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3 years ago

Using the slope formula, find the slope of the line through the points (0,0) and (5,10).

Mathematics

1 answer:

pychu [463]3 years ago

8 0

<h2>Answer:</h2>

First, we need to find the slope of the line using <u><em>slope formula*</em></u>.

$m = \frac{10 - 0}{5 - 0} = \frac{10}{5} = 2$

Slope of the line: <em>2</em>

Second, we determine the <em><u>y-intercept</u></em> using the slope we just found, one of the given points, and <em><u>slope-intercept form**</u></em>.

$10 = 2(5) + b\\\\10 = 10 + b\\\\0 = b$

Because <em>b = 0</em>, this means that the y-intercept is the origin, (0,0), so it is not written in the equation.

Finally, we create the equation of the line.

$y = 2x$

Slope formula: <em>y₂ - y₁/x₂ - x₁</em>

Slope-intercept form: <em>y = mx + b</em>

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I need the answer :(

madreJ [45]

Answer:

z = 62

y = 117

Step-by-step explanation:

118 and z are supplementary.

z + 118 = 180 Supplementary angles add to 180. Subtract 118 from both sides.

z = 180 - 118 Do the subtraction

z = 62 Answer

The interior angles of all quadrilaterals (convex) add up to 360 degrees.

y + z + 84 + 97 = 360 Given

62 + y + 84 + 97=360 Add

y + 243 = 360 Subtract 243 from both sides

y = 360 - 243 combine

y = 117 Answer

5 0

3 years ago

Let X be a set of size 20 and A CX be of size 10. (a) How many sets B are there that satisfy A Ç B Ç X? (b) How many sets B are

Svetlanka [38]

Answer:

(a) Number of sets B given that

A⊆B⊆C: 2¹⁰. (That is: A is a subset of B, B is a subset of C. B might be equal to C)
A⊂B⊂C: 2¹⁰ - 2. (That is: A is a proper subset of B, B is a proper subset of C. B≠C)

(b) Number of sets B given that set A and set B are disjoint, and that set B is a subset of set X: 2²⁰ - 2¹⁰.

Step-by-step explanation:

Let $x_1, x_2, \cdots, x_{20}$ denote the 20 elements of set X.

Let $x_1, x_2, \cdots, x_{10}$ denote elements of set X that are also part of set A.

For set A to be a subset of set B, each element in set A must also be present in set B. In other words, set B should also contain $x_1, x_2, \cdots, x_{10}$ .

For set B to be a subset of set C, all elements of set B also need to be in set C. In other words, all the elements of set B should come from $x_1, x_2, \cdots, x_{20}$ .

$\begin{array}{c|cccccccc}\text{Members of X} & x_1 & x_2 & \cdots & x_{10} & x_{11} & \cdots & x_{20}\\[0.5em]\displaystyle\text{Member of}\atop\displaystyle\text{Set A?} & \text{Yes}&\text{Yes}&\cdots &\text{Yes}& \text{No} & \cdots & \text{No}\\[0.5em]\displaystyle\text{Member of}\atop\displaystyle\text{Set B?}& \text{Yes}&\text{Yes}&\cdots &\text{Yes}& \text{Maybe} & \cdots & \text{Maybe}\end{array}$ .

For each element that might be in set B, there are two possibilities: either the element is in set B or it is not in set B. There are ten such elements. There are thus $2^{10} = 1024$ possibilities for set B.

In case the question connected set A and B, and set B and C using the symbol ⊂ (proper subset of) instead of ⊆, A ≠ B and B ≠ C. Two possibilities will need to be eliminated: B contains all ten "maybe" elements or B contains none of the ten "maybe" elements. That leaves $2^{10} -2 = 1024 - 2 = 1022$ possibilities.

Set A and set B are disjoint if none of the elements in set A are also in set B, and none of the elements in set B are in set A.

Start by considering the case when set A and set B are indeed disjoint.

$\begin{array}{c|cccccccc}\text{Members of X} & x_1 & x_2 & \cdots & x_{10} & x_{11} & \cdots & x_{20}\\[0.5em]\displaystyle\text{Member of}\atop\displaystyle\text{Set A?} & \text{Yes}&\text{Yes}&\cdots &\text{Yes}& \text{No} & \cdots & \text{No}\\[0.5em]\displaystyle\text{Member of}\atop\displaystyle\text{Set B?}& \text{No}&\text{No}&\cdots &\text{No}& \text{Maybe} & \cdots & \text{Maybe}\end{array}$ .

Set B might be an empty set. Once again, for each element that might be in set B, there are two possibilities: either the element is in set B or it is not in set B. There are ten such elements. There are thus $2^{10} = 1024$ possibilities for a set B that is disjoint with set A.

There are 20 elements in X so that's $2^{20} = 1048576$ possibilities for B ⊆ X if there's no restriction on B. However, since B cannot be disjoint with set A, there's only $2^{20} - 2^{10}$ possibilities left.

5 0

3 years ago

How do you solve for A

ExtremeBDS [4]

More information please

4 0

3 years ago

What is the distance between the two points (5,-2) and (-3,8)

bearhunter [10]

You need to use the distance formula
$d = \sqrt{ {(x - x)}^{2} + {(y - y)}^{2} }$

$\sqrt{ {(5 + 3)}^{2} + {( - 2 - 8)}^{2} }$
so the distance between points (5,-2) and (-3,8) is
$2 \sqrt{41}$
which won't simplify so it stays as is

4 0

3 years ago

What is the midpoint of (2,-2,4) and (-2,0,6)

Mekhanik [1.2K]

Midpoint of (a,b,c) and (e,f,g) is
((a+e)/2,(b+f)/2,(c+g)/2)
just average them

the x value
(2+-2)/2=0/2=0

the y value
(-2+0)/2=-2/2=-1

the z value
(4+6)/2=10/2=5

(0,-1,5) is da midopint

6 0

3 years ago