Answer:
C)
region C
Step-by-step explanation:
We have to use what is called the zero-interval test [test point] in order to figure out which portion of the graph these inequalities share:
0 ≤ 2 ☑ [We shade the portion of the graph that CONTAIN THE ORIGIN, which is the bottom portion.]
0 ≥ −3 ☑ [We shade the portion of the graph that CONTAINS THE ORIGIN, which is the left side.]
So, now that we got that all cleared up, we can tell that both graphs share a region where the ORIGIN IS VISIBLE. Therefore region C matches the above inequalities.
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The maximum height is 144 feet.
The maximum height is the y-coordinate of the vertex. To find the vertex, we first use x = -b/2a. For our information, that is x=-64/2(-16) = -64/-32 = 2.
Now we substitute this into the equation:
y = -16(2²) + 64(2) + 80 = -64 + 128 + 80 = 144
The activity pictured is called goat tying.
BC is 10 units and AC is 
units
Step-by-step explanation:
Let us revise the sine rule
In ΔABC:
- AB is opposite to ∠C
- BC is opposite to ∠A
- AC is opposite to ∠B
Let us use this rule to solve the problem
In ΔABC:
∵ m∠A = 45°
∵ m∠C = 30°
- The sum of measures of the interior angles of a triangle is 180°
∵ m∠A + m∠B + m∠C = 180
∴ 45 + m∠B + 30 = 180
- Add the like terms
∴ m∠B + 75 = 180
- Subtract 75 from both sides
∴ m∠B = 105°
∵ 
∵ AB = 
- Substitute AB and the 3 angles in the rule above
∴ 
- By using cross multiplication
∴ (BC) × sin(30) = × sin(45)
∵ sin(30) = 0.5 and sin(45) = 
∴ 0.5 (BC) = 5
- Divide both sides by 0.5
∴ BC = 10 units
∵ 
- Substitute AB and the 3 angles in the rule above
∴ 
- By using cross multiplication
∴ (AC) × sin(30) = × sin(105)
∵ sin(105) = 
∴ 0.5 (AC) = 
- Divide both sides by 0.5
∴ AC = units
BC is 10 units and AC is units
Learn more:
You can learn more about the sine rule in brainly.com/question/12985572
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Answer:
y = 
and x = 
Step-by-step explanation:
To solve simultaneous equations, you need to have the number in front of both x's or y's the same. (signs doesn't matter)
To get -x to -10x we simply need to multiply the first equation by 10:
-x * 10 = -10x
-9y * 10 = -90y
16 * 10 = 160
-10x - 90y = 160
Now we can add the two equations:
-10x + 10x = 0
-90y + 20y = -70y
160 + 20 = 180
-70y = 180
70y = -180
7y = -18
y =
Now plug into the second equation:
10x + 20() = 20
10x - 
= 20
Move the over to the other side, making it a positive:
10x = 20 +
10x = 
Divide both sides by 10:
x =
So y = and x =
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