Three businesses donated money to charity.
5. Business B pledged $20 million less
than twice the amount pledged by
Business A. Business C pledged $200
million less than twice the amount
pledged by Business B. If x represents
the amount pledged by the Business A,
write expressions to show the amounts
pledged by Business B and Business C
in terms of x.
6. The combined pledges of Business A,
Business B, and Business C totaled
$1035 million. Write an equation that
can be used to determine how much
each business pledged.
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3. PYRAMIDS When climbing an ancient
Mayan pyramid, the Johnson family
noticed that the bottom of each side of
the pyramid started with 50 large
stones. The next step up had 45 large
stones, the next step up had 40 stones,
and so on. Write an equation to
represent the number of stones on each
level. How many levels can the pyramid
have?
Steps 1 = 45 stones
Steps 2 = 40 stones
Steps 3 = 34
?
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TRIANGULAR NUMBERS By arranging
bowling pins in their proper order, a
triangle is created. The table below
shows the number of rows of bowling
pins and the total number of pins in the triangle. The formula:
n * (n+1) / 2
can be used to find t, the total number of items in n rows. How many bowling pins would there be if 10 rows of pins were set up?
Rows 1 2 3 4
Pins 1 3 6 10
--------------------------------
PASCAL’S TRIANGLE For Exercises 5 and
6, use the following information.
Blaise Pascal is known for a special
triangular arrangement of numbers, calledPascal’s Triangle.. Each number insuccessive rows of the triangle is created by adding the two numbers in the row above the number.
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
5. Starting with the second row from thetop, what is the sequence of the diagonal
(1 2 3 4 5 6 7)?
6. The sum of each row represents 2n,
starting with the first row, which is
20 = 1. Write an exponential expression
for the sum of the values in the sixth
row. Simplify the expression.
answer for,5. Business B pledged $20 million less
than twice the amount pledged by
Business A. Business C pledged $200
million less than twice the amount
pledged by Business B. If x represents
the amount pledged by the Business A,
write expressions to show the amounts
pledged by Business B and Business C
in terms of x. is
A=x
B=2X-20
C=4X-240
id be glad to check your answers if you showed the work that you tried and the answer you think is correct
For 5 & 6. Business I have no clue where to start. :{
---------------------------
4. TRIANGULAR NUMBERS I tried this:
t= 10x(10+1)
t= 10x(11)
t= 110/2 = 55
but this also looks wrong and doesn't seem right.
---------------------------
Again with PASCALS TRIANGLE 6 I have no idea where to start.
--------------------------
With 3 PYRAMIDS i tried this:
45-5 (1-9)
45-5 (8)
45+40
= 85
Also it appears wrong.
Please. I am having extreme difficulties with this :(
5. To find the amounts pledged by Business B and Business C in terms of x:
Business B pledged $20 million less than twice the amount pledged by Business A. So, the amount pledged by Business B can be expressed as 2x - 20 million.
Business C pledged $200 million less than twice the amount pledged by Business B. So, the amount pledged by Business C can be expressed as 2(2x - 20 million) - 200 million.
Therefore, the expressions to show the amounts pledged by Business B and Business C in terms of x are:
Business B = 2x - 20 million
Business C = 2(2x - 20 million) - 200 million
6. The combined pledges of Business A, Business B, and Business C totaled $1035 million. To write an equation to determine how much each business pledged:
The amount pledged by Business A is x.
The amount pledged by Business B is 2x - 20 million.
The amount pledged by Business C is 2(2x - 20 million) - 200 million.
Therefore, the equation would be: x + (2x - 20 million) + (2(2x - 20 million) - 200 million) = 1035 million.
3. To write an equation representing the number of stones on each level of the pyramid:
The number of stones on each level decreases by 5 compared to the previous level.
Let n represent the level number.
So, the equation would be: Number of stones = 50 - 5(n-1).
To find the number of levels the pyramid can have, you can solve the equation when the number of stones on a level becomes zero.
50 - 5(n-1) = 0
=> 50 - 5n + 5 = 0
=> 55 - 5n = 0
=> 5n = 55
=> n = 11
Therefore, the pyramid can have a maximum of 11 levels.
TRIANGULAR NUMBERS:
To find the number of bowling pins in a given number of rows:
Use the formula: t = n * (n + 1) / 2, where t represents the total number of items and n represents the number of rows.
For example, if you want to find the number of bowling pins in 10 rows:
t = 10 * (10 + 1) / 2
t = 10 * 11 / 2
t = 110 / 2
t = 55
So, if 10 rows of pins were set up, there would be a total of 55 bowling pins.
PASCAL’S TRIANGLE:
5. To find the sequence of the diagonal (1 2 3 4 5 6 7) starting from the second row:
In Pascal's Triangle, each number in successive rows is created by adding the two numbers in the row above.
The sequence of the diagonal can be found by looking at the second number in each row. So, the sequence would be: 1 2 3 4 5 6 7.
6. The sum of each row represents 2n, starting with the first row, which is 20 = 1.
So, for the sixth row, the sum of the values would be 2^6 = 64.
Therefore, the exponential expression for the sum of the values in the sixth row is 64.