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1 year ago

Write an equation for each line.

Mathematics

1 answer:

Tems11 [23]1 year ago

5 0

Answer:

Step-by-step explanation:

Equation of blue line:

blue line is parallel to y-axis

⇒ x = 5

Equation of green line:

Green line is parallel to x-axis.

y = 2

Equation of red line:

At y-intercept x = 0. Point on red line is (0,5)

So, y-intercept = 5

y = mx + b Here, m is slope any b is y-intercept.

y = mx + 5

Now, choose any other point in red line. ((1,7)

Substitute this value in the above equation and we can find m

7 = m*1 + 5

7 - 5 = m

m = 2

y = 2x + 5

Equation of black line:

Black line and red line are parallel and so, they have same slope.

y = 2x + b

y-intercept (0,-6) ; b = -6

y = 2x - 6

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If the ratio of the corresponding side lengths of two similar polygons is 6:11, what is the ratio of their areas?

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Its a function of the square of the sides. = 36:121

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3 years ago

A sweater originally priced at $80 was marked down by 25%. What was the sale price of the sweater?

crimeas [40]

The original price of the sweater is $80 which is 100% of the price.
If the price is reduced by 25%, then the new price is 75% of the original price since 100% - 25% = 75%.
Now we need to find 75% of $80.

To find a percent of a number, multiply the percent by the number.
To convert a percent into a decimal, divide the percent by 100 which is the same as moving the decimal point two places to the left.

Here's how to change 75% into a decimal.
75% = 75/100 = 0.75

Here's how you calculate 75% of $80.
75% of $80 =

= 75% * 80

= 0.75 * $80

= $60

Answer: The sale price is $60.

6 0

3 years ago

Read 2 more answers

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.