Jacob just bought a new pair of basketball shoes. He expects the shoes to last for two hundred twenty-five games. He plays two games a week. Define a unit for the time Jacob has been using his new pair of basketball shoes. Enter a variable for the time Jacob has been using his new pair of basketball shoes and use this variable to write an expression for the number of games remaining for the shoes.

The cardinal number of G = 0 for the given set G = {x|x ∈ N and x is a negative}.

A set is defined as a group of objects in mathematics. Set names and symbols begin with a capital letter. According to set theory, a set's constituent parts can be included in anything.

The set is given in the question, as follows:

G = {x|x ∈ N and x is a negative}

We have to determine the cardinal number of set G = {x|x ∈ N and x is a negative}

Cardinal numbers, also known as Cardinals of a Set, are the numbers used to count the number of elements in a Set.

Simply expressed, the cardinal number of a set equals the number of items in a set.

Let A = {a, b, c, d}  be a set then Cardinal number of A is 4

Given G = {x|x ∈ N and x is a negative}

Here, x belongs to N, and a negative number

Since Natural Number (N) = 1, 2, 3, 4 ...

There is no negative value that corresponds to N.

Thus, G = { } or G is an empty set.

Hence, the cardinal number of G = 0

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The question seems incomplete, the complete question would be as:

Find the cardinal number of set G = {x|x ∈ N and x is a negative}

The function that describes the sequence maps each index or position to its corresponding value.

A sequence space is a vector space that contains endless sequences of real or complex numbers. It is used in functional analysis and related mathematical fields. It is, in essence, a function space whose constituents are functions from the natural numbers to the field K of real or complex numbers.

The notation f(2) = 4 indicates that a term in a sequence defined by a function has a value of 4 when the term's index or position is 2.

Because sequences are a collection of ordered pairs with the first element being the index or position of the term and the second being the term's value, they can be characterised as functions. The function that represents the series maps each index or location to its associated value, and these ordered pairs can be seen as points on a coordinate plane.

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The rule for the arithmetic sequence in this problem is defined as follows:

[tex]a_n = 4.5 - 0.625(n - 1)[/tex]

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The general rule of an arithmetic sequence is given as follows:

[tex]a_n = a_1 + (n - 1)d[/tex]

The common ratio for the sequence is given as follows:

d = 3.25 - 3.875 = 3.875 - 4.5 = -0.625.

The first term of the sequence is given as follows:

[tex]a_1 = 4.5[/tex]

Hence the rule is defined as follows:

[tex]a_n = 4.5 - 0.625(n - 1)[/tex]

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Answer:

C(t) = 0.50 * t + 2.50

Step-by-step explanation:

The function C(t) to represent the cost of a taxicab ride can be written as:

C(t) = 2.50 + 0.50 * t

where t is the distance traveled in tenths of a mile.

The slope of the graph of this function is 0.50, which represents the cost per tenth of a mile.

The y-intercept of the graph of this function is 2.50, which represents the fixed fee that must be paid regardless of the distance traveled.

So, the equation of the graph of this function is:

C(t) = 0.50 * t + 2.50

The statement is true. Matrix multiplication is not commutative, so the product of the transposes of the matrices must be applied in the same order as the initial product, not in a reverse order.

The statement that the transpose of a product of matrices equals the product of their transposes in the same order is true. Matrix multiplication is not commutative, which means that the order in which the matrices are multiplied matters. That is, for two matrices A and B, AB does not necessarily equal BA. Thus, when taking the transpose of a product of matrices, the order in which the transposes of the matrices are multiplied must be the same as the order in which the original matrices were multiplied. Otherwise, the result will not be the same. For example, if two matrices A and B are multiplied to give AB, the transpose of AB will be (AB)^T = B^T A^T, not A^T B^T. This is why the product of the transposes must be applied in the same order as the initial product.

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The total number of seeds Frank is going to plant is 6b + 6 seeds.

From the question, we have the following parameters that can be used in our computation:

Graden 1 = b

Graden 2 = 5b + 6

Frank is going to plant b seeds in one garden and 5b + 6 seeds in another garden.

The total number of seeds Frank is going to plant is:

b + (5b + 6) = 6b + 6

So Frank is going to plant 6b + 6 seeds.

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Answer:

Step-by-step explanation:

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Answer:

The first one is 3/5 & The second one is 3/8 & The the third one is 1/8

Step-by-step explanation:

Hope this helps :)

A. The properties of parallelogram involving slope is the slope of opposite sides of parallelogram are equal as the lines are parallel. Hence, the vertices ABCD form a parallelogram.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces.

A. The properties of parallelogram involving slope is the slope of opposite sides of parallelogram are equal as the lines are parallel.

B. The opposite sides of the parallelogram are parallel and equal, and their slopes are equal.

C. The given vertices of a parallelogram are:

A(-2, 0), B(0, 9), C(2, 0) and D(0, -9).

Calculate the slope of segment AB and CD.

The slope is given as:

m = (y2 - y1) / (x2 - x1)

For AB:

m = (9 - 0) / (0 + 2) = 9/2

For CD:

m = (-9 - 0) / (0 - 2) = 9/2

Since the slopes of the segments AB and CD are equal the two lines are parallel to each other. Hence, the vertices ABCD form a parallelogram.

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The angle that is adjacent to the angle CED is the angle DEA.

When two angles have a similar vertex and side, they are referred to as neighbouring angles. The vertex of an angle is the point at which the rays that make up its sides come to an end. When adjacent angles have a same vertex and side, they can be a complimentary angle or supplemental angle.

An adjacent angle is complementary to another if the total of its adjacent angles is 90 degrees.

When the total of two adjacent angles is 180 degrees, they are supplementary to one another.

Two angles are said to be adjacent angles when they share a common vertex.

In the given figure the angle that shares the common vertex to angle CED is angle DEA.

Hence, the angle that is adjacent to the angle CED is the angle DEA.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 2545.10\\ P=\textit{original amount deposited}\dotfill &\pounds 2000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]2545.10 = 2000\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 4} \implies \cfrac{2545.10}{2000}=\left( 1+\cfrac{r}{100} \right)^4 \\\\\\ \cfrac{2545.10}{2000}=\left( \cfrac{100+r}{100} \right)^4\implies \sqrt[4]{\cfrac{2545.10}{2000}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[4]{\cfrac{2545.10}{2000}}=100+r\implies 100\sqrt[4]{\cfrac{2545.10}{2000}}-100=r\implies \boxed{6.2\approx r}[/tex]

Answer:

Step-by-step explanation:

I am not sure what you mean with that question but a short definition of bullying is:

Bullying can result in physical injury, social and emotional distress, self-harm, and even death. It also increases the risk for depression, anxiety, sleep difficulties, lower academic achievement, and dropping out of school.

the measurement of the ∠R will be 101 degrees.

A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, while a quadrilateral with equal sides is known as a rhombus.

Given TPRS is a parallelogram. in that ∠T = (4x +1) and ∠S = (3x +4)°

Since in a parallelogram, opposite angles are equal Thus,

∠P = ∠S = 3x + 4

∠R = ∠T = 4x +1

Since we know the sum of all angles of a quadrilateral is 360°

3x +4 + 4x +1 + 3x +4 + 4x +1 = 360

14x + 10 = 360

14x = 350

x = 350/14

x = 25

Thus,

∠R = 4x +1

∠R = 4 *25 + 1

∠R = 101°

therefore, the measurement of the ∠R will be 101 degrees.

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The requried measure of the angle ∠2 = ∠5 = ∠15 = 125, ∠11 = 88, ∠3 = ∠9 = ∠13 =  102°, ∠4 = ∠14 = 78°, ∠7 = 37, ∠8 = 41, ∠1 = ∠6 = ∠10 = 16 = 55°.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

here,
from figure,
∠2 = ∠5 = ∠11 + ∠12 = ∠15 = 125

From the above expression,
∠2 = ∠11 + 37°
125 - 37 = ∠11
∠11 = 88°

Similarly.
∠3 = ∠9 = ∠13 = ∠18 = 102°
∠4 = ∠7+∠8 = ∠14 = ∠17= 78°
∠1 = ∠6 = ∠10 = 16 = 55°

Thus, the requried measure of the angle ∠2 = ∠5 = ∠15 = 125, ∠11 = 88, ∠3 = ∠9 = ∠13 =  102°, ∠4 = ∠14 = 78°, ∠7 = 37, ∠8 = 41, ∠1 = ∠6 = ∠10 = 16 = 55°.

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Alexander's white paint will be more lighter.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that in art class students are mixing black and white paint to make gray paint. Allison mixes 1 cup of black paint and 2 cups of white paint. Alexander mixes 6 cups of black paint and 11 cups of white paint.

We will compare the percent of white paint in a mixture.

We can write -

Therefore, Alexander's white paint will be more lighter.

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The equation 15 - x = 7 models the scenario because it represents the decrease in the number of cats that the zoo now nurses. It can be read as "15 (the number of cats originally) minus x (the number of cats moved) equals 7 (the number of cats the zoo now nurses)".

is really "x", which oddly enough is the 100%, but we also know that 0.40% of "x" is 29, so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 29& 0.40 \end{array} \implies \cfrac{x}{29}~~=~~\cfrac{100}{0.40}\implies \cfrac{x}{29}=\cfrac{100}{~~ \frac{ 40}{100 } ~~}\implies \cfrac{x}{29}=\cfrac{10000}{40} \\\\\\ \cfrac{x}{29}=250\implies x=7250[/tex]

Answer:

61

Step-by-step explanation:

√(2+3)^2+(2+4)^2

=√5^2+6^2

=√25+36

=√61

So the number is 61

Answer:

60

Step-by-step explanation:

15x3=45

5x3=15

15+45=60

(a) f(x) =  [tex]log_2(x)[/tex] is a logarithmic function

(b) g(x) = ∜x is a root function

(c) h(x) = [tex]2x^3/(1 - x^2)[/tex] is a rational function

(d) u(t) = 1 - 1.1t + [tex]2.54t^2[/tex] is a polynomial of degree 2

(e) v(t) = [tex]5^t[/tex]is an exponential function

(f) w(θ) = sin θ [tex]cos^{2}\theta[/tex] is a trigonometric function.

(a) f(x) = [tex]log_2(x)[/tex] is a logarithmic function. Logarithmic functions have the logarithm of the independent variable as the output. Here, the logarithm base is 2.

(b) g(x) = ∜x is a root function. Root functions have the square root or higher roots of the independent variable as the output. Here, the root is a cube root.

(c) h(x) = [tex]2x^3/(1 - x^2)[/tex] is a rational function. Rational functions are functions that are expressed as the quotient of two polynomials. Here, the numerator is a cubic polynomial and the denominator is a quadratic polynomial.

(d) u(t) = 1 - 1.1t + [tex]2.54t^2[/tex] is a polynomial of degree 2. Polynomials are functions that are expressed as a sum of powers of the independent variable, with coefficients. The degree of a polynomial is the highest power of the independent variable.

(e) v(t) = [tex]5^t[/tex] is an exponential function. Exponential functions have the independent variable as the exponent. Here, the base is 5.

(f) w(θ) = sin θ [tex]cos^{2}\theta[/tex] is an algebraic function and a trigonometric function. Algebraic functions are functions that can be expressed using arithmetic operations and algebraic expressions. Trigonometric functions are functions that involve the ratios of the sides of a right triangle. Here, the function is a combination of sine and cosine functions.

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The complete question is -

Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.

(a) f(x) =  [tex]log_2(x)[/tex]    

(b) g(x) = ∜x    

(c) h(x) = [tex]2x^3/(1 - x^2)[/tex]    

(d) u(t) = 1 - 1.1t + [tex]2.54t^2[/tex]                    

(e) v(t) = [tex]5^t[/tex]    

(f) w(θ) = sin θ [tex]cos^{2}\theta[/tex]

Answer:

y=-3x+7

its the same thing  

Step-by-step explanation:

The expression for (h·g)(x) is 4x²+17.8x+19.8.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are g(x)=9+4x and h(x)=x+ [tex]2\frac{1}{5}[/tex].

Now, (h·g)(x)=h(x)×g(x)

= (x+ [tex]2\frac{1}{5}[/tex])×(9+4x)

= (x+11/5)×(9+4x)

= 9x+99/5+4x²+44x/5

= 9x+19.8+4x²+8.8x

= 4x²+17.8x+19.8

Therefore, the expression for (h·g)(x) is 4x²+17.8x+19.8.

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The fraction does the third girl gets is 3c - b/3c

A fraction can be defined as the part of a whole number or element.

The different types of fraction are;

From the information given, we have that;

3 girls shares an amount of money

The eldest = b/3x

The youngest = b/6c

This is represented as;

1 - b/3c + b/6c

Add the fractions

1 - 2b - b /6c

add the values

1 - 3b/6c

1 - b/3c

3c - b/3c

Hence, the expression is 3c - b/3c

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The required  sum of the first n odd numbers is equal to n².

The first few odd numbers are 1, 3, 5, 7, 9, 11, and so on. When we add up the first few of these numbers, we get the following sums:

1 = 1

1 + 3 = 4

1 + 3 + 5 = 9

1 + 3 + 5 + 7 = 16

1 + 3 + 5 + 7 + 9 = 25

We can see that the nth odd number is equal to 2n - 1. And the sum of the first n odd numbers is equal to n². This can be verified geometrically by considering a square with sides of length n.

The sum of the first n odd numbers can be thought of as the sum of the diagonal elements of the square, which forms a square of length n.

Thus, the sum of the first n odd numbers is equal to n².

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Drone 1 is traveling faster than Drone 2.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The table and equation below show the proportional relationship between time, in seconds, x, and distance traveled, in feet, y, for two drones.

For drone 1;

The equation is,

⇒ y = 6x

For drone 2;

x = 8, 10, 13

y = 24, 30, 39

Now, For drone 1;

The distance in 8 seconds is,

⇒ y = 6x

⇒ y = 6 × 8

⇒ y = 48

The distance in 10 seconds is,

⇒ y = 6x

⇒ y = 6 × 10

⇒ y = 60

Thus, Drone 1 is traveling faster than Drone 2.

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