Answer:
4 minutes and 25 seconds (4.25)
Step-by-step explanation:
153/36
Based on the calculations, Kirk bought 2.4 bags of popcorn and 7.2 sodas.
- Let the number of sodas bought be s.
- Let the number of bags of popcorn be p.
<u>Given the following data:</u>
a. To write a system of equations that models this scenario:
<h3>What is a system of
equations?</h3>
A system of equations can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).
<h3>For the
soda and
popcorn:</h3>
...equation 1.
Translating the word problem into an algebraic expression, we have;
Three times as many bags of popcorn as sodas:
...equation 2.
b. To determine how many of each item Kirk bought:
Substituting eqn. 2 into eqn. 1, we have:

p = 2.4 bags of popcorn
<u>For soda:</u>

s = 7.2 sodas.
Read more on word problems here: brainly.com/question/13170908
Answer:
y = x² + 7x + 4
Step-by-step explanation:
<u>First option</u>
System of equations:
y = x² + x – 4
y = x – 5
Replacing:
x - 5 = x² + x – 4
0 = x² + x – 4 - x + 5
0 = x² + 1
Discriminant:
b²-4*a*c
0²-4*1*1
-4 < 0 then the equation has no real roots
<u>Second option</u>
System of equations:
y = x² + 2x – 1
y = x – 5
Replacing:
x - 5 = x² + 2x – 1
0 = x² + 2x - 1 - x + 5
0 = x² + x + 4
Discriminant:
b²-4*a*c
1²-4*1*4
-15 < 0 then the equation has no real roots
<u>Third option</u>
System of equations:
y = x² + 6x + 9
y = x – 5
Replacing:
x - 5 = x² + 6x + 9
0 = x² + 6x + 9 - x + 5
0 = x² + 5x + 4
Discriminant:
b²-4*a*c
5²-4*1*4
9 > 0 then the equation has two different real roots
<u>Fourth option</u>
System of equations:
y = x² + 7x + 4
y = x – 5
Replacing:
x - 5 = x² + 7x + 4
0 = x² + 7x + 4 - x + 5
0 = x² + 6x + 9
Discriminant:
b²-4*a*c
6²-4*1*9
0 then the equation has one real root
Answer:



Step-by-step explanation:
Let 




We have the relation





