1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Kruka [31]
3 years ago
12

How to simplify this expression??

Mathematics
2 answers:
sdas [7]3 years ago
8 0

Answer :

1

Step-by-step-explanation :

{x}^{2}  + 4x + 5 -  {(x + 2)}^{2}  \\  {x}^{2}  + 4x + 5 - ( {x}^{2}  + 4x + 4)   \\

{x}^{2}  + 4x + 5 -  {x}^{2}  - 4x - 4 =  {x}^{2}  -  {x}^{2}  + 4x - 4x + 5 - 4 = 5 - 4 = 1

Mars2501 [29]3 years ago
3 0

Answer:

(x+1)  •  (x-5)

Step-by-step explanation:

The first term is,  x2  its coefficient is  1 .

The middle term is,  -4x  its coefficient is  -4 .

The last term, "the constant", is  -5  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -5 = -5  

Step-2 : Find two factors of  -5  whose sum equals the coefficient of the middle term, which is   -4 .

     -5    +    1    =    -4    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  1  

                    x2 - 5x + 1x - 5

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-5)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x-5)

Step-5 : Add up the four terms of step 4 :

                   (x+1)  •  (x-5)

You might be interested in
Andrea is at the grocery store buying fruit for a smoothie stand. She needs 7 boxes of raspberries for every 5 bunches of banana
Degger [83]

Answer:

The greatest number of bunches of bananas that Andrea can buy is 15 and the greatest number of boxes of raspberries that Andrea can buy is 21 to maintain the ratio 7:5

Step-by-step explanation:

Let

x ---->the greatest number of boxes of raspberries that Andrea can buy

y ---->the greatest number of bunches of bananas that Andrea can buy

we know that

100\%+8\%=106\%=108/100=1.08 ---> sales tax

\frac{x}{y} =\frac{7}{5}

x=\frac{7}{5}y ----> equation A

1.08[2.50x+3.00y]\leq 135 ----> inequality B

substitute equation A in the inequality B

1.08[2.50(\frac{7}{5}y)+3.00y]\leq 135

solve for y

Multiply by 5 both sides to remove the fraction

18.9y+16.2y\leq 675

35.1y\leq 675

y\leq 19.23

so

The maximum value of y is 19

Find the value of x

replace the value of y in equation A until you get an integer value that satisfies the ratio 7:5  

For y=19

x=\frac{7}{5}(19)

x=26.6

For y=18

x=\frac{7}{5}(18)

x=25.2

For y=17

x=\frac{7}{5}(17)

x=23.8

For y=16

x=\frac{7}{5}(16)

x=22.4

For y=15

x=\frac{7}{5}(15)

x=21

therefore

The greatest number of of bunches of bananas that Andrea can buy is 15 and the greatest number of boxes of raspberries that Andrea can buy is 21 to maintain the ratio 7:5

<u><em>Verify the inequality B</em></u>

1.08[2.50(21)+3.00(15)]\leq 135

1.08[52.5+45]\leq 135

105.3\leq 135 ----> is true

4 0
3 years ago
The sum of two numbers is 9. And the sum of their reciprocals is 1/2.find the numbers
Musya8 [376]
Set up a system of equations:

x + y = 9
1/x +1/y = 1/2

The easiest way to solve would be substitution.
x + y = 9 can be solved for y:

y = 9 - x

Then plug this into the second equation and solve for x:

1/x + 1/(9-x) = 1/2
(9-x) + x = x(9-x)/2
9 = (9x-x²)2
18 = 9x - x²
x² - 9x + 18 = 0
(x-6)(x-3) = 0
x = 6, 3

You can check your answer by plugging the two numbers back into both of the equations:

6 + 3 = 9
1/6 + 1/3 = 1/2

The two numbers are 6 and 3.
7 0
3 years ago
How do you simplify a complex fraction
forsale [732]
A compound fraction is simplified by multiplying the numerator by the reciprocal of the denominator fraction. This process is repeated as often as necessary at every level of the fraction.

Examples:
(a/b)/(c/d) = (ad)/(bc)
a/(b/c) = (ac)/b
(a/b)/c = a/(bc)

_____
When the fraction has numerators or denominators that are fractions, you need to be very clear about what is being divided by what. If it isn't clear by the typesetting (length or boldness of fraction bars), then parentheses are required around numerators and around denominators.
6 0
3 years ago
Clare is in charge of getting snacks for a road trip with her friends and her dog. She has
Eduardwww [97]

Answer:

$15 and 50 cents

Step-by-step explanation:

3.25x2=6.50+9=15.50

6 0
3 years ago
Read 2 more answers
Which statement is true regarding the graphed functions?
just olya [345]

ANSWER

f(0) = g(0)

EXPLANATION

From the graph we

g(0) =  - 2

because this is where the line x= 0 meets the graph of g(x).

Also

f(0) =  - 2

because this is where the line x= 0 meets the graph of f(x).

This implies that,

f(0) = g(0)

The correct choice is A.

6 0
3 years ago
Other questions:
  • I don't know how to do any of this
    14·1 answer
  • Which is an advantage of using a credit card? You can make purchases even when you don't have cash. You don't indulge in impulse
    13·2 answers
  • You're playing a fantasy game that allows you to create your own character. There are 555 options for the race of the character,
    6·2 answers
  • HELPPP FAST??? LOTS OF POINTS/BRAINEST
    10·1 answer
  • Leslie wants to place a square rug in the center of her bedroom. Her bedroom is square-shaped with a length of 13 3/4 feet. Her
    13·1 answer
  • Find the polynomial. (3m − 2n) and (4m − n) are the factors of
    14·2 answers
  • What is the answer to this
    7·2 answers
  • I have a piece of string that is 5ft and 7 inches. How many inches is the string. (include the inches 2 steps)​
    10·1 answer
  • If M is the set of all square of integers that are less than 100 and N is the set of all positive even numbers that are under 30
    10·1 answer
  • Which function has a constant additive rate of change of -1/4?​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!