 medium jerseys you can pick from.

The probability of you randomly grabbing a medium sized jersey is 4/19.

After taking out another medium sized jersey, there are 18 jerseys left in the box and 3 medium jerseys you can pick from.

The probability of you randomly grabbing a medium sized jersey is 3/18.

To get the answer, you do 1/4 * 4/19 * 3/18, and get 1/114, or 0.00877192982.

If you round that to the nearest millionth, it's 0.008772

Don't judge me, it might not be correct.

4 0

3 years ago