Answer:
each notebook costs $2.70
each pack of pencils costs $1.50
Step-by-step explanation:
system of equations:
let p = pack of pencils
let n = notebook
3p + 5n = 18
4p + 4n = 16.8
I used the elimination method by multiplying the first equation by 4 and the second equation by -3
4(3p + 5n = 18) = 12p + 20n = 72
-3(4p + 4n = 16.8) = -12p -12n = -50.4
adding the new equations together you get: 8n = 21.6
n = 21.6/8
n = $2.70
solve for 'p':
3p + 5(2.7) = 18
3p + 13.5 = 18
3p = 4.5
p = $1.50
Answer:
They are congruent by HL
Step-by-step explanation:
Answer:
- The circumference of the circle in term of pi = 10π inches
- The circumference of the circle us 3.14 as pi = 31.4 inches
Step-by-step explanation:
Given
The radius of the circle = r = 5 in
We know that diameter is twice the radius.
so d = 2r = 2(5) = 10 in
<u>Finding the circumference of the circle in terms of pi</u>
Using the formula to find the circumference of the circle
C = dπ
C = 10×π
C = 10π inches
Thus, the circumference of the circle in term of pi = 10π inches
<u>Finding the circumference of the circle using π = 3.14</u>
We know that the formula to find the circumference of the circle
C = dπ
Given
π = 3.14
substituting π = 3.14 to find the circumference of the circle
C = 10×3.14
C = 31.4 inches
Thus, the circumference of the circle = 31.4 inches
Answer:
2.67 inches.
Step-by-step explanation:
Assuming that we represent the size of the squares with the letter y, such that after the squares are being cut from each corner, the rectangular length of the box that is formed can now be ( 23 - 2y), the width to be (13 - 2y) and the height be (x).
The formula for a rectangular box = L × B × W
= (23 -2y)(13-2y) (y)
= (299 - 46y - 26y + 4y²)y
= 299y - 72y² + 4y³
Now for the maximum volume:
dV/dy = 0
This implies that:
299y - 72y² + 4y³ = 299 - 144y + 12y² = 0
By using the quadratic formula; we have :
where;
a = 12; b = -144 and c = 299
Since the width is 13 inches., it can't be possible for the size of the square to be cut to be 9.33
Thus, the size of the square to be cut out from each corner to obtain the maximum volume is 2.67 inches.
Answer:
=250(1.025)∧4t
Step-by-step explanation:
Using the compound interest formula we can find the expression for the total amount that accumulates in the given time t.
A=P(1+R/n)ⁿᵇ
where A is the amount, P the principal amount, R the rate as a decimal n is the number of times it is compounded and b the time.
When compounded annually, the expression becomes
A=250(1.1)∧t
When compounded quarterly, we introduce the n in our expression.
A=250(1+0.1/4)∧4t
=250(1.025)∧4t
