Consider the system:
2 answers:
Answer:
Step-by-step explanation:
In this problem, we have the following linear equations:
y=3x+5
y=ax+b
We know that a linear equation is an equation for a line. In a system of linear equations, two or more equations work together.
1. What values for a and b make the system inconsistent?
A system is inconsistent if and only if the lines are parallel in which case the system has no solution. This is illustrated in the first Figure bellow. Two lines are parallel if they share the same slope. So, the system is inconsistent for:
a=3
for any value of b
2. What values for a and b make the system consistent and dependent?
A system is consistent if and only if the lines are the same in which case the system has infinitely many solutions. This is illustrated in the second Figure bellow. So, the system is consistent and dependent for:
a=3 and b=5
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Answer:
840 cubic inches
Step-by-step explanation:
Given:
The wooden steps have two parts.
Both of which are rectangular prisms.
The top part is 6 inches tall, 5 inches wide and 10 inches long.
The bottom part is 6 inches tall, 9 inches wide and 10 inches long.
Question asked:
What is the volume of the steps?
Solution:
<u>For top part</u>
Length = 10 inches
Width = 5 inches
Height = 6 inches
<u><em>As we know:</em></u>
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<u>For bottom part</u>
Length = 10 inches
Width = 9 inches
Height = 6 inches
Similarly
Volume of two steps = 300 + 540 = 840 cubic inches
<em>Therefore, the volume of the steps are 840 cubic inches.</em>
<em></em>
The first thing we must do for this case is find the number of total guitarists.
We have then:
We now look for the relationship between the number of guitarists playing jazz alone to the total number of guitarists.
We have then:
Where,
x: number of guitarists playing jazz alone
From here, we clear the value of x.
Then, the number of guitarists who play classical solo is:
Answer:
30 guitarists play classical solos in the contest