A contractor can spend at most $250 a day on operating costs and payroll. It costs $45 each day to operate the forklift and $60 a day for each crew member. Write an inequality to represent the contractor's budget for the day.

60x + 45 ≥ 250
60x + 45 ≤ 250
60 − 45x ≥ 250
60 − 45x ≤ 250

[tex]x~~ : ~~(x+5)~~ = ~~4~~ : ~~5\qquad \implies \qquad \cfrac{x}{x+5}=\cfrac{4}{5} \\\\\\ 5x=4x+20 \implies x=20[/tex]

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?.

The sine function graphed is given as follows:

y = 0.5sin(x - π/4).

The sine function for this problem is defined as follows:

y = Asin(Bx - C).

For which the parameters are given as follows:

The difference between the highest value and the lowest value is of 1, hence the amplitude of the function is givne as follows:

2A = 1

A = 1/2

A = 0.5.

The period of the function is of 2π, hence the parameter b is obtained as follows:

2π/B = 2π

B = 1.

The sine function, without phase shift, should pass through the origin, while the function here was shifted right π/4 units, hence the parameter C is given as follows:

C = π/4.

Hence the function is:

y = 0.5sin(x - π/4).

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Answer:

2.29 pounds.

Step-by-step explanation:

The following is the analysis for the response to this query:

There must be some relationship among both the volume and the weight.

According to the given label's information, one cup weighs 99 grams. Given that there are 99/453.6 pounds for every cup as well as you require 7*1 1/2 cups, multiplying 10.5 cups by 99/453.6 pounds for every cup results in 2.3 pounds. A pound (avoirdupois) is defined as 453.6 grammes.

Another way to write this would be:

7 (pecan pie) * 1.5 (cup/pecan pie) * 99 (gram/cup) * 0.0022 (pounds/gram) = 2.292 pounds

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There are several methods that can be used to solve a system of nonlinear equations, but three common ones are: substitution method, elimination method and graphing method.

Substitution method: This involves isolating one variable in one equation and substituting it into the other equation to eliminate that variable. You can then solve for the remaining variable and substitute it back into the original equation to find the solution.

Elimination method: This method involves adding or subtracting the equations in such a way as to eliminate one of the variables. Then you can solve for the remaining variable and substitute it back into the original equation to find the solution.

Graphical method: This method involves graphing both equations on the same coordinate plane and finding the point of intersection of the two lines. The coordinates of this point will be the solution to the system of equations.

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A linear expression is in polynomials when it is expressed as the product of it's factor

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1. For example, x² is a variable raised to the second power, but x is a variable raised to the first power.

When two linear factors are expressed together the result forms a polynomial.

A polynomial is an expression in which the power of it's variable is higher than 1. quadratic expression is also an example of polynomial.

For example if an expression is given as (x+2)(x+3). The result of the expression will give x²+5x+6 which is a quadratic expression and a polynomial.

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To write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10.

To write 10 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.

In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 10 + Number = N+10.

This notation means that we are adding 10 to a number, which results in N+10. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+10.

Another way to write 10 more than a number is to use the phrase "10 plus a number". This phrase indicates that we are adding 10 to a number to get N+10.

Therefore, In short, to write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10. This means that we are adding 10 to a number, resulting in N+10. It can also be written as "10 plus N", indicating the same operation.

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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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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 )

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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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.

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:

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]

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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Answer:

that even a complete problem?

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

Cross multiply

[tex]x + 147° = 180°[/tex]

simplify

x = 180° - 147°

answer : x = 33°

Answer:

4

Step-by-step explanation:

8x + 15 = 5.5x +25

so 2.5x =10

x=4

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: Commutative, associative, distributive

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

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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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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Answer: it mean 7-9.

Step-by-step explanation:

7 is smaller than 9, so the answer is going to be negative. I like to do

7-9

Is basically just 9-7, just put a negative label

So 7-9 can be solved as 9-7=2 slap on a negative sign and -2! Hope this helps!

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

The solution is the set of values for the two variables (x, y) that satisfy both equations.

To solve a system of two equations with two variables that are both quadratic (2nd degree), you can use the following steps:

Write the two equations in standard form, which is ax² + bx + c = 0 for each equation, where a, b, and c are coefficients.

Solve each equation separately for one variable by factoring or by using the quadratic formula.

Substitute the value of one variable from one equation into the other equation, and solve for the other variable.

Substitute the value of the other variable from the previous step back into one of the original equations to find the value of the first variable.

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Answer:

#1) [tex]\frac{1}{7}[/tex]

#2) 4

Step-by-step explanation:

#1) 37x=9x+4

37x=9x+4

-9x

28x=4

28   28

answer: [tex]\frac{4}{28} = \frac{1}{7}[/tex]

#2) 2x+3=11

2x+3=11

        -3

2x= 8

2     2

answer: [tex]\frac{8}{2} =4[/tex]

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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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°

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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