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2 years ago

(x - 4)(x + 2) in factored form, use the FOIL method to turn it into standard form

Mathematics

1 answer:

Verdich [7]2 years ago

7 0

Answer:

${x}^{2} - 2x - 8$

Step-by-step explanation:

(X - 4)(X+2)

$( {x}^{2} + 2x - 4x - 8) \\ ( {x}^{2} - 2x - 8)$

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If x^2+1/x^2=3 find the value of x^2/(x^2+1)^2<br> Express answer as a common fraction.<br> Thanks!!

timama [110]

$x^2+\dfrac1{x^2}=3\implies x^4+1=3x^2\implies x^4-3x^2+1=0$

By the quadratic formula,

$x^2=\dfrac{3\pm\sqrt5}2\implies x^2+1=\dfrac{5\pm\sqrt5}2$

Then

$(x^2+1)^2=\dfrac{25\pm10\sqrt5+5}4=\dfrac{15\pm5\sqrt5}2$

$\implies\dfrac{x^2}{(x^2+1)^2}=\dfrac{\frac{3\pm\sqrt5}2}{\frac{15\pm5\sqrt5}2}=\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}$

Multiply numerator and denominator by the denominator's conjugate:

$\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}\cdot\dfrac{15\mp5\sqrt5}{15\mp5\sqrt5}=\dfrac{45\pm15\sqrt5\mp15\sqrt5-25}{15^2-(5\sqrt5)^2}=\dfrac{20}{100}=\dfrac15$

3 0

2 years ago

Define four symbolic constants that represent integer 25 in decimal, binary, octal, and hexadecimal formats

stealth61 [152]

Answer:

1) Decimal $25= (25)_{10}$

2) Binary $25= (11001)_2$

3) Octal $25= (31)_8$

4) Hexadecimal $25= (19)_{16}$

Step-by-step explanation:

Given : Integer is 25

To find : Represent integer in decimal, binary, octal, and hexadecimal formats.

Solution :

1) Integer into decimal - To convert into decimal the base goes to 10.

So, $25= (25)_{10}$

2) Integer into binary - To convert into binary the base goes to 2, it form in 0 and 1 and we divide integer by 2.

Divide 25 by 2 and note down the remainders.

2 | 25

2 | 12 R=1 ←

2 | 6 R=0 ↑

2 | 3 R=0 ↑

2 | 1 → R=1 ↑

So, $25= (11001)_2$

3) Integer into octal - To convert into octal the base goes to 8 and we divide integer by 8.

Divide 25 by 8 and note down the remainders.

8 | 25

| 3 → R=1

So, $25= (31)_8$

4) Integer into hexadecimal - To convert into hexadecimal the base goes to 16 and we divide integer by 16.

Divide 25 by 16 and note down the remainders.

16 | 25

| 1 → R=9

So, $25= (19)_{16}$

3 0

3 years ago

Simplify 3x + (-12x) - 5x.

lutik1710 [3]

3x - 12x - 5x
= 3x - 17x
= - 14x

answer
-14x

4 0

2 years ago

Read 2 more answers

Which pair of numbers, if included in this set, would not change the median?

sattari [20]

Answer:

Step-by-step explanation:

Order the set first

27, 28, 35, 37, 43, 47

Median now is: 36 (which is the mean between 35 and 37, the two central numbers )

If you add A) 35,50 then you will still have to compute the mean between 35 and 37 in order to find the median, because you have:

27,28,35,35,37,43,47,50

7 0

3 years ago

Read 2 more answers

The cost of having photos taken includes a sitting fee and $12 for each portrait. The cost of 3,6, and 9 photos respectively is

Eddi Din [679]

Answer:The sitting fee is 15 dollars

Step-by-step explanation:If you were to use the formula y=mx+b then the starting equation would be y=12x+b. It already gave you the cost for the amount of photos respectively so 51=12(3)+b. 12 times 3 equals 36 and 51 minus 36 equals 15. The same way would be used for 87 dollars and 123 dollars while using the amount of photos respectively. 87=12(6)+b. 12 times 6 equals 72. 72 plus 15 equals 87. 123=12(9)+b. 12 times 9 equals 108. 108 plus 15 equals 123. Therefore the sitting fee is 15. (51=12(3)+15, 87=12(6)+15, 123=12(9)+15)

4 0

2 years ago