When you divide any number by a fraction less than one, what happens to the original number?

alpha and beta are the zeros of the polynomial x^2 -(k +6)x +2(2k -1). Find the value of k if alpha + beta = 1/2 alpha beta(ITS

serious [3.7K]

Answer:

$k=\frac{-11}{2}$ .

Step-by-step explanation:

We are given $\alpha$ and $\beta$ are zeros of the polynomial $x^2-(k+6)x+2(2k-1)$ .

We want to find the value of $k$ if $\alpha+\beta=\frac{1}{2}$ .

Lets use veita's formula.

By that formula we have the following equations:

$\alpha+\beta=\frac{-(-(k+6))}{1}$ (-b/a where the quadratic is ax^2+bx+c)

$\alpha \cdot \beta=\frac{2(2k-1)}{1}$ (c/a)

Let's simplify those equations:

$\alpha+\beta=k+6$

$\alpha \cdot \beta=4k-2$

If $\alpha+\beta=k+6$ and $\alpha+\beta=\frac{1}{2}$ , then $k+6=\frac{1}{2}$ .

Let's solve this for k:

Subtract 6 on both sides:

$k=\frac{1}{2}-6$

Find a common denominator:

$k=\frac{1}{2}-\frac{12}{2}$

Simplify:

$k=\frac{-11}{2}$ .

7 0

3 years ago

How do the values of the 5s in 581.03 and 5.472 compare

Nonamiya [84]

The value of the 5 in 581.03 is 100 times the value of the 5 in 5.472

Step-by-step explanation:

Each digit in a number has a place value.

The place value of 4 in 453.56 is hundreds (100), because 4 is in the hundred place

The place value of 2 in 1782.56 is ones (1), because 2 is in the unit place

The place value of 3 in 2.345 is tenth (0.1), because 3 is in the tenth place

∵ The number is 581.03

- Find the place of 5 in the number

∵ 5 is in the hundred place

∴ The place value of 5 is 100

∵ The number is 5.472

- Find the place of 5 in the number

∵ 5 is in the unit place

∴ The place value of 5 is 1

To find the value of the 5 in 581.03 is how many times the value of the 5 in 5.472 divide the place values of them

∵ 100 ÷ 1 = 100

∴ The value of 5 in 581.03 = 100 times the value of 5 in 5.472

The value of the 5 in 581.03 is 100 times the value of the 5 in 5.472

6 0

3 years ago

Find the slope of the line passing through the points (-2, 5) and (-6, 7).

Vlad1618 [11]

The slope would be - 1/2 !!

you would number the x and y values of the coordinates.

( -2 , 5 ) ( -6 , 7 )
x1. y1. x2. y2

then do the formula that gives you the slope y2 - y1 / x2 - x1

this gives you:

7 - 5 / -6 - (-2) = 2/ -4 (simplify) -1/2

so this would give you m= -1/2

5 0

4 years ago

Holly has $462 in her bank account and takes out $15 each week but does not put any back in. Write an equation/expression to rep

Degger [83]

Answer:

Therefore required expression is

y =462 - t×15

where y represents the amount of money in her bank account in dollar after t week.

Step-by-step explanation:

Given that,

Holly has $462 in her bank account and takes out $15 each week but does not put any back in.

She takes out $15 on first week.

The remaining amount of her bank account is =$(462-15)

=$(462 - 1×15)

If she withdraws $15 on second week.

The remaining amount of her bank account is =$(462-15-15)

=$(462 - 2×15)

Similarly after third the amount in her account is =$(462 - 3×15)

From the above it is cleared that

The amount in her account after t week is

=$(462 - t×15)

Therefore required expression is

y =462 - t×15

where y represents the amount of money in her bank account in dollar after t week.

3 0

3 years ago

How do I do that it's systems of equations

Tpy6a [65]

You have to get y alone,

6 0

4 years ago