10 points
What is an irrational number between 7.7 and 7.9?

and no, 7.8 is not irrational.

Final answer:

Jacob bought 2 adult tickets and 7 children's tickets to see his favorite singer, spending a total of $76 for 9 tickets with adult tickets costing $10 each and children's tickets $8 each.

Explanation:

Jacob bought a total of 9 tickets, consisting of adult tickets and children's tickets. Adult tickets cost $10 each while children's tickets cost $8 each, and Jacob spent a total of $76 on tickets. To find out the number of adult and children's tickets he bought, we can set up a system of equations:

Let the number of adult tickets be represented by a and the number of children's tickets be represented by c. We are given two pieces of information:

We can solve the system of equations by substitution or elimination. If we rearrange the first equation (a + c = 9) to get a = 9 - c, we can substitute this into the second equation 10a + 8c = 76:

Now that we have the value for c, we can find a:

Jacob bought 2 adult tickets and 7 children's tickets.

The multiplication 12 x 6 can be represented by a 2-dimensional array model, where you arrange 72 items into 12 rows (or columns) with 6 items in each. It visually illustrates that 12 groups of 6 equals 72.

To represent 12 x 6 using a model, you can create a two-dimensional array. In this array, you would have 12 rows (or columns, as per your preference), and 6 items in each row (or column). Essentially, you need a total of 72 (12 x 6) items arranged in this way.

Here's a small representation for the purpose of understanding:

In this representation, X denotes an item. We have 12 rows with 6 items in each, which shows the product of 12 x 6 as 72. This type of model is also known as an area or array model in mathematics.

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16 liters x 0.78 = 12.48 liters

0.25x +12.48 = 0.41(16+x)

0.25x+12.48 = 6.56 +0.41x

5.92 = 0.16x

x = 5.92/0.16 = 37 liters

Answer:

B) -2

Step-by-step explanation:

-7-3/ 4+1= -10/5 = -2

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-1, 3) and (4, -7). Substitute:

[tex]m=\dfrac{-7-3}{4-(-1)}=\dfrac{-10}{5}=\boxed{-2}\to\boxed{B.}[/tex]

Answer:

64

Step-by-step explanation:

The rate of paddling in still water is 3 times than the speed of the current.

What is Speed?

The formula for the speed is calculated as;

Speed = Distance / Time

Given that;

Jennifer can paddle a certain distance with the current in 2.5 hr.

And, To cover the same distance against the current, she takes 5 hr.

Let distance be D , speed is S and the current speed will be C.

The we can formulate two conditions as;

(S + C) × 2.5 = D  .... (I)

And, (S - C) × 5 = D  .... (II)

Solve equation (i) and (ii) we get;

S = 3C

Thus, we can say that;

The rate of paddling in still water is 3 times than the speed of the current.

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Mike can cut 14 pieces from his 9 inch sub sandwich.

To find out how many 2/3 inch pieces Mike can cut from his 9 inch sub sandwich, we can use division. Here's the step-by-step calculation:

First, we need to determine how many 2/3 inch pieces fit in one inch. This is found by dividing 1 by 2/3.

[tex]\[ \frac{1}{\frac{2}{3}} = 1 \times \frac{3}{2} = \frac{3}{2} = 1.5 \][/tex]

So, one inch can hold 1.5 pieces.

Now, to find out how many pieces can fit in the entire 9 inch sandwich, we multiply the number of pieces per inch by the length of the sandwich.

[tex]\[ 1.5 \times 9 = 13.5 \][/tex]

So, Mike can cut 13.5 pieces from the 9 inch sandwich.

However, as we can't have a fraction of a piece, we round down since we can't have part of a piece.

[tex]\[ \text{Floor}(13.5) = 14 \][/tex]

Therefore, Mike can cut 14 pieces from his 9 inch sub sandwich.

To find the coordinates of point S, we can use the midpoint formula by taking the average of the x-coordinates and the average of the y-coordinates. Substituting the given values into the formula, we find that the coordinates of S are (3, 8).

To find the coordinates of S, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (M) between two points (R and S) can be found by taking the average of the x-coordinates and the average of the y-coordinates.

Given that the coordinates of M are (-1, 5) and the coordinates of R are (-5, 2), we can use the formula:

M = ((x1 + x2) / 2, (y1 + y2) / 2)

Substituting the known values, we get:

(-1, 5) = ((-5 + x2) / 2, (2 + y2) / 2)

Solving for x2 and y2, we find that the coordinates of S are (3, 8).

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The inequality x/-10 > 6 is solved by multiplying both sides by -10, which flips the inequality symbol, yielding x < -60 as the solution. This approach accounts for the rule that multiplication or division by a negative number reverses the inequality sign.

To solve the inequality x/-10 > 6, we need to manipulate the inequality while preserving the relationship between the two sides. When multiplying or dividing both sides of an inequality by a negative number, the inequality symbol must be reversed. Here is the step-by-step process:

This solution demonstrates how to properly handle an inequality involving a negative divisor. It's important to note that if this problem were part of a larger context, such as solving for a concentration in a chemical solution (for which negative values might be physically impossible), one would need to consider the context to determine the relevance of the solution.

In a context where x represents a concentration, a negative value might be discarded as physically impossible, leaving only the physically plausible positive values. As an example, in solution preparation, one might encounter information such as 'solving for x gives a negative root and a positive root', where the negative root would be discarded, and the positive root, such as x = 7.2 x 10-2, would be the correct solution.

Moreover, when dealing with approximate solutions, you might encounter situations where x is very small relative to another value, and thus the value of x might be ignored in the solving process to simplify the equation. However, this approach is not applicable to our inequality since we are not approximating but rather finding the exact set of values for x that satisfy the inequality.

To solve the inequality x/-10 > 6, multiply both sides of the inequality by -10 and reverse the inequality sign. The solution is all values of x that are less than -60.

To solve the inequality x/-10 > 6, we can multiply both sides of the inequality by -10, but remember that when we multiply or divide by a negative number, we need to reverse the inequality sign. So the inequality becomes x < -60. Thus, the solution to the inequality is all values of x that are less than -60.

Answer:In this question, the buying price will be lower if the quantity bought is higher. But the markup ratio for retail price is constant at 80% of buying price. If the price of the range is x, then the equation of retail price would be:

Retail price= x * (100%+80%)

Retail price= x * 180%=

Retail price=  1.8 x

The equation should be same because the markup ratio is same. Only the buying price that will be different based on the quantity of shoe purchased.

THANKS

129

Step-by-step explanation: