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3 years ago

I just need help on 4

Mathematics

1 answer:

Fittoniya [83]3 years ago

6 0

Answer:

4) alternate interior angles theorem

Step-by-step explanation:

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If the sum of the zereos of the quadratic polynomial is 3x^2-(3k-2)x-(k-6) is equal to the product of the zereos, then find k?

lys-0071 [83]

Answer:

Step-by-step explanation:

So I'm going to use vieta's formula.

Let u and v the zeros of the given quadratic in ax^2+bx+c form.

By vieta's formula:

1) u+v=-b/a

2) uv=c/a

We are also given not by the formula but by this problem:

3) u+v=uv

If we plug 1) and 2) into 3) we get:

-b/a=c/a

Multiply both sides by a:

-b=c

Here we have:

a=3

b=-(3k-2)

c=-(k-6)

So we are solving

-b=c for k:

3k-2=-(k-6)

Distribute:

3k-2=-k+6

Add k on both sides:

4k-2=6

Add 2 on both side:

4k=8

Divide both sides by 4:

k=2

Let's check:

$3x^2-(3k-2)x-(k-6) \text{ with }k=2$ :

$3x^2-(3\cdot 2-2)x-(2-6)$

$3x^2-4x+4$

I'm going to solve $3x^2-4x+4=0$ for x using the quadratic formula:

$\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\frac{4\pm \sqrt{(-4)^2-4(3)(4)}}{2(3)}$

$\frac{4\pm \sqrt{16-16(3)}}{6}$

$\frac{4\pm \sqrt{16}\sqrt{1-(3)}}{6}$

$\frac{4\pm 4\sqrt{-2}}{6}$

$\frac{2\pm 2\sqrt{-2}}{3}$

$\frac{2\pm 2i\sqrt{2}}{3}$

Let's see if uv=u+v holds.

$uv=\frac{2+2i\sqrt{2}}{3} \cdot \frac{2-2i\sqrt{2}}{3}$

Keep in mind you are multiplying conjugates:

$uv=\frac{1}{9}(4-4i^2(2))$

$uv=\frac{1}{9}(4+4(2))$

$uv=\frac{12}{9}=\frac{4}{3}$

Let's see what u+v is now:

$u+v=\frac{2+2i\sqrt{2}}{3}+\frac{2-2i\sqrt{2}}{3}$

$u+v=\frac{2}{3}+\frac{2}{3}=\frac{4}{3}$

We have confirmed uv=u+v for k=2.

4 0

3 years ago

Find the area of the shape shown below.

oee [108]

Answer:

=6 units squared

Step-by-step explanation:

area=1/2h(a+b)

=1/2×2(4+2)

7 0

3 years ago

Hey! I'v been struggling with this question lately. Can someone just lend me a hand?

Dominik [7]

So, this problem is asking us to find the value of our variable u.

How can you do this? By isolating the variable, or having only it on one side of the equals sign.

Here's the step by step approach. It's just simple algebra and reverse order of operation (which is what you should do whenever you are solving for a variable).

$\frac{u+88}{11} = 17$

Multiply both sides by 11 to get rid of the 11 denominator.
$u + 88 = 187$

Then, subtract both sides by 88 to get u by itself.
$u = 99$

Therefore, u is equal to 99.

6 0

3 years ago

Read 2 more answers

Express 8 sin^2x - 10sinxcosx in the form a+b sin(2x+c).

ladessa [460]

8 sin2x - 10sinxcosx = 8*2sinXcosX-10sinXcosX = 16sinXcosX - 10sinXcosX = 6sinXcosX=3sin2x

7 0

3 years ago

Factor. (help plz!)<br><br> x^2+7x+10

yawa3891 [41]

Answer:

$(x + 5) \times (x + 2)$