Greg is running a marathon while running he should drink 22 ounces of water per hour if he runs for 4 hours how much water should he drink

To prove the divisibility lets expand each number first to get the complete picture of the problem

51^7 =   8.974106779 . 10^11

51^6 =  1.75962878 . 10^10

(51^7 - 51^6) =  8.974106779 . 10^11 -  1.75962878 . 10^10

                    = 8.798143901. 10^11

[tex]\frac{8.798143901. 10^11}{25}[/tex]

= 3.51925756. 10^10

That is the answer expressed in scientific notation

= 35192575600

Which means the divisibility is proven

Step-by-step explanation:

[tex]51^7-51^6=51^{6+1}-51^6\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=51^6\cdot51^1-51^6\cdot1\\\\\text{use the distributive property}\ a(b-c)=ab-ac\\\\=51^6\cdot(51-1)=51^6\cdot50=51^6\cdot(2\cdot25)=25\cdot(51^6\cdot2)[/tex]

[tex]\text{One of the factors of the product is the number 25.}\\\\\bold{CONCLUSION:}\\\\\text{The whole product is divisible by 25.}[/tex]

[tex]\text{Therefore}\ 51^7-51^6\ \text{is divisible by 25.}[/tex]

Final answer:

Miguel ran different distances on Monday and Friday. We calculate how much farther he ran on Friday than on Monday to find the difference in distance.

Explanation:

Miguel ran 1 3/10 miles on Monday. On Friday, Miguel ran 3 times as far as he did on Monday. To find out how much farther Miguel ran on Friday than on Monday, we first calculate how far he ran on Friday, which is 1 3/10 miles x 3 = 3 9/10 miles. The difference in distance is 3 9/10 - 1 3/10 = 2 6/10 miles.

light would travel approximately [tex]\( 1.35 \times 10^{12} \)[/tex] meters in 4,500 seconds.

To find out how far light travels in 4,500 seconds, we can use the formula:

[tex]\[ \text{Distance} = \text{Speed} \times \text{Time} \][/tex]

Given that the speed of light is approximately [tex]\( 3.0 \times 10^8 \)[/tex] meters per second and the time is 4,500 seconds, we can plug these values into the formula:

[tex]\[ \text{Distance} = 3.0 \times 10^8 \text{ m/s} \times 4,500 \text{ s} \][/tex]

Calculating this gives us:

[tex]\[ \text{Distance} = 1.35 \times 10^{12} \text{ meters} \][/tex]

So, light would travel approximately [tex]\( 1.35 \times 10^{12} \)[/tex] meters in 4,500 seconds.

Starting from your school's location (2,-1), by subtracting 5 from the x-coordinate for walking west, and adding 2 to the y-coordinate for walking north, the location of your house corresponds the ordered pair (-3,1).

Given your school is at (2,-1) and you walk 5 blocks west and 2 blocks north to reach your school, we can determine the location of your house. If we think of the coordinate system with east being positive along the x-axis and north as positive along the y-axis, then walking west (the opposite direction of positive x) means subtracting from the x-coordinate and walking north (the positive y direction) means adding to the y-coordinate.

So, starting from the school's location (2,-1), to account for your walk, subtract 5 (for walking west) from the x-coordinate, resulting in -3, and add 2 (for going north) to the y-coordinate, resulting in 1. Thus, the location of your house corresponds to the ordered pair (-3,1).

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Answer: This represented a exponential growth function.

Step-by-step explanation:

Exponential growth is demonstrated when the rate of change of the value of any mathematical function[the change per unit of time] is proportional to the function's present value, resulting in its value at any time being an exponential function of time or becomes a function in which the time value is the exponent.

Given : A function has a constant tripling time. So it is highly increasing (exponentially) with the time i.e. the function is exponential function.

Answer: Hello mate!

A constant tripling time means that there is a time T, a quantity triples when t = T, then triples again when t = 2T, and again when t = 3T.

Then if A is the initual cuantity; we have a function of the form

f(t) = A*3^(t/T)

and you can see that:

f(0) = A

f(T) = A*3

f(2T) = A*3^2 = (A*3)*3

and so on:

This function describes an exponential growth (because f(t) increases exponentialy over time)

The store has increased the price per dozen eggs by approximately 64.57%.

To calculate the percent increase in price per dozen eggs, we can compare the old price per dozen eggs to the new price per dozen eggs. The original price per dozen eggs is $3.50, and the new price per dozen eggs can be calculated by dividing the total cost of the bucket of eggs by the number of dozens it contains. Since there are 450 eggs in the bucket and a dozen is equal to 12 eggs, the new price per dozen eggs is $16.20 / (450 / 12) = $5.76.

To find the percent increase, we can use the formula:
Percent increase = (new price - original price) / original price * 100%
Substituting the values into the formula, we have:
Percent increase = ($5.76 - $3.50) / $3.50 * 100%
Percent increase = $2.26 / $3.50 * 100%
Percent increase ≈ 64.57%

The store increased the price per dozen eggs by approximately 710.19%.

To determine by what percent the store has increased the price per dozen eggs, we first need to calculate the original price per dozen and then compare it to the selling price per dozen.

Step-by-Step Calculation:

1. Calculate the original price per egg:

  [tex]\[ \text{Total cost of 450 eggs} = \$16.20 \][/tex]

  [tex]\[ \text{Cost per egg} = \frac{\$16.20}{450} = \$0.036 \text{ per egg} \][/tex]

2. Convert the cost per egg to the cost per dozen:

  [tex]\[ \text{Cost per dozen} = \$0.036 \times 12 = \$0.432 \][/tex]

3. Given selling price per dozen:

  [tex]\[ \text{Selling price per dozen} = \$3.50 \][/tex]

4. Calculate the price increase per dozen:

  [tex]\[ \text{Price increase per dozen} = \$3.50 - \$0.432 = \$3.068 \][/tex]

5. Calculate the percent increase:

  [tex]\[ \text{Percent increase} = \left( \frac{\$3.068}{\$0.432} \right) \times 100 = 710.19\% \][/tex]

- The store has increased the price per dozen eggs by approximately 710.19%.

The slope of the line passing through the points (−3, 8) and (4, −6) is calculated using the slope formula and results in a slope of −2.

To find the slope of the line that passes through the points (−3, 8) and (4, −6), we apply the slope formula m = (y2 − y1) / (x2 − x1). Let's designate the first point (−3, 8) as (x1, y1) and the second point (4, −6) as (x2, y2). Plugging these values into the formula, we get:

m = (−6 − 8) / (4 − (−3))

m = −14 / 7

m = −2

Therefore, the slope of the line between the two points is −2. The negative sign indicates that the line is descending from left to right.

Final answer:

To calculate the slope of a line that goes through the points (-3, 8) and (4, -6), apply the slope formula m = (y2 - y1) / (x2 - x1). After substituting the values, the slope is found to be -2.

Explanation:

To find the slope of the line that passes through the points –(3, 8) and (4, –6), we can use the slope formula, which is m = (y2 - y1) / (x2 - x1).

Using the given points, Point 1 (x1, y1) is (-3, 8) and Point 2 (x2, y2) is (4, -6). Substituting these values into the slope formula gives us:

m = (-6 - 8) / (4 - (-3))

m = (-14) / (7)

m = -2

Therefore, the slope of the line that passes through the given points is -2.

To find the dimensions of the volleyball court, set up a system of equations using the perimeter and area formulas. Solve the equations to find the possible dimensions of the court.

To find the dimensions of the volleyball court, we can set up a system of equations using the given information. Let's represent the length of the court as 'l' and the width as 'w'. We know that the perimeter of a rectangle is given by the formula 2l + 2w, so we can set up the equation 2l + 2w = 52. Additionally, we know that the area of a rectangle is given by the formula lw, so we can set up the equation lw = 153.

Using these equations, we can solve for the dimensions of the volleyball court. Let's solve the first equation for l: 2l = 52 - 2w. Dividing both sides by 2 gives us l = 26 - w. Now we can substitute this value of l into the second equation: (26 - w)w = 153. Expanding this equation gives us w^2 - 26w + 153 = 0. We can solve this quadratic equation using factoring, the quadratic formula, or by graphing. After solving for w, we can substitute this value back into the equation l = 26 - w to find the length of the court.

After solving the quadratic equation, we find two possible values for the width: w = 9 and w = 17. Plugging each value into the equation l = 26 - w, we find the corresponding lengths: l = 17 and l = 9. Therefore, the possible dimensions of the volleyball court are 17m by 9m or 9m by 17m.

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The choice that describes the meaning of the result is,

all values of x make the equation true.

The correct option is d.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

Owen used these steps to solve the equation,

4x+7 = 1+2(2x+3).

Simplifying,

4x + 7 = 1 + 4x + 6

4x + 7 = 4x + 6 + 1

4x + 7 = 4x + 7

Subtract 4x to both sides,

7 = 7.

That means, the equation has infinitely many solutions.

Therefore, all values of x make the equation true.

To learn more about the equation;

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Answer:

This is a Trapezoid! It has 22 [tex]units{2}[/tex]

Answer: [tex]76\ m^2[/tex]

Step-by-step explanation:

The surface area of a rectangular prism is given by :-

[tex]\text{Surface area}=2(lw+wh+hl)\\\\\Rightarrow\ \text{Surface area}=2(4\cdot5+2\cdot5+2\cdot4)\\\\\Rightarrow\ \text{Surface area}=2(20+10+8)\\\\\Rightarrow\ \text{Surface area}=2(38)\\\\\Rightarrow\ \text{Surface area}=76\ m^2[/tex]

Hence, he surface area of this right rectangular prism= [tex]76\ m^2[/tex]

Answer:

2,15 and 4,9

Step-by-step explanation:

this is because these two points are in between the other two sets of points.

We want to see how to find a linear equation by only looking at the line graph.

First, a general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know that the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of that line is given by:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Then the line is something like:

[tex]y = (\frac{y_2 - y_1}{x_2 - x_1})*x + b[/tex]

To get the value of b, we use the fact that if the function passes through  (x₁, y₁), it means that when x = x₁ we also must have y = y₁, replacing that in the equation we get:

[tex]y_1 = (\frac{y_2 - y_1}{x_2 - x_1})*x_1 + b\\\\y_1 - (\frac{y_2 - y_1}{x_2 - x_1})*x_1 = b[/tex]

Then the linear equation is:

[tex]y = (\frac{y_2 - y_1}{x_2 - x_1})*x + y_1 - (\frac{y_2 - y_1}{x_2 - x_1})*x_1[/tex]

So what we need to do is just look at the graph and find two points, then you can use the above guide to find the linear equation.

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Answer:

26%

because I did the Math so don't ask OKAY!