1/2(x-4)=4. Solve for x

Answers

Answer 1

Answer: 1/2(x-4)=4
1/2x-2=4 (expand the brackets)
1/2x=6 (added 2 to both sides)
x= 6/(1/2)
x= 6*2
x=12

Answer 2

Answer:
1/2(x-4) = 4

Multiply each side of the equation by 2 : (x- 4) = 8

Add 4 to each side of the equation: x = 12

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Use the REMAINDER THEOREM to explain whether or not (x-2) is a factor of F(x)=x^4-2x^3+3x^2-10x+3

Answers

$(P(x))/(R(x))|(D(x))/(Q(x))$

$\frac{x^4-2x^3+3x^2-10x+3}{}|\frac{x-2}{}$

$(x^4-2x^3+3x^2-10x+3)/(-x^4+2x^3)|(x-2)/(x^3)$

$(3x^2-10x+3)/(-3x^2+6x)|(x-2)/(x^3+3x)$

$(-4x+3)/(4x-8)|(x-2)/(x^3+3x-4)$

$\frac{-5}{}|(x-2)/(x^3+3x-4)$

$\boxed{\boxed{(x^4-2x^3+3x^2-10x+3)/(-5)|(x-2)/(x^3+3x-4)}}$

$R(x)=-5$

4. Find the sum of the first eighteen terms of the arithmetic sequence whose nthterm is an = 15 + 8n.
a. 1438
b. 1638
c. 1836
d. 1783

Answers

Answer:

The sum of first eighteen terms of the arithmetic sequence is $\mathbf{S_(18)=1638}$

Option B is correct option.

Step-by-step explanation:

We need to find the sum of the first eighteen terms of the arithmetic sequence whose nth term is an = 15 + 8n

The formula used to calculate sum of arithmetic sequence is: $S_n=(n)/(2)(a_1+a_n)$

Finding a₁ by putting n=1

$a_n=15+8n\na_(1)=15+8(1)\na_(1)=15+8\na_(1)=23$

We have $a_1=23$

Finding 18th term n=18

$a_n=15+8n\na_(18)=15+8(18)\na_(18)=15+144\na_(18)=159$

So, the sum of first eighteen terms of the arithmetic sequence is:

$S_n=(n)/(2)(a_1+a_n)\nS_(18)=(n)/(2)(a_1+a_(18))\nS_(18)=(18)/(2)( 23+159)\nS_(18)=9(182)\nS_(18)=1638$

So, the sum of first eighteen terms of the arithmetic sequence is $\mathbf{S_(18)=1638}$

Option B is correct option.

DAILY MATH QUESTIN
CAN YOU SOLVE THE PROBLEM?

Answers

Answer:

Step-by-step explanation:

9-3x3+1

9-9+1

Answer:

Step-by-step explanation:

Start with the division. 3 ÷ 1/3 = 9

Now continue to add/subtract in the order it comes.

9 - 9 = 0

0 + 1 = 1

A pet store has 2 gray rabbits. one eighth of the rabbits at the pet store are gray. How many rabbits does the pet store have?

Answers

We know that 1 out of 8 rabbits are gray. And there is 2 gray rabbits.

You have to be proportionate:

there will be 16 rabbits total, because we keep the proportion of 1 out of 8

How many ways are there to distribute three different teddy bears and nine identical lollipops to four children (a) Without restriction? (b) With no child getting two or more teddy bears? (c) With each child getting three ""goodies""?

Answers

Answer:a) 14080, b) 5280, c) 64.

Step-by-step explanation:

Since we have given that

Number of teddy bears = 3

Number of identical lollipops = 9

Total number of things = 3+9 =12

Number of children = 4

(a) Without restriction?

Number of ways would be

$4^3* ^(12)C_3\n\n=14080$

(b) With no child getting two or more teddy bears?

$4* 3!* ^(12)C_9\n\n=5280$

(c) With each child getting three ""goodies""?

$4^3=64$

Hence, a) 14080, b) 5280, c) 64.

What is 0.375 as a percentage and decimal

Answers

Decimal = 0.375
Percentage = 0.375/1
= 0.375*100 / 1*100
= 37.5 / 100
= 37.5 %
Fraction = 37.5 / 100
= 3/8 ( 12.5*3 is 37.5 and 12.5*8 is 100)

Hope it helps

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