Let's use J for James's age and A for Austin's age. The equations are:
J = A - 4
3J + A² = 28
Just plug (A - 4) in the place of J in the second equation. This gives you:
3(A - 4) + A² = 28
-->
A² + 3A - 12 = 28
-->
A² + 3A - 40 = 0
-->
(A - 5)(A + 8) = 0
-->
A = 5 or -8
-8 is nonsense, so Austin is 5 years old. Therefore, James is 1 year old.
Answer:
Step-by-step explanation:
step 1
Determine the slope of the dashed line
The formula to calculate the slope between two points is equal to
we have
(-3,1) and (0,3)
substitute
step 2
Find the equation of the dashed line in slope intercept form
we have
---> given problem
substitute
step 3
Find the equation of the inequality
we know that
Is a dashed line and everything to the left of the line is shaded
so
see the attached figure to better understand the problem
Answer:
f(t) = 4(t − 1)2 + 4; the minimum height of the roller coaster is 4 meters from the ground
Step-by-step explanation:
The function is a quadratic where t is time and f(t) is the height from the ground in meters. You can write the function f(t) = 4t2 − 8t + 8 in vertex form by completing the square. Complete the square by removing a GCF from 4t2 - 8t. Take the middle term and divide it in two. Add its square. Remember to subtract the square as well to maintain equality.
f(t) = 4t2 − 8t + 8
f(t) = 4(t2 - 2t) + 8 The middle term is -2t
f(t) = 4(t2 - 2t + 1) + 8 - 4 -2t/2 = -1; -1^2 = 1
f(t) = 4(t-1)^2 + 4 Add 1 and subtract 4 since 4*1 = 4.
The vertex (1,4) means at a minimum the roller coaster is 4 meters from the ground.
- f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 2 meters from the ground
- f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 4 meters from the ground
- f(t) = 4(t − 1)2 + 4; the minimum height of the roller coaster is 1 meter from the ground
- f(t) = 4(t − 1)2 + 4; the minimum height of the roller coaster is 4 meters from the ground
Answer:
$501,049.37
Step-by-step explanation:
For computing the amount after 22 years we need to applied the future value which is shown in the attachment below:
Given that
PMT = $9,000
NPER = 22 years
Annual rate = 0.078
Quarterly= 0.078 ÷ 4 = 0.0195
Effective annual rate = (1.0195^4) - 1 = 0.0803113041
Now applied the formula which is given below
= -FV(RATE;NPER;PMT;PV)
After applying the above formula, the future value is $501,049.37
