Two cars leave the same location traveling in opposite directions. One car leaves at 3:00 p.m. traveling at an average rate of 55 miles per hour. The other car leaves at 4:00 p.m. traveling at an average rate of 75 miles per hour. Let x represent the number of hours after the first car leaves. How many hours after the first car leaves will the two cars be 380 miles apart?

Absolutely, it is correct.

[tex]\boxed{ \ 60 \div 5 (7 - 5) = 24 \ }[/tex]

In the 1500s the specific rules of the order of operation were promptly issued. The order of these workings states which processes take precedence (as a key priority) before which other operations.

Operation priorities are as follows.

Let's implement the rule.

[tex]\boxed{ \ 60 \div 5 (7 - 5) = \ ? \ }[/tex]

Subtract 7 by 5 in parentheses.

[tex]\boxed{ \ 60 \div 5 (2) = \ ? \ }[/tex]

Properly apply rule number 3 from the priority operation above. Initially, we have to divide 60 by 5.

[tex]\boxed{ \ 12(2) = \ ? \ }[/tex]

Continuing with multiplication 12 by 2 proves the exact result.

[tex]\boxed{ \ 12 \times 2 = 24 \ }[/tex]

Thus, this equation is correct.

[tex]\boxed{ \ 60 \div 5 (7 - 5) = 24 \ }[/tex]

Note:

What is the result if we don't follow operation priorities? Let's see.

At this crucial point.

[tex]\boxed{ \ 60 \div 5 (2) = \ ? \ }[/tex]

We decide to multiply 5 by 2, even though there are no parentheses from them, only parentheses for 2.

[tex]\boxed{ \ 60 \div 5 \times 2 = \ ? \ }[/tex]

[tex]\boxed{ \ 60 \div 10 = 6 \ }[/tex]

[tex]\boxed{ \ 60 \div 5 (7 - 5) = 6 \ }[/tex]

That's what happens if we don't follow operating priorities.

Unless the problem like this:

[tex]\boxed{ \ 60 \div (5 (7 - 5)) = 6 \ }[/tex]

[tex]\boxed{ \ 60 \div (5 (2)) = 6 \ }[/tex]

[tex]\boxed{ \ 60 \div 10 = 6 \ }[/tex]

Thus, the difference must be considered. Consequently, follow the priority of the operation and look at the problem in detail.

Keywords: the order of operation, operation priorities are as follows, parentheses, brackets, simplify, exponent, multiplication, division, from left to right, add, subtract

The height of the tallest model is 81 cm and the model is  [tex]y ( x ) = 3^x[/tex].

Given data:

Let x be the height of the tallest model.

According to the information given, the height of each model is three times the height of the previous model.

So, represent the heights of the models as and exponential model where [tex]y ( x ) = 3^x[/tex].

1st model: 3 centimeters (3 cm)

2nd model: 3 times the height of the 1st model = 3 * 3 cm = 9 centimeters (9 cm)

3rd model: 3 times the height of the 2nd model = 3 * 9 cm = 27 centimeters (27 cm)

4th model: 3 times the height of the 3rd model = 3 * 27 cm = 81 centimeters (81 cm)

So, the height of the tallest model can be represented as:

x = 81 centimeters

Hence, the height of the tallest model is 81 centimeters.

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divide the total gallons by the number of containers

40.8 / 8 = 5.1 gallons each

Answer:

21.9 ft

Step-by-step explanation:

The area of a square is the square of the side length, so the side length is the square root of the area:

... s = √(479 ft²) ≈ 21.886 ft

This is approximately 21.9 ft.

area of a square = S^2

 S^2 = 123

S = sqrt(123)

S = 11.0905

 rounded to nearest tenth = 11.1 feet

1 is the remainder of 21 divided by 4

A division is a process of splitting a specific amount into equal parts.

The number which is getting divided here is called the dividend.

21 is the dividend.

The number which divides a given number is the divisor.

4 is the divisor

And the number which we get as a result is known as the quotient.

The divisor which does not divide a number completely produces a number, which is referred to as remainder.

21 ÷ 4 = 5 with a remainder of 1.

Hence, 1 is the remainder of 21 divided by 4

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The slope of the given line is 14 and y intercept is 17.

The equation of a line is y = mx + b.Where m is slope and b is y intercept.

According to the given question a straight line defined by the points (3, 59) and (5, 87).

We know slope (m) = (y₂ -y₁)/(x₂ - x₁)

∴ m = (87 - 59)/(5 - 3)

m = 28/2

m = 14.

Now the equation of the line will be of the form y = 14x + b.

Now we will put any of the values of the given pair of points.

∴ 59 = 14(3) + b

   b = 59 - 42

   b = 17.

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The expression [tex]e^{2t} + 2 + e^{-2t[/tex] is a quadratic equation in terms of exponentials. Without additional information, simplification beyond this stage is not generally feasible. This concept is a typical part of high school algebra, with applications in several fields.

The provided expression [tex]e2t + 2 + e-2t[/tex] belongs to a class of mathematical problems often seen in high school algebra. It involves exponentials, which introduces the concept of exponential functions.

The expression is in a form of a quadratic equation in terms of exponentials, which can be solved via appropriate methods such as factoring, quadratic formula, or completing the square. However, without additional information or context like an equation being set to zero, simplification beyond this stage is not generally feasible. Exponential functions often have applications in fields like physics, economics, and engineering, especially in phenomena that exhibit growth or decay properties.

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Answer:

Option C. 4 Units

Step-by-step explanation:

From the intersecting chords theorem we know that if two chords are intersecting each other in a circle then the products of the lengths of the line segments of each chord are equal.

Therefore AY.YC =YB.YD

Here AY = x, BY = 3, YC = 6, YD = 8

So x.6 = 3.8

6x = 24

x = 24/6 = 4 Units

Option C 4 units is the correct option.

Final answer:

Both schools will serve chicken wraps again on March 29th.

Explanation:

The question involves finding the next calendar date when both the high school and middle school will serve chicken wraps again. To solve this problem, we need to find the Least Common Multiple (LCM) of the two repeating cycles, which are 6 days for the high school and 8 days for the middle school.

First, let's calculate the LCM of 6 and 8:

We find that the smallest common multiple is 24 days.

Since both schools served chicken wraps on March 5th, we simply add 24 days to that date. This gives us:

Therefore, both schools will serve chicken wraps again on March 29th.

 29 feet = 348 inches

352 yards = 0.2 miles

372 feet = 124 yards

2 miles = 10560 feet 

 you can actually just google for the answers lol

29 feet = 348 inches

352 yards = 0.2 miles

372 feet = 124 yards

2 miles = 10560 feet  

To find the amount of salt in the tank at any time t, we can use the equation S(t) = 10 - 10(W(t)/20), where W(t) represents the amount of water in the tank at time t. Substituting the given values, we can calculate the amount of salt in the tank.

To find the amount of salt in the tank at any time t, we need to consider the rate at which pure water enters and leaves the tank. Since water enters the tank at a rate of 5 gallons/minute, the amount of water in the tank at any time t can be represented by the equation: W(t) = 5t, where t represents time in minutes. The concentration of salt in the tank remains constant, so the amount of salt in the tank at any time t can be represented by the equation: S(t) = 10 - 10(W(t)/20), where S(t) represents the amount of salt in pounds and W(t) represents the amount of water in gallons.

Let's solve for S(t) when t = 10 minutes:
S(10) = 10 - 10(5/20) = 10 - 10(1/4) = 10 - 10/4 = 10 - 2.5 = 7.5 pounds of salt.

To solve the equation y = 2mx + 9b for x, subtract 9b from both sides, and then divide by 2m. The result is x = (y - 9b) / (2m). This manipulation is emblematic of solving linear equations which are foundational in algebra.

The student is asking to solve the linear equation y = 2mx + 9b for the variable x. This type of problem involves algebraic manipulation to isolate the variable of interest. Here are the steps to solve for x:

In this case, y is the dependent variable, m is the slope of the line, and b would be the y-intercept if this equation were graphed on a coordinate plane. To better understand this concept, let's take the specific equation y = 9 + 3x as an example which is a linear equation with b set to 9 and m set to 3.

To visualize this equation, one can construct a table of values by selecting various x values and calculating the corresponding y values. Then, these points are plotted on a graph to show the linear relationship. This process is depicted in Table A1 and Figure A1, with the equation illustrated in a graph.

The general form of a linear equation is y = mx + b, where m represents the slope and b the y-intercept. In these exercises, understanding and manipulating this form helps us find relationships between variables and understand how changes in one variable affect another.

Answer:

I'm terrible at explaining so here's a ss

- Ripper

Step-by-step explanation:

Answer:

C. 6

Step-by-step explanation:

It is given that the rectangles in the figure are similar.

Thus, the corresponding sides of the two rectangles will be equal.

So, we get,

[tex]\frac{3}{x}=\frac{5}{x+4}[/tex]

i.e. [tex]3(x+4)=5x[/tex]

i.e. [tex]3x+12=5x[/tex]

i.e. [tex]2x=12[/tex]

i.e. x = 6.

Hence, the value of x is 6.

since the thousands place is a 3 which is lower than a 5

 it would be rounded to 20,000

Answer:

Nearest ten thousands 20000,

Step-by-step explanation:

Given  :23,569

To find : Rounded to the nearest ten thousands

Solution: We have given that 23,569

We can write it as 23,569

Step 1 : Identify the ten thousands digit 2 in 23,569

Step 2: Identify the next smallest place value 3 in 23,569

Step 2: We can the digit less  than five, so it would be rounded down

Step 3 : The ten thousands remain same   and Every digit after becomes a zero.

Step 4 : Number become 20000.

Therefore,  nearest ten thousands 20000,