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4 years ago

A line is drawn so that it passes through the points (-3,0) and (1.4). What is the slope of the line?

Mathematics

1 answer:

vladimir2022 [97]4 years ago

4 0

Answer: $m=1$

Step-by-step explanation:

For this exercise you can use the following formula for calculate the slope:

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

In this case you know that the given line passes through the points (-3,0) and (1.4). Therefore you can identify that:

$y_2=0\\y_1=4\\\\x_2=-3\\x_1=1$

Then, in order to calculate the slope of this line, you must substitute the coordinates of the points into the formula:

$m=\frac{0-4}{-3-1}$

Finally, evaluating, you get that the slope of this line is the following:

$m=\frac{-4}{-4}\\\\m=1$

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3 years ago

Read 2 more answers

) Determine the probability that a bit string of length 10 contains exactly 4 or 5 ones.

yanalaym [24]

Answer: 0.4512

Step-by-step explanation:

A bit string is sequence of bits (it only contains 0 and 1).

We assume that the 0 and 1 area equally likely to any place.

i.e. P(0)= P(1)= $\dfrac{1}{2}$

The length of bits : n = 10

Let X = Number of getting ones.

Then , $X \sim Bin(n=10,\ p=\dfrac{1}{2})$

Binomial distribution formula : $P(X=x)=^nC_x p^x q^{n-x}$ , where p= probability of getting success in each event and q= probability of getting failure in each event.

Here , $p=q=\dfrac{1}{2}$

Then ,The probability that a bit string of length 10 contains exactly 4 or 5 ones.

$P(X= 4\ or\ 5)=P(x=4)+P(x=5)\\\\=^{10}C_4(\dfrac{1}{2})^{10}+^{10}C_4(\dfrac{1}{2})^{10}$

$=\dfrac{10!}{4!6!}(\dfrac{1}{2})^{10}+\dfrac{10!}{5!5!}(\dfrac{1}{2})^{10}$

$=(\dfrac{1}{2})^{10}(\dfrac{10!}{4!6!}+\dfrac{10!}{5!5!})$

$=(\dfrac{1}{2})^{10}(210+252)$

$=(0.0009765625)(462)$

$=0.451171875\approx0.4512$

Hence, the probability that a bit string of length 10 contains exactly 4 or 5 ones is 0.4512.

3 0

4 years ago

The grid shows figure Q and its image figure Q’ after a transformation. Which transformation was applied on figure Q?

photoshop1234 [79]

Answer:

B.) Clockwise rotation of 90° about the origin.

Step-by-step explanation:

We see that the co-ordinates of the figure Q are (2,4), (3,7), (7,5), (5,4) and (4,2).

It can be seen that the co-ordinates changed after the transformation are (4,-2), (7,-3), (5,-7), (4,-5) and (2,-4).

That is,

Q Q'

(2,4) ---------------------> (4,-2)

(3,7) ----------------------> (7,-3)

(7,5) ----------------------> (5,-7)

(5,4) ----------------------> (4,-5)

(4,2) ----------------------> (2,-4)

Thus, the co-ordinates are changing by the rule (x,y) → (y,-x).

Hence, the transformation applied is 'Clockwise rotation of 90° about the origin'.

So, option B is correct.

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4 years ago

Is (-1,-2) a solution to the equation 2x-3y=4?<br> No<br> O Yes

a_sh-v [17]

Answer:

Yes

Step-by-step explanation:

Plug in (-1 , -2) in the LHS of the equation.

2x - 3y = 2*(-1) - 3*(-2)

= -2 + 6

= 4 = RHS

So, (-1 , -2) is a solution

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3 years ago

If the sum of the tast

tensa zangetsu [6.8K]

Answer:

Step-by-step explanation:

x + 1, x + 2

2x + 3 = 71

71 - 3 = 68 / 2 = 35, 36

x = 34

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3 years ago