When adding two numbers, such as 123 and 423, care is taken to first line them up and then add like digits. How does expanding this expression to [(1 × 10^2 ) + (2 × 10^1 ) + (3 × 10^0 )] + [(4 × 10^2 ) + (2 × 10^1 ) + (3 × 10^0 )] make the operation more like a polynomial addition problem?

The equation 4x + √y = 12 is a non-linear function because of the square root term. Non-linear functions do not have a constant rate of change and their graphs are not straight lines.

The equation 4x + √y = 12 is not a linear function. A linear function is defined as a function that can be represented by a straight line. However, this equation contains a square root term, which makes it a non-linear function. To determine the type of function, it is important to consider the rules and properties of different function types.

In this case, the equation represents a non-linear function because of the square root term. Non-linear functions do not have a constant rate of change and their graphs are not straight lines. The square root term introduces a curve in the graph.

For example, let's say y = 4, then we can solve for x: 4x + √y = 12, which simplifies to 4x + 2 = 12. Solving for x, we get x = 2. So, for y = 4, x = 2. If we continue to substitute different values for y, we will see that the relationship between x and y is not linear.

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Answer:

Distribute the 3 to each term in the parentheses by multiplying.

Step-by-step explanation:

3(2x – 6 – x + 1)^2 – 2 + 4x

In Step 1 she simplified within the parentheses.

The expression becomes [tex]3(x-5)^2 - 2 + 4x[/tex]

In Step 2 she expanded the exponent.

After expanding the exponent (x-5)^2 it becomes (x^2-10+25)

[tex]3(x^2-10+25)  - 2 + 4x[/tex]

In the next step we distribute 3 inside the parenthesis in order to remove the parenthesis .

Answer: Distribute the 3 to each term in the parentheses by multiplying.

Answer:

To change from one unit to another in the metric system, multiply or divide by multiples of 10.

Step-by-step explanation:

The value of this expression is [tex] 3 x 10^{6} [/tex]

In order to find this, you divide each term separately. First we'll start with the numbers in the front.

[tex] \frac{4.8}{1.6} = 3 [/tex]

Now that we have the first number, we look to the 10s and the powers they are raised to. Since we are looking at powers of the same number, we can use the properties of exponents to simply subtract the numbers they are raised to.

[tex] \frac{10^{9}}{10^{3}} = 10^{6} [/tex]

Then we put the two back together for the final answer.

[tex] 3 x 10^{6} [/tex]

To drag the coach at a constant speed, each player needs to apply a force of approximately 583.89 N to counteract the friction force of 1140 N on the sled, calculated using trigonometry and Newton's Second Law of Motion.

The key concept in this question involves Newton's Second Law of Motion and the dynamics of forces acting at angles. The friction force on the sled is given as 1140 N, and since the football coach is moving at a steady speed, we can infer that the net force is zero, implying that the pulling forces balance out the friction force.

To find the force each player must exert, we first determine the total force needed to overcome friction. Since the rope's angle is 25.0° (half the angle between the ropes), the total horizontal force exerted by the two players (F-total) needs to match the friction force. Using trigonometry, the force each player exerts (F-player) can be expressed as:

F-player = F-total / (2 × cos(25.0°/2)) = 1140 N / (2 × cos(12.5°))

So, we calculate the force:

F-player = 1140 N / (2 × cos(12.5°)) = 1140 N / (2 × 0.9763) = 1140 N / 1.9526 = 583.89 N

Therefore, each player needs to exert approximately 583.89 N to drag the coach at a steady speed of 2.30 m/s.

Final answer:

To find the height h, divide the area A (96) by the base b (12) to get h = 8.

Explanation:

The problem statement A = bh is a formula to calculate the area of a rectangle, where A is the area, b is the base or width, and h is the height. You're given that the area A is 96 and the base b is 12; you need to find the height h. You can rearrange the formula to solve for h by dividing both sides by b:

h = A / b.

Plug in the values that you know:

h = 96 / 12 = 8.

So, the height h equals 8.

Answer:

Check: He used an incorrect time ratio converting hours to minutes

Check: He incorrectly concluded that she is not running fast enough

Do not check: His units do not cancel

Do not check: He used an incorrect distance ratio converting miles to feet

Do not check: He cannot determine her average rate in miles per hour after only 15 minutes

Step-by-step explanation:

You're welcome bud :)

Answer:

[tex]\frac{60x^{20}y^{24}}{30x^{10}y^{12}}[/tex] in simplest form would be [tex]2x^{10}y^{12}.[/tex]

Step-by-step explanation:

Given expression [tex]\frac{60x^{20}y^{24}}{30x^{10}y^{12}}[/tex].

Let us simplify given rational expression in smaller parts.

[tex]\frac{60}{30} = 2[/tex]

[tex]\frac{x^{20}}{x^{10}} = x^{20-10} = x^{10}[/tex]

[tex]\frac{y^{24}}{y^{12}} = y^{24-12} = y^{12}.[/tex]

Combining all terms together, we get

[tex]2x^{10}y^{12}.[/tex]

Therefore,

[tex]\frac{60x^{20}y^{24}}{30x^{10}y^{12}}[/tex] in simplest form would be [tex]2x^{10}y^{12}.[/tex]

Final answer:

To find the number of large bags of dog food Doug bought, use the given prices and total spent in the store.

Explanation:

Doug bought 3 large bags of dog food.

To solve this problem, we can set up the equation: $57x + $9 = $180. From here, we can find x by rearranging the equation to solve for x.

Therefore, Doug bought 3 large bags of dog food, as each large bag costs $57 and he spent $180 in total.

Answer:

D.

Step-by-step explanation:

The range is the (y) value. And you never repeat a number when finding the relation or domain (x).  Therefor the best answer would be D.

Its not A because the numbers are for the domain (X value; First column)

Not B because its also for the Domain and it repeats -1 twice

Not C because it repeats 2 twice

Making D the reasonable answer

I hope this helps :))

Given AB = BC = 6, and DE = 2(AB), then DE = 2 * 6 = 12. Therefore, DE equals 12 units.

In the problem, it's stated that AB = BC = 6 units. This means that both AB and BC are equal in length, each measuring 6 units. As per the given relationship, DE is twice the length of AB. Substituting the known value of AB as 6 units into the expression for DE, we get DE = 2 * 6 = 12 units.

The equality of AB and BC implies that the triangle ABC is an isosceles triangle, where AB and BC are the congruent sides. Consequently, the line segment DE, which is related to AB, shares the same length as BC, making DE also equal to 6 units. However, as per the given relationship DE = 2 * AB, DE is calculated as 2 times the length of AB. Substituting AB = 6 units into the equation, DE = 2 * 6 = 12 units.

Therefore, following the given relationship between DE and AB and using the fact that AB = BC, we can confidently conclude that the length of DE is 12 units. This is determined by doubling the known length of AB, which is established by the equality of AB and BC in the context of an isosceles triangle.

1 mile = 5280 feet

45 x 5280 = 237,600 feet per hour

Actually I believe that Coach Link is incorrect in saying that he can only make 91 teams of 1 or 1 team of 91.

To find the number of teams he can make, we have to find the whole number that can divide 91 and give also a whole number answer. In this case, I found it to be 7.

91 / 7 = 13

So this means that Coach Link can also make 7 teams of 13 or 13 teams of 7.

To write an equation for a vertical translation, subtract the amount of the translation from the original equation. In this case, the equation y = 1/2x becomes y = 1/2x - 18, representing a vertical translation of 18 units downwards.

To write an equation for the vertical translation, we start with the equation y = 1/2x. Since we need to shift the graph 18 units down, the equation becomes y = 1/2x - 18. This equation represents a vertical translation of 18 units downwards.

To maximize the atrium area with a 756-ft perimeter, the dimensions should be 189 ft x 189 ft, with an area of 35,721 sq ft.

To find the dimensions that will maximize the area of the rectangular atrium, we need to set up an equation based on the given perimeter and then use calculus to find the dimensions that maximize the area.

Let's denote the length of the atrium as "L" and the width as "W."

The perimeter of a rectangle is given by the formula:

Perimeter = 2L + 2W

In this case, the perimeter is 756 ft, so we have:

2L + 2W = 756

Divide both sides of the equation by 2 to solve for L:

L + W = 378

Now, we can express L in terms of W:

L = 378 - W

The area of a rectangle is given by the formula:

Area = L * W

Substitute the expression for L in terms of W:

Area = (378 - W) * W

Area = 378W - W^2

To maximize the area, we need to find the critical points.

Take the derivative of the area formula with respect to W and set it equal to zero:

d(Area)/dW = 378 - 2W = 0

Solve for W:

2W = 378

W = 189

Now, we can find the corresponding value of L using L = 378 - W:

L = 378 - 189

L = 189

So, the dimensions that will maximize the area of the atrium are:

Length (L) = 189 ft

Width (W) = 189 ft

The maximum area of the atrium will be:

Area = L * W

Area = 189 ft * 189 ft

Area = 35,721 square feet.

For similar question on perimeter.

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