If The Reciprocal Of A Number Is Subtracted From The Original Number, The Difference Is 8/3. Find The Number, The Length Of A Rectangle Is 14m What R.
If the reciprocal of a number is subtracted from the original number, the difference is 8/3. Find the number
The length of a rectangle is 14m what R.E. the possible width that will give a perimeter less than 48m? Also Determine the linear inequality
A collection of 27 coins consisting of 5 peso coins and one peso coins has a value of 79 pesos. How many coins of each kind are there? Also, what is the system of linear equations that represents the problem
A retiring worker has 860,000 to invest.He invested part of it in bonds getting 5% interest, and the remainder in mortgage getting 6% interest.Find the investment at each rate if the total investment in a year is 50,000 pesos. Also, what is the system of linear equations that represents the problem.
A triangle is a polygon. Determine the if-then form of the statement.
With solution please answer ASAP thanks
Answer:
1. x = 3 or x = -`1/3
2. 2l + 2w < 48 ( linear inequality)
w < 10
3. x + y = 27
5x + y = 79
13 five peso coins and 14 one peso coins
two equations two unknowns linear equation
4. one variable linear equation
160,000 ( invested in bonds)
700,000 ( invested in mortgage)
5. If a polygon has 3 sides, then it is a polygon.
Step-by-step explanation:
1. If the reciprocal of a number is subtracted from the original number, the difference is 8/3. Find the number
let x be the number
x - (1/x) = 8/3
x^2 - 1 = (8/3)x
x^2 - (8/3)x - 1 = 0
solve for x
use quadratic formula
a = 1, b = -8/3, c= -1
x = -b ± √(b² - 4ac)/ 2a
x = (8/3) ± √((-8/3)² - 4(1)(-1))/ 2(-1)
x = (8/3) ± √(100/9)/ -2
x = (8/3) ± 10/3/ -2
x = 3 or x = -`1/3
2. The length of a rectangle is 14m what R.E. the possible width that will give a perimeter less than 48m? Also Determine the linear inequality
l = 14
let w be the width
perimeter = 2l +2w
perimeter < 48
2l + 2w < 48 (linear inequality)
2(14) + 2(w) < 48
28 + 2w < 48
2w < 20
w < 10
Therefore, the width must be less than 10 m to have a perimeter of less than 48 m
3. A collection of 27 coins consisting of 5 peso coins and one peso coins has a value of 79 pesos. How many coins of each kind are there? Also, what is the system of linear equations that represents the problem
let x be the 5 peso coins
y be the one peso coins
x + y = 27
5x + y = 79
solve for x and y by elimination method
-4x = -52
x = 13
y = 79 - (5 × 13)
y = 14
13 five peso coins and 14 one peso coins
It is a two variable / two unknowns/ two equations linear equation
4. A retiring worker has 860,000 to invest.He invested part of it in bonds getting 5% interest, and the remainder in mortgage getting 6% interest.Find the investment at each rate if the total investment in a year is 50,000 pesos. Also, what is the system of linear equations that represents the problem.
let x be the amount invested in bonds
860,000 - x = be the amount invested in mortgage
0.05x = interest of invested in bonds
0.06(860000 - x) = interest of invested in mortgage
0.05x + 0.06(860000 - x) = 50,000
x = 160,000 (invested in bonds)
860,000 - 160,000 = 700,000 (invested in mortgage)
it is a one variable linear equation
5. A triangle is a polygon. Determine the if-then form of the statement.
If a polygon has 3 sides, then it is a polygon.
Below are other practice problems:
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