If a 50 foot cable supporting a circus tent

In 1997 there were 31 laptop computers at grove high school. starting in 1998 the school bought 20 more laptop computers at the

Ksenya-84 [330]

We have equation:
t=20x+31
x is number of years after 1997.

To calculate number of laptops in 2005:
x=2005-1997
x=8

t=20*8+31
t=160+31
t=191

In year 2005 school had 191 laptops.

7 0

3 years ago

Please help, will mark you as the brainiest! Please do NOT answer if you don’t know it!

Sholpan [36]

Answer:

if oq or and os are bisectors then MN is 40, also it is a perpendicular angle so it would also be 40

Step-by-step explanation:

3 0

3 years ago

Determine the first four terms of the sequence in which the nth term is a_n=(n+1)!/(n+2)!

Vilka [71]

Answer: Choice B) 1/3, 1/4, 1/5, 1/6

=============================================

Plug in n = 1 to find the first term

a_n = ( (n+1)! )/( (n+2)! )

a_1 = ( (1+1)! )/( (1+2)! )

a_1 = ( 2! )/( 3! )

a_1 = ( 2*1 )/( 3*2*1 )

a_1 = 2/6

a_1 = 1/3

The first term is 1/3. Optionally you can stop here because only choice B has 1/3 listed as the first term, so this must be the answer. However, I'm going to keep going to show how to find the three other terms. This will help confirm why choice B is the answer, and it will be handy for those times when you aren't given multiple choice answers.

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

Plug in n = 2

a_n = ( (n+1)! )/( (n+2)! )

a_2 = ( (2+1)! )/( (2+2)! )

a_2 = ( 3! )/( 4! )

a_2 = ( 3*2*1 )/( 4*3*2*1 )

a_2 = 6/24

a_2 = 1/4

The second term is 1/4

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

Plug in n = 3

a_n = ( (n+1)! )/( (n+2)! )

a_3 = ( (3+1)! )/( (3+2)! )

a_3 = ( 4! )/( 5! )

a_3 = ( 4*3*2*1 )/( 5*4*3*2*1 )

a_3 = 24/120

a_3 = 1/5

The third term is 1/5

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

Plug in n = 4

a_n = ( (n+1)! )/( (n+2)! )

a_4 = ( (4+1)! )/( (4+2)! )

a_4 = ( 5! )/( 6! )

a_4 = ( 5*4*3*2*1 )/( 6*5*4*3*2*1 )

a_4 = 120/720

a_4 = 1/6

The fourth term is 1/6

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The first four terms are: 1/3, 1/4, 1/5, 1/6, so that confirms why choice B is the answer.

4 0

3 years ago

Question included in the image - geometry problem.

iren [92.7K]

Answer:

y = 116°

Step-by-step explanation:

Given that L₁ || L₂:

The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the two opposite and non-adjacent remote interior angles.

Also, ∠y° and ∠2x° are same-side interior angles formed by the intersection of the hypotenuse of the triangle that acts as a transversal to the parallel lines, L₁ and L₂. Given that ∠y° and ∠2x° are same-side interior angles, then it means that they are the supplements of each other, such that the sum of their measures is 180°.

Now that we have established these definitions, we can proceed with the solution.

Equation 1: ∠y° + ∠2x° = 180° ⇒ Same-side interior angles

Equation 2: ∠y° = ∠x° + ∠84° ⇒ exterior angle theorem

Substitute the value of m∠y° from Equation 2 into Equation 1 to solve for the value of x:

∠y° + ∠2x° = 180°

∠x° + ∠84° + 2x° = 180°

Combine like terms:

∠3x° + ∠84° = 180°

Subtract ∠84° from both sides:

∠3x° + ∠84° - ∠84° = 180° -∠84°

∠3x° = 180° - ∠84°

∠3x° = 96°

Divide both sides by 3 to solve for x:

$\frac{3x}{3} = \frac{96}{3}$

∠x° = 32°

Substitute the value of x into Equation 2 to solve for y:

∠y° = ∠x° + ∠84°

∠y° = ∠32° + ∠84°

∠y° = 116°

Verify whether the values for x and y are correct by substituting their values into Equation 1 and 2:

<h3>Equation 1:</h3>

∠y° + ∠2x° = 180°

116° + 2(32)° = 180°

116° + 64° = 180°

180° = 180° (True statement).

<h3>Equation 2:</h3>

∠y° = ∠x° + ∠84°

116° = 32° + 84°

116° = 116° (True statement)

Therefore, the correct answer is: y = 116°.

5 0

3 years ago

HELP what is 5.476 rounded to hundreths and how do you round the numbers GIVING 12 POINTS

Bond [772]

Hundredths are the second number after the decimal, which is the 7. The number, 5.476, rounded is 5.48. You round numbers by looking at the number after what place you want to round by. For example, if I had 5.28 and wanted to round it to the nearest tenths, I would look at the number after 2, which is 8. If the number is 5 or higher and one to the place you need to the round. If it’s 4 or lower, just take away the numbers after the place you need to round, so it would be 5.3. However, if it was 5.23 and I wanted to round it to the tenths, I would just take away the three, making it 5.2

7 0

3 years ago