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4 years ago

According to the Ruler Postulate, what does the set of points on any line correspond to?

Mathematics

2 answers:

S_A_V [24]4 years ago

8 0

The correct answer is real numbers

Nesterboy [21]4 years ago

3 0

Answer:

The answer is real numbers.

Step-by-step explanation:

The Ruler Postulate states that on any given number line, every point can be paired with a number and every number can be paired with a point called the coordinates.

We know that on a number line, there are both positive and negative numbers.

The numbers on the right side of 0 are positive and the number on left side of 0 are negative.

So, the numbers in the coordinates of the number line are all real numbers.

You might be interested in

Which choices are equivalent to the expression below? √14 x √10

Nataly [62]

Answer:

11.8321595662

Step-by-step explanation:

thats all I know

4 0

3 years ago

Read 2 more answers

Select the correct answer.

EleoNora [17]

Answer:

Option (B)

Step-by-step explanation:

There are two lines on the graph representing the system of equations.

First line passes through two points (-3, 1) and (-2, 3).

Slope of the line = $\frac{y_2-y_1}{x_2-x_1}$

= $\frac{3-1}{-2+3}$

m = 2

Equation of the line passing through (x', y') and slope = m is,

y - y' = m(x - x')

Equation of the line passing through (-3, 1) and slope = 2 will be,

y - 1 = 2(x + 3)

y = 2x + 7 ----------(1)

Second line passes through (0, 1) and (-1, 4) and y-intercept 'b' of the line is 1.

Let the equation of this line is,

y = mx + b

Slope 'm' = $\frac{y_2-y_1}{x_2-x_1}$

= $\frac{4-1}{-1-0}$

= -3

Here 'b' = 1

Therefore, equation of the line will be,

y = -3x + 1 ---------(2)

From equation (1) and (2),

2x + 7 = -3x + 1

5x = -6

x = $-\frac{6}{5}$

x = $-1\frac{1}{5}$

From equation (1),

y = 2x + 7

y = $-\frac{12}{5}+7$

= $\frac{-12+35}{5}$

= $\frac{23}{5}$

= $4\frac{3}{5}$

Therefore, exact solution of the system of equations is $(-1\frac{1}{5},4\frac{3}{5})$ .

Option (B) will be the answer.

5 0

3 years ago

If(x) = x + 2 and h(x) = x-1, what is f • h](-3)?

deff fn [24]

Answer/Step-by-step explanation:

Composition functions are functions that combine to make a new function. We use the notation ◦ to denote a composition.

f ◦ g is the composition function that has f composed with g. Be aware though, f ◦ g is not

the same as g ◦ f. (This means that composition is not commutative).

f ◦ g ◦ h is the composition that composes f with g with h.

Since when we combine functions in composition to make a new function, sometimes we

define a function to be the composition of two smaller function. For instance,

h = f ◦ g (1)

h is the function that is made from f composed with g.

For regular functions such as, say:

f(x) = 3x

2 + 2x + 1 (2)

What do we end up doing with this function? All we do is plug in various values of x into

the function because that’s what the function accepts as inputs. So we would have different

outputs for each input:

f(−2) = 3(−2)2 + 2(−2) + 1 = 12 − 4 + 1 = 9 (3)

f(0) = 3(0)2 + 2(0) + 1 = 1 (4)

f(2) = 3(2)2 + 2(2) + 1 = 12 + 4 + 1 = 17 (5)

When composing functions we do the same thing but instead of plugging in numbers we are

plugging in whole functions. For example let’s look at the following problems below:

Examples

• Find (f ◦ g)(x) for f and g below.

f(x) = 3x + 4 (6)

g(x) = x

2 +

(7)

When composing functions we always read from right to left. So, first, we will plug x

into g (which is already done) and then g into f. What this means, is that wherever we

see an x in f we will plug in g. That is, g acts as our new variable and we have f(g(x)).

g(x) = x

2 +

(8)

f(x) = 3x + 4 (9)

f( ) = 3( ) + 4 (10)

f(g(x)) = 3(g(x)) + 4 (11)

f(x

2 +

) = 3(x

2 +

) + 4 (12)

f(x

2 +

) = 3x

2 +

+ 4 (13)

Thus, (f ◦ g)(x) = f(g(x)) = 3x

2 +

x + 4.

Let’s try one more composition but this time with 3 functions. It’ll be exactly the same but

with one extra step.

• Find (f ◦ g ◦ h)(x) given f, g, and h below.

f(x) = 2x (14)

g(x) = x

2 + 2x (15)

h(x) = 2x (16)

(17)

We wish to find f(g(h(x))). We will first find g(h(x)).

h(x) = 2x (18)

g( ) = ( )2 + 2( ) (19)

g(h(x)) = (h(x))2 + 2(h(x)) (20)

g(2x) = (2x)

2 + 2(2x) (21)

g(2x) = 4x

2 + 4x (22)

Thus g(h(x)) = 4x

2 + 4x. We now wish to find f(g(h(x))).

g(h(x)) = 4x

2 + 4x (23)

f( ) = 2( ) (24)

f(g(h(x))) = 2(g(h(x))) (25)

f(4x

2 + 4x) = 2(4x

2 + 4x) (26)

f(4x

2 + 4x) = 8x

2 + 8x (27)

(28)

Thus (f ◦ g ◦ h)(x) = f(g(h(x))) = 8x

2 + 8x.

4 0

3 years ago

A rectangular has sides that measure 9 centimeters by 12 centimeters by 23 centimeters. Joan filled the container to its brim wi

Svet_ta [14]

So you need to find the volume of the rectangular prism and the equation for that is V=l×w×h. If you plug those numbers in you'd get 9×12×23=2,484. If you multiply 2,484 by $\frac{1}{3}$ because you'd have to pour out $\frac{1}{3}$ of the water out so that it's only $\frac{2}{3}$ of the volume of water is left. 2,484× $\frac{1}{3}$ = 828mm.

8 0

3 years ago

A stock of food is enough to fees 50 persons for 14 days. How many days will the foos last if 20 persons will be added?

stellarik [79]

Answer:

solution

Step-by-step explanation:8 days

7 0

3 years ago