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3 years ago

The quotient of 8 times a number and 6 is -2. What is the number?

Mathematics

1 answer:

Reika [66]3 years ago

7 0

Answer:

-3/2

Step-by-step explanation:

8n/6 = -2 . . . the quotient of 8 times a number and 6 is -2

n = -12/8 = -3/2 . . . . multiply by 6/8

The number is -3/2.

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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

Cameron's book log shoes he reads total of 4\1/4 hours last month how many minutes is that

Romashka-Z-Leto [24]

260 minutes. 4 times 60 = 240 + 20 minutes i s the quarter

8 0

3 years ago

Read 2 more answers

Every one reading this please help! I don't understand this and I will give brainliest to the person that helps first with a goo

stira [4]

Since the area of the poster doesn't change by putting it in a frame, we presume the question is asking what the area of the framed poster is.

The length of the poster in its frame is ...
(frame width on one side) + (poster length) + (frame width on the other side)
2 in + 32 in + 2 in = 36 in

Likewise, the width of the poster in its frame is ...
2 in + 24 in + 2 in = 28 in

The area of a rectangle 36 in by 28 in is the product of these dimensions:
Area = (36 in)×(28 in) = (36×28) in² = 1008 in²

6 0

3 years ago

Read 2 more answers

What is the cube root for 3000??

Alona [7]

$\sqrt[3]{3000}=\sqrt[3]{1000\times3}=\sqrt[3]{1000}\times\sqrt[3]3=10\sqrt[3]3$

4 0

3 years ago

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Which method or methods listed below describe a solid system for keeping financial records? I. Making a mental note of all purch

Nikitich [7]

Financial records are important records and thus, needs to be saved safely. The method for solid system to keep it is: Option d. I, II, and III

<h3>How to safely keep financial records and why?</h3>

Financial records are records of all financial transactions and receipts. They're needed for future cases like some contradictions, to get past details, to analyze data to make prediction about future sale and for development of the organization etc.

For keeping them, they should be saved in an easily accessible, and hardly destroy-able place. So that its prevented safely but accessible faster with correct authentication.

For the given case, for solid system for keeping financial records, we can actually follow all the three steps provided.

I. Making a mental note of all purchases made during the week. II. Recording money spent in a hand-held notebook. III. Organizing receipts and transactions on a computer.

Thus,

The method for solid system to keep it is: Option d. I, II, and III

Learn more about financial records here:

brainly.com/question/4954869

7 0

2 years ago