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The statement D is false that No irrational number is rational.

The set of real numbers includes integers, rational numbers, and irrational numbers.

This implies that all irrational numbers and integers are also real numbers.

Thus, statements A and B are correct.

Rational numbers are numbers that can be written as the division of two integers, which thus also include all integers.

The set of irrational numbers then contains all real numbers that are NOT rational numbers

Therefore, the set of irrational numbers does not include integers, which implies that statement D is false.

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The sum of the triangular numbers is [tex]\frac{n(n+1)(n+2)}{6}[/tex]

According to the question, the series of triangular numbers is given as in the form of the number of dots constituting the equilateral triangles i.e.
1, 3, 6, 10, 15 . . . . .n

triangular number are the sequence and series of the numbers and each number represents and constitute in visualization of  series of  equilateral triangle.

given series in the figure
1, 3, 6, 10, 15, . . . . . .  ., n
each number represents the number of dots containing in triangle
now the series can be given by
[tex]S = \frac{n(n+1)}{2}[/tex]  for n = 1, 2, 3, 4,. . . . .n
now , according to the question the sum of the series can be given as
⇒  ∑S
⇒   ∑[tex]\frac{n^2+n}{2}[/tex]
⇒  [tex]\frac{1}{2}[\sum n^2+\sum n]\\\frac{1}{2}[\frac{n(n+1)(2n+1)}{6}+\frac{n(n+1)}{2}] \\\frac{n(n+1)}{4}[\frac{(2n+1)}{3}+1] \\\frac{n(n+1)}{4}[\frac{(2n+1+3)}{3}] \\\frac{n(n+1)}{4}[\frac{(2n+4)}{3}] \\\frac{n(n+1)}{4}2[\frac{(n+2)}{3}]\\\frac{n(n+1)(n+2)}{6}[/tex]

Thus, the sum of the triangular number is given by [tex]\frac{n(n+1)(n+2)}{6}[/tex]

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[tex]\textsf {Simplifying the exponents :}[/tex]

[tex]\mathsf {\frac{3x^{-6}y^{-3}}{15x^{2}y^{10}}}[/tex]

[tex]\mathsf {\frac{1}{5x^{(2+6)}y^{(10+3)}}}[/tex]

[tex]\mathsf {\frac{1}{5x^{8}y^{13}}}[/tex]

The statement about using the line of best fit for the given scatter plot is; False

When we have a scatter plot, it is always best to look for the line of best fit or curve of best fit depending on the nature of the variation of the plotted points.

Now, from the scatter plot image attached, we can see that the points are already looking like a curved plot form and so what we will need her will be a curve of best fit and not a line of best fit plot and as such the statement about using a line of best fit plot is false.

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All the solution of the equation x³ + 8x² + 100x + 800 = 0 will be 10i, -10i, and -8. Then the correct option is D.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The equation is given below.

          x³ + 8x² + 100x = -800

x³ + 8x² + 100x + 800 = 0

Then the factor of the equation will be

x³ + 8x² + 100x + 800 = 0

x² (x + 8) + 100(x + 8) = 0

        (x² + 100)(x + 8) = 0

Then all the solution of the equation will be

x = 10i, -10i, and -8.

Then the correct option is D.

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Answer:

d

Step-by-step explanation:

Answer:

An obtuse triangle can not have more than one angle measured greater than 90.

Step-by-step explanation:

Obtuse triangles have 2 acute angles (less than 90 degrees) and 1 obtuse angle (greater than 90).

Solution: 8p+44

Detailed explanation:

First we can "expand" by multiplying 6 times the parentheses and then 2 times the other set of parentheses.

[tex]--\mapsto\boldsymbol{6(p+6)+2(p+4)}\\\\---\mapsto\boldsymbol{6p+36+2p+8}[/tex]

To make life easier let's just put the p's next to each other.

[tex]--\mapsto\boldsymbol{6p+2p+36+8}[/tex]

Now let's add the p's

[tex]---\mapsto\boldsymbol{8p+44}[/tex]

Voila! There's our answer!

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Hope I helped! Best wishes.

Reach far. Aim high. Dream big.

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If x is the largest side :

If 4.1 is the greatest side :

Range of possible sizes for side 'x' :

The expression which represents the other factor, or factors, of the given polynomial is option (C) (2x-1)(x+1)

A cubic equation in algebra is a one-variable equation of the form ax3+bx2+cx+d=0 where an is nonzero. The roots of the cubic function defined by the left side of this equation are the solutions to this equation.

Given expression 2x³-3x²-3x+2 whose one of factor is (x-2)

We have to find second factor of given equation

First we will be rational root theorem to given expression so will get following expression:

[tex]\left(x+1\right)\frac{2x^3-3x^2-3x+2}{x+1}[/tex]

So one factor is (x-1) and now simplifying [tex]\frac{2x^3-3x^2-3x+2}{x+1}[/tex]  we get              2x² - 5x +2 and the factor of 2x² - 5x +2 will be (2x-1)(x-2)

Hence the expression which represents the other factor, or factors, of the given polynomial is option (C) (2x-1)(x+1)

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Answer:

x=(y-3)/4

Step-by-step explanation:

y=4x+3

y-3=4x

x=(y-3)/4

Answer:

it would look like this

Step-by-step explanation:

The solution to the given compound inequality 2x - 3 < x + 2 ≤ 3x + 5 is 5 > x ≥ -3/2

2x - 3 < x + 2 ≤ 3x + 5

solve differently

2x - 3 < x + 2

2x - x < 2 + 3

x < 5

x + 2 ≤ 3x + 5

x - 3x ≤ 5 - 2

-2x ≤ 3

x ≥ 3/-2

x ≥ -3/2

Therefore, the solution of the compound inequality is 5 > x ≥ -3/2

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We will apply the Pythagoras theorem to find the measure of the unknown leg in a triangle when one leg and the hypotenuse are provided dimensions.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometric function.

According to Pythagoras, the sum of the squares of two sides equals the square of the longest side.

[tex]\rm h^2 = p^2+ b^2[/tex]

Where,

h is the hypotenuse

p is the perpendicular

b is the base

If any of the two is given the third side will be obtained using the  Pythagoras theorem.

In a triangle with given measurements for one leg and the hypotenuse, we will determine the measure of the unknown leg by the Pythagoras theorem.

Hence we willl apply the pythogorous theorem for finding the unknown side.

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Each step of the proof are:

The given parameter is:

Lines a and b are parallel.

This is represented as; a || b

Corresponding angles are equal.

∠1 and ∠5 are corresponding angles.

So, we have: ∠1 ≅ ∠5

Also, they are congruent.

So, we have ∠1 ≅ ∠5

Vertical angles are equal.

∠5 and ∠7 are vertical  angles.

So, we have: ∠5 ≅ ∠7

Also, they are congruent.

So, we have ∠5 ≅ ∠7

According to the transitive property;

If ∠1 ≅ ∠5 and ∠5 ≅ ∠7, then ∠1 ≅ ∠7

Hence, it has been proved that ∠1 ≅ ∠7

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Answer:

i think the answer would be 53?

Step-by-step explanation:

i could be wrong

Step-by-step explanation:

the answer is d= -46/-7

or in simplest form

d= 6.57

hope this is correct...

Answer:

The group that is most likely able to have a lower mean age of painting students is Group A

Step-by-step explanation:

mean = sum of all terms divided by total number of terms

Looking at the graph data you have provided you can see that group A's students are a younger than students in Group B.

Which means when you calculate the mean the group which would give you the lower ratio with the same denominator of K (let there is K number of students in the class) will have lower mean age

here group A students are younger therefore their ratio will be lower

hence lower mean age

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The correct answer is option B that is Each white blood cell contains millions of haemoglobin molecules. All blood cells come from one pool of stem cells.

The complete question is given below:-

Which of the following statements are true?

I. Each white blood cell contains millions of haemoglobin molecules.

II. In a sample of blood, there are more red blood cells than white blood cells.

III. HIV destroys red blood cells.

IV. All blood cells come from one pool of stem cells.

A. II and IV only

B. I and IV only

C. II and III only

D. I, III, and IV only

E. I, II, and IV only

The most prevalent form of blood cell and the main source of oxygen for the bodily tissues of vertebrates, red blood cells are also known as red cells, red blood corpuscles, haematids, erythroid cells, or erythrocytes. They circulate through the blood through the circulatory system.

Therefore the correct answer is option B that is Each white blood cell contains millions of haemoglobin molecules. All blood cells come from one pool of stem cells.

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The conversion to logarithm function will be that log3 27 = 3.

From the information given, we are to convert the exponential equation to logarithm function. This will be:

log 3 27

This will be log 3 3³

= 3 × log 3^3

= 3 × 1

= 3

Therefore, x = 3.

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The correct expression is : [tex]\frac{4 cm }{1 year}[/tex] x [tex]\frac{10 mm}{1 cm}[/tex] x [tex]\frac{ 1 year }{365 days}[/tex]

What is the correct expression?

The first step is to convert year to days.

1 year = 365 days

The next step is to convert cm to mm.

1cm = 10 mm

4 x 10 = 40mm

Now, divide 40 mm by 365 days

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Placing the equations under the correct solution, we get

x = 3                                      x ≠ 3

-14x = -42                              -5 + x = -9

[tex]-\frac{3}{5} +x = \frac{12}{5}[/tex]                          [tex]\frac{x}{3} =9[/tex]

[tex]\frac{x}{4} =\frac{6}{8}[/tex]                                    

x -5 = -2            

From the question, we are to place the equations under the correct solution

To do this, we will solve the equations one after the other

x = -42/-14

x = 3

x = -9 + 5

x = -4

∴ x ≠ 3

[tex]x = \frac{12}{5} +\frac{3}{5}[/tex]

[tex]x = \frac{12+3}{5}[/tex]

[tex]x = \frac{15}{5}[/tex]

x = 3

[tex]x=\frac{6\times 4}{8}[/tex]

[tex]x=\frac{24}{8}[/tex]

x = 3

x = 3 × 9

x = 27

∴ x ≠ 3

x = -2 + 5

x = 3

Hence, placing the equations under the correct solution, we get

x = 3                                      x ≠ 3

-14x = -42                              -5 + x = -9

[tex]-\frac{3}{5} +x = \frac{12}{5}[/tex]                          [tex]\frac{x}{3} =9[/tex]

[tex]\frac{x}{4} =\frac{6}{8}[/tex]                                    

x -5 = -2            

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The formula for number of buses per person is b = p/50

This is a way of using a variable to represent other variables in a function.

Given the expression

p = kb

If k = 50, then;

p = 50b

Make b the subject of the formula

p/50 = 50b/50
b = p/50

Hence the formula for number of buses per person is b = p/50
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Using linear function concepts, it is found that a set of ordered pairs with a slope of 3 is perpendicular to the set (12,3), (9,4).

A linear function is modeled by:

y = mx + b

In which:

If two lines are perpendicular, the multiplication of their slopes is of -1. The set (12,3), (9,4) has the slope given by:

m = (4 - 3)/(9 - 12) = -1/3.

Hence, for the perpendicular set:

[tex]-\frac{1}{3}m = -1[/tex]

m = 3.

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Answer:

(2*2*1.5*1/3)+(2*1.5*4)= 14

Step-by-step explanation:

To find the area of a pyramid, you use the equation of 1/3 *lwh. When we place the values in there, we get 2*2*1.5*1/3, which is equal to 2. Then we solve the bottom part. Since it is a rectangular prism, we use the equation of lwh. When we insert the values, we get 2*1.5*4, which is equal to 12. Now, we take these two values of 2 and 12 and we combine them, giving us our final answer of 14.

Answer:

x^2-3x-1

Step-by-step explanation:

So we have the equation:

x^3-2x^2-4x-1/x+1

First factor the equation:

(x+1)(x^2-3x-1)/x+1

Then cancel the common factor: x+1 to solve the equation:

x^2-3x-1

since we were given the key ( how it should be sort out or used )

then we get all the numbers out which are:

21, 23, 30, 32, 32, 35, 43, 44, 46, 48, 49, 49, 50, 52, 52, 53, 55

then we go ahead to answer the questions:

a) Range = highest number minus Lowest number

55 - 21 = 34

b) 17 (by counting all individual ages ).

c) Median = the middle age

(but before that, we must arrange the ages either a cording to their sizes either from biggest to smallest (descending order) or from smallest to biggest (ascending order)

so we arrange in ascending order but the numbers are already arranged so we don't have to stress ourselves:

Median = 46 (the number in the middle ).

Hope you ace your tests, Good luck ✅.

The statements that describe a triangular prism are:

A triangular prism is a three-dimensional object that is made up of one base that has the shape of a triangle and three lateral sides that have the shape of a rectangle. A triangular prism has 5 faces, 9 edges and 6 vertices.

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There is no absolute value function when graphed, will be wider than the graph of the parent function f(x) = |x|

An absolute value function is a function such that,

[tex]|x|=-1 when x\geq 0 and |x|=1 when x\leq 0[/tex]

For the given example,

We have been given a parent function f(x) = |x|

We need to find the absolute value function, when graphed, will be wider than the graph of the parent function.

Consider the graph of all absolute value functions.

The graph of f(x) = |x| + 3 is represented blue color.

The graph of f(x) = |x − 6| is represented green color.

The graph of f(x) = |x| is represented red color.

The graph of f(x) = 9|x| is represented violet color.

From this graph, we can observe that,

f(x) = |x| + 3 is as wise as the parent absolute value function f(x) = |x| translated up by 3 units.

Similarly, the function f(x) = |x - 6| is as wise as the parent absolute value function f(x) = |x| translated right by 6 units.

This means, there is no absolute value function when graphed, which will be wider than the graph of the parent function f(x) = |x|

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Answer:

I believe the answer is C. F(x)= 1/3|x|

Step-by-step explanation:

i hope this helps.

Δ DGC is right angled triangle because Line E G is perpendicular-to CC', Option D is the correct answer.

Triangle is a polygon with three sides , angles and vertices.

It is given that the there are two Triangles , ABC and A'B'C' as an image of the ABC

* Line segment AA' has a midpoint at point F

*D is the mid point of the line joining BB' .*

The figure is attached with the answer.

the line of reflection of the object is always perpendicular to the object and the image.

it is also given that CGF is a right angle.

Therefore triangle DGC is right angled triangle , (the option given in the question is incorrect ) ,  Line E G is perpendicular-to CC'.

Option D is the correct answer.

Please Refer to the image for correct coordinates.

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