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levacccp [35]
1 year ago
13

Determine the slope of the line passing through the points (5,6) and (-5,-1)m=____

Mathematics
1 answer:
EleoNora [17]1 year ago
6 0

GIVEN:

We are given two points on a line and these are;

A=(5,6),\text{ }B=(-5,-1)

Required;

We are required to determine the slope of the line passing through these points.

Step-by-step solution;

The slope of a line is given by the formula;

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

The variables are;

\begin{gathered} (x_1,y_1)=(5,6) \\  \\ (x_2,y_2)=(-5,-1) \end{gathered}

We can now substitute these into the formula and then simplify;

\begin{gathered} m=\frac{-1-6}{-5-5} \\  \\ m=\frac{-7}{-10} \\  \\ m=\frac{7}{10} \end{gathered}

ANSWER:

The slope of the line passing through the given points is;

m=\frac{7}{10}

You might be interested in
5. Show that the following points are collinear. a) (1, 2), (4, 5), (8,9) ​
Irina-Kira [14]

Label the points A,B,C

  • A = (1,2)
  • B = (4,5)
  • C = (8,9)

Let's find the distance from A to B, aka find the length of segment AB.

We use the distance formula.

A = (x_1,y_1) = (1,2) \text{ and } B = (x_2, y_2) = (4,5)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-4)^2 + (2-5)^2}\\\\d = \sqrt{(-3)^2 + (-3)^2}\\\\d = \sqrt{9 + 9}\\\\d = \sqrt{18}\\\\d = \sqrt{9*2}\\\\d = \sqrt{9}*\sqrt{2}\\\\d = 3\sqrt{2}\\\\

Segment AB is exactly 3\sqrt{2} units long.

Now let's find the distance from B to C

B = (x_1,y_1) = (4,5) \text{ and } C = (x_2, y_2) = (8,9)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(4-8)^2 + (5-9)^2}\\\\d = \sqrt{(-4)^2 + (-4)^2}\\\\d = \sqrt{16 + 16}\\\\d = \sqrt{32}\\\\d = \sqrt{16*2}\\\\d = \sqrt{16}*\sqrt{2}\\\\d = 4\sqrt{2}\\\\

Segment BC is exactly 4\sqrt{2} units long.

Adding these segments gives

AB+BC = 3\sqrt{2}+4\sqrt{2} = 7\sqrt{2}

----------------------

Now if A,B,C are collinear then AB+BC should get the length of AC.

AB+BC = AC

Let's calculate the distance from A to C

A = (x_1,y_1) = (1,2) \text{ and } C = (x_2, y_2) = (8,9)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-8)^2 + (2-9)^2}\\\\d = \sqrt{(-7)^2 + (-7)^2}\\\\d = \sqrt{49 + 49}\\\\d = \sqrt{98}\\\\d = \sqrt{49*2}\\\\d = \sqrt{49}*\sqrt{2}\\\\d = 7\sqrt{2}\\\\

AC is exactly 7\sqrt{2} units long.

Therefore, we've shown that AB+BC = AC is a true equation.

This proves that A,B,C are collinear.

For more information, check out the segment addition postulate.

7 0
2 years ago
If $17,000 is invested in an account for 25 years. Calculate the total interest earned at the end of 25 years if the interest is
KATRIN_1 [288]

Answer:

a.) $29,750.00   simple interest

b.) $75,266.35  Compounded annually

c.) $79,358.65 compunded  quarterly

d.) $80,332.11 compounded monthly

Step-by-step explanation:

a.) Formula: I = p x r x t

Where:

P is the principal amount, $17000.00.

r is the interest rate, 7% per year, or in decimal form, 7/100=0.07.

t is the time involved, 25....year(s) time periods.

So, t is 25....year time periods.

To find the simple interest, we multiply 17000 × 0.07 × 25 to get that:

The interest is: $29750.00

______________________________

b.) $75,266.35

c.) $79,358.65

d.) $80,332.11

5 0
3 years ago
Estimate the problem 3,844 ÷75​
blondinia [14]

Answer:88

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Please help with the following question
sasho [114]
  We have:
  The generic equation of the line is:  y-yo = m (x-xo)
  The slope is:
  m = (y2-y1) / (x2-x1)
  m = (- 2-0) / (3-0)
  m = -2 / 3
  We choose an ordered pair
  (xo, yo) = (0, 0)
  Substituting values:
  y-0 = (- 2/3) (x-0)
  Rewriting:
  y = (- 2/3) x
  Answer:
  The equation of the line is:
  y = (- 2/3) x


5 0
3 years ago
A real estate agent has 19 properties that she shows. She feels that there is a 30% chance of selling any one property during a
netineya [11]

Answer:

P(X \geq 5)=1-P(X

We can find the individual probabilities:

P(X=0)=(19C0)(0.3)^0 (1-0.3)^{19-0}=0.00114

P(X=1)=(19C1)(0.3)^1 (1-0.3)^{19-1}=0.0092

P(X=2)=(19C2)(0.3)^2 (1-0.3)^{19-2}=0.0358

P(X=3)=(19C3)(0.3)^3 (1-0.3)^{19-3}=0.0869

P(X=4)=(19C4)(0.3)^4 (1-0.3)^{19-4}=0.1491

And replacing we got:

P(X \geq 5) = 1-[0.00114+0.009282+0.0358+0.0869+0.149]= 0.7178

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

X \sim Binom(n=19, p=0.3)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

And we want to find this probability:

P(X \geq 5)

And we can use the complement rule:

P(X \geq 5)=1-P(X

We can find the individual probabilities:

P(X=0)=(19C0)(0.3)^0 (1-0.3)^{19-0}=0.00114

P(X=1)=(19C1)(0.3)^1 (1-0.3)^{19-1}=0.0092

P(X=2)=(19C2)(0.3)^2 (1-0.3)^{19-2}=0.0358

P(X=3)=(19C3)(0.3)^3 (1-0.3)^{19-3}=0.0869

P(X=4)=(19C4)(0.3)^4 (1-0.3)^{19-4}=0.1491

And replacing we got:

P(X \geq 5) = 1-[0.00114+0.009282+0.0358+0.0869+0.149]= 0.7178

4 0
3 years ago
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