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Scrat [10]
3 years ago
12

What is the ninth term of the arithmetic sequence defined by the rule A(n)= -14+(n-1)(2)

Mathematics
1 answer:
Kruka [31]3 years ago
3 0
If you start counting from 0, you ninth term will be 8. Replace n=8 and calculate:
A(8) = -14 + (8-1)(2) = -14 + (7)(2) = -14 + 14 = 0

If you start counting from 1, your ninth term will be 9. Replace n=9 and calculate:
A(9) = -14 + (9-1)(2) = -14 + (8)(2) = -14 + 16 = 2

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Solve the given linear Diophantine equation. Show all necessary work. A) 4x + 5y=17 B)6x+9y=12 C) 4x+10y=9
aliina [53]

Answer:

A) (-17+5k,17-4k)

B)  (-4+3k,4-2k)

C) No integer pairs.

Step-by-step explanation:

To do this, I'm going to use Euclidean's Algorithm.

4x+5y=17

5=4(1)+1

4=1(4)

So going backwards through those equations:

5-4(1)=1

-4(1)+5(1)=1

Multiply both sides by 17:

4(-17)+5(17)=17

So one integer pair satisfying 4x+5y=17 is (-17,17).

What is the slope for this equation?

Let's put it in slope-intercept form:

4x+5y=17

Subtract 4x on both sides:

     5y=-4x+17

Divide both sides by 5:

      y=(-4/5)x+(17/5)

The slope is down 4 and right 5.

So let's show more solutions other than (-17,17) by using the slope.

All integer pairs satisfying this equation is (-17+5k,17-4k).

Let's check:

4(-17+5k)+5(17-4k)

-68+20k+85-20k

-68+85

17

That was exactly what we wanted since we were looking for integer pairs that satisfy 4x+5y=17.

Onward to the next problem.

6x+9y=12

9=6(1)+3

6=3(2)

Now backwards through the equations:

9-6(1)=3

9(1)-6(1)=3

Multiply both sides by 4:

9(4)-6(4)=12

-6(4)+9(4)=12

6(-4)+9(4)=12

So one integer pair satisfying 6x+9y=12 is (-4,4).

Let's find the slope of 6x+9y=12.

6x+9y=12

Subtract 6x on both sides:

      9y=-6x+12

Divide both sides by 9:

       y=(-6/9)x+(12/9)

Reduce:

       y=(-2/3)x+(4/3)

The slope is down 2 right 3.

So all the integer pairs are (-4+3k,4-2k).

Let's check:

6(-4+3k)+9(4-2k)

-24+18k+36-18k

-24+36

12

That checks out since we wanted integer pairs that made 6x+9y=12.

Onward to the last problem.

4x+10y=9

10=4(2)+2

4=2(2)

So the gcd(4,10)=2 which means this one doesn't have any solutions because there is no integer k such that 2k=9.

6 0
3 years ago
Type a digit that makes this statement true.<br><br> 768,72<br> is divisible by 6.<br><br> Help Me
kiruha [24]

Answer:

6

Step-by-step explanation:

Rule for divisibilty of 6:

  • sum of place values is a multiple of 3
  • an even number

Step 1: dd the integers

  • 7 + 6 + 8 + 7 + 2 + x
  • 30 + x

Now, we have a couple options:

  • x = 3
  • x = 6
  • x = 9

You can use any of these three values,

But the number has to be even, so the last digit has to be even. The correct answer is 6.

-Chetan K

8 0
2 years ago
Read 2 more answers
I need help on questions 48 49 and 50 and u need to find the surface area of the 3 polyhedras please and thank you!
White raven [17]

48. The surface area of a cylinder is given by

... A = 2πr² + 2πrh = 2πr(r+h)

For r = 13 mi and h = 7 mi, this becomes

... A = 2π(13 mi)(13 mi + 7 mi) = 520π mi²

The surface area of the cylinder is 520π mi² ≈ 1634 mi².

49. The surface area of a rectangular prism is

... A = 2(LW + H(L+W))

For L = 20 m, W = 10 m, H = 7 m, this becomes

... A = 2((20 m)(10 m) + (7 m)(20 m + 10 m)) = 2(200 m² + 210 m²) = 820 m²

The surface area of the prism is 820 m².

50. The formula is the same as for problem 48.

For r = 10 m and h = 13 m, this becomes

... A = 2π(10 m)(10 m + 13 m) = 460π m² ≈ 1445 m²

The surface area of the cylinder is 460π m² ≈ 1445 m².

_____

When calculations are repetitive, it is convenient to let a calculator or spreadsheet do them.

7 0
3 years ago
Y=3x^2+11x-4 and y=10x-1. solve the system of equations
Mashcka [7]
3x^2+11x-4=10x-1
3x^2+11x-10x-4+1=0
3x^2+x-3=0
Δ=1^1-4*3*(-3)=1+36=37
x1=(-1+V37)/6

x2=( -1-V37)/6
7 0
3 years ago
Please help me with the problem
mixas84 [53]
Let's see what we're working on here 

\frac{1}{2}  - 2(m) =?
            ? = 0
Simplify this → \frac{1}{2}

\frac{1}2y} - 2(m) = ?

\frac{2(m)(2)}{2}

\frac{1 - 4(m)}{2} = ?

\frac{1 - 4(m)}{2} = 2

-4(m) + 1 = 0
 Subtract ( - )the number 1 from each of your sides on this part

4(m) = 1 
Multiply( ×) the number -1 to your sides for this part of the equation 

Therefore, the value of m is \frac{1}{4}
m =  \frac{1}{4}


3 0
3 years ago
Read 2 more answers
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