Answer with explanation:
Two Quadratic expressions are said to be equivalent,if they have same zeroes.But here it has been asked about ,expression which are of the same form,means Instead of being congruent they should be similar.
Expression Equivalent Expression
1. x²+ 3 x + 15 ---------------------- x² + 6 x + 34
2. x² + 8 --------------------- x² + 16
3. x² - 5 x + 5 -------------- x² -12 x + 37
Answer:
Step-by-step explanation:
Cost (C) depends on the number of miles traveled (x).
So C is the dependent variable.
Or C(x) if they want you to be more specific.
x is your independent variable.
Miles driven do not depend on anything.
Initial salary = $50,000 .
Rate of raise = 5% each year.
Therefore, each next year salary would be 105% that is 1.05 times.
5% of 50,000 = 0.05 × 50000 = 2500.
Therefore raise is $2500 each year.
According to geometric sequence first term 50000 and common ratio 1.05.
Applying geometric sequence formula
1) 
2) In order to find salary in 5 years we need to plug n=5, we get
= 50000(1.21550625)
<h3>=$60775.3125.</h3>
3) In order to find the total salary in 10 years we need to apply sum of 10 terms formula of a geometric sequence.
Plugging n=10, a = 50000 and r= 1.05.
= 628894.62678.
<h3>Therefore , you will have earned $ 628894.62678 in total salary by the end of your 10th year.</h3>
Answer:
2. Judy =$5
Ben= $4
Step-by-step explanation:
2. Let Judy = x and Ben = y
8x + 10y = 80
9x + 5y = 65
Solve these simultaneous equations.
8
x + 10
y = 80
18
x + 10
y = 130
Take the second equation away from the first equation
−
10
x = −
50
x = 5
This means that Judy gets paid $5 an hour.
Therefore, Ben gets paid $4 an hour.
Answer:
3. 24 quarters and 16 dimes
Step-by-step explanation:
3. Let the number of dimes = x and the number of quarters = y
Value Value
Type Number of of
of of EACH ALL
coin coins coin coins
-------------------------------------------
dimes x $0.10 $0.10x
quarters y $0.25 $0.25y
-------------------------------------------
TOTALS 40 $7.60
x + y = 40
0.10x + 0.25y = 7.60
Get rid of decimals by multiplying every term by 100:
10x + 25y = 760
So we have the system of equations:
x + y = 40
10x + 25y = 760
We solve by substitution. Solve the first equation for y:
x + y = 40
y = 40 - x
Substitute (40 - x) for y in 10x + 25y = 760
10x + 25(40 - x) = 760
10x + 1000 - 25x = 760
-15x + 1000 = 760
-15x = -240
x = 16 = the number of dimes.
Substitute in y = 40 - x
y = 40 - (16)
y = 24 quarters.
$1.60 + $6.00 = $7.60
I hope that helped, sorry for taking so long :-)
