All categories

3 years ago

What are the domain restrictions of the expression h^2+3h−10/h^2−12h+20 ?

Mathematics

2 answers:

vovangra [49]3 years ago

8 0

Answer:

h≠10.

Step-by-step explanation:

The expression is

$\frac{h^2+3h-10}{h^2-12h+20}.$

To find the restrictions we can factor the numerator and the denominator by searching two numbers that multiplied are -10 and subtracted are 3, also for the denominator:

$\frac{h^2+3h-10}{h^2-12h+20}= \frac{(h+5)(h-2)}{(h-10)(h-2)} = \frac{(h+5)}{(h-10)}.$

When we have a fraction the denominator can not be zero. Then, for our expression h needs to be different to 10 or the denominator would be zero.

Grace [21]3 years ago

3 0

The denominator cannot be 0, so if h^2-12h+20=0
(h-2)(h-10)=0
h=2 or h=10
So h cannot be 2 or 10, the first and third choices are correct.

You might be interested in

Lucy makes green paint by mixing yellow and blue paint in the ratio 5:2. Blue paint costs

ahrayia [7]

Answer:

No, she won’t make a profit

Step-by-step explanation:

Here, we are interested in determining if Lucy made a profit or a loss.

The cost of blue paint is 30 pounds for 5 liters. This means that a liter of blue paint is 30/5 = 6 pounds per liter

The cost of yellow paint is 28 pounds per 7 liters, the cost per liter is 28/7 = 4 pounds per liter

Now, in her mixing, she mixes 5 parts of yellow paint and 2 parts of blue paint.

This means that she mixed them the ratio as follows per liter;

For yellow, we have; 5/(5+2) = 5/7

For blue we have 2/(5+2) = 2/7

Now since a liter of yellow paint cost 4 pounds

5/7 of a liter will cost 5/7 * 4 = 20/7 pounds

For the blue paint, a liter cost 6 pounds, 2/7 of a liter will cost 2/7 * 6 = 12/7

The total cost in pounds in this;

20/7 + 12/7 = 32/7 = £4.57 pounds to 2 decimal place

Now she sells her green paint product at £4.5 per liter. Since this is less than the cost price of production which is £4.57, she is running at a loss

8 0

3 years ago

What is the solution to 2x^2-3x-1=0

Tems11 [23]

x=43+√17,43−√17 Is the answer.

I hope this helps. :)

7 0

3 years ago

I dont understand and this is very urgent so can someone help me out please?

wariber [46]

Answer:

Please Find the solution below

Step-by-step explanation:

Let us say the two equations are

x+y=5 --------------(A)

x-y=1 -------------(B)

Let us solve them for x and y by adding them

2x=6

x=3

Hence from (A)

3+y=5

y=2

Hence our solution is

x=3, y=2

Adding same number to equation (A) say 2 we get

x+y+2=5+2

x+y=5+2-2

x+y=5

Hence equation remains the same while adding same number to each side.

Same thing happens if we add same number to equation (B)

Hence we draw the conclusion that the solution remains the same if same number is added to each side of the original equation.

6 0

3 years ago

An experiment consists of choosing objects without regards to order. Determine the size of the sample space when you choose the

sdas [7]

Answer:

$n= 75, 582$

$n= 2300$

$n = 253$

Step-by-step explanation:

Generally the size of the sample sample space is mathematically represented as

$n = \left N } \atop {}} \right. C_r$

Where N is the total number of objects available and r is the number of objects to be selected

So for a, where N = 19 and r = 8

$n = \left 19 } \atop {}} \right. C_8 = \frac{19 !}{(19 - 8 )! 8!}$

$= \frac{19 *18 *17 *16 *15 *14 *13 *12 *11! }{11 ! \ 8!}$

$n= 75, 582$

For b Where N = 25 and r = 3

$n = \left 25 } \atop {}} \right. C_3 = \frac{25 !}{(19 - 3 )! 3!}$

$= \frac{25 *24 *23 *22 ! }{22 ! \ 3!}$

$n= 2300$

For c Where N = 23 and r = 2

$n = \left 23 } \atop {}} \right. C_2 = \frac{23 !}{(23 - 2 )! 2!}$

$= \frac{23 *22 *21! }{21 ! \ 3!}$

$n = 253$

4 0

3 years ago

There were 3 apple, 1 mixed fruit, 2 grape, and 4 tropical fruit juice boxes in the cooler at the picnic. What is the probabilit

goldenfox [79]

There are 10 juice boxes in the cooler altogether.
2 of them are grape.

The first time Jill pulls one out with her eyes closed,
the probability that it's a grape is

2 / 10 .

If that try is successful, then there are 9 boxes left in the cooler,
and one of them is grape.

If she already has one grape, and reaches in again with her eyes
closed, the probability of pulling out the second grape is

1 / 9 .

The probability of both events happening in two tries is

(2/10) x (1/9) = 2/90 = 1/45 = (2 and 2/9) percent .

6 0

3 years ago

Read 2 more answers