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:
Just do 60 divided by 10
Step-by-step explanation:
60=10 x 10 times 6 = 60 so x=6
the answer is false because it can be in the Y or the X axis
Answer:
15.6km
Step-by-step explanation:
Given the map scale 1:200000
1cm on the map represents 200000 cm on ground or in actual distance
Hence, if distance from Belfast to Larne is 7.8vm on map ;
Actual distance will be :
7.8 * 200000 = 1560000 cm
Converting to km :
Recall :
1000 m = 1km
100 cm = 1 m
Hence,
100000 cm = 1km
Therefore, (1560000 / 100000) km
= 15.6km
Hence, distance between Belfast and Larne is 15.6km
Answer:
The answer is 8 quarters, 16 nickles, and 32 dimes
Step-by-step explanation:
- First, the equation would be (2/4d) x 5 +d x 10 +1/4d x 25= 600 (Don't put 6.00, that's dollars. We put 6 dollars into cents to make it easier.)
- Then we slowly start to solve: 10/4d + 10d + 25/4d = 600
- 10d+40d+25d/4 = 600 (Put all of that over 4, not first 25d)
- 75d= 600 x 4
- d=600 x 4/75 (same here put everything over 75)
- d=32
- So then n= 2 x 32/4 = 16
- Then n would be equal to : 1/4d= 1/4 x 32 = 8
- So your answer would be 8 quarters, 16 nickles, and 32 dimes.
Hope this helped :)
