А. х²-4=0; х²=4; х=±2, true.
B. x²=-4; there is no solution.
C. 3x²+12=0; 3x²=-12; x²=-4; there is no solution.
D. 4x²=16; x²=4; x=±2, true.
E. 2(x-2)²=0; 2(x²-4x+4)=0; 2x²-8x+8=0; x²-4x+4=0; x1=2; x2=2. False. The answer: A, D.
We can often solve inequalities by adding or subtracting a number from both sides
The graph at option 1 shows the given inequality y < x² + 1. The domain and range of the given inequality is {x: x ∈ (-∞, ∞)} and {y: y ∈ [1, ∞)}.
<h3>How to graph an inequality?</h3>
The steps to graph an inequality equation are:
- Solve for the variable y in the given equation
- Graph the boundary line for the inequality
- Shade the region that satisfies the inequality.
<h3>Calculation:</h3>
The given inequality is y < x² + 1
Finding points to graph the boundary line by taking y = x² + 1:
When x = -2,
y = (-2)² + 1 = 4 + 1 = 5
⇒ (-2, 5)
When x = -1,
y = (-1)² + 1 = 2
⇒ (-1, 2)
When x = 0,
y = (0)² + 1 = 1
⇒ (0, 1)
When x = 1,
y = (1)² + 1 = 2
⇒ (1, 2)
When x = 2,
y = (2)² + 1 = 5
⇒ (2, 5)
Plotting these points in the graph forms an upward-facing parabola.
So, all the points above the vertex of the parabola satisfy the given inequality. Thus, that part is shaded.
From this, the graph at option 1 is the required graph for the inequality y < x² + 1. The boundary line is dashed since the inequality symbol is " < ".
Learn more about graphing inequalities here:
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Answer:
27
Step-by-step explanation:
Factory A proportion:
3 : 2,000
Factory B proportion:
5 : 4,500 (this can be simplified):
1 : 900
Now plug in 18,000 to each proportion:
Factory A:
x : 18,000
3 : 2,000
x = 27
Factory B:
x : 18,000
1 : 900
x = 20
Factory A had the greater amount of defects, 27
Answer:
10=y/11-13
We move all terms to the left:
-10-(y/11-13)=0
-y/11+13-10=0
We multiply all the terms by the denominator
-y+13*11-10*11=0
We add all the numbers together, and all the variables
-1y+33=0
We move all terms containing y to the left, all other terms to the right
-y=-33
y=-33/-1
y=+33
