For the seagull to catch the crab, h(t)=g(t) so:
-16t^2+45=-13t+23 add 16t^2 to both sides
45=16t^2-13t+23 subtract 45 from both sides
16t^2-13t-22=0 using the quadratic equation:
t=(13±√1577)/32, since t>0
t=(13+√1577)/32 seconds
t≈1.65 seconds (to nearest hundredth of a second)
And the height that this occurs using either original equation is:
h((13+√1577)/32)≈1.59 ft (to nearest hundredth of a foot)
Answer:
? is 24
Step-by-step explanation:
Lets consider SAM's age is 'x' and Hank's age is 'y'
So as per given data Sam's age is 5/3 times of Hank's age
so x = 5/3 * y
3x = 5y --> equation 1
and also sum of their ages is 24
so, x + y = 24
we need to find Hank's age (y)
so x = 24 - y
Now replace x value in equation 1
3(24-y) = 5y
72-3y = 5y
72 = 3y+5y
8y= 72
y= 72/8
y = 9 years.
So the Hank's age is 9 years
.
9514 1404 393
Answer:
$491.65
Step-by-step explanation:
The pay for the first 8 hours is $5.40 per hour × 8 hours = $43.20. Hours over 8 are paid at 1.5 × $5.40 = $8.10 per hour. There are at least 8 hours every day for the 6-day week. There are hours over 8 on Monday, Wednesday, Thursday, and Friday totaling 7 hours of overtime.
The amount of sales is more than $3000, so 4% will be paid on $3000, and 5% will be paid on the $1115 in excess of $3000.
So, the gross pay is ...
$43.20 × 6 + 8.10 × 7 = $315.90 . . . . wages
$3000 × .04 +1115 × .05 = $175.75 . . . commission
$315.90 +1.75.75 = $491.65 . . . . gross pay for the week
_____
It can be less tedious to let a spreadsheet do the calculations.