For this case we have the following inequality: y < 3x + 1 < br/ >
What we must do is to evaluate a point of the Cartesian plane and verify if it is in the shaded region.
The shaded region represents the solution of the system of equations.
For the point (0, 0) we have:
0 < 3(0) + 1 < br / >
0 < 0 + 1 < br / >
0 < 1 < br / >
Therefore, the point (0, 0) is in the shaded region because it satisfies the inequality.
Then, the points that are on the line, are not part of the solution because the sign is of less strict.
Hope I helped ~~Laurel
In the given question, it is given that
ramp is 17 feet long, rises 8 feet above the floor, and covers a horizontal distance of 15 feet.
And we have to find the value of tan B.
And tangent of any angle is equal to the ratio of vertical by horizontal. That is
And that's the required missing ratio for tan B .
Answer:
Samuel is correct i.e there are infinitely many solutions
Step-by-step explanation:
Given that Samuel and Hayden solved the system of equations –6x – 6y = –6 and 7x + 7y = 7. we have to find that whether the system of equations has infinitely many solutions or not.
A system of linear equations has infinite solutions if the graphs are the exact same line i.e the the equations are equivalent.
The first equation: –6x – 6y = –6 ⇒ x+y=1 ⇒ y=-x+1
∴ the slope of its line is -1 and the y-intercept is 1
The second equation: 7x + 7y = 7 ⇒ x+y=1 ⇒ y=-x+1
∴ the slope of its line is -1 and the y-intercept is 1.
Here, we get the equation which has the same slope and y-intercept as that of the first equation.
In other words, the two equations are represented by the same line. This implies that the lines intersect infinitely many times, or that the system has infinitely many solutions.
Hence, Samuel is correct.
Answer:
Step-by-step explanation:
x= money earned per hour working as a cashier.
y=money earned per hour working delivering newspapers.
We propose the following system of equations:
5x + 4y =77
6x + 3y=78
We solve the system by reduction method:
-6*(5x+4y=77) ⇒ -30x-24y=-462
5*(6x+3y=78)⇒ 30x+15y=390
---------------------------
-9y=-72 ⇒ y=-72 /-9=8
Now, we get the value of "x" replacing the value of "y" by "8" in any part of the equation above.
5x + 4(8)=77
5x+32=77
5x=77-32
5x=45
x=45/5=9
therefore;
money earned per hour working as a cashier= $9/ hour
money earned per hour working delivering newspapers=$8/hour
Answer:
The gestation period of rhinos (487 days) is 121. 3 percent longer than the gestation period of bears (220 days).
Step-by-step explanation:
Given:
Gestation period of rhinos = 487 days
Gestation period of bears = 220 days
To Find:
Percentage increase = ?
Solution:
The percentage increase =
On substituting the values,
= 
=
=>
=> 121.3 %
