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Fed [463]
2 years ago
9

Help me please 8. Match each angle pair with the corresponding drawing. Choose the best answer!

Mathematics
1 answer:
sdas [7]2 years ago
5 0

Answer:

1. D

2. B

3.  A

4. C

Step-by-step explanation:

1. Vertical angles are a pair of opposite angles formed by the intersection of lines. Choice D has two lines intersecting, and two opposite angles formed by it.

2. Adjacent angles are two angles that have a common vertex and common side but do not overlap. Choice B is two angles with a common vertex and common side, and they don't overlap.

3. Supplementary angles are angles that add up to 180 degrees/make a straight angle. Choice A has two angles that add up to 180 degrees, and the two angles combined make a straight angle/line.

4. Two angles are called complementary angles if they add up to 90 degrees and form a right angle. Choice C has two angles that form a right triangle, meaning it adds up to 90 degrees.

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Country days scholarship rounds receive a gift of $135000. The money is invested in stock, bonds, and CDs. CDs pay 2.75% interes
Vsevolod [243]

Answer:

  • CDs — $10,000
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  • stocks — $45,000

Step-by-step explanation:

Let the variables c, b, s represent the dollar amounts invested in CDs, stocks, and bonds, respectively. Then the problem statement gives us 3 relations between these 3 variables:

  c + b + s = 135000 . . . . . . . . . . . . . . . . . total invested

  0.0275c +.045b +0.104s = 8555 . . . . . total income earned

  -c + b = 70000 . . . . . . . . . . . . . . . . . . . . . 70,000 more was in bonds than CDs

Using the third equation to write an expression for b, we can substitute into the other two equations.

  b = 70000 +c . . . . . . . . . . . . . . . . expression we can substitute for b

  c + (70000 +c) +s = 135000 . . . . substitute for b in the first equation

  2c +s = 65000 . . . . . . . . . . . . . . . . [eq4] simplify

  .0275c +.045(70000 +c) +.104s = 8555 . . . . . substitute for b in 2nd eqn

  .0725c +.104s = 5405 . . . . . . . . . . [eq5] simplify

Using [eq4], we can write an expression for s that can be substituted into [eq5].

  s = 65000 -2c . . . . . . . expression we can substitute for s

  0.0725c +0.104(65000 -2c) = 5405

  -0.1355c = -1355 . . . . . . . . . . . . . . . . . . . . subtract 6760, simplify

  c = 1355/.1355 = 10,000

  s = 65000 -2×10000 = 45,000

  b = 70000 +10000 = 80,000

The amounts invested in stocks, bonds, and CDs were $45,000, $80,000, and $10,000, respectively.

_____

Alternatively, you can reduce the augmented matrix for this problem to row-echelon form using any of several calculators or on-line sites. That matrix is ...

\left[\begin{array}{ccc|c}1&1&1&135000\\0.0275&0.045&0.104&8555\\-1&1&0&70000\end{array}\right]

6 0
3 years ago
Reduce the ratio to its lowest form. 72:8​
dmitriy555 [2]

Answer:

9:1

Step-by-step explanation:

Try to reduce the ratio further with the greatest common factor (GCF).  

The GCF of 72 and 8 is 8  

Divide both terms by the GCF, 8:

72 ÷ 8 = 9

8 ÷ 8 = 1  

The ratio 72 : 8 can be reduced to lowest terms by dividing both terms by the GCF = 8 :  

72 : 8 = 9 : 1  

Therefore:

72 : 8 = 9 : 1

4 0
2 years ago
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