# What is the coefficient of x when you simplify the following expression?1/2 (-6x– 4) + 4x

###### Question:

1/2 (-6x– 4) + 4x

## Answers

1. 74 because 8(10) - 6

2.4(4) - 5(3) = 1

3. 7(3)+8(4) * 2 = 106

4. A

5.a

6. 20.5

7.26

8.a

9.a

10a

32 -40x +20x^2-5x^3 +5/8x^4 -x^5/32-4 13/3231.92 (accurate to 3 decimal places); 32 to 2 significant figures

Step-by-step explanation:

a) The full expansion of a binomial to the 5th power is ...

[tex](a+b)^5=a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5[/tex]

For the given binomial, a=2, b=-1/2x, so the expansion is ...

[tex](2-\dfrac{x}{2})^5=2^5-5(2^4)\dfrac{x}{2}+10(2^3)\dfrac{x^2}{2^2}-10(2^2)\dfrac{x^3}{2^3}+5(2)\dfrac{x^4}{2^4}-\dfrac{x^5}{2^5}\\\\=\boxed{32-40x+20x^2-5x^3+\dfrac{5}{8}x^4-\dfrac{x^5}{32}}[/tex]

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b) The sum of coefficients of x^3, x^4 and x^5 is ...

-5 +5/8 -1/32 = -4 13/32

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c) 1.999^5 = (2 -.001)^5 = (2 -0.002/2)^5

So, we can use the above expansion with x=.002. The result from part (b) tells us that the error from neglecting 3rd-power terms and higher will be on the order of 40×10^-9, far less than that necessary for the required accuracy.

1.999^5 ≈ 32 -.002(40 -.002(20)) = 32 -.002(39.96) = 32 -0.07992

1.999^5 ≈ 31.92

= 32 (to 2 significant figures)

[tex]1.\\(4x^2+15x-3)-(-3x^2+5)\\=4x^2+15x-3+3x^2-5\\=7x^2+15x-8\leftarrow A.[/tex]

[tex]2.\\-3f^2+4f-3+8f^2+7f+1\\=5f^2+11f-2\leftarrow C.[/tex]

[tex]3.\\(2x^2+6x+1)+(-7x^2+2x-3)\\=2x^2+6x+1-7x^2+2x-3\\=-5x^2+8x-2\leftarrow B.[/tex]

[tex]4.\\4x^2+3x-3\\\{4;\ 3;-3\}[/tex]

[tex]5.\\6x^4+3x^3-2x^2+15x-14\\\{6;\ 3;-2;\ 15;-14\}\to5\leftarrow A.[/tex]

[tex]6.\\-7x-5x^2+5\\\{-7\}\leftarrow D.[/tex]

[tex]7.\\(2.5\cdot10^4)(4\cdot10^3)=2.5\cdot4\cdot10^{4+3}=10\cdot10^7\\=10^{1+7}=10^8=1\cdot10^8\leftarrow C.[/tex]

[tex]8.\\2^2\cdot2^8=2^{2+8}=2^{10}\leftarrow B.[/tex]

[tex]1.\\(4x^2+15x-3)-(-3x^2+5)\\=4x^2+15x-3+3x^2-5\\=7x^2+15x-8\leftarrow A.[/tex]

[tex]2.\\-3f^2+4f-3+8f^2+7f+1\\=5f^2+11f-2\leftarrow C.[/tex]

[tex]3.\\(2x^2+6x+1)+(-7x^2+2x-3)\\=2x^2+6x+1-7x^2+2x-3\\=-5x^2+8x-2\leftarrow B.[/tex]

[tex]4.\\4x^2+3x-3\\\{4;\ 3;-3\}[/tex]

[tex]5.\\6x^4+3x^3-2x^2+15x-14\\\{6;\ 3;-2;\ 15;-14\}\to5\leftarrow A.[/tex]

[tex]6.\\-7x-5x^2+5\\\{-7\}\leftarrow D.[/tex]

[tex]7.\\(2.5\cdot10^4)(4\cdot10^3)=2.5\cdot4\cdot10^{4+3}=10\cdot10^7\\=10^{1+7}=10^8=1\cdot10^8\leftarrow C.[/tex]

[tex]8.\\2^2\cdot2^8=2^{2+8}=2^{10}\leftarrow B.[/tex]

im back.

Step-by-step explanation:holy guacomole, ill answer in chat. Imma get paper.

(1) A

(2) C

(3) B

(4) The coefficients are 4,3,-3.

(5) A

(6) D

(7) C

(8) B

Step-by-step explanation:

(1)

The given expression is

[tex](4x^2 + 15x - 3) - (-3x^2 + 5)[/tex]

Using distributive property.

[tex](4x^2 + 15x - 3) - (-3x^2) -( 5)[/tex]

[tex]4x^2 + 15x - 3 + 3x^2 - 5[/tex]

On combining like terms.

[tex](4x^2+3x^2) + 15x +(- 3 - 5)[/tex]

[tex]7x^2 + 15x-8[/tex]

Therefore, the correct option is A.

(2)

The given expression is

[tex]-3f^2 + 4f - 3 + 8f^2 + 7f + 1[/tex]

On combining like terms.

[tex](-3f^2+ 8f^2) +( 4f + 7f )+(- 3 + 1)[/tex]

[tex]5f^2 +11f -2[/tex]

Therefore, the correct option is C.

(3)

The given expression is

[tex](2x^2 + 6x + 1) + (-7x^2 + 2x - 3)[/tex]

Combined like terms.

[tex](2x^2-7x^2) + (6x+ 2x) + (1 - 3)[/tex]

[tex]-5x^2 + 8x -2[/tex]

Therefore, the correct option is B.

(4)

The given expression is

[tex]4x^2 + 3x - 3[/tex]

A number before variable terms are called coefficient of that term.

Therefore, the coefficients are 4,3,-3.

(5)

The given expression is

[tex]6x^4 + 3x^3 - 2x^2 + 15x - 14[/tex]

It this polynomial, the number of terms is 5.

Therefore the correct option is A.

(6)

The given expression is

[tex]-7x - 5x^2 + 5[/tex]

The coefficient to x is -7.

Therefore, the correct option is D.

(7)

The given expression is

[tex](2.5\cdot 10^4)(4\cdot 10^3)[/tex]

[tex](2.5\cdot 4)\cdot (10^4\cdot 10^3)[/tex]

Using product property of exponent.

[tex](10)\cdot 10^{4+3}[/tex]

[tex]1\cdot 10^{1+4+3}[/tex]

[tex]1\cdot 10^{8}[/tex]

Therefore, the correct option is C.

(8)

The given expression is

[tex]2^2\cdot 2^8[/tex]

Using product property of exponent.

[tex]2^{2+8}[/tex]

[tex]2^{10}[/tex]

Therefore, the correct option is B.

(1) A

(2) C

(3) B

(4) The coefficients are 4,3,-3.

(5) A

(6) D

(7) C

(8) B

Step-by-step explanation:

(1)

The given expression is

[tex](4x^2 + 15x - 3) - (-3x^2 + 5)[/tex]

Using distributive property.

[tex](4x^2 + 15x - 3) - (-3x^2) -( 5)[/tex]

[tex]4x^2 + 15x - 3 + 3x^2 - 5[/tex]

On combining like terms.

[tex](4x^2+3x^2) + 15x +(- 3 - 5)[/tex]

[tex]7x^2 + 15x-8[/tex]

Therefore, the correct option is A.

(2)

The given expression is

[tex]-3f^2 + 4f - 3 + 8f^2 + 7f + 1[/tex]

On combining like terms.

[tex](-3f^2+ 8f^2) +( 4f + 7f )+(- 3 + 1)[/tex]

[tex]5f^2 +11f -2[/tex]

Therefore, the correct option is C.

(3)

The given expression is

[tex](2x^2 + 6x + 1) + (-7x^2 + 2x - 3)[/tex]

Combined like terms.

[tex](2x^2-7x^2) + (6x+ 2x) + (1 - 3)[/tex]

[tex]-5x^2 + 8x -2[/tex]

Therefore, the correct option is B.

(4)

The given expression is

[tex]4x^2 + 3x - 3[/tex]

A number before variable terms are called coefficient of that term.

Therefore, the coefficients are 4,3,-3.

(5)

The given expression is

[tex]6x^4 + 3x^3 - 2x^2 + 15x - 14[/tex]

It this polynomial, the number of terms is 5.

Therefore the correct option is A.

(6)

The given expression is

[tex]-7x - 5x^2 + 5[/tex]

The coefficient to x is -7.

Therefore, the correct option is D.

(7)

The given expression is

[tex](2.5\cdot 10^4)(4\cdot 10^3)[/tex]

[tex](2.5\cdot 4)\cdot (10^4\cdot 10^3)[/tex]

Using product property of exponent.

[tex](10)\cdot 10^{4+3}[/tex]

[tex]1\cdot 10^{1+4+3}[/tex]

[tex]1\cdot 10^{8}[/tex]

Therefore, the correct option is C.

(8)

The given expression is

[tex]2^2\cdot 2^8[/tex]

Using product property of exponent.

[tex]2^{2+8}[/tex]

[tex]2^{10}[/tex]

Therefore, the correct option is B.

1. Evaluate 8a - b if a = 10 and b = 6

8×10 - 6 = 80 - 6 = 74

2. Evaluate expression if a=3 and b=4. 4b-5a

4×4 - 5×3 = 16 - 15 = 1

3. Evaluate Expressions a=3 b=4, 7a + 8b x 2

7×3 + 8×4×2 = 21 + 64 = 85

4.Strawberries are $1.95 a pound. Write an expression for p pounds of strawberries.

1 pound is $1.95; 2 pounds is 2×$1.95; 3 pounds is 2×$1.95

So p pounds is p×$1.95 = $1.95p

5. Kenneth has g gumballs. Maggie has 29 fewer gumballs than Kenneth. Choose the expression that shows how many gumballs Maggie has.

fewer means less than Kenneth; means we need tu subtract

g - 29

6)

5 + 36 ÷ 2 × 3 - 4 = 5 + 18 × 3 - 4 = 5 + 54 - 4 = 55

7)

18 + (6 – 2) × 2 = 18 + 4×2 = 18 + 8 = 26

8. Expand

-3( 2r + 5s). = -3×2r + (-3)×5s = -6r - 15s

9. Expand and simplify

5(2 - 3y) = 5×2 + 5×(-3y) = 10 - 15y

10.Factor:

7x + 49y = 7×x + 7×7y = 7(x + 7y)

11. Factor

6p − 36 = 6×p − 6×6 = 6(p − 6)

12. Which expression contains exactly 3 terms?

B. 8 + 2y - 5x

13. What is the coefficient of x? 8 + 5x - y

8 + 5x - y

C. 5

14. Identify the "like terms" in the expression: 2x + 4y - 3x + y - x

2x and -3x and -x; 4y and y

15. Factor 5x − 25

5x − 25 = 5×x − 5×5 = 5(x − 5)

a) [tex](3x+y)^5=243x^5+405x^4y+270x^3y^2+90x^2y^3+15xy^4+y^5[/tex].

b) The middle term in the expansion is [tex]\frac{6}{x}[/tex].

c) The coefficient of [tex]x^{11}[/tex] is 120.

Step-by-step explanation:

Remember that the binomial theorem say that [tex](x+y)^n=\sum_{k=0}^{n} \binom{n}{k}x^{n-k}y^{k}[/tex]

a) [tex](3x+y)^5=\sum_{k=0}^5\binom{5}{k}3^{n-k}x^{n-k}y^k[/tex]

Expanding we have that

[tex]\binom{5}{0}3^5x^5+\binom{5}{1}3^4x^4y+\binom{5}{2}3^3x^3y^2+\binom{5}{3}3^2x^2y^3+\binom{5}{4}3xy^4+\binom{5}{5}y^5[/tex]

symplifying,

[tex](3x+y)^5=243x^5+405x^4y+270x^3y^2+90x^2y^3+15xy^4+y^5[/tex].

b) The middle term in the expansion of [tex](\frac{1}{x} +\sqrt{x})^4=\sum_{k=0}^{4}\binom{4}{k}\frac{1}{x^{4-k}}x^{\frac{k}{2}}[/tex] correspond to k=2. Then [tex]\binom{4}{2}\frac{1}{x^2}x^{\frac{2}{2}}=\frac{6}{x}[/tex].

c) [tex](x^2+\frac{1}{x})^{10}=\sum_{k=0}^{10}\binom{10}{k}x^{2(10-k)}\frac{1}{x^k}=\sum_{k=0}^{10}\binom{10}{k}x^{20-2k}\frac{1}{x^k}=\sum_{k=0}^{10}\binom{10}{k}x^{20-3k}[/tex]

Since we need that 11=20-3k, then k=3.

Then the coefficient of [tex]x^{11}[/tex] is [tex]\binom{10}{3}=120[/tex]

The correct options are 1, 2, 4 and 6.

Step-by-step explanation:

The given expression is

[tex](-5x-3y)-(-x-3z)[/tex]

To subtract like term subtract like terms, subtract the coefficients, not the variables.

Therefore option 1 is correct.

Like terms are terms that contain the same variable, raised to the same power. For example: 3xy and 5xy, 4x² and 3x².

Therefore, option 2 is correct.

Using distributive property we get

[tex]-5x-3y-(-x)-(-3z)[/tex]

[tex]-5x-3y+x+3z[/tex]

Only combine terms which contain the same variable.

Therefore option 4 is correct.

[tex](-5x+x)-3y+3z[/tex]

[tex]-4x-3y+3z[/tex]

The simplified expression is -4x-3y+3z. Therefore option 6 is correct.