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3 years ago

A linear pair of angles have measures of 3m - 6 and 3m + 18. What is the value of m?

Mathematics

1 answer:

timama [110]3 years ago

4 0

Answer:

the value of m = 28°

Step-by-step explanation:

the sum of adjacent angles which form linear pair is 180°

so,

=》3m - 6° + 3m + 18° = 180°

=》6m + 12° = 180°

=》6m = 180° - 12°

=》m = 168° ÷ 6

=》m = 28°

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Given the geometric sequence where a1 = 3 and r = √2 find a9

Zigmanuir [339]

Answer:

$a_9=48$

Step-by-step explanation:

we are given

sequence is geometric

so, we can use nth term formula

$a_n=a_1(r)^{n-1}$

we have

$a_1=3$

$r=\sqrt{2}$

we have to find a9

so, we can plug n=9

we get

$a_9=3(\sqrt{2})^{9-1}$

$a_9=2^4\cdot \:3$

$a_9=48$

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3 years ago

What two rational expressions sum to <img src="https://tex.z-dn.net/?f=%5Cfrac%7B4x%2B2%7D%7Bx%5E%7B2%7D-9%2B8%20%7D" id="TexFor

bulgar [2K]

Answer:

$\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}$

Step-by-step explanation:

Given

$\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}$

Required

Fill in the gaps

Going by the given parameters, we have that

$\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}$

$x^2 - 9x + 8$ , when factorized is $(x-1)(x-8)$

Hence; the expression becomes

$\frac{4x+2}{(x-1)(x-8)} = \frac{A}{(x-8)(x-1)} + \frac{B}{(x-1)(x-8)}$

Combine Fractions

$\frac{4x+2}{(x-1)(x-8)} = \frac{A + B}{(x-8)(x-1)}$

Simplify the denominators

$4x + 2 = A + B$

By direct comparison

$A = 4x$

$B = 2$

Hence, the complete expression is

$\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}$

3 0

3 years ago

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A frame contains 4 pounds of gold. Suppose gold is worth $1,277 per ounce. How much would the gold in the crown be worth? $5,108

Art [367]

Answer:

5108

Step-by-step explanation:

4 0

2 years ago

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Which linear equation has no solution?

olga_2 [115]

Answer:

Option A

Step-by-step explanation:

Given:

a. 3x-5= 3x + 5
b. 3x-5= 3x - 5
c. 3x - 5 = 2x+5
d. 3x-5 = 2x + 10

To find:

Which one of the linear equations have no solution.

Solution:

a) 3x-5= 3x + 5

Add 5 to both sides

3x-5= 3x + 5

3x - 5 + 5 = 3x + 5 + 5

Simplify

(Add the numbers)

3x - 5 + 5 = 3x + 5 + 5

3x = 3x + 5 + 5

(Add the numbers)

3x = 3x + 5 + 5

3x = 3x + 10

Subtract 3x from both sides

3x = 3x + 10

3x - 3x = 3x + 10 - 3

Simplify

(Combine like terms)

3x -3x = 3x + 10 - 3

0 = 3x + 10 - 3

(Combine like terms)

0 = 3x + 10 - 3

0 = 10

The input is a contradiction: it has no solutions

b) 3x-5= 3x - 5

Since both sides equal, there are infinitely many solutions.

c) 3x - 5 = 2x+5

Add 5 to both sides

3x = 2x + 5 + 5

Simplify 2x + 5 + 5 to 2x + 10

3x = 2x + 10

Subtract 2x from both sides

3x - 2x = 10

Simplify 3x - 2x to x.

x = 10

d) 3x-5 = 2x + 10

Add 5 to both sides

3x = 2x + 10 + 5

Simplify 2x + 10 + 5 to 2x + 15

3x = 2x + 15

Subtract 2x from both sides

3x - 2x = 15

Simplify 3x -2x to x.

x = 15

--------------------------------------------

Answer:

As you can see all c and d both have solutions, eliminating them as options. Option B has infinite solutions leaving Option A which has no solutions.

Therefore, <u><em>Option A</em></u> is the linear equation that has no solution.

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Step-by-step explanation:

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3 years ago