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2 years ago

What is the common factor of 10 15and 35

Mathematics

1 answer:

anygoal [31]2 years ago

7 0

Answer:

the common factor of all the numbers is 5

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Find the product of all real values of r for which 1/2x=r-x/7

Dahasolnce [82]

Answer:

$r = \±\sqrt{14$

$Product = -14$

Step-by-step explanation:

Given

$\frac{1}{2x} = \frac{r - x}{7}$

Required

Find all product of real values that satisfy the equation

$\frac{1}{2x} = \frac{r - x}{7}$

Cross multiply:

$2x(r - x) = 7 * 1$

$2xr - 2x^2 = 7$

Subtract 7 from both sides

$2xr - 2x^2 -7= 7 -7$

$2xr - 2x^2 -7= 0$

Reorder

$- 2x^2+ 2xr -7= 0$

Multiply through by -1

$2x^2 - 2xr +7= 0$

The above represents a quadratic equation and as such could take either of the following conditions.

(1) No real roots:

This possibility does not apply in this case as such, would not be considered.

(2) One real root

This is true if

$b^2 - 4ac = 0$

For a quadratic equation

$ax^2 + bx + c = 0$

By comparison with $2x^2 - 2xr +7= 0$

$a = 2$

$b = -2r$

$c =7$

Substitute these values in $b^2 - 4ac = 0$

$(-2r)^2 - 4 * 2 * 7 = 0$

$4r^2 - 56 = 0$

Add 56 to both sides

$4r^2 - 56 + 56= 0 + 56$

$4r^2 = 56$

Divide through by 4

$r^2 = 14$

Take square roots

$\sqrt{r^2} = \±\sqrt{14$

$r = \±\sqrt{14$

Hence, the possible values of r are:

$\sqrt{14$ or $-\sqrt{14$

and the product is:

$Product = \sqrt{14} * -\sqrt{14}$

$Product = -14$

8 0

2 years ago

What is 2+ 9-x divided by 4 = 10

N76 [4]

Here is the work for this equation:

2+9-x/4 =10

11-x/4=10

11-x=40

x=29

7 0

2 years ago

A student had 500 milliliters of water in a water bottle. She drank 25% of the water before soccer practice. After practice, she

AlladinOne [14]

Step-by-step explanation:

25\100*500=125

1/3*125=41.66

41.66 millilites is left in the bottle

4 0

3 years ago

Rachel received a monthly raise of $105.25. If this represented a 5.5% increase, what is her monthly salary after the raise?

crimeas [40]

Answer:

Step-by-step explanation:

105,25:5,5*105.5=2018,89

8 0

2 years ago

Find an equation for the line below.

Taya2010 [7]

Answer:

y = 1/2x + 5/2

Step-by-step explanation:

4 0

2 years ago

What is the common factor of 10 15and 35​

What is the common factor of 10 15and 35