The line l cuts the y-axis at (0,5).
l also passes through the point (2, 1).
find the equation of the line which is parallel to l and which passes through the point
(3,0).

One is a unique number as it is only a positive integer that is neither prime nor composite.

If the numeral is a positive integer and there are no duplicate digits, it will be considered unique. The fact that one is the only positive integer that is neither prime nor composite makes it a unique number. It is the only positive integer that can be divided by each other and itself. As a result, only one can be regarded as the lowest common denominator among all other integers.

Given that it is the identity element for multiplication, every integer multiplied by one equals the original number. Additionally, it is the additive identity element, which means that any integer plus one equals itself. Every number may be stated as a power of one, which is the foundation of the number system.

Read more about the unique numbers on:

https://brainly.com/question/27963346

#SPJ4

Answer:

A) 2 B) 6 C)0

Step-by-step explanation:

A)

f(6) = 6/3 - 1 = 1

g(3) = 2(3) - 5 = 1

f(6) + g(3) = 1 + 1 = 2

B)

Find the inverse of the function g(x)

x = 2y-5

-2y = -x-5

2y = x+5

y = (x+5)/2

g^-1(7) = 12/2 = 6

C)

g^-1(7) = 6

Find the inverse of the function f(x)

x = y/3 - 1

x+1 = y/3

y = 3x+3

f^-1(1) = 3+3 = 6

g^-1(7) – f^-1(1)​ = 6-6 = 0

Since 4x2+1 cannot equal 0, the solution to the above expressions issue indicates that (4x20+1) has no real factors.

It is necessary to substitute a number for each variable and conduct arithmetic operations in order to verify an algebraic equation. The response variable in the example above is comparable to 6, as 6 plus 6 = 12. Knowing the values of the variables will enable us to replace the original values with those known, allowing us to evaluate the expression.

Here,

It is significant to remember that the current ratio of a term's coefficient

Words 8x3 and 2x have a coefficient ratio of 8:2 (4:1), whereas phrases 12x2 and 3 have a coefficient ratio of 12:3 (4:1) This implies that the original sentence should be divided into the following categories: This indicates that the original phrase, which is written as, should be combined as follows:

=> (8x³+2x)(12x²+3)=2x(4x²+1))3(4x²+1),

before figuring out that (4x2+1)=(2x3)(4x2+1) is the common component.

Since 4x2+1 cannot equal 0 due to the fact that 4x20 for x R, (4x20+1) has no real factors. Since 4x2+1 cannot equal 0, the solution to the above expression issue indicates that (4x20+1) has no real factors.

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

Let ww represent the number of hours washing cars, and tt represent the number of hours tutoring.

The inequality representing the total number of hours Arianna must work between both jobs is:

ww + tt ≥ 10

This inequality states that the number of hours spent washing cars plus the number of hours spent tutoring must be greater than or equal to 10 hours. This represents all possible combinations of hours washing cars and hours tutoring that Arianna can work in a given week while meeting the requirement that she must work no less than 10 hours altogether between both jobs.

The type of data that would be used to describe the number of students enrolled at Evergreen Valley College is quantitative - discrete.

What is algebra ?

Algebra is a branch of mathematics in which arithmetic operations and other formal manipulations are applied to abstract symbols rather than specific numbers. Geometry is the branch of mathematics that deals with the shape of objects, their spatial relations, and the properties of the space the objects are in.

It's going to be quantitative because the number of students at a college can only take on certain numerical values, those that are into jurors continuous. All values can be taken by quantitative variables. Maybe 479.4, not just 479 or 480.

The type of data that would be used to describe the number of students enrolled at Evergreen Valley College is quantitative - discrete.

To learn more about algebra visit : brainly.com/question/24875240

#SPJ4

Answer:

Quantitative discrete due to the fact that’s the current quantity

Answer:

Step-by-step explanation:

1. When multiplying, exponents must be added, not multiplied as shown in the problem.

Error: [tex]3(-2)x^{2*4}[/tex]

Correct: [tex]3(-2)x^{2+4} = -6x^{6}[/tex]

2. The coefficients have been added, not multiplied.

Error: [tex](4+3)a^{2+5}[/tex]

Correct: [tex](4*3)a^{2+5} = 12a^{7}[/tex]

3. The exponent was miscalculated.

Error: [tex]x^{6+3}[/tex]

Correct: [tex]x^{6+3+1} = x^{10}[/tex]

4. The exponent was miscalculated, the two values have different bases, so they cannot be calculated using that method.

Error: [tex]6^{4+3}[/tex]

Correct: [tex]3^4*2^3 = (3*2)^3*3 = 3*6^3[/tex]

Answer:

See below.

Step-by-step explanation:

Given:

[tex]\left(3x^2\right)\left(-2x^4\right)=3\left(-2\right)x^{2 \cdot 4}=-6x^8[/tex]

Error:

The exponent product rule has been used incorrectly.

The exponents should be added not multiplied.

Correction:

[tex]\left(3x^2\right)\left(-2x^4\right)=3\left(-2\right)x^{2 +4}=-6x^6[/tex]

Correct answer:

[tex]-6x^6[/tex]

------------------------------------------------------------------------------------------

Given:

[tex]4a^2 \cdot 3a^5=(4+3)a^{2+5}=7a^7[/tex]

Error:

The numbers 4 and 3 have been added when they should have been multiplied.

Correction:

[tex]4a^2 \cdot 3a^5=(4 \cdot 3)a^{2+5}=12a^7[/tex]

Correct answer:

[tex]12a^7[/tex]

------------------------------------------------------------------------------------------

Given:

[tex]x^6 \cdot x \cdot x^3=x^{6+3}=x^9[/tex]

Error:

The exponent of the x-term has been ignored:  x = x¹

Correction:

[tex]x^6 \cdot x \cdot x^3=x^{6+1+3}=x^{10}[/tex]

Correct answer:

[tex]x^{10}[/tex]

------------------------------------------------------------------------------------------

Given:

[tex]3^4 \cdot 2^3=6^{4+3}[/tex]

Error:

The exponent product rule is only applicable when the bases are the same:  a⁴ · a³ = a⁴⁺³

Correction:

[tex]3^4 \cdot 2^3=81 \cdot 8=648[/tex]

Correct answer:

[tex]648[/tex]

Answer:

To find the cost price (C.P.) of the watch, we need to use the following formula:

C.P. = Selling Price / (1 - Loss Percentage)

In this case, we know that the Selling Price is Rs 484 and the Loss Percentage is 12%. To use this formula, we first need to convert the Loss Percentage to a decimal:

12% = 0.12

Now we can plug in the values into the formula:

C.P. = 484 / (1 - 0.12)

Solving for C.P., we get:

C.P. = 484 / 0.88

C.P. = Rs 550

Therefore, the cost price (C.P.) of the watch is Rs 550.

Therefore , the solution of the quadratic equation comes out to be x value is 4.

The quadratic solution x = ax2 + foo + c=0 is a regression model for one variable equations. According to the First Theorem of Algebra, this polynomial only has one solution because of its second order. Both straightforward and complex solutions are viable options. The term "quadratic formula" refers to a formula with four variables. According to this, there can only be a single squared word present. Mathematical variables or variables a, b, and c are often used to represent the unknown variable "X" in the formula "ax2 + bx + c = 0," which is frequently used to solve arithmetic problems.

Here,

Given :

=> 4x²+ 6x-2+6 - 4x² - 6x

=>  4x² - 4x² + 6x -6x -2 +6

=> 0 + 0 +4

=> 4

Therefore , the solution of the quadratic equation comes out to be x value is 4.

To know more about quadratic equation visit:

https://brainly.com/question/30098550

#SPJ4

duri will stay warm in their sleeping bag when the temp is at least 30f. the situation will be written in inequality as  30F ≤ T. An inequality is used to express a comparison between two values.

In this case, the inequality states that the temperature, represented by the variable T, must be less than or equal to 30F in order for the person in the sleeping bag to stay warm. This means that if the temperature is 30F or higher, the person in the sleeping bag will stay warm.   Inequalities use a few different symbols to represent the comparison relationship between two values.

In this case, the symbol used is ≤, meaning "less than or equal to". This symbol is used to indicate that the temperature must be 30F or lower in order for the person in the sleeping bag to stay warm.  In more general terms, an inequality represents a comparison between two values that can be expressed on a number line.

To know more about inequality refer to the link  brainly.com/question/30231190

#SPJ4

Angles BAD and ADC are both right angles (definition of a rectangle).

Rectangle ABCD is provided in Statement 1.

Because the opposing sides of a rectangle are congruent, claim number two

By the reflexive quality of congruence, according to Statement 3. Statement

Because a rectangle's angles are all right angles, claim 4

Statement 5: Because all right angles are congruent, angles BAD and ADC are congruent.

Statement 6: According to SAS, triangles BAD and CDA are congruent.

7th statement: CPCTC

The statement Statement 4 was omitted:

Angles BAD and ADC are both right angles (definition of a rectangle) is statement below completes Anastasia's proof.

To learn more about Angles refer to:

https://brainly.com/question/25716982

#SPJ1

Answer:

x=27.5 hope it helps you..... and hi

Answer:

Step-by-step explanation:

1....Re-order terms so constants are on the left;

2(x - 3) =49

2.. Distribute;

2x-6 =49

3... Add 6 to both sides;

2x-6+6=49+6

4... Simplify;

2x=55

5..Divide both sides by the same factor;

2x=55

[tex]\frac{2x}{2}[/tex]  = [tex]\frac{55}{2}[/tex]

6...Simplify;

x=[tex]\frac{55}{2}[/tex]

The minimum number of terms needed to find the sum of the infinite series 1/n2 with an error less than 0.001 is 11.

1. Calculate the sum of the first 10 terms of the series.

S10 = 1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/36 + 1/49 + 1/64 + 1/81 + 1/100

   = 2.405

2. Calculate the 11th term of the series.

T11 = 1/121 = 0.00826

3. Calculate the sum of the first 11 terms of the series.

S11 = S10 + T11 = 2.405 + 0.00826 = 2.41326

4. Calculate the 12th term of the series.

T12 = 1/144 = 0.00694

5. Calculate the difference between the sum of the first 11 terms and the sum of the first 12 terms.

Difference = S11 - S12 = 2.41326 - (2.41326 + 0.00694) = -0.00694

6. Check if the difference is less than 0.001.

Yes, the difference is less than 0.001. Therefore, the minimum number of terms needed to find the sum of the infinite series 1/n2 with an error less than 0.001 is 11.

learn more about number here

https://brainly.com/question/10547079

#SPJ4

The US GDP (Gross Domestic Product) for 2014 was reported to be the nearest hundredth is 17. 56 trillion dollars. The current US population is about 320 million people to the nearest hundredth.

The gross domestic product (GDP) is a commonly used indicator of the value added produced by the production of goods and services in a country over a certain time period (GDP). As a result, it also takes into account the money made from that manufacturing or the sum of money spent on finished goods and services (fewer imports). Although the gross domestic product (GDP) is the most important indicator for gauging economic activity, other metrics may be better suitable for gauging people's material well-being.

To learn more about hundredth here:

https://brainly.com/question/29016830

#SPJ4

 If a symmetric matrix can be inverted into a diagonal matrix using another matrix, then it is diagonalizable. Accordingly, it may be said that there is a matrix P that can be inverted such that P-1 * A * P = D, where D is a diagonal matrix and A is the symmetric matrix. The diagonal entries of D are the appropriate eigenvalues, while the columns of P are the eigenvectors of A.

  The matrix P is the foundation of the vector space because its columns are linearly independent and it is invertible. The inner product of any two different eigenvectors is 0, as A's eigenvectors are orthogonal to one another due to its symmetry.

 We can divide each eigenvector by its norm to get an orthonormal basis from this collection of eigenvectors. As a result, a group of eigenvectors that are orthonormal to one another and serve as the vector space's orthonormal basis are produced.

  Therefore, A symmetric matrix is diagonalizable and has an orthonormal eigen basis  consisting of orthonormal eigenvectors, which can be obtained by dividing each eigenvector by its norm.

 To know more about matrices at :

brainly.com/question/12088021

#SPJ4

The probability that x equals 1 is 0.3151.

What are examples and probability?

The quantity of success-producing options. the total number of outcomes that could occur.

                     For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). We specify P(heads) = 12.

0.05x0.6302 1!(10-1)! =10x0.05x0.6302 = 0.3151 ">

Since the binomial distribution is a discrete distribution, it accepts discrete random variables. This shows that the random variable x can only accept integer values and cannot take the value 0.5000 because it is on an interval scale (continuous). Therefore, the statement that the maximum probability happens when x equals 0.5000 is false.

Learn more about probability

brainly.com/question/30034780

#SPJ4

With 20 counselors, there should be 250 boys at Laura's summer camp.

To determine how many boys should be at camp with 20 counselors, we can use the proportion of boys to counselors that existed at the camp when there were 200 boys and 16 counselors.

The proportion of boys to counselors when there were 200 boys and 16 counselors is 200/16 = 12.5 boys per counselor.

If we want to know how many boys should be at camp with 20 counselors, we can use this proportion and the number of counselors we have (20) to calculate the number of boys.

To calculate this, we can use the following formula:

Number of boys = (Proportion of boys to counselors) x (Number of counselors)

So for 20 counselors, the number of boys should be:

12.5 x 20 = 250 boys

So with 20 counselors, there should be 250 boys at Laura's summer camp.

To learn more about the Proportion, visit:

brainly.com/question/25938439

#SPJ4

Solution Grade 7 is a saturated, neutral pH liquid solution made up of a mixture of water and salt, or other electrolyte, with a specific gravity of 1.0, a boiling point of 100°C, and a high electrical conductivity.

Solution Grade 7 is a type of liquid solution used in science experiments. It is typically made up of a mixture of water and salt, or some other electrolyte. It has the following properties:

1. It is a saturated solution, meaning that it contains the maximum amount of dissolved solute that the solvent can hold at a given temperature.

2. It has a neutral pH, meaning that it is neither acidic nor basic.

3. It has a specific gravity of 1.0, meaning that it has a density equal to that of pure water.

4. It has a boiling point of 100°C (212°F), meaning that it boils at the same temperature as pure water.

5. It has a high electrical conductivity, meaning that it can easily conduct electricity.

Learn more about grade here

https://brainly.com/question/29618342

#SPJ4

Answer: The father will be twice as old as the son in 24 years.

Step-by-step explanation:

12+24=36

48+24=72

72/2=36

Hope this helps!!!

According to the Pythagorean theorem length of the third side is  [tex]\sqrt{5}[/tex].

What is Pythagorean theorem?

The hypotenuse square in a right-angled triangle is equal to the sum of the squares of the other two sides, according to the Pythagoras theorem. A and B are the triangle's two legs, and C is the hypotenuse, hence this theorem can be written as c2 = a2 + b2. These triangles are also referred to as Pythagorean triangles.

Here in given right triangle side = 2 and hypotenuse = 3.

Now using Pythagorean theorem then,

=> [tex]side^2+side^2=hypotenuse^2[/tex]

=> [tex]side^2+2^2=3^2[/tex]

=> [tex]side^2[/tex]+4=9

=>  [tex]side^2[/tex] = 9-4 = 5

=> side = [tex]\sqrt{5}[/tex]

Hence third side length of the right triangle is [tex]\sqrt{5}[/tex].

To learn more about Pythagorean theorem refer the below link

https://brainly.com/question/343682

#SPJ1

The difference between the estimate in part a and the actual value calculated in part b is the equation (Estimate - Actual Value). In this case, the equation is (50 - 41.2) = 8.8.

An equation is a mathematical statement that two expressions are equal. It is usually written using an equal sign (=) and may also include numbers, variables, operators, and other mathematical symbols. Equations are used to describe relationships between different values, such as the area of a circle or the slope of a line. Equations can be used to solve for a single unknown value, or to find the relationship between different values.

Given that the difference between the estimate and actual value is 8.8, I think my estimate was reasonable. This is because the difference between the estimate and actual value is relatively small, which suggests that my estimate was close to the actual value. Therefore, my estimate was reasonable.

To know more about Equation click-
https://brainly.com/question/2972832
#SPJ4

Check the picture below.

Answer: The height above ground at which the tree broke is 8 meters.

Step-by-step explanation:

Let the standing part of tree be of 'l' meters.

Therefore the broken part is of 24 - l meters.

By using trignometric functions

sin(30°) =[tex]\frac{Perpendicular}{Hypotenuse}[/tex]

[tex]\frac{1}{2}[/tex]=[tex]\frac{l}{24-l}[/tex]

⇒ 2 × l = 24 - l

⇒3 × l = 24

⇒ l = 8

∴ The height above ground at which the tree broke is 8 meters.

The difference between the given values of |-10| and 19 is - 9

What is an algebraic expression ?

Algebraic expression can be defined as the combination of variables , constants and exponents .

Algebraic expressions are the idea of expressing numbers the use of letters or alphabets with out specifying their actual values. The fundamentals of algebra taught us the way to explicit an unknown value the use of letters such as x, y, z, and so on. these letters are called here as variables. An algebraic expression may be a aggregate of both variables and constants. Any cost this is placed before and extended by way of a variable is a coefficient.

Given values ,

|-10| and 19

the difference ,

|-10| - 19 = 10-19

= -9

Hence, The difference between the given values of |-10| and 19 is - 9

To learn more about algebraic expression from the given link.

https://brainly.com/question/953809

#SPJ1

Therefore , the solution of the given problem of median comes out to be  R students still present (maximum) =35

The number that precisely falls in the center of a sorted collection is the median value. An average or maximum probability metric is the difference between the initial and final 50% of the data. Different algorithms are employed to compute the average and mode depending on if you do have an unusual or perhaps even number of data points.

Here,

Median is 55

P :Q: R :S :average of 45 :50: 55 :65

The number of pupils within every section needs to be as low as possible 

R is a mean

P differs by 1: 10 from the mean.

Q is 1.5 away from the mean.

Then S will just have three students, or three times five, to keep the population's mean constant.

R students still present (maximum):

=> 40 - 1- 1-3

=> 35

Therefore , the solution of the given problem of average comes out to be  R students still present (maximum) =35

To know more about median , visit

brainly.com/question/28060453

#SPJ4

Answer:

i think u are in 10th standard srry if i am wrong

B. The third term in the sequence has a value of 1.

The notation f(3) = 1 means that the value of the function f at the input 3 is equal to 1. In other words, when the input of the function is 3, the output is 1.

This notation does not indicate anything about the first term or common difference or common ratio of the sequence.

So, theta = arctan(sqrt(500^2-d^2) / d) would give us the angle between the ground and the ladder where d is distance from the base of the ladder to the building.

The angle between the ground and the ladder can be found using the inverse tangent function (also known as arctan) and the Pythagorean theorem.

First, we need to find the ratio of the height of the ladder to the distance from the base of the ladder to the building. This ratio is known as the tangent of the angle between the ground and the ladder.

Let h be the height of the ladder and d be the distance from the base of the ladder to the building.

tan(theta) = h/d

Next, we can use the Pythagorean theorem to find the value of h:

d^2 + h^2 = 500^2

Now we can substitute the value of h in the first equation.

tan(theta) = sqrt(500^2-d^2) / d

To find the angle between the ladder and the ground, you can use the inverse tangent function on the above equation.

theta = arctan(sqrt(500^2-d^2) / d)

To find the exact value of the angle, you would need to know the value of d (distance from the base of the ladder to the building).

To learn more about inverse tangent function

visit; brainly.com/question/29342276

#SPJ4

Answer:

Hi!

slope of a line passing through the point (2,1) and (2,-1)

as you can see the abscisas of the point is same which means x-axis

now by formula

m = slope y2-y1/x2-x1

-9-1/2-2

-10/0 when there's zero in denominator this mean answer is infinity ♾️

This mean line is parallel to Y-axis

so when we're hanging out

Answer: the slope is undefined

Step-by-step explanation:

Slope = y2-y1 divided by x2-x1

slope = -9 - 1 divided by 2 - 2

slope = -10 divided by 0

Any slope with 0 as the denominator is always undefined.

The equation for the vertex's x-coordinate and the axis of symmetry is:

[tex]$x=\frac{-b}{2 a}[/tex]

The standard form of a parabola is y = a x² + + bx + c, where [tex]$a \neq 0$[/tex]

A parabola's vertex is its minimum or maximum point. The vertex is the smallest point and the parabola widens upward if a>0. Vertex is maximal point and parabola widens downward if a=0.

You must ascertain the x and y coordinates in order to determine the vertex.

The equation for the vertex's x-coordinate and the axis of symmetry is:

[tex]$x=\frac{-b}{2 a}[/tex]

To find the y-coordinate of the vertex, substitute the value for x into the equation and solve for y.

[tex]$y=a\left(\frac{-b}{2 a}\right)^2+b\left(\frac{-b}{2 a}\right)+c[/tex]

To learn more about vertex, refer to:

https://brainly.com/question/1503262

#SPJ1