What is the log2 function?

The statement that is true on the system of equations is that A. The system has no solution.

There is no solution in the given system of equations because the lines formed by the equations are parallel to each other. This means that they will never intersect with each other.

A solution is only derived at the points where the systems of equations intersect with each other. As there is no point where these equations intersect, it means there is no solution for these system of equations.

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a) Issac get £10.75 as change after buying all masks

b) The price of the e-scooter in the sale is £277.50

a)

Isaac buys 17 anti-pollution masks for £5.25 each, so the total cost is

17 * 5.25 = £89.25

He pays with five £20 notes, which is a total of 5 * 20 = £100

So, the change he should get is £100 - £89.25 = £10.75

Therefore, Isaac should get £10.75 as change.

b)

In the sale, there is 1/4 off the cost price of the e-scooter, which means that the scooter is discounted by 1/4 * £370 = £92.50.

To work out the price of the e-scooter in the sale, you need to subtract the discount from the normal price, so

£370 - £92.50 = £277.50

Therefore, the price of the e-scooter in the sale is £277.50

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The maximum possible value for the greatest common divisor (GCD) of 11n + 3 and 2n + 1 as n ranges over the positive integers is 1.

The GCD of two integers is the largest integer that divides both integers without leaving a remainder. We can use the Euclidean algorithm to find the GCD of two numbers.

The Euclidean algorithm states that for two integers a and b, we can find the GCD of a and b by repeatedly applying the following steps:

Divide a by b to get a quotient q and a remainder r

Replace a with b and b with r

Repeat the process until r is 0

If we apply this algorithm to 11n + 3 and 2n + 1, we get the following:

GCD(11n+3, 2n+1)

As 11n + 3 = 3(2n + 1) + 5n

= GCD(2n+1, 5n )

As 2n + 1 = (2/5)(5n) + 1

= GCD(5n, 1)

= GCD(1, 0)

= 1

So as n ranges over the positive integers, the maximum possible value for the GCD of 11n + 3 and 2n + 1 is 1.

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The degree of the polynomial 7x³ 5x 4x³ 2x² is 3.

The degree of a polynomial is the highest power of x in the polynomial.

In this case, the polynomial is 7x³ 5x 4x³ 2x², and the highest power of x is x³. This means that the degree of this polynomial is 3.

It's important to note that when working with polynomials it's important to pay attention to the signs of the coefficients. In this case, we have 7x³, 5x, 4x³, 2x². The x³ term has the highest degree and it's coefficient is 7, the x term has the second highest degree and it's coefficient is 5, the x³ term has the same degree as the first x³ term, but the coefficient is different, and the x² term has the fourth highest degree and it's coefficient is 2.

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Answer:

$6.51

Step-by-step explanation:

To make a percent a decimal, divide by 100

62% = .62

.62 x 10.50 = 6.51

We know that half of 10.50 is 5.25 and 625 would be a little higher and 6.51 is a little higher.

Answer:

[tex]13^{\circ}[/tex]

Step-by-step explanation:

Consider the smaller of the two triangles with angle [tex]x[/tex].

Using vertically opposite angles, one of the angles of this triangle is [tex]85^{\circ}[/tex].

Using corresponding angles combined with angles on a straight line, one of the angles is [tex]82^{\circ}[/tex].

Angles in a triangle add to [tex]180^{\circ}[/tex], so [tex]x=13[/tex].

Answer:

awser is D. I did the text

The range of the accidents reported from the grouped frequency table is 22.

The range is the difference between the highest value and the lowest value of a given set of data.

We have,

The number of accidents reported from the grouped frequency table.

The largest number of accidents = (19 - 25)

The smallest number of accident = (3 - 7)

Now,

Range.

= 25 - 3

= 22

Thus,

The range of the reported accidents is 22.

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Answer:

Slope = -2  Y intercept is (0,4)

Step-by-step explanation:

Answer:

65?

Step-by-step explanation:

im not to sure but maybe 65

It means that the grocer has to pay $1.38 for each pound of strawberries. So the constant of proportionality for this scenario is $1.38

Proportionality is a mathematical relationship between two variables, where the ratio of one variable to the other is always the same, regardless of the values of the variables. The variables are said to be in proportion if there is a constant of proportionality "k" such that one variable is equal to "k" times the other variable. In other words, if y is proportional to x, the relationship is represented by an equation of the form y = kx, where "k" is the constant of proportionality.

A constant is a value that does not change. In mathematical terms, it refers to a value in an equation that remains the same and does not depend on the variables. For example, in the equation y = kx, "k" is a constant. It is a fixed numerical value that relates two variables in a proportionality relationship. Constants can be represented by a number, a letter or a symbol.

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The following presumption has to be verified in order to establish whether the collection of ordered pairs fulfills an exponential function: The x-coordinates must have the same increment or a consistent difference.

A mathematical function of form f (x) = aˣ is an exponential function. "x" is a variable, while "a" is a constant that serves as the function's basis and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the foundation for exponential functions that are most frequently utilized.

Characteristics are:

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Answer:

b and d

Step-by-step explanation:

slope is  -0.632 which is quite literally what d is saying, (on terms of graphs) for every 1 square over it goes -0.63 squares down

A one million sided shape called as Megagon.

We know that a polygon is noting but a closed two-dimensional figure which is enclosed by line segments.

These line segments are known as sides.

A polygon has at least three straight sides and angles.

Polygons are classified mainly into four categories. Regular polygon, Irregular polygon, Convex polygon and Concave polygon

We know that a polygon with n sides is called n-gon.

For n = 1000000, i.e., a polygon with one million sides is called as Megagon.

A number of edges and vertices = 1000000

And the internal angle of megagon is about 179.99 degrees.

Therefore, a shape with  1 million sides is known as a Megagon

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Teo can fill 28 glasses in  4 2/3 pitches of juice.

Teo  has 4 2/3 pitches of juice.

First we write the improper fraction (mixed fraction) as a proper fraction.

4 2/3

= [(4 × 3) + 2] / 3

= (12 + 2) / 3

= 14/3

One glass holds 1/6 of a pitcher.

Let m number of glasses hold 14/3 pitches of juice.

By unitary method,

m × (1/6) =  14/3

To find the value of m we need to divide fractions.

m = (14/3) / (1/6)

m = (14/3) × (6/1)

m = 14 × 2

m = 28

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In the late 19th century, the Russian press used the phrase 2 + 2 = 5 to describe the moral confusion of social decline at the turn of a century, because political violence characterised much of the ideological conflict among proponents of humanist democracy and defenders of tsarist autocracy in Russia

Answer: No, it is not a solution.

Step-by-step explanation:

   We will substitute the point given, and if the inequality is true after simplifying then it is a solution.

 Given:

3x + 11y ≤ 8

 Substitue:

3(1) + 11(7) ≤ 8

 Multiply:

3 + 77 ≤ 8

 Add:

80 ≤ 8 ✗

According to the compound interest formula, the population is 5 years is 422,385.

The term compound interest in math is defined as the interest calculated on the principal and the interest accumulated over the previous period.

Here we have given that the population of 210,000 people is increasing by 15% each year.

And then while looking into the given question, we have identified that the value of

interest rate = 15%

principal count = 210,000

time period = 5

Here we have to convert R as a percent to r as a decimal, then we get

=> r = R/100

=> r = 15/100

=> r = 0.15 rate per year,

Now, we have to solve the equation for A

[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]

Apply the values on it , then we get,

[tex]A = 210,000.00(1 + \frac{0.15}{1} )^{(1)(5)}[/tex]

When we simplify this one then we get

[tex]A = 210,000.00(1 + 0.15)^5[/tex]

Therefore, the value of A is 422,385.

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In mathematics, a plane is a two-dimensional surface that can be enlarged indefinitely. In order to make a plane we need at least 3 points.

In order to make a plane we need at least 3 points. Let A, B and C are three points which can be defined by two particular vector AB and AC.

As the two vectors is located on the plane, we can use their cross product to define a normal vector on the plane.

As we see a triangle which is a two-dimensional geometric figure that is developed based on 3 points. Triangle is the smallest polygon. The other polygon needs more point for creation.

Therefore, it is proved that minimum three points is mandatory for plane formation.

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The domain and range of function Y = 4x² are:

Domain: (-∞, ∞) {x | x ∈ R}

Range: [0, ∞) {y | y ≥ 0}

Now, According to the question:

What are the domain and range?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

We have,

Y = 4x²

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation: (-∞, ∞)

Set-Builder Notation:  {x | x ∈ R}

The range is the set of all valid y values: [0, ∞)

Set-Builder Notation: {y | y ≥ 0}

Hence, the domain and range of function Y = 4x² are:

Domain: (-∞, ∞) {x | x ∈ R}

Range: [0, ∞) {y | y ≥ 0}

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The complete question is this:

What is the domain of the function Y = 4x²

Answer: standard form of (6.31×10⁵ ) + (2.6×10⁴) is 65.7 × 10⁴.

What is a simplification of an expression?

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

As given,

(6.31×10⁵ ) + (2.6×10⁴) = ( 6.31× 10⁴ ×10 ) + (2.6 × 10⁴ )

                                   =  ( 6.31 × 10 + 2.6 )

                                   =  ( 63.1 + 2.6 )

                                   =  ( 65.7 )

                                   = 65.7 × 10⁴

Hence, the standard form of ( 6.31× 10⁵) + (2.6 × 10⁴) = 65.7 × 10⁴.

[tex](6.31\times 10^{5})+(2.6\times 10^{4})\implies 6\underline{31000}+2\underline{6000} \implies \text{\LARGE 657000}[/tex]

Since points D and F are the intersections of sides AC and AE, In triangle respectively, DF is parallel to EC and so EC is twice as long as DF. Thus, the value of side EC is 32.

Given that it has 3 components and three vertices, a triangle qualifies as a polygon. It has a fundamental geometric form. Triangle ABC is the name given to a triangular with the corners A, B, and C. When the three aspects are not collinear, Euclidean geometry yields a single plane and triangle. Triangles are regarded as polygons since they have 3 components and three corners. The points where a triangle's three sides meet are referred to as its corners. Three triangle angles are multiplied to get 180 degrees.

Given :

Triangle ACE

The midpoint of EC is side, where AC = 38 B.

D sits in the middle of EC.

The center of AE is F.

DF = 16.

Given that D is the midpoint of EC and that F is the midpoint of AE, it follows that DF is parallel to AC.

If DF and AC are parallel, then DF and AC are equal to twice each other and DF equals 16. Thus, EC equals 32.

=>EC = 2*DF

=>EC = 2*16

=>EC = 32

It follows that if points B, D, and F are the midpoints of the sides of the triangle ACE, then DF is parallel to AC and EC = 2 x DF = 32.

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Answer: The answer is 11 1/4

Step-by-step explanation:

The table representing the given absolute function should be completed as follows;

x          f(x)

6          8

-1          6

4          4

9         14

Based on the information provided, we have the following absolute function:

f(x) = |-2x + 4|

When x = 6, the value of the absolute function is given by;

f(6) = |-2(6) + 4|

f(6) = |-12 + 4|

f(6) = |-8|

f(6) = 8

When x = -1, the value of the absolute function is given by;

f(-1) = |-2(-1) + 4|

f(-1) = |2 + 4|

f(-1) = |6|

f(-1) = -6.

When the value of the absolute function y = 4 is given by;

4 = |-2x + 4|

±4 = -2x + 4

2x = 4 ± 4

2x = 8

x = 4 or 0.

When the value of the absolute function y = 14 is given by;

14 = |-2x + 4|

±14 = -2x + 4

2x = 4 ± 14

2x = 18

x = 9 or 5.

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Anael can not use the fourth board measurement. This can be solved by using the concept of inch scale.

A centimeter is smaller than an inch. On the other side of the centimeter ruler, inches are denoted by the large, continuous hash marks that are inscribed above the digits. On a ruler, the inch is the largest unit and is denoted by the longest line. There is a number next to each 1-inch line on the ruler that designates.

Since the international yard was adopted in the 1950's and 1960's, standards for the precise length of an inch have fluctuated, but the inch is now based on the metric system and is defined as precisely 25.4 mm.

The question given here,

the first board measurement: [tex]99\frac{3}{4} =[/tex] 99 inch ± 0.75 inch

the second board measurement: [tex]99\frac{7}{8} =[/tex] 99 inch ± 0.875 inch

the third board measurement: [tex]100\frac{1}{6} =[/tex] 100 inch ± 0.16 inch

the fourth board measurement: [tex]100\frac{5}{16} =[/tex] 100 inch ± 0.3125 inch

the fifth board measurement: [tex]99\frac{13}{16} =[/tex] 99 inch ± 0.8125 inch

Thus, Anael can not use the fourth board measurement.

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the given triangle A 45-45-90 triangle is a right triangle having interior angles measuring 45°, 45°, and 90° in degrees.

A 45-45-90 triangle is also an isosceles triangle, which means that its two legs are equal in length.

All 45-45-90 triangles are similar to each other.

Line segments DE and FG are perpendicular to side AB of the 45-45-90 triangle, ABC. Triangles ADE and AFG are also 45-45-90 triangles now, △ABC~△ADE~△AFG.

The ratio of the side lengths of a 45-45-90 triangle is:

                                          ratio= 1:1: √2

The legs of opposite the 45° angles (the shorter sides) are √2÷2of the length of the hypotenuse (the side opposite the 90° angle)

The hypotenuse is √2 times the length of either leg.

Since a 45-45-90 triangle is also an isosceles triangle, then, the two legs are equal on measuring. Assuming x is the length of the leg and b is the length of the hypotenuse and using the Pythagorean Theorem:

x^2 + x^2= b^2

Thus, the ratio of the side lengths of a 45-45-90 triangle are x:x:√2 or 1:1: √2 respectively.

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Answer:

hectogon or hecatontagon or 100-gon

Step-by-step explanation:

It is a hundred - sided polygon ( shape ). The sum of all hectogon's interior angles are 17640 degrees.

Answer:

Regular exercise has been shown to aid in the prevention and management of noncommunicable illnesses such as diabetes, heart disease, stroke, and a number of malignancies. Additionally, it lowers blood pressure, supports healthy body weight, and enhances well-being through enhancing mental health.

Step-by-step explanation:

With 10 faces and 16 vertices, an octagonal prism is depicted.Two octagonal bases and eight rectangular sides define an octagonal prism, which has two of each shape.

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The dual formula is a formula which we get when we replace the symbol ∨ by ∧ , ∧ by ∨ , T by F  or F by T.

Basically , we can say that it is obtained by replacing tautology by contradiction.

There are certain rules which are to be followed while applying dual formula which are,

S1 is a tautology if and only if S2 is a contradiction.

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Answer:

PF = 9

Step-by-step explanation:

the incentre of a triangle is equally distant from the triangle's 3 sides, that is

PD = PE = PF

using PD = PE to solve for x

5x - 6 = 3x ( subtract 3x from both sides )

2x - 6 = 0 ( add 6 to both sides )

2x = 6 ( divide both sides by 2 )

x = 3

then

PE = 3x = 3 × 3 = 9

PF = PE = 9