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zhenek [66]
2 years ago
14

What is the slope of (-2,2) (-4,-4)

Mathematics
2 answers:
Flauer [41]2 years ago
7 0

Answer:

3

Step-by-step explanation:

slope = (y2-y1)/(x2-x1)

(-4-2)/(-4--2)

-6/-2

3

Andrei [34K]2 years ago
7 0

Answer:

to find slope we use the following methods

Step-by-step explanation:

given

X1 -2

X2= -4

Y1= 2

Y2= -4

slope=y2-Y1 ÷X2-X1

= -4-2÷ -4-(-2)

=-6 ÷-4+2

= -6÷-2

= 3

slop of (-2,2) (-4,-4) = 3

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Find x so that the points (x,x+1), (x+2,x+3) and (x+3,2x+4) form a right-angled triangle.
azamat

Let <em>a</em>, <em>b</em>, and <em>c</em> be vectors each starting at the origin and terminating at the points (<em>x</em>, <em>x</em> + 1), (<em>x</em> + 2, <em>x</em> + 3), and (<em>x</em> + 3, 2<em>x</em> + 4), respectively.

Then the vectors <em>a</em> - <em>b</em>, <em>a</em> - <em>c</em>, and <em>b</em> - <em>c</em> are vectors that point in directions parallel to each of the legs formed by the triangle with these points as its vertices.

If this triangle is to contain a right angle, then exactly one of these pairs of vectors must be orthogonal. In other words, one of the following must be true:

(<em>a</em> - <em>b</em>) • (<em>a</em> - <em>c</em>) = 0

<em>or</em>

(<em>a</em> - <em>b</em>) • (<em>b</em> - <em>c</em>) = 0

<em>or</em>

(<em>a</em> - <em>c</em>) • (<em>b</em> - <em>c</em>) = 0

We have

<em>a</em> - <em>b</em> = (<em>x</em>, <em>x</em> + 1) - (<em>x</em> + 2, <em>x</em> + 3) = (-2, -2)

<em>a</em> - <em>c</em> = (<em>x</em>, <em>x</em> + 1) - (<em>x</em> + 3, 2<em>x</em> + 4) = (-3, -<em>x</em> - 3)

<em>b</em> - <em>c</em> = (<em>x</em> + 2, <em>x</em> + 3) - (<em>x</em> + 3, 2<em>x</em> + 4) = (-1, -<em>x</em> - 1)

Case 1: If (<em>a</em> - <em>b</em>) • (<em>a</em> - <em>c</em>) = 0, then

(-2, -2) • (-3, -<em>x</em> - 3) = (-2)×(-3) + (-2)×(-<em>x</em> - 3) = 2<em>x</em> + 12 = 0   ==>   <em>x</em> = -6

which would make <em>a</em> - <em>c</em> = (-3, 3) and <em>b</em> - <em>c</em> = (-1, 5), and their dot product is not zero. Then the triangles vertices are at the points (-6, -5), (-4, -3), and (-3, -8).

Case 2: If (<em>a</em> - <em>b</em>) • (<em>b</em> - <em>c</em>) = 0, then

(-2, -2) • (-1, -<em>x</em> - 1) = (-2)×(-1) + (-2)×(-<em>x</em> - 1) = 2<em>x</em> + 4 = 0   ==>   <em>x</em> = -2

which would make <em>a</em> - <em>c</em> = (-3, -1) and <em>b</em> = (-1, 1), and their dot product is also not zero. The vertices are the points (-2, -1), (0, 1), and (1, 0).

Case 3: If (<em>a</em> - <em>c</em>) • (<em>b</em> - <em>c</em>) = 0, then

(-3, -<em>x</em> - 3) • (-1, -<em>x</em> - 1) = (-3)×(-1) + (-<em>x</em> - 3)×(-<em>x</em> - 1) = <em>x</em> ² + 4<em>x</em> + 6 = 0

but the solutions to <em>x</em> here are non-real, so we throw out this case.

So there are two possible values of <em>x</em> that make a right triangle, <em>x</em> = -6 and <em>x</em> = -2.

3 0
3 years ago
Can someone please explain to me how to solve this equation?
Nikolay [14]

Answer:

first of all erase what u have written

Step-by-step explanation:

<h2>Q: 25-(3x+5)=2(x+8)+x</h2>
  • 25-3x-5=2x+16+x
  • 20-6x=16
  • 6x=4
  • x=2/3
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3 years ago
155 divided by 17. .......
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155 divided by 17 =
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3 years ago
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For the given term, find the binomial raised to the power, whose expansion it came from: 15(5)^2 (-1/2 x) ^4
Elina [12.6K]

Answer:

<em>C.</em> (5-\frac{1}{2})^6

Step-by-step explanation:

Given

15(5)^2(-\frac{1}{2})^4

Required

Determine which binomial expansion it came from

The first step is to add the powers of he expression in brackets;

Sum = 2 + 4

Sum = 6

Each term of a binomial expansion are always of the form:

(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......

Where n = the sum above

n = 6

Compare 15(5)^2(-\frac{1}{2})^4 to the above general form of binomial expansion

(a+b)^n = ......+15(5)^2(-\frac{1}{2})^4+.......

Substitute 6 for n

(a+b)^6 = ......+15(5)^2(-\frac{1}{2})^4+.......

[Next is to solve for a and b]

<em>From the above expression, the power of (5) is 2</em>

<em>Express 2 as 6 - 4</em>

(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......

By direct comparison of

(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......

and

(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......

We have;

^nC_ra^{n-r}b^r= 15(5)^{6-4}(-\frac{1}{2})^4

Further comparison gives

^nC_r = 15

a^{n-r} =(5)^{6-4}

b^r= (-\frac{1}{2})^4

[Solving for a]

By direct comparison of a^{n-r} =(5)^{6-4}

a = 5

n = 6

r = 4

[Solving for b]

By direct comparison of b^r= (-\frac{1}{2})^4

r = 4

b = \frac{-1}{2}

Substitute values for a, b, n and r in

(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......

(5+\frac{-1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......

Solve for ^6C_4

(5-\frac{1}{2})^6 = ......+ \frac{6!}{(6-4)!4!)}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{6!}{2!!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{6*5*4!}{2*1*!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{6*5}{2*1}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{30}{2}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+15*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+15(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+15(5)^2(\frac{-1}{2})^4+.......

<em>Check the list of options for the expression on the left hand side</em>

<em>The correct answer is </em>(5-\frac{1}{2})^6<em />

3 0
3 years ago
Simultaneous equations 2x+3y=13 4x-y=-2
Rufina [12.5K]

Answer:

(0.5, 4 )

Step-by-step explanation:

Given the 2 equations

2x + 3y = 13 → (1)

4x - y = - 2 → (2)

Multiplying (2) by 3 and adding to (1) will eliminate the term in y

12x - 3y = - 6 → (3)

Add (1) and (3) term by term to eliminate y

14x = 7 ( divide both sides by 14 )

x = 0.5

Substitute x = 0.5 into either of the 2 equations and evaluate for y

Substituting into (1)

2(0.5) + 3y = 13

1 + 3y = 13 ( subtract 1 from both sides )

3y = 12 ( divide both sides by 3 )

y = 4

Solution is (0.5, 4 )

3 0
3 years ago
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