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Tju [1.3M]
3 years ago
5

write the point slope form of the line that passes through -8, 2 and is perpendicular to the line with a slope of negative 8​

Mathematics
1 answer:
Karolina [17]3 years ago
3 0

Answer:

y = -1/8x + 1

Step-by-step explanation:

Line perpendicular to 8 is -1/8

If the line were to start at the origin, then y- intercept would be 0, and it would pass through the point (-8, 1) To pass through point (-8, 2), add 1 to y in the first example.

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7 apples cost $5. How many apples can i buy with $8?
brilliants [131]

Answer:

7 Bc ur gonna b to broke to buy some more

Step-by-step explanation:

8-5

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2 years ago
​ y=3x−5 y=x−1 ​ Is ( 2 , 1 )a solution of the system?
kotegsom [21]

Answer: Yes, (2,1) is a solution.

Point for : (2,1)

Equation form : x=2 , y=1

Step-by-step explanation: Solve for the first variable in one of the equations, then substitute the result into the other equation.

Hope this helps you out! ☺

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3 years ago
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What is the slope of this line!
vesna_86 [32]

Answer:

-1/3

Step-by-step explanation:

Slope is rise over run which is -1 over 3

3 0
3 years ago
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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:

<h3>(a)</h3>

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.

<h3>(b)</h3>

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
2 years ago
There are 4 cups in a quart and 4 quarts in a gallon how many cups in a 5 gallon jug of water
Marysya12 [62]
80 cups in a 5 gallon jug of water.

1 quart has 4 cups
1 gallon has 4 quarts
1 gallon = 4 quarts * 4 cups = 16 cups

5 gallons = has 80 cups of water.

(4 cups / 1 quart) x (4 quarts / 1 gallon) x (5 gallons) = 4 x 4 x 5 = 80 cups <u>
</u>
6 0
3 years ago
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