X = ones, y = fives
x + y = 19....x = 19 - y
x + 5y = 59
19 - y + 5y = 59
19 + 4y = 59
4y = 59 - 19
4y = 40
y = 40/4
y = 10 <=== there are 10 five dollar bills
x + y = 19
x + 10 = 19
x = 19 - 10
x = 9 <=== there are 9 one dollar bills
Answer:
Olivia invested $2900 in a savings account that paid 4.5%/yr and $900 in a government bond that paid 5.5%/yr.
Step-by-step explanation:
With the information provided you can write the following equations:
x+y=3800 (1)
0.045x+0.055y=180 (2), where:
x is the amount invested in a savings account
y is the amount invested in a government bond
First, you can solve for x in (1):
x=3800-y (3)
Next, you can replace (3) in (2) and solve for y:
0.045(3800-y)+0.055y=180
171-0.045y+0.055y=180
0.01y=9
y=9/0.01
y=900
Finally, you can replace the value of y in (3) to find x:
x=3800-900
x=2900
According to this, the answer is that Olivia invested $2900 in a savings account that paid 4.5%/yr and $900 in a government bond that paid 5.5%/yr.
Answer:
The slope - intercept equation for this line is y = 17x - 55
Step-by-step explanation:
The general form of the slope-intercept form is
y = mx +b
where m is the slope and b is the y-intercept.
We are given slope m = 17
we need to find b the y-intercept.
To find y-intercept we would use point(3,-4) and formula
y = -4
x = 3
m = 17
b=?
y = mx + b
-4 = (17)(3) + b
-4 = 51 + b
b = -4 -51
b = -55
So, y-intercept is -55
The slope - intercept equation for this line is y = 17x - 55
Right square pyramid V=189cm³
Answer:
The number of hours Jackie worked = 80hours
Step-by-step explanation:
Last summer:
Jackie made $960
Rachel made $960
let number of hours Jackie worked = x
Rachel worked 16 hours more than Jackie:
Number of hours Rachel worked = x + 16
if Jackie earned $y per hour
Rachel earned $2 less per hour = y-2
Jackie: 960 = x × y = xy
Rachel: 960 = (x+16)(y-2)
960 = xy -2x +16y -32
recall xy = 960, insert the value for xy
960 = 960 - 2x +16y -32
- 2x +16y -32 = 0
2x -16y = -32
x-8y = -16
x = 8y-16
recall xy = 960, insert the expression for x
(8y-16)y = 960
8y² -16y = 960
y² -2y - 120 = 0
y²+10y-12y -120 = 0
y(y+10) -12(y+10) = 0
(y-12) = 0 or (y+10) = 0
y = 12 or -10
since y can't be negative, y = 12
x = 8y-16
x = 8(12) -16 = 80
The number of hours Jackie worked = x = 80 hours