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Radda [10]
3 years ago
5

The Point-Slope Equation: Pt 3

Mathematics
1 answer:
NARA [144]3 years ago
3 0

Answer:

y = -1/20x + 22

Step-by-step explanation:

The family trip is a linear model and its equation can be written as a linear equation y = mx + b where m is the slope and b is the y-intercept. The slope is the constant rate of change. The rate of change here is 1 gallon per 20 miles or -1/20 since each gallon used decreases from the overall gas tank. Substitute m = -1/20.

The y-intercept is the starting point or the number of gallons the tank in the van holds. Since the van had 16 gallons after 120 miles, this means there was 22 gallons. Since 120 miles has been spent at 20 miles a gallon, it took 120 / 20 = 6 gallons to drive that far. So 16 + 6 = 22 gallons. Substitute b = 22.

y = mx + b

y = -1/20x + 22

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Calculate the value of angle A and C of ∆ ABC. Where b=1435cm, a= 782cm and B= 115.6°.​
Monica [59]

The Law of Sines says

\dfrac{\sin A}{a} = \dfrac{\sin B}{b} = \dfrac{\sin C}{c}

\sin A = \dfrac a b \sin B

A = \arcsin( \dfrac{782}{1435} \sin 115.6 ) = 29.44^\circ

We don't have to worry about the obtuse supplement because a triangle can only have one obtuse angle, and that's B.

C = 180 - 115.6 - 29.44 = 34.96^\circ

Answer: A=29.44°, C=34.96°

5 0
3 years ago
The French Club is sponsoring a bake sale. If their goal is to raise at least $140, how many pastries must they sell at $3.50 ea
weeeeeb [17]

Let x be the number of pastries they must sell.

$3.50x≥140

This inequality states that for the number of pastries at 3.50 dollars each must be greater than or equal to 140. Solve for x.

3 0
3 years ago
Tangent please help me
atroni [7]
A^2+ b^2= c^2
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6 0
3 years ago
Look at this triangle work out length AB
Paha777 [63]

Answer:

2√137

Step-by-step explanation:

To find AB, we can use the Pythagorean Theorem (a² + b² = c²). In this case, a = 22, b = 8 and we're solving for c, therefore:

22² + 8² = c²

484 + 64 = c²

548 = c²

c = ± √548 = ± 2√137

c = -2√137 is an extraneous solution because the length of a side of a triangle cannot be negative, therefore, the answer is 2√137.

3 0
3 years ago
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How do you combine like terms and solve for the variable?<br> 8 - 3x - 5x = -8
Nitella [24]
<span>8 - 3x - 5x = -8
8 - 8x = -8
-8x = -8 - 8
-8x = -16
8x = 16
x = 16/8
x = 2</span>
7 0
3 years ago
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