Show why this statement is true: the square root of four times nine equals the square root of four times the square root of nine

To estimate the total cost, round the numbers and calculate, we get an estimate of $2000. The exact answer for the total cost is $2009.

To estimate the total cost of the MP3 players, we can round the number of blue MP3 players down to 20 and the number of red MP3 players up to 30. So, estimating each at $40, we have a total of $40 x 20 + $40 x 30 = $800 + $1200 = $2000.

To find the exact answer for the total cost, we multiply the cost of each MP3 player ($41) by the number of blue and red MP3 players separately. So, the blue MP3 players cost $41 x 22 = $902, and the red MP3 players cost $41 x 27 = $1107. Adding these together gives a total of $902 + $1107 = $2009.

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Left and right motion indicates change in x-value.

If we subtract 6 from the x-coordinate of each point,

A(3, 4) will be transferred to A'(3-6, 4) = A'(-3, 4).

B(4, 0) will be transferred to B'(4-6, 0) = B'(-2, 0).

C(2, 1) will be transferred to C'(2-6, 1) = C'(-4, 1).

Hence, the correct option is c. Δ ABC is congruent to Δ A'B'C' because you can mapΔ ABC to Δ A'B'C' using a translation 6 units to the left, which is a rigid motion.

Answer:

8(10) + 8(9)

2(9) + 2(3)

Step-by-step explanation:

m∠C=m∠Dx=−3x+804x=80x=20

m∠C=x∘=20∘

The overnight low temperature was -14 degrees F, calculated by subtracting the temperature drop from the initial temperature.

In the context of determining the overnight low temperature, it's essential to consider the initial temperature and the subsequent change. In this specific scenario, the starting point is a temperature of 0 degrees Fahrenheit. However, as the night progresses, the temperature experiences a decrease of 14 degrees.

To pinpoint the overnight low temperature, we employ a straightforward subtraction method. By subtracting the amount of change, which is 14 degrees, from the initial temperature of 0 degrees Fahrenheit, we arrive at the final result of -14 degrees Fahrenheit.

This calculation demonstrates the mathematical approach to determining temperature variations, which is especially pertinent in weather forecasting and climatology. It showcases how understanding temperature fluctuations and changes is crucial for assessing climatic conditions and their impact on various aspects of daily life and scientific research.

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Final answer:

The selling price for the running shoes should be $40.79 to include the cost price of $22.29 and the desired profit of $18.50.

Explanation:

To calculate the selling price of the running shoes to achieve a desired profit of $18.50, we simply add the cost of the shoes to the desired profit.

The cost of the shoes is $22.29, and the store owner wants to make a profit of $18.50.

Therefore, the selling price should be:

Cost of shoes: $22.29

Desired profit: +$18.50

Total selling price: $40.79

The store owner should set the selling price at $40.79 to make a profit of $18.50 on the pair of running shoes.

1 foot = 12 inches

5.5* 12 = 66 inches long

Melvin's mass expressed as a fraction of Kok Yang's mass is 7/2. The ratio of Kok Yang's mass to Melvin's mass is 2:7, and the ratio of Melvin's mass to the total mass of both combined is 7:9.

If Kok Yang's mass is 2/7 of Melvin's mass, we need to express Melvin's mass as a fraction of Kok Yang's mass. To do this, we set Kok Yang's mass to 1 (as a convenient reference) and Melvin's mass then becomes 7/2 times Kok Yang's mass, since 1 is 2/7 of 7/2. Therefore, Melvin's mass in terms of Kok Yang's mass is 7/2.

The ratio of Kok Yang's mass to Melvin's mass, given that Kok Yang's mass is 2/7 of Melvin's mass, is simply 2:7.

Final answer:

The equation 17x × 1 = 17x illustrates the Identity Property of Multiplication, indicating that multiplying by one does not change the value of a number.

Explanation:

The equation 17x × 1 = 17x demonstrates the Identity Property of Multiplication. This property states that when any number is multiplied by one, the result is the original number. It's called the identity property because one is the identity element for multiplication. Multiplication or division by the same number on both sides of an equation will not change the equality. Therefore, multiplying by one does not alter the value of the quantity.

For example, the equation could also be expressed as 1 × 17x = 17x, showcasing the Commutative Property of Multiplication, which allows us to change the order of the factors without changing the product. However, the main focus here is the identity property, as the number stays the same after multiplication by one.

descended would mean he was -1400 feet from the entrance

he then rose 800 feet so

-1400 + 800 = -600 feet

he then went down 450 feet

-600 - 450 = -1050 feet

net loss was 1050 feet

The speed of Natalie in miles per hour is 1.2 mph.

The given parameters;

The speed of Natalie in miles per hour is obtained by dividing the distance covered by Natalie by the time of motion.

The value of this speed is  calculated as;

[tex]speed = \frac{distance }{time} \\\\speed = \frac{3/5}{1/2} = \frac{3\times 2}{5} = \frac{6}{5} = 1.2 \ mph[/tex]

Thus, the speed of Natalie in miles per hour is 1.2 mph.

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Final answer:

To find the two consecutive odd integers, we set up the equation n + 44 = 3(n + 2), where n is the lesser integer. Solving the equation gives us n = 19, so the integers are 19 and 21.

Explanation:

The question asks to find two consecutive odd integers such that 44 more than the lesser is three times the greater. Let's denote the lesser integer as n and the greater as n + 2, as consecutive odd integers differ by 2. We can set up the following equation based on the given information: n + 44 = 3(n + 2).

Now, we solve for n:

n + 44 = 3n + 6

Subtract n from both sides: 44 = 2n + 6

Subtract 6 from both sides: 38 = 2n

Divide both sides by 2: 19 = n

Therefore, the lesser integer is 19, and the greater integer is 19 + 2 = 21.

A hiker has the following items:

A sleeping bag that weighs 3.4 lb

A Camping bag that weighs 4.6 lb

And a water bottle that weighs 2.2 lb.

The expression would be:

3.4x + 4.6x + 2.2x = x

Where x is the weight that each x hikers are carrying.

You just need to add the three items and the answer would be 10.2 pounds.

We want to find the total weight that each hiker carries by adding the weights of all individual items that they carry. And then we want an expression for the total weight that x hikers carry.

These items can be seen in the image at the end of the answer.

We will see that the total weight carried by x hikers is given by:

W(x) = (10.2lb)*x

--------------------------------

First, let's find the weight that each hiker carries.

Each hiker carries:

The total weight is:

T = 3.4 lb + 4.6 lb + 2.2 lb = 10.2 lb

Then if each hiker carries 10.2 lb of weight, and there are x hikers, the total weight carried by them will be x times 10.2 lb

We have:

W(x) = (10.2lb)*x

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