The ordered pair which makes both inequalities true is: D. (3, 0).
<h3>How to determine ordered pair?</h3>
In Mathematics, an inequality can be used to show the relationship between two (2) or more integers and variables in an equation.
In order to determine ordered pair which makes both inequalities true, we would substitute the points into the inequalities as follows:
At (0, 0), we have:
y > -2x + 3
0 > -2(0) + 3
0 > 3 (false).
y < x – 2
0 < 0 - 2
0 < -2 (false)
At (0, -1), we have:
y > -2x + 3
-1 > -2(0) + 3
-1 > 3 (false).
y < x – 2
-1 < 0 - 2
-1 < -2 (false)
At (1, 1), we have:
y > -2x + 3
1 > -2(1) + 3
1 > -1 (true).
y < x – 2
1 < 1 - 2
1 < -1 (false)
At (3, 0), we have:
y > -2x + 3
0 > -2(3) + 3
0 > -3 (true).
y < x – 2
0 < 3 - 2
0 < 1 (true).
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Using the slope line formula,
The slope of line y = mx is 1.0315.
We have given that,
parabola equation is y = 5x - 3x²
line passing through origin is in the form of y = mx
==> mx = 5x - 3x²
==> 3x²+ mx - 5x = 0
==> 3x² + x(m -5) = 0
==> x(3x + (m -5)) = 0
==> x = 0 , x = (5 -m)/3
The total area of the bounded region is then the integral of 5x - 3x² from x = 0 to x = (5-m)/3
Area under y = 5x - 3x2 and y = mx is (125/54)/2 = 125/108
==> [0 to (5 -m)/3] ∫(5x - 3x²-mx )dx = 125/108
==> [0 to (5 -m)/3]∫( (5 - m)x - 3x2 )dx = 125/108
==> [0 to (5 -m)/3] ((5 - m)x²/2 - x³ )= 125/108
==> (5 - m)[(5 -m)/3]²/2 - ((5 -m)/3)³ = 125/108
==> (5 -m)³/18 - (5 -m)³/27 = 125/108
==> (5 -m)³/54 = 125/108
==> (5 -m)³ = 125/2
==> (5 -m) = 3.9685
==> m = 5 - 3.9685
==> m = 1.0315
Hence slope of line = 1.0315
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Answer C explanation: Alternate interior angles are always congruent
C(X)
Only one that's goes up 2 and has a slope of 2/3
Answer:
A
Step-by-step explanation:
It is A, because it tells you the equation of
-5x + 8 ≥ -7
Because the key on the right tells you that shaded squares are negative and white ones are positive.
You can then subtract both sides by 8 to isolate the -5x and the equation becomes:
-5x ≥ -7 - 8
Which simplifies to
-5x ≥ -15
which you can now divide both sides by -5 to get
x ≥ 3
BUT WAIT
the general rule is that when you divide a variable (in this case x) by a negative number, you have to flip the inequality sign
so ≥
should become ≤
so the equation is x ≤ 3
