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lesya692 [45]
3 years ago
6

Name each pair of angles as corresponding, alternate interior, alternate exterior, or consecutive. Then solve for x.

Mathematics
1 answer:
Studentka2010 [4]3 years ago
4 0

Answer:

x = -2

Step-by-step explanation:

These 2 angles are <u>alternate exterior</u> so they're equal to each other.

x + 127 = 125

x = 125 - 127

x = -2

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Find all geometric sequences such that the sum of the first two terms is 24 and the sum of the first three terms is 26.
Serga [27]

Answer:

<h3>The nth term Tn = -8(-1/4)^(n-1) or Tn = 6(1/3)^(n-1) can be used to find all geometric sequences</h3>

Step-by-step explanation:

Let the first three terms be a/r, a, ar... where a is the first term and r is the common ratio of the geometric sequence.

If the sum of the first two term is 24, then a/r + a = 24...(1)

and the sum of the first three terms is 26.. then a/r+a+ar = 26...(2)

Substtituting equation 1 into 2 we have;

24+ar = 26

ar = 2

a = 2/r ...(3)

Substituting a = 2/r into equation 1 will give;

(2/r))/r+2/r = 24

2/r²+2/r = 24

(2+2r)/r² = 24

2+2r = 24r²

1+r = 12r²

12r²-r-1 = 0

12r²-4r+3r -1 = 0

4r(3r-1)+1(3r-1) = 0

(4r+1)(3r-1) = 0

r = -1/4 0r 1/3

Since a= 2/r then a = 2/(-1/4)or  a = 2/(1/3)

a = -8 or 6

All the geometric sequence can be found by simply knowing the formula for heir nth term. nth term of  a geometric sequence is expressed as

if r = -1/4 and a = -8

Tn = -8(-1/4)^(n-1)

if r = 1/3 and a = 6

Tn = 6(1/3)^(n-1)

The nth term of the sequence above can be used to find all the geometric sequence where n is the number of terms

6 0
3 years ago
A game-show spinner has these odds of stopping on particular dollar values: 40% for $5, 25% for $100, 20% for $500, and 15% for
Yakvenalex [24]

Answer:

13÷ 23

Step-by-step explanation:

The computation of the odds of player winning is shown below;

For $5 it is 40%

And, for $100 it is 25%

so for total it is

= 40% + 25%

= 65%

And, the total percentage is 100%

So, the odds in favor is

65:100

13:20

Now for winning it would be 13÷ 23

5 0
2 years ago
I have no idea how to do this, please help!
Marta_Voda [28]

Answer:

24

Step-by-step explanation:

7 0
3 years ago
A recipe uses 1/4 teaspoons of baking soda for every ½ cup of flour. What is the unit rate in cups per teaspoon?
Verizon [17]

Answer:

2 cups per teaspoon, 2 cups/1 tsp

Step-by-step explanation:

to get the teaspoon amount to 1 (you have to for a unit rate), you multiply both sides by 4.

1/2 x 4 = 2

1/4 x 4 = 1

8 0
2 years ago
Which of the following is equivalent to (16^3/2)^1/2? 6 8 12 64
Pani-rosa [81]
\bf a^{\frac{{ n}}{{ m}}} \implies  \sqrt[{ m}]{a^{ n}} \qquad \qquad&#10;\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\&#10;-------------------------------\\\\&#10;\left( 16^{\frac{3}{2}} \right)^{\frac{1}{2}}\implies 16^{\frac{3}{2}\cdot \frac{1}{2}}\implies 16^{\frac{3}{4}}\qquad \boxed{16=2^4}\qquad (2^4)^{\frac{3}{4}}\implies 2^{4\cdot \frac{3}{4}}&#10;\\\\\\&#10;2^3\implies 8
6 0
3 years ago
Read 2 more answers
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