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3 years ago

Triangle UVW has a perimeter of 11.5 units. Solve for y.

Mathematics

1 answer:

vodomira [7]3 years ago

8 0

Answer:

y = 3.2 units

Step-by-step explanation:

Find the missing angle measure x. Use the fact that all interior angle measures in a triangle add up to 180 degrees.

55 + 50 + x = 180
105 + x = 180
x = 75

We can use the Law of Cosines to determine the missing side length y.

a² = b² + c² - 2bc · cos(A)

Let's set UW (y) as a, WV as b, and UV as c. Therefore, ∠V must be A, ∠U must be B, and ∠W must be C.

Use the Law of Cosines to solve for a (side length y).

a² = b² + c² - 2bc · cos(A)
a² = (4)² + (3.5)² - 2(4)(3.5) · cos(50)
a² = 28.25 - 28cos(50)
a² = 28.25 - 17.99805307
a² = 10.25194693
a = 3.20186616366

Side length y is equal to 3.2 units.

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18. Determine the common difference, the fifth term, and the sum of the first 100 terms of the following sequence:

Ksenya-84 [330]

$a_1=1,\ a_2=2.5,\ a_3=4,\ a_4=5.5,\ ...\\\\a_2-a_1=2.5-1=1.5\\a_3-a_2=4-2.5=1.5\\a_4-a_3=5.5-4=1.5\\a_{n+1}-a_n=1.5=constans\\\\\text{It's an arithmetic sequence with}\\a_1=1,\ \boxed{d=1.5}\\\\a_n=a_1+(n-1)d\to a_n=1+(n-1)(1.5)=1+1.5n-1.5\\\\a_n=1.5n-0.5\\\\a_5=1.5(5)-0.5=7.5-0.5=7\\\boxed{a_5=7}\\\\\text{The formula of a Sum of the First n Terms of an Arithmetric Sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{We have:}\\a_1=1,\ d=1.5,\ n=100\\\\\text{Substitute}$

$S_{100}=\dfrac{(2)(1)+(100-1)(1.5)}{2}\cdot100=\dfrac{2+(99)(1.5)}{1}\cdot50\\\\=(2+148.5)\cdot50=150.5\cdot50=7,525\\\\\boxed{S_{100}=7,525}\\\\Answer:\\the\ common\ difference:\ d=1.5\\the\ fifth\ term:\ a_5=7\\the\ sum\ of\ first\ 100\ terms:\ S_{100}=7,525$

8 0

3 years ago

4. Use the substitution method to determine the solution to this system of equations.

N76 [4]

Answer:

No solution

Step-by-step explanation:

6X - 3Y = -9--------------(1)

- 2 X +Y= 5---------------(2)

from equation two,

Y = 5+2X------------------(3)

substitute equation (3) into equation (1)

6X-3(5+2X)= -9

opening bracket

6X-15-6X= -9

6X- 6X = -9+15

0 = 6

<h2>therefore the answer is no solution</h2>

3 0

2 years ago

What is the relationship between the continental drift hypothesis and the theory of

Pepsi [2]

Answer:

Plate tectonics explains why Earth's continents are moving; the theory of continental drift did not provide an explanation. Therefore, the theory of plate tectonics is more complete. It has gained widespread acceptance among scientists.

Step-by-step explanation:

Do some research on it.

5 0

2 years ago

Ryan measure the perimeter of his square painting so he can make a wooden frame . find the perimeter of the painting in centimet

egoroff_w [7]

Answer:

Perimeter = 122 cm or 1.22 m

Step-by-step explanation:

The complete question with image is attached.

We know the perimeter is the sum of all the sides.

Since it's already given that one side is 30.5 and we know it is a square, so perimeter would be sum of all the 4 sides [each 30.5 cm].

Perimeter = 30.5 + 30.5 + 30.5 + 30.5 = 122 cm

Also, to get the answer in meters, we need to know that 100 cm = 1 m, hence

We got to divide by 100 to get our answer in meters, so

122/100 = 1.22 meters

Hence

Perimeter = 1.22 m

6 0

3 years ago

When placed in the box below, what expression will complete an example of the commutative property of addition 7(2+9)= ?

ANEK [815]

The expression for 7(2+9) IS A(B+C) which is distributive property of addition over multiplication.

Only two arithmetic procedures are subject to the commutative property: Multiplication and Addition

A + B = B + A Which is Commutative property of addition

A.B = B.A, which is a commutative property of multiplication.

Distributive property is A(B+C) =AB+AC

The operation on numbers that are available in brackets can be distributed for each number outside the bracket, according to the distributive property. It is one of the mathematical properties that is used the most. Commutative and associative qualities are the other two important features.

from the given data 7(2+9) =7*2+7*9

=14+63

=77

Now, we can clear that 7(2+9) =7(9+2)

Hence, the expression for commutative property of addition is A(B+C) = AB+AC.

To learn more about commutative property, visit

brainly.com/question/28387735

#SPJ1

6 0

1 year ago