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Jgarciar541
01.07.2020 •
Mathematics
Which statement is true about the graphed function?
F(x) < 0 over the interval (-4,-4)
OF(x) < 0 over the interval (0, -3)
F(x) > 0 over the interval (-4,-3)
F(x) > 0 over the interval (--4)
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Ответ:
Statement 1 : True
Statement 2: False
Statement 3: False
Statement 4:True
Statement 5:False
Statement 6:True
Step-by-step explanation:
Given :![2y = x + 10](/tpl/images/0338/8962/dc4ad.png)
To Find: Which statements about the system are true?
Solution:
Slope intercept form:![y =mx+c](/tpl/images/0338/8962/a4a1e.png)
where m is the slope
Convert the given equations in slope intercept form
Equation 1:![2y = x + 10](/tpl/images/0338/8962/dc4ad.png)
On comparing with general form
Slope = m =![\frac{1}{2}](/tpl/images/0338/8962/9cdae.png)
Equation 2:![3y = 3x + 15](/tpl/images/0338/8962/d7fa6.png)
On comparing with general form
Slope = m = 1
Substitute the value of x form B in A
Substitute the value of y in B to get value of x
Thus the solution is (0,5)
Thus The system has one solution.
So, Statement 1 is true
Since the slopes of the given lines are not same so the lines are not parallel
Thus the statement 2 is false.
Slope of line 1 is
and slope of line 2 is 1
Since the slopes are not same
So, statement 3 is false.
Equation 1:![2y = x + 10](/tpl/images/0338/8962/dc4ad.png)
To find y intercept substitute x =0
Equation 2:![3y = 3x + 15](/tpl/images/0338/8962/d7fa6.png)
To find y intercept substitute x =0
So,statement 4 is true Both lines have the same y-intercept.
Statement 5: The equations graph the same line.
Statement 5 is false (refer the attached graph)
Statement 6 is true The solution is the intersection of the 2 lines (refer the attached graph)