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3 years ago

Which equation represents a line that passes through the two points in the table?

Mathematics

1 answer:

Sveta_85 [38]3 years ago

3 0

Answer:

$\large\boxed{A.\ y-3=\dfrac{2}{3}(x-3)}$

Step-by-step explanation:

The point-slope form of an equation of a line:

$y-y_1=m(x-x_1)$

m - slope

(x₁, y₁) - point on a line

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (3, 3) and (6, 5).

Substitute:

$m=\dfrac{5-3}{6-3}=\dfrac{2}{3}$

Take the point (3, 3):

$y-3=\dfrac{2}{3}(x-3)$

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Jacob runs 5 miles in 1 1/2 hours . Robert runs 3 miles in 45 minutes or 3/4 hour. Who runs faster

IgorLugansk [536]

Answer:

Robert

Step-by-step explanation:

If Robert runs 3 miles in 45 minutes, by the end of 90minutes, Robert would have covered 6miles, while Jacob covered 5miles in 90 minutes, therefore, Robert ran faster than Jacob.

5 0

3 years ago

What is the GCF of 40 and 21

trasher [3.6K]

40 and 21 do not have common factors, except for one. So the answer is 1.

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3 years ago

Read 2 more answers

A cyclist traveled 9 kilometers per hour faster than an in-line skater. In the time it took the cyclist to travel 45 kilometers,

coldgirl [10]

Answer:

18 kmh

Step-by-step explanation:

Given: Speed of cyclist is 9 km/h more than skater´s speed.

Distance covered at the given time by cyclist is 45 km and by skater is 30 km.

Let´s assume the speed of skater be "x"

∴ Speed of cyclist will be $(x+9) km/h$

Remember; time= $\frac{Distance}{speed}$

We know the time taken by both cyclist and skater are same.

∴ we can form an equation to find the speed of skater.

Time taken by cyclist= time taken by skater

⇒ $\frac{45}{(x+9)} = \frac{30}{x}$

Multiplying both side by $(x+9)\ and\ x$

⇒ $45x= 30\times (x+9)$

Using distributive property of multiplication

⇒ $45x= 30x+270$

Subtracting both side by 30x

⇒ $15x= 270$

Dividing both side by 15

⇒ $x= \frac{270}{15}$

∴ $x= 18\ kmh$

Hence, speed of the skater is 18 kmh

6 0

4 years ago

Translate this word phrase into an equation. one increased by two equals the quotient of nine and three

34kurt

Here is the equation for this word phrase:
1 + 2 = 9 / 3
Quotient is the result of division.

4 0

3 years ago

A box contains four bowling balls numbered 2, 4, 6, and 10 according to their weight. Two are drawn randomly without replacement

Lilit [14]

Answer:

E(M) = 23/3

Var(M) = 53/9.

Step-by-step explanation:

There are three possible values for M: 4, 6, and 10.

$\begin{array}{|l|l|}\cline{1-2}\\[-1em]\text{Larger Number} & \text{Smaller Number}\\ \cline{1-2}\\[-1em]4 & 2 \\\cline{1-2}\\[-1em]6 & 2, ~4\\\cline{1-2}\\[-1em] 10 & 2, ~4, ~6\\\cline{1-2} \end{array}$ .

That's six unique combinations in total. If the balls are drawn randomly, the probability for getting each combination shall be equal. That is:

$\begin{array}{|c|c|}\cline{1-2}\\[-1em]m & P(\text{M} = m)\\\cline{1-2}\\[-1em] 2 & 0\\\cline{1-2}\\[-1em] 4 & 1/6 \\\cline{1-2}\\[-1em] 6 & 2/6\\\cline{1-2}\\[-1em] 10 & 3/6\\\cline{1-2}\end{array}$ .

Consider the formula for the expected value of a discrete random variable:

$\begin{aligned} E({\rm M})& = \sum{[m \cdot P(\mathrm{M} = m)]}\\ &= 4 \times \frac{1}{6} + 6\times \frac{2}{6} + 10 \times \frac{3}{6}\\ &= \frac{23}{3}\end{aligned}$ .

Formula for the variance of a discrete random variable (note that this formula can take many other forms):

$\begin{aligned}Var(\mathrm{M}) &= \sum{[m^{2}\cdot P(\mathrm{M}= m)]} - \mu^{2}\\&= 4^{2}\times \frac{1}{6} + 6^{2} \times \frac{2}{6} + 10^{2} \times \frac{3}{6} - \left(\frac{23}{3}\right)^{2}\\&= \frac{53}{9}\end{aligned}$ .

5 0

3 years ago