So say for example u have -7 - (-5), think of subtracting integers as adding the opposite, so ur adding the opposite of -5, the opposite of -5 is 5, so ur adding -7 and 5= -2
another one: -15 - (-18)
again, adding the opposite. -15 plus positive 18= 3
Answer:
The scatter plot is attached.
Step-by-step explanation:
In a scatter plot, we graph the independent variable on the x-axis and the dependent variable on the y-axis.
In this case, age is independent and weight is dependent.
This means the points we plot are:
(7, 50); (7, 60); (8, 65); (8, 70); (9, 70); (9, 80); (10, 75); and (10, 90).
Answer:
2.04 km
Step-by-step explanation:
there are 1,000 m in 1 km
she was 680 x 3 meters = 2,040 m
2,040 m = 2.04 km
Answer:
d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))
Step-by-step explanation:
The Law of Sines tells us that sides of a triangle are proportional to the sine of the opposite angle. This can be used along with a trig identity to demonstrate the required relation.
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<h3>top triangle</h3>
The law of sines applied to the top triangle is ...
BC/sin(A) = AC/sin(θ)
Triangle ABC is isosceles, so the base angles at B and C are congruent. Then the angle at vertex A is ...
∠A = 180° -θ -θ = 180° -2θ
A trig identity tells us the sine of an angle is equal to the sine of its supplement. That means the sine of angle A is ...
sin(A) = sin(180° -2θ) = sin(2θ)
and our above Law of Sines equation tells us ...
BC = sin(A)/sin(θ)·AC = k·sin(2θ)/sin(θ)
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<h3>bottom triangle</h3>
The law of sines applied to the bottom triangle is ...
DC/sin(B) = BC/sin(D)
d/sin(α) = BC/sin(β)
Multiplying by sin(α) we have ...
d = BC·sin(α)/sin(β)
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Using our expression for BC gives the desired relation:
d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))
Answer: The system of equations that could be used to determine the number of small cups sold and the number of large cups sold is
6x + 18y = 780
y = 4x
Step-by-step explanation:
Let x represent the number of small cups that were sold.
Let y represent the number of large cups that were sold.
Each small cup holds 6 ounces of lemonade and each large cup hold 18 ounces of lemonade. Lincoln used 780 ounces. This is expressed as
6x + 18y = 780- - - - - - - - - - 1
Lincoln sold 4 times as many large cups as small cups. This is expressed as
y = 4x
