MATHEMATICS HIGH SCHOOL

Can u Simplify 1 1/16

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Answer 1

Answer:

Answer:

11/16 they cannot be divided, it would remain ig

answer

11/16÷1= 11/16

11/16÷2 I don't know they can divide :)

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Which of the following relations is a function? {(-6, 4), (-6, 2), (2, 9), (1, 4)}

{(8, 2), (9, -2), (7, 0), (-3, 6)}

{(1, 2), (4, -1), (1, 2), (-3, 4)}

{(8, -2), (-4, 3), (8, 4), (-2, 3)}

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The formal definition of a function states that: "A function relates each element of a set with exactly one element of another set (possibly the same set)."

The part "..with exactly one element.." means that for every input (x-coordinate), it cannot give back 2 or more return values (y-coordinates). With that rule alone, we can look at the different groups of coordinate points, and find which of the groups don't have repeating x-coordinates.

Let us look at each group:
{(-6, 4), (-6, 2), (2, 9), (1, 4)} contains 2 pairs with the -6 x-coordinate, so this is not a function.

{(1, 2), (4, -1), (1, 2), (-3, 4)} contains 2 pairs with the 1 x-coordinate so this is not a function.

{(8, -2), (-4, 3), (8, 4), (-2, 3)} contains 2 pairs with the 8 x-coordinate so this is not a function.

{(8, 2), (9, -2), (7, 0), (-3, 6)} does not have any repeating x-coordinates, so this relation is a function.

The point-slope form of the equation of the line that passes through (–4, –3) and (12, 1) is y – 1 = (x – 12). What is the standard form of the equation for this line?

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The equation of line passes through points $\left({ - \,4, - \,3}\right)$ and $\left({12,1}\right)$ in standard form is $\boxed{{\mathbf{x - 4y = 8 }}}$ .

Further explanation:

It is given that a line passes through points $\left({ - 4, - 3}\right)$ and $\left({12,1}\right)$ .

The slope of a line passes through points $\left({{x_1},{y_1}}\right)$ and $\left({{x_2},{y_2}}\right)$ is calculated as follows:

$m=\frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}{\text{ }}$ ......(1)

Here, the slope of a line is denoted as and points are $\left({{x_1},{y_1}}\right)$ and $\left({{x_2},{y_2}}\right)$ .

Substitute for ${x_1}$ , $-3$ for ${y_1}$ , $12$ for ${x_2}$ and $1$ for ${y_2}$ in equation (1) to obtain the slope of a line that passes through points $\left({ - 4, - 3}\right)$ and $\left({12,1}\right)$ .

$\begin{aligned}m&=\frac{{1 - \left({ - 3}\right)}}{{12 - \left({ - 4}\right)}}\n&=\frac{{1 + 3}}{{12 + 4}}\n&=\frac{4}{{16}}\n&=(1)/(4)\n\end{aligned}$

Therefore, the slope is $(1)/(4)$ .

The point-slope form of the equation of a line with slope $m$ passes through point $\left({{x_1},{y_1}}\right)$ is represented as follows:

$y - {y_1}=m\left({x - {x_1}}\right){\text{}}$ ......(2)

Substitute for ${x_1}$ , $1$ for ${y_1}$ and $(1)/(4)$ for $m$ in equation (2) to obtain the equation of line.

$\begin{aligned}y - 1&=(1)/(4)\left({x - 12}\right)\n4\left({y - 1}\right)&=x - 12\n4y - 4&=x - 12\nx - 4y&=8\n\end{aligned}$

Therefore the standard equation of line that passes through points $\left({ - 4, - 3}\right)$ and $\left({12,1}\right)$ is $x - 4y = 8$ .

Thus, theequation of line passes through points $\left({ - 4, - 3}\right)$ and $\left({12,1}\right)$ in standard form is $\boxed{{\mathbf{x - 4y = 8 }}}$

Learn more:

1. Which classification best describes the following system of equations? brainly.com/question/9045597

2. What is the value of in the equation when ? brainly.com/question/3965451

3. What are the values of x?brainly.com/question/2093003

Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Coordinate Geometry

Keywords:Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics,equation of line, line, passes through point

Chris has a collection of 20 baseball cards and Kyle has collection of 40 baseball cards. Chris is adding 3 baseball cards per month to his collection while Kyle is adding one baseball card per month to his collection. After how many months will Chris and Kyle have the same number of baseball cards?

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Answer:

11 months

Step-by-step explanation:

The initial number of baseball cards that Chris has is 20.

This is like the first term of a sequence.

If Chris is adding 3 baseball cards per month, then there will be a constant difference of 3.

The number of baseball cards after $n$ months is given by the formula;

$C_n=20+(n-1)3$

$\Rightarrow C_n=20+3n-3$

$\Rightarrow C_n=3n+17$ where $n\ge1$

Similarly, Kyle initially has 40 baseball cards and adds one base ball card per month to his collection;

The number of his baseball cards after $n$ months is given by the formula;

$K_n=40+(n-1)1$

$K_n=40+n-1$

$\Rightarrow K_n=n+39$

To determine the number of months that will pass before Kyle and Chris have the same number of base ball cards, we equate both equations to get;

$\Rightarrow 3n+17=n+39$

We group like terms to get;

$3n-n=39-17$

$\Rightarrow 2n=22$

$\Rightarrow n=11$

Therefore Chris and Kyle will have the same number of baseball cards after 11 months.

Final answer:

By setting equal the linear expressions for how many baseball cards Chris and Kyle have after a given number of months, we find that it will take 10 months for them to have the same number.

Explanation:

The question is essentially asking how long it will take for Chris and Kyle to have the same number of baseball cards. It's a problem about linear expressions, rooted in mathematics. Chris starts with 20 baseball cards and adds 3 per month. We can express this as C = 20 + 3m, where m is the number of months. Kyle starts with 40 baseball cards and adds 1 per month. We express this as K = 40 + m.

We want to find out when Chris and Kyle will have the same number of cards, so we set C = K, which results in 20 + 3m = 40 + m. By solving this equation, we can condense it to 2m = 20 or m = 10. Therefore, it will take 10 months for Chris and Kyle to have the same number of baseball cards.

Learn more about Linear Equations here:

brainly.com/question/32634451

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Can someone please help

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Answer:

I think its Your Values, but try and a get a second opinion

If A and B are independent events, P(A and B) =

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Answer:

If A and B are independent events, then the events A and B' are also independent. Proof: The events A and B are independent, so, P(A ∩ B) = P(A) P(B). From the Venn diagram, we see that the events A ∩ B and A ∩ B' are mutually exclusive and together they form the event A.

Answer:

Step-by-step explanation:

Given A and B are independent events, P(A and B) = P(A)*P(B)

a community hall is in the shape of a cuboid. the hall is 20m long, 15m wide and 4m high. the community hall needs re-decorating with new paint for the walls and ceiling, and new tiles on the floor. a 20l tin of paint covers 40 squared metres and costs £15. 1 squared metre floor tiles cost £3 each. work out the total cost of paint and tiles needed to decorate the community hall.

Answers

Answer:

the total cost of paint and tiles needed to decorate the community hall is £105 + £900 = £1005.

Step-by-step explanation:

Area of the walls:

- The community hall is shaped like a cuboid, so the walls are the four rectangular sides.

- The length and height of each wall are given as 20m and 4m, respectively.

- The total area of the walls is the sum of the areas of all four walls: 2 * (length * height + width * height).

- Substituting the given values, we have: 2 * (20m * 4m + 15m * 4m).

2. Area of the ceiling:

- The ceiling is also a rectangle, with the same length and width as the floor.

- The area of the ceiling is given by length * width: 20m * 15m.

3. Area of the floor:

- The area of the floor is the same as the area of the ceiling: 20m * 15m.

Now, let's calculate the areas:

1. Area of the walls:

- 2 * (20m * 4m + 15m * 4m) = 2 * (80m^2 + 60m^2) = 2 * 140m^2 = 280m^2.

2. Area of the ceiling:

- 20m * 15m = 300m^2.

3. Area of the floor:

- 20m * 15m = 300m^2.

Next, we can calculate the number of tins of paint and tiles needed and their costs:

- Number of tins of paint needed = Area of walls / Coverage per tin = 280m^2 / 40m^2/tin = 7 tins.

- Cost of paint = Number of tins * Cost per tin = 7 tins * £15/tin = £105.

- Number of tiles needed = Area of floor / Area per tile = 300m^2 / 1m^2/tile = 300 tiles.

- Cost of tiles = Number of tiles * Cost per tile = 300 tiles * £3/tile = £900.

Therefore, the total cost of paint and tiles needed to decorate the community hall is £105 + £900 = £1005.

yes, i am a student

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