The price of a new car is $29990. If the sales tax rate is 6.5%, then how much sales tax is being charged? What is the total cost of the car including tax?

Two different methods used to solve the system of linear equation is given by :

a. Elimination method.

b. Substitution method

As given in the question,

Let us consider system of linear equation  be :

2x + 5y = 3  __(1)

3x + 4y = 1  __(2)

a. Elimination method :

Multiply (1) by 3 and ( 2) by -2 and add them we get,

6x + 15y = 9

-6x -8y = -2

     7y  = 7

⇒ y = 1

b. Substitution method :

Substitute the value of y = 1 in any one equation we get,

2x + 5(1) = 3

⇒ 2x = 3 - 5

⇒ x = -1

While solving two equation substitute the value of one variable from one equation into the other.

Therefore, the two methods used to solve the system of linear equation is equal to :

a. Elimination method.

b. Substitution method

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It will take 20.6 hours to paint the house if both painter A and painter B worked together.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Suppose we have two ratio p : q and r : s.

If both these ratios are proportional, then we can write it as p: q : : r : s.

This is same as p : q = r : s or p/q = r/s

Let F represent the house fully painted.

Painting done by painter A in 50 hours = F

Painting done by painter A in 1 hour = F/50

Painting done by painter B in 35 hours = F

Painting done by painter B in 1 hour = F/35

If they both paint together,

Painting done by painter A and painter B in 1 hour = F/50 + F/35

                                                                                    = 85/1750 F

                                                                                    = 17/350 F

Time taken to paint 17/350 F = 1 hour

Time taken to paint F = 1 / (17/350)

                                    = 20.588

                                    ≈ 20.6 hours

Hence time taken to paint the house by both working together is 20.6 hours.

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[tex] \frac{x}{3° } + 49° = 180° \\ [/tex]

Cross multiply

[tex]x + 147° = 180°[/tex]

simplify

x = 180° - 147°

answer : x = 33°

The slope of y = -3x + 3 is -3, it's the coefficient of the x variable.

What is slope ?

Slope, also known as gradient, is a measure of the steepness of a line. It is the ratio of the change in the y-coordinate to the change in the x-coordinate between any two distinct points on the line. It is represented by the letter "m" in the slope-intercept form equation of a line y = mx + b, where m is the slope, x is the independent variable, y is the dependent variable and b is the y-intercept, the point where the line crosses the y-axis.

The slope of a line is a measure of its steepness or incline. It is the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run) between two points on the line. The slope is represented by the letter "m" and it is the coefficient of the x variable in the equation of the line y = mx + b, where b is the y-intercept.

In this case, the equation of the line is y = -3x + 3,

The slope of y = -3x + 3 is -3, it's the coefficient of the x variable.

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The three types of multiplication properties are given by :

1. Commutative property : a × b = b × a , a, b ∈R

2. Identity property : a × 1 = a , a ∈ R

3. Distributive property : a × ( b + c ) = a × b + a × c , a, b, c ∈R.

As given in the question,

Three types of multiplication property is given by :

Let us consider variable a, b, c belongs to real number R.

1. Commutative property :

Order of the multiplication having no affect on the final outcome.

a × b = b × a

Example : 5 × 4 = 20

4 × 5 = 20

2. identity property :

Multiplying one to any real number always gives the same number.

a × 1 = a

Example : 3 × 1 = 3

3. Distributive property :

Adding first two numbers and then multiplying or first multiplying each pair and then adding result remain same.

a × ( b + c ) = a × b + a × c

Example:

5 × ( 2 + 1 )  = 5 × 2 + 5 × 1

Therefore, the three types of multiplication property are given by :

1. Commutative property

2. Identity property

3. Distributive property

The above question is incomplete , the complete question is :

What are the 3 types of multiplication properties ?.

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Answer: Commutative, associative, distributive

Step-by-step explanation: I hope this helped!

To find the factored form of the quadratic equation x^2 + 8x + 16, we can use the technique of factoring by grouping.

First, we write the equation in the form of (x^2 + ax + b) + (x + c) = 0

x^2 + 8x + 16 = 0

Next, we find two numbers that multiply to b and add to a, in this case, b = 16 and a = 8

We can factor out a common factor of x from the first two terms and x + 4 from the last two terms: x^2 + 8x + 16 = (x^2 + 8x) + (16)

Finally, we can factor out a common factor of x + 4 from both terms:

x^2 + 8x + 16 = x(x + 8) + 4(4)

So the factored form of x^2 + 8x + 16 is (x+4)^2.

You can also find the factored form of the quadratic equation x^2 + 8x + 16 by using the difference of squares method:

x^2 + 8x + 16 = (x+4)^2

It's worth noting that this is a perfect square trinomial, which means that it can be factored into the square of a binomial.

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The difference between the greatest 6-digit and smallest 6-digit numbers is 899999.

The aim is to find the smallest and largest 6-digit numbers, and then we need to find how many numbers are between these two values.

Let's start by finding the smallest 6-digit number.

We know that 0 is the smallest digit that can not be used in the highest place value, so we will consider the next smallest digit; that is, 1 and 1 can be used in the highest place value.

Thus, we can create the required 6-digit smallest number with 0 and 1.

Hence, the smallest 6-digit number is 100000.

Now, we will discover the largest 6-digit number.

As we know, the largest digit is 9, which can be used anywhere. So, we will form the largest 6-digit number with the digit 9.

Thus, the largest 6-digit number is 999999.

Next, we need to find the difference between these two values.

So, we can determine the difference between the smallest 6-digit number and the largest 6-digit number by subtracting the smallest from the largest.

Thus, we get,

⇒999999−100000

⇒899999

Hence, 899999 is the difference between the smallest 6-digit and the largest 6-digit numbers.

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Answer:

but it is not possible to determine the value of X with the information provided. The numbers 3, 4, 5, 6, and 8 are all different values, and without any additional context or information, it is impossible to determine which one is X.

It would be helpful if you could provide more information such as an equation or some context, to help determine the value of X.

The point opposite to point A is not labeled in the number line.

A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.

Given a number line,

for any number line points left of zero are negative numbers and points right to the zero are positive numbers,

Given points,  Point A is 2 units to the right = +2

Point B is 4 units to the right = +4

Point C is 2 units to the right of zero = +2

Point D is 3 units to the left of zero = -3

Point E is 5 units to the left of zero = -5

so the point opposite to +2 is -2 which is 2 units left of zero,

but it is not given on the labeled points.

Therefore, the opposite point of A is not labeled.

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Answer:

89

Step-by-step explanation:

fibonacci sequence is a famous sequence where each number is the sum of the last two.

Therefore :

34+55 will give us the next number which is 89

Answer:

u = -69

Step-by-step explanation:

Now we have to,

→ find the required value of u.

The equation is,

→ -11u = 759

Then the value of u will be,

→ -11u = 759

→ u = 759/-11

→ u = -(759/11)

→ [ u = -69 ]

Hence, the value of u is -69.

Answer:

(3, 8 )

Step-by-step explanation:

given 2 points (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = P (1, 6 ) and (x₂, y₂ ) = Q (5, 10 ) , then

midpoint = ( [tex]\frac{1+5}{2}[/tex], [tex]\frac{6+10}{2}[/tex] ) = ( [tex]\frac{6}{2}[/tex] , [tex]\frac{16}{2}[/tex] ) = (3, 8 )

Answer:

x = 39

m ∠1 = 63°

m ∠2 = 117°

Step-by-step explanation:

m∠1 + m∠2 = 180° since they are adjacent linear angles lying on the same straight line

Therefore x + 24 + 3x = 180

4x + 24 = 180

4x = 180-24 = 156

x = 156/4 = 39

Therefore x = 39 (a)

FOr (b) substitute this value of x = 39 into each equation

m∠1 = x + 24 = 39 + 24 = 63°

m∠2 = 3x = 3(39) = 117°

The volume of solid₁ and solid₂ is related with y = x + 1 where x = 1 × 2 units.

The amount of actual space a 3D object takes up is measured by its volume. It represents the area in three dimensions of a two-dimensional shape. It is measured in cubic units like cm3, for example. This can be determined by multiplying the object's length, height, and width.

Based on a fundamental equation, which is one of the first equations that students encounter in school, this method of measuring volume was developed. Because it lays the foundation for further equation study, math volume is very important.

We cane see that

y = x + 1

1/2 of 2 = x/2 = 1

x = 2

Lets find the value of the variables

y = (2)+ 1

y = 3

Volume of solid₁ = x × y × 2 = 2 × 3 × 2 = 12 cube unit

Volume of solid₂ = x × y × 2 = 2 × 3 × 2 = 12 cube unit

Thus, the volume of solid₁ and solid₂ is related with y = x + 1 where x = 1 × 2 units.

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A scatter plot or scattergram chart will show the relationship between two different variables or reveals distribution trends.

Now, According to the question:

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.

Use a scatter plot to determine whether or not two variables have a relationship or correlation. Are you trying to see if your two variables might mean something when put together? Plotting a scattergram with your data points can help you to determine whether there's a potential relationship between them.

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There are 198 passengers in each car.

What is division?

The division is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and multiplication. It is the inverse operation of multiplication.

To determine the number of passengers in each car, we need to divide the total number of passengers by the total number of cars.

We know that:

There are 4,752 passengers in total

There are 8 cars per train and 3 trains

So, the total number of cars is 8 cars/train x 3 trains = 24 cars

To find the number of passengers per car, we divide the total number of passengers by the total number of cars:

4,752 passengers / 24 cars = 198 passengers per car.

Hence, there are 198 passengers in each car.

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Answer: [tex]x-\frac{x}{9}[/tex]

Step-by-step explanation:

1) quotient is the answer of a division problem

with that in mind and letting "a number" = x . . .

"The quotient of a number and nine..." would be [tex]\frac{x}{9}\\[/tex]

2) "is less than" always means you but the previous statement BEHIND . . .

[tex]x-\frac{x}{9}[/tex]

Answer:

that even a complete problem?

Answer:

Domain: is -4 ≤ x ≤ 1
which can be expressed in interval notation as

[-4, 1]

Range is -3 ≤ y ≤ 2

or in interval notation: [-3, 2]

Step-by-step explanation:

The domain is the set of x values from minimum to maximum

The range is the set of y values again from minimum to maximum

Minimum value of x = -4

Maximum value = 1

So range is -4 ≤ x ≤ 1 which can be expressed in interval notation as

[-4, 1]

Minimum y-value is -3 and maximum y-value is 2

Range is -3 ≤ y ≤ 2

or in interval notation: [-3, 2]

The second transformation that is applied to rectangle A B C D is a translation.

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Answer:

  9xy² -6x²y +5x³

Step-by-step explanation:

You want the additive inverse of –9xy² + 6x²y – 5x³.

The additive inverse is the value that gives zero when added to the original. It can be formed by changing the signs of the terms in the sum:

  9xy² -6x²y +5x³

On simplifying the given quadratic equation , we get that the solution of the quadratic equation  3x² -14x -5 = 0 are x = -1/3 and  x = 5     .

The Quadratic Equation are given as : 3x² -14x -5 = 0 ;

to find the solutions of this equation , we use the split the middle term method ;

⇒ 3x² -14x -5 = 0 ;

we split "-14" as the sum of -15 and 1 .

⇒ 3x² -15x + x -5 = 0 ;

⇒ 3x(x - 5) +1(x - 5) = 0;

⇒ (3x + 1)(x - 5) = 0  ;

Solving the factors separately ,

we have ;

⇒ 3x + 1 = 0    and   x - 5 = 0  ;

⇒  x = -1/3    and  x = 5  ;

Therefore , the solutions of given quadratic are x = -1/3    and  x = 5 .

The given question is incomplete , the complete question is

What are the solutions of the quadratic equation 3x² -14x -5=0 ?

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Yes, the numbers 2 and 9 are co-prime numbers, i.e., HCF(2,9) = 1.

Two numbers a and b are relatively prime if their only common divisor is 1. If the only highest common factor of two numbers a and b is 1, then a and b are co-prime numbers. In this case,(a, b) is said to be a co-prime pair. Properties of relatively prime numbers:

We have, two numbers say 2 and 9 and we have to check they are co-prime or not. The factors of 2 are 1 and 2. Factors of 9 are 1, 3 and 9. So, highest common factor between 2 and 9 is 1. As 9 and 2 have no common factor other than 1, they are co-prime.

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Complete question:

Is 2 co-prime number with 9?.

Answer: A

Step-by-step explanation:

when you have a number to a negative power, putting it as a fraction under 1 will turn the negative power positive

Answer:c

Step-by-step explanation:

Julie is approximately 40.6 ft away from the base of the tower.

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. One of the main uses of trigonometry is to calculate distances in a triangle when the lengths of two sides and the measure of the angle between them are known.

We can calculate this by using the formula:

Distance = (tower height) / (tan(angle of depression))

Distance = (83 ft) / (tan(49))

Distance = 40.6 ft (rounded to the nearest tenth)

Therefore, Julie is approximately 40.6 ft away from the base of the tower.

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The factor of 9x² 24xy 16y² is (3x−4y)²

A number or other mathematical object is factorized or factored when it is written as the product of numerous factors, usually smaller or simpler things of the same kind.

Factorization in mathematics is the method of dividing a large number into tiny ones that, when multiplied together, give you the original number. Factorization is the split of a number into its factors or divisors.

9x²−24xy+16y²

=(3x)²−24xy+(4y)²

=(3x)²−2(3x)(4y)+(4y)²

Using (a−b)²=a²−2ab+b², we get

=(3x−4y)²

Factorization, also known as factoring, is the process of dividing or decomposing a thing into factors that, when multiplied together, form the original number, matrix, etc.

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