Harvey collects rare marbles. He has 112 marbles in his collection. Each tray holds an equal number of marbles. If he uses 7 trays to hold all of the marbles will he display on 3 trays?

f(x) = 75x represents the distance covered by a train traveling at a constant speed of 75 mi/h. The graph is a line with a constant slope of 75, originating from (0,0). The domain and range of the function are both all non-negative real values ([0, +∞)).

To graph the function f(x) = 75x, where x represents time in hours and f(x) represents distance in miles, we construct a simple 2D graph. In this case, the graph will be a straight line sloped upward, starting from the origin (0,0), since the time and distance both start from zero. The slope of the line corresponds to the speed of the train, 75 mi/h, indicating that the train covers 75 miles each hour.

The domain, or possible x-values, of this function are all non-negative real numbers since time cannot be negative. In mathematical terms, this is [0, +∞). The range, or possible f(x)-values, are also all non-negative real numbers as the distance covered also cannot be negative. So, the range is also [0, +∞).

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To determine the number of loaves of bread needed to make the cost of the machine and ingredients less than buying bread at the store, set up an inequality and solve for 'x'. With the given values, you would need to make at least 5 whole loaves of bread.

To determine how many loaves of bread will need to be made for the cost of the machine and ingredients to be less than the cost of buying bread at the store, we need to compare the costs of making bread and buying bread.

The cost of making a one pound loaf of bread using the machine and ingredients is $0.45. The cost of buying a one pound loaf of bread at the store is $2.19.

Let's assume the cost of making each whole loaf of bread is $0.45. We can set up an inequality to represent the situation:

0.45x < 2.19

Where 'x' is the number of loaves of bread that need to be made.

To solve for 'x', we divide both sides of the inequality by 0.45:

x > 2.19/0.45

Using a calculator, we find that x > 4.87. Rounded up, this means you would need to make at least 5 whole loaves of bread in order for the cost of the machine and ingredients to be less than buying bread at the store.

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Final answer:

The length of Chalene's hair in relation to her shoulders can be described using the expression:

Length of hair = 11.5 - 1.5n,

where 'n' represents the number of weeks. Each week, Chalene cuts 1.5 inches off her hair.

Explanation:

To describe the length of Chalene's hair in relation to her shoulders, we can use the expression:

Length of hair = 11.5 - 1.5n

where 'n' represents the number of weeks.

Each week, Chalene cuts 1.5 inches off her hair, so we subtract 1.5 from the previous length to get the new length.

For example, after 1 week, the length of her hair will be 11.5 - 1.5(1) = 10 inches past her shoulders.

Answer:

Part a) [tex]x^{2}+4x+4[/tex]

Part b) [tex]x^{2}-10x+25[/tex]

Step-by-step explanation:

we know that

A perfect square trinomial is equal to

[tex](x+a)^{2} =x^{2}+2ax+a^{2}[/tex]

Part a) we have

[tex]x^{2}+4x[/tex]

Compare with the formula of a perfect square trinomial

[tex]x^{2}+4x=x^{2}+2ax+a^{2}[/tex]

so

[tex]4x=2ax[/tex]

[tex]4=2a[/tex]

[tex]a=2[/tex]

therefore

[tex](x+a)^{2} =(x+2)^{2}=x^{2}+4x+4[/tex]

Part b) we have

[tex]x^{2}-10x[/tex]

Compare with the formula of a perfect square trinomial

[tex]x^{2}-10x=x^{2}+2ax+a^{2}[/tex]

so

[tex]-10x=2ax[/tex]

[tex]-10=2a[/tex]

[tex]a=-5[/tex]

therefore

[tex](x+a)^{2} =(x-5)^{2}=x^{2}-10x+25[/tex]

The values are needed to make each expression a perfect square trinomial x^2 + 4x + 4 and x^2 – 10x + 25.

A perfect square is a number system that can be expressed as the

square of a given number from the same system.

A. [tex]x^{2} +4x+4[/tex]

A perfect square trinomial is

[tex](x+a)^2 = x^2 + 2ax + a^2[/tex]

Compare with the formula of a perfect square trinomial

4x = 2ax

4 = 2a

a = 2

Therefore, [tex](x+a)^2 = (x+2)^2 = x^{2} +4x+4[/tex]

B. [tex]x^{2} -10x + 25[/tex]

A perfect square trinomial is

[tex](x+a)^2 = x^2 + 2ax + a^2[/tex]

Compare with the formula of a perfect square trinomial

-10x = 2ax

-10 = 2a

a = -5

Therefore, [tex](x+a)^2 = (x-5)^2 = x^{2} -10x+25[/tex].

Learn more about a perfect square;

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Final answer:

To find out how much a coral reef grows in 12 weeks, with a weekly growth of 0.13 m, multiply the growth rate by the number of weeks, resulting in a total growth of 1.56 m.

Explanation:

If a coral reef grows 0.13 m every week, to find out how much it grows in 12 weeks, we simply need to multiply the weekly growth rate by the number of weeks:

Weekly growth rate = 0.13 m

Number of weeks = 12

Therefore, the total growth over 12 weeks is:

0.13 m/week × 12 weeks = 1.56 meters.

In 12 weeks, the coral reef grows by a total of 1.56 meters.

Answer:

The three prime numbers are, 31, 37, and 41.

How I got the answer:

1. 31 is a prime number: 31 x 1 = 31  

                                        1 x 31 = 31

2. 37 is a prime number: 37 x 1 = 37

                                          1 x 37 = 37

3. 41 is a prime number: 41 x 1= 41

                                         1 x 41 = 41

Final answer:

To evaluate  [tex](-B)^2[/tex] for A=5, B=-4, and C=2, substitute the given values into the expression. The result is 16.

Explanation:

To evaluate [tex](-B)^2[/tex] for A=5, B=-4, and C=2, we substitute the given values into the expression. Since B=-4, we have [tex](-B)^2=(-(-4))^2=4^2=16.[/tex]

The significance of raising a number to a power lies in its ability to represent repeated multiplication in a concise and efficient manner. Powers allow us to express large numbers and complex mathematical relationships in a compact form. They are fundamental in various mathematical operations, such as arithmetic, algebra, calculus, and number theory. Additionally, powers play a crucial role in scientific notation, where they facilitate the representation of very large or very small numbers in a more manageable format. Overall, understanding powers is essential for comprehending a wide range of mathematical concepts and applications.

Answer: . $50

Step-by-step explanation:

The formula to find the compound amount (compounded quarterly) is given by :-

[tex]A=P(1+\dfrac{r}{4})^{4t}[/tex], where P Is principal amount, r is the rate of interest in decimal and t is the time in years.

Given : Aaron puts $1,000 in an account that pays 10% interest compounded quarterly.

Then, P=1000, r=10%=0.1 ; t=[tex]\dfrac{6}{12}=0.5[/tex] year

Now, [tex]A=1000(1+\dfrac{0.1}{4})^{4(0.5)}[/tex]

[tex]A=1000(1.025)^{2}=1050.625[/tex]

Then , Compound interest=[tex]A-P=1050.625-1000=50.625\approx\$50[/tex]

Hence, he earns the estimated interest of $50.