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2 years ago

What is the value of x in the equation 32(4x − 2) − 3x = 5 − (x + 2)?

Mathematics

2 answers:

Gwar [14]2 years ago

8 0

Answer:

x = 0.53

Step-by-step explanation:

32(4x − 2) − 3x = 5 − (x + 2)

128x - 64 - 3x = 5 - x - 2

125x - 64 = -x + 3

126x = 67

x = -0.53

Ierofanga [76]2 years ago

7 0

Step-by-step explanation:

Use the given functions to set up and simplify

(

−

)

−

(

)

126

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Tank A has a capacity of 9.5 gallons. 6 1\3 gallons of the tank"s water are poured out. How many gallons of water are left in th

dezoksy [38]

Since 1/3 can't be turned into a decimal, change .5 into 1/2. In order to subtract, the fractions need a common denominator. The least common denominator is 6. So 1/3 turns into 2/6, and 1/2 turns into 3/6. Now you need to take 9 3/6 minus 6 2/6. The answer is 3 1/6 gallons of water.

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2 years ago

List all the factors of 19. Tell whether 19 is prime or composite.

andreyandreev [35.5K]

Answer:

19 is a prime number, thus making the only factors 1, 2, 19. (Not necessary to include 1)

Step-by-step explanation:

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2 years ago

Started off with 25 gallons drove a 150mills how many gallons is left

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It depends on your fuel economy, how much fuel the car burns per 100 miles etc.

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2 years ago

A teacher places n seats to form the back row of a classroom layout. Each successive row contains two fewer seats than the prece

Alex_Xolod [135]

Answer:

The number of seat when n is odd $S_n=\frac{n^2+2n+1}{4}$

The number of seat when n is even $S_n=\frac{n^2+2n}{4}$

Step-by-step explanation:

Given that, each successive row contains two fewer seats than the preceding row.

Formula:

The sum n terms of an A.P series is

$S_n=\frac{n}{2}[2a+(n-1)d]$

$=\frac{n}{2}[a+l]$

a = first term of the series.

d= common difference.

n= number of term

l= last term

$n^{th}$ term of a A.P series is

$T_n=a+(n-1)d$

n is odd:

n,n-2,n-4,........,5,3,1

Or we can write 1,3,5,.....,n-4,n-2,n

Here a= 1 and d = second term- first term = 3-1=2

Let $t^{th}$ of the series is n.

$T_n=a+(n-1)d$

Here $T_n=n$ , n=t, a=1 and d=2

$n=1+(t-1)2$

⇒(t-1)2=n-1

$\Rightarrow t-1=\frac{n-1}{2}$

$\Rightarrow t = \frac{n-1}{2}+1$

$\Rightarrow t = \frac{n-1+2}{2}$

$\Rightarrow t = \frac{n+1}{2}$

Last term l= n,, the number of term $=\frac{ n+1}2$ , First term = 1

Total number of seat

$S_n=\frac{\frac{n+1}{2}}{2}[1+n}]$

$=\frac{{n+1}}{4}[1+n}]$

$=\frac{(1+n)^2}{4}$

$=\frac{n^2+2n+1}{4}$

n is even:

n,n-2,n-4,.......,4,2

Or we can write

2,4,.......,n-4,n-2,n

Here a= 2 and d = second term- first term = 4-2=2

Let $t^{th}$ of the series is n.

$T_n=a+(n-1)d$

Here $T_n=n$ , n=t, a=2 and d=2

$n=2+(t-1)2$

⇒(t-1)2=n-2

$\Rightarrow t-1=\frac{n-2}{2}$

$\Rightarrow t = \frac{n-2}{2}+1$

$\Rightarrow t = \frac{n-2+2}{2}$

$\Rightarrow t = \frac{n}{2}$

Last term l= n, the number of term $=\frac n2$ , First term = 2

Total number of seat

$S_n=\frac{\frac{n}{2}}{2}[2+n}]$

$=\frac{{n}}{4}[2+n}]$

$=\frac{n(2+n)}{4}$

$=\frac{n^2+2n}{4}$

4 0

2 years ago

What are the factors of

Veronika [31]

Step 1: Trying to factor as a Difference of Squares:

Factoring: x²⁰⁰² - 1

Theory : A difference of two perfect squares, A² - B² can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A² - AB + BA - B² =

A² - AB + AB - B²

A² - B²

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1

Check: x²⁰⁰² is the square of x¹⁰⁰¹

Factorization is : (x¹⁰⁰¹ + 1) × (x¹⁰⁰¹ - 1)

7 0

2 years ago