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3 years ago

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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What decimal equivalent to 5/6

victus00 [196]

Answer:

0.83333333

Step-by-step explanation:

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3 years ago

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Triangle J K L is shown. Angle J L K is 105 degrees. The length of J K is 4.7 and the length of J L is 2.7.

cluponka [151]

Answer:

The approximate measure of angle K is 34°

Step-by-step explanation:

In ΔJKL

∠L = 105°

JK = 4.7

JL = 2.7

Sine Rule:

$\frac{SinA}{a} = \frac{SinB}{b}= \frac{SinC}{c}$

So, $\frac{SinL}{JK} = \frac{SinK}{JL}\\\frac{SinL}{4.7} = \frac{SinK}{2.7}\\\frac{Sin 105}{4.7} = \frac{SinK}{2.7}\\\frac{Sin 105 \times 2.7}{4.7} = SinK\\\frac{(0.9659 \times 2.7)}{4.7} = Sin K\\\frac{2.60793}{4.7} = Sin K\\0.5549 = Sin K\\Sin^{-1}(0.5549)= K\\K = 33.70$

K ≈ 34°

So, Option B is true

Hence The approximate measure of angle K is 34°

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3 years ago

4. Ten less than the product of six and eight less than a number

ICE Princess25 [194]

Answer: 38

Step-by-step explanation:

6 x 8 = 48

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3 years ago

Consider rolling two fair dice one 3-sided the other 5-sided

Ne4ueva [31]

Since the dice are fair and the rolling are independent, each single outcome has probability 1/15. Every time we choose

$1\leq x\leq 3,\quad 1\leq y \leq 5$

We have $P(X=x)=\frac{1}{3}$ and $P(Y=y)=\frac{1}{5}$ , because the dice are fair.

Now we use the assumption of independence to claim that

$P(X=x, Y=y) = P(X=x)\cdot P(Y=y) =\dfrac{1}{3}\cdot\dfrac{1}{5} = \dfrac{1}{15}$

Now, we simply have to count in how many ways we can obtain every possible outcome for the sum. Consider the attached table: we can see that we can obtain:

2 in a unique way (1+1)
3 in two possible ways (1+2, 2+1)
4 in three possible ways
5 in three possible ways
6 in three possible ways
7 in two possible ways
8 in a unique way

This implies that the probabilities of the outcomes of $W=X+Y$ are the number of possible ways divided by 15: we can obtain 2 and 8 with probability 1/15, 3 and 7 with probability 2/15, and 4, 5 and 6 with probabilities 3/15=1/5

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3 years ago

Five small apples have about 390 calories.

Dvinal [7]

78 calories per apple :)

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