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kolezko [41]
2 years ago
13

In a diagram showing two parallel lines cut by a trasversal, the measures of two same side interior angles are both given as 3x.

Without writing and solving an equation, can you determine the measures of both angles? Explain. Then write and solve an equation to find the measures
Mathematics
1 answer:
Andre45 [30]2 years ago
3 0

Answer:

90 degrees

Step-by-step explanation:

Same side interior angles, or consecutive angles, are supplementary (angle measures add up to 180 degrees). Since both angles have measures 3x degrees, the angles are congruent (same angle measure). In Geometry, when two angles are congruent and supplementary, the two angles are right angles (angles measuring 90 degrees). Therefore the angle measures of the two angles are 90 degrees and 90 degrees.

Or, to solve this algebraically, add 3x and 3x, let it equal to 180 degrees, solve for x, and find the angle measures by substituting x into the expression.

3x + 3x = 180

6x = 180

x = 30


3x = 3*30 = 90

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Rewrite the following without an exponent 4^-2
Paul [167]

Answer:

1/16

Step-by-step explanation:

4^-2 is the same as 1/4^2

and then calculate 4^2 to get 16, making it 1/16.

6 0
4 years ago
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For Lilly‘s birthday she takes her for friends to the movies she buys herself all of her friends the movie tickets which cost 72
VladimirAG [237]

Answer:

6536.25

Step-by-step explanation:

Given that :

Number of friends = 4

Cost of movie ticket = 725 each

At concession stand:

Pop corn = 850

Number of popcorn = 2

Large soda = 575

Number of large sodas = 3

Discount given = 15%

Amount spent on movie ticket :

725 * 5 = 3625

Amount spent at concession stand :

Cost of popcorn + cost of large soda

(850 * 2) + (575 * 3) = 3425

15% discount on purchase :

Discount = ((1-0.15) * 3425) = 2911.25

Total amount spent :

3625 + 2911.25

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5 0
3 years ago
Cindy plants a daffodil plant. If the plant has one daffodil flower to start with, and the number of daffodils triples every wee
Romashka [77]

Answer:

There will be 729 daffodils in the sixth week

Step-by-step explanation:

Given

a = 1 --- start

r = 3 --- weekly rate

Required

Number of daffodils in 6th week

This question illustrates an exponential function which is represented as

f(x) = ab^x

Where

f(x) = Number of daffodils at x week

x = The week

a = Initial number of daffodils

b= rate

So, we have:

a = 1

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Hence:

f(x) = 1 * 3^x

f(x) = 3^x

At the 6th week

x = 6

So:

f(6) = 3^6<em> ---- as a power</em>

f(6) = 3 * 3 * 3 * 3 * 3 * 3<em> --- related multiplication</em>

f(6) = 729<em> --- standard form</em>

4 0
3 years ago
L will mark you brainiest if correct
Strike441 [17]
4 years

I hope it’s right
Best luck with your studying
4 0
3 years ago
What is the present occupancy rate of a 555-bed facility that only has 333 inmates booked? please show work i keep finding my wo
babunello [35]

Answer:

60%.

Step-by-step explanation:

We are asked to find the present occupancy rate of a 555-bed facility that only has 333 inmates booked.

The total number of beds is 555 and 333 beds are occupied by inmates. So we will find out 333 is what percent of 555.

\text{Present occupancy rate}=\frac{333}{555}\times 100

Upon dividing 333 by 555 we will get,

\text{Present occupancy rate}=0.6\times 100

\text{Present occupancy rate}=60\%

Therefore, present occupancy rate is 60%.

8 0
3 years ago
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