Answer:
12, 23, 48, 325
Step-by-step explanation:
So, when given two inequalities and asked to find the values that make both true, it is considered a system of equations. To solve a system of equation, you have to graph the inequalities and find where they intersect.
Inequality 1:
(-3x) + 5 < (-10)
Inequality 2:
7x + x - 4 > 28
simplifies to: 8x - 4 > 28
When graphed, the inequalities don't intersect, but rather have a similar shaded area overlapping from the point of 5 and greater.
Answers that apply from given list would be:
12, 23, 48, 325
Answer:
y = - 
x + 
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 4y = 5x + 3 into this form by dividing the 3 terms by 4
y = 
x + 
← in slope- intercept form
with slope m =
Given a line with slope m then the slope of a line perpendicular to it is
= - 
= - 
= - , thus
y = - x + c ← is the partial equation
To find c substitute (3, - 2) into the partial equation
- 2 = - 
+ c ⇒ c = - 2 + =
y = - x + ← equation of perpendicular line
They are inverse functions though to be completely thorough your teacher should have also put g(f(x)) = x as well. Though I can see what your teacher is aiming for at least.
The idea is that whatever the output of g(x) is, it's plugged into f(x) and the initial input is the result. So g(x) takes a step forward and f(x) takes a step back undoing everything g(x) did. Which is exactly what an inverse operation does.
So, let’s represent the number as n:
n+7=2n+3
Subtract both sides by 3:
n+4=2n
Now by n:
2n=4
Divide:
n=2
The number is 2
