Answer:
Step-by-step explanation:
Arithmetic sequence:
Here a is the first term and d is the common difference.
⇒ 
------------(I)
⇒ a + 19d = 100 ---------(II)
Subtract equation (I) from (II)
(I1) a + 19d = 100
(II) a + 13d = 46
<u>- - -</u>
6d = 54
d = 54 ÷ 6
Substitute d = 9 in equation(I) and find 'a',
a + 13*9= 46
a + 117 = 46
a = 46 - 117
a = -71
= -71 + 18
= -53
= -71 + 54
= -17
= -71 + 9*n - 1 *9
= -71 + 9n - 9
= -71 - 9 + 9n
= - 80 + 9n
Answer:
Equation 1 = Equation 2
165 - 4x = 145 - 3.50x
Step-by-step explanation:
Let x represent the number of 30-day periods.
Tavon has a gift card for $165 that loses $4 for each 30-day period it is not used.
Therefore the equation =
$165 -$4 × x
= 165 - 4x.......... Equation 1
He has another gift card for $145 that loses $3.50 for each 30-day period it is not used.
$145 -$3.50 × x
= 145 - 3.50x........... Equation 2
Hence, an equation for the number of 30-day periods until the value of the gift cards will be equal is obtained by equating Equation 1 and Equation 2 together
So, we have
Equation 1 = Equation 2
165 - 4x = 145 - 3.50x
We simplify further:
165 - 145 = -3.50 + 4.0x
20 = 0.5x
x = 20/0.5
x = 40
Therefore, number of each 30-day periods until the value of the gift cards will be equal is 40
Answer: 322
Step-by-step explanation:
23 students × 14 homework
=322 problems
The teacher will have to grade 322 problems
4x=20-8y
x=5-2y now use this value of x in the second equation...
3(5-2y)+6y=15
15-6y+6y=15
15=15 This is true for any y or x value.
So there are infinitely many solutions as the two equations describe the same line.
Answer:
Decreased by 20%.
16 lbs is 80% of 20 lbs.
Step-by-step explanation:
y × 20 = 16 × 100
20y = 1600
20y ÷ 20 = 1600 ÷ 20
y = 80
100% - 80% = 20%
