MATHEMATICS HIGH SCHOOL

63360 inches, and the risers of the steps of the capitol building are 8 inches high. Barry is visiting the capitol, and as he climbs up from the one-mile step, his altitude above sea level, in inches, is given by the following sequence: 63,360, 63,368, 63,376, 63,384, 63,392, ... What is Barry's altitude above sea level, in inches, when he is standing on the 55th step above the one-mile step (counting the one-mile step itself as step #1)?

Answers

Answer 1
Answer: This is an arithmetic sequence question
The formula for the nth term of a sequence is 1+(n-1)d where a is the first term(63360), n is the 55th term, d is the common difference between consecutive terms(63368-63360)=8
Altitude on 55th step= 63360+(55-1)8
                              =63360+(54x8)
                              =63360+432
                              =63792 inches

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#1. What term describes a line segment that connects a vertex of a triangle to a point on the line containing the opposite side, so that the line segment is perpendicular to that line? #2. Which term describes a line segment that connects a vertex of a triangle to the midpoint of the opposite side?

Answers

#1
The ALTITUDE is a line segment that connects a vertex of a triangle to a point on the line containing the opposite side, so that the line segment is perpendicular to that line.

#2
The MEDIAN  a line segment that connects a vertex of a triangle to the midpoint of the opposite side

Answer:

# 1

        Altitude of a triangle.

# 2

        Median of a triangle.

Step-by-step explanation:

Altitude--

An altitude is a line that passes through a vertex and it intersects the opposite side of that vertex at 90 degree i.e. the line is perpendicular to the opposite side.

The point where the three altitudes of a triangle meet is called the Orthocenter of the triangle.

Median of a triangle--

The median of the triangle is the line which passes through a vertex and meets the midpoint of the opposite side of the triangle.

The point where the three medians of a triangle meet is called the Centroid of the triangle.

Find the distance between the pair of parallel lines, y = x-11 & y = x-7

Answers

k:\ y = x-11\ \ \ \Leftrightarrow\ \ \ x-y-11=0\n and\n l:\ y = x-7\ \ \ \Leftrightarrow\ \ \ x-y-7=0\n\nthe\ distance:\n\n d(k;l)= \frac{\big{|-11-(-7)|}}{\big{ √(1^2+1^2) }} =\frac{\big{|-11+7|}}{\big{ √(2) }} =\frac{\big{|-4|}}{\big{ √(2) }} =\frac{\big{4\cdot √(2) }}{\big{ √(2)\cdot √(2) }} =\frac{\big{4 √(2) }}{\big{2 }} =2 √(2)
Given \ the \ equations \ of \ two \ non-vertical \ parallel \ lines:\n\ny = mx+b_1\ny = mx+b_2\n\nthe \ distance \ between \ them \ can \ be \ expressed \ as : \n\nd= (|b_(1)-b_(2)|)/( √( m^2+1) )

y = x-11 \n y = x-7 \n\n\nd= (| -11- (-7)|)/( √( 1^2+1) ) =(| -11+7|)/( √( 1+1) ) = (|-4|)/( √(2) ) = (4)/( √(2) )\cdot (√(2))/(√(2))=(4√(2))/(2)=2√(2)
 

Emil's backpack weighs six and three eights pounds. He removes a book that weighs three fourth pound. Then he removes a book that weighs one half pound .How much does Emil's back pack weigh now

Answers

Answer:

Emil's back pack weigh now 5(1)/(8)\ pounds.

Step-by-step explanation:

Given:

Total Weight of backpack = 6(3)/(8)\ pounds

6(3)/(8)\ pounds can be Rewritten as (51)/(8)\ pounds

Weight of backpack =  (51)/(8)\ pounds

Weight of Book 1 = (3)/(4)\ pound

Weight of Book 2 = (1)/(2)\ pound

We need to find weight of back pack after removing books.

Solution:

Now we can say that;

weight of back pack after removing books can be calculated by Subtracting Weight of Book 1 and Weight of Book 2 from Total Weight of backpack.

framing in equation form we get;

weight of back pack after removing books = (51)/(8)-(3)/(4)-(1)/(2)

Now to solve the equation we will first make the denominator common using LCM.

weight of back pack after removing books =(51*1)/(8*1)-(3*2)/(4*2)-(1*4)/(2*4)=(51)/(8)-(6)/(8)-(4)/(8)

Now the denominators are common so we will solve the numerator.

weight of back pack after removing books = (51-6-4)/(8)=(41)/(8)\ pounds \ \ OR \ \ 5(1)/(8)\ pounds

Hence Emil's back pack weigh now 5(1)/(8)\ pounds.

PLEASE HELP DUE IN 5 MINS

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Answers

Answer:

it might be 2,-2

Step-by-step explanation:

The perimeter of a rectangular field is 344 yards.  If the width of the field is 74 yards, what is its length

Answers

The perimeter of a rectangle is the length of two widths plus two lengths.  You have the width as 74 yard so your formula is 2(74) + 2L = 344.  2x74=148 so 148 + 2L=344.  Subtract 148 from both sides and get 196. 2L=196. Divide both sides by 2 and you get L= 98

P = 2L + 2w

344 = 2L + 2·74

344 - 148 = 2L

2L = 196

L = 196 : 2

L = 98 yards

A test has 10 true/false questions. How many different tests can be turned in to the teacher?

Answers

The same as the greatest number that can be written
with 10 binary bits:  1,024
Each question has 2 possible answers. There are 10 questions. 

1 - 2 
2 - 2 
3  - 2 
4 - 2 
5 - 2 
6 - 2 
7 - 2 
8 - 2 
9 - 2 
10 2                                                                                      There can be 20 different tests. 
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