Let x be the number of boys in a family of 4 children. Determine the values of the variable x. please answer.

By setting up and solving the equation based on the work rates of the maids, we find that the faster maid would need 4.5 hours to clean the complete house alone.

Let's denote the time it takes for the faster maid to clean the house alone as x hours and for the slower maid as 3x hours (since she is three times slower). When they clean the house together, their combined work rate is 1 house per 3 hours.

We can set up an equation based on the work done: The faster maid's work + the slower maid's work = the total work done. Here, the 'work' is a fraction of the house cleaned per hour, so the equation can be written as: 1/x + 1/(3x) = 1/3.

By solving this equation, we find that x = 4.5. Hence, the faster maid would need 4.5 hours to clean the house alone.

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Answer:

61.848 million

Step-by-step explanation:

Answer:I know the answer is 24-2d. But can anyone give me the Step-by-step explanation of how to solve it in the comments below.

The best representation of the number of bottles she has left at the end of d days is,

⇒ 24 - 2d

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Marjorie bought 24 bottles of juice.

And, She drinks 2 bottles each day.

Now, We get;

First day;

⇒ 24 - 2

Second day;

⇒ 24 - 2 x 2

After d days;

⇒ 24 - 2d

Thus, The best representation of the number of bottles she has left at the end of d days is,

⇒ 24 - 2d

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The expression after simplification is -57

Given the expression  14+{−2+3[1+3(−6−2)]}

Using the PEDMAS method

P is parenthesis

E is exponent

D is division

M is multiplication

A is addition

S is subtraction

14+{−2+3[1+3(−6−2)]}

=  14+{−2+3[1+3(-8)]}

= 14+{−2+3[1+(-24)]}

=  14+{−2+3[1-24]}

= 14+{−2+3[-23]}

=  14+{−2+[-69]}

= 14+{−2-69}

= 14+(-71)

= 14 - 71

= -57

Hence the value of the expression after simplification is -57

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Answer:

Yes, there is a direct variation, where the constant is 195 miles\hr

Step-by-step explanation:

Consider the provided information.

An airplane travels 780 miles in 4 hours.

780 miles = 4 hours

Divide both the sides by 4.

780/4 miles = 4/4 hours

195 miles = 1 hours

we need to make a table and graph to show the mileage for 2,8 and 12 hours.

The required table is shown below:

hr        Mileage (Miles)

2         2×195 = 390 miles

8         8×195 = 1560 miles

12       12×195 = 2340 miles

From the table we can observe that there is a direct variation, where the constant is 195 miles\hr

The graph of the table is shown below.

The graph is a line passing through the origin.

Thats the same problem mr kagey  gave me

Step-by-step explanation:

They're pretty much the same thing but when you hear the word rate of change, your thinking of it more in the context of a word problem and interpreting what it means. So labels are pretty much the key difference.

So like slope is here is a random coordinate plane, here's random points or just tell me what the slope is whereas rate of change is like it's number of meters per minute or its number of miles per hour so rate of change means you're comparing two quantities but you have units or labels attached to it.

You're calculating it in the same way but when we say rate of change we're really being asked in the context what does it mean.

Answer:

we need to see the diagram..

Step-by-step explanation:

For the polar curve r = θ, the tangent lines are horizontal when θ = 0 and θ = π, and the tangent lines are vertical when θ = π/2 and θ = 3π/2.

The question is asking us to find the values of θ for which the tangent lines to the polar curve r = θ are horizontal and vertical. To do this, we need to first derive the slope of the tangent line in polar coordinates.

The derivative dr/dθ represents the slope of the radius with respect to θ, or in other words, the slope of the curve. When r = θ, the derivative dr/dθ = 1. This slope is equal to the tangent of the angle that the tangent line makes with the positive x-axis.

Therefore, for the tangent lines to be horizontal, the angle needs to be 0 or π rad (0 or 180 degrees). For the tangent lines to be vertical, the angle needs to be π/2 or 3π/2 rad (90 or 270 degrees). Using the equation r = θ in rad, we find the horizontal tangents are when θ = 0 and θ = π, while the vertical tangents are when θ = π/2 and θ = 3π/2.

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To make things easier for you, the correct answer is C: 3.69 × 10^5

Answer:   24,975 tickets and 25,875 tickets

Step-by-step explanation:

Given : The number of tickets sold at the movie palace theaters during the weekend =  24,875

If we add the the number of tickets sold to 100 tickets, we get

[tex]24,875+100=24,975[/tex]

If we add the the number of tickets sold to 1000 tickets, we get

[tex]24,875+1000=25,875[/tex]

Hence, when we add 100 tickets and 1000 tickets to the number of tickets sold we get 24,975 tickets and 25,875 tickets

A. Finding the slope

The slope of the function is simply the ratio of the value of the dependent variable over the independent variable, so in this case it is:

slope = 6/ 3 = 2

B. Finding the y – intercept

The y – intercept is simply the value of the dependent variable when the independent variable is equal to zero, therefore:

y – intercept (b) = 4

C. Finding the function of the graph

The general equation of a line is given as:

y = m x + b

where m is the slope and b is the y intercept therefore:

y = 2 x + 4

D. Finding the x – intercept

The x – intercept is simply the value of the independent variable (x) when the dependent variable (y) is equal to zero, therefore:

0 = 2 x + 4

x = - 2

E. Graph the function

Check out the image attached

The linear function described is y = -2x + 4, with a slope of -2 and a y-intercept at (0,4). The line for this function will pass through the points (0,4) and (2,0), the latter being the x-intercept.

The question asks to graph a linear function in which the dependent variable decreases 6 units for every 3 units the independent variable decreases, and the function's value at 0 is 4. The nature of this relationship implies that the slope of this function is -2 (calculated as -6 divided by 3). Therefore, the equation for this linear function, using the slope-intercept form y = mx + b, will be y = -2x + 4. In this equation, -2 is the slope (m) and 4 is the y-intercept (b, the function's value when x is 0).

To graph this function, you start by marking the point (0,4) on your graph. From this point, you then go down 2 units (as the slope is -2) and 1 unit to the right (as the decrease in y for a 1 unit increase in x). You will continue this pattern to graph the line. The x-intercept—the point at which the line crosses the x-axis (i.e., where y = 0)—occurs at x = 2, because plugging in 0 for y in the equation gives us -2x + 4 = 0, which simplifies to x = 2. So the final line should pass through the points (0,4) and (2,0).

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We are taking the difference between x and the 98 we must borrow from x.

The addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.

let us assume that we subtract 98 from the number x.

∴ We are taking the difference of x and 98 we have to borrow 98 from that number x.

For example -: We have to subtract 98 from 299, here we will borrow 98 from 299 which is (299 - 98) = 101.

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