The ages of Edna, Ellie, and Elsa are consecutive integers. The sum of their ages is 108. What are their ages?

Answer:

The graph of given equation is shown below.

x-intercept is 3 and y-intercept is -1.

Step-by-step explanation:

The given function is

[tex]f(x)=\frac{1}{3}x-1[/tex]

We need to draw the graph of given equation.

At x=0,

[tex]f(0)=\frac{1}{3}(0)-1=-1[/tex]

So, y-intercept is -1.

Equate f(x)=0 to find x-intercept.

[tex]\frac{1}{3}x-1=0[/tex]

[tex]\frac{1}{3}x=1[/tex]

Multiply both sides by 3.

[tex]x=3[/tex]

So, x-intercept of the line is 3.

Plot these two points (0,-1) and (3,0) on coordinate plane and connect them by a straight line.

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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Answer:

64

Step-by-step explanation:

x = hours worked so her hourly pay would be 8.25x

then you add 30 in tips

 so it would be 8.25x+30

 Answer is A

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 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.

The approximate average number of people per square mile in Australia is approximately 8.47.

To find the approximate average number of people per square mile in Australia, we can divide the total population of Australia by the area in square miles. According to the Australian Bureau of Statistics, the population of Australia is approximately 25 million. To calculate the average number of people per square mile, we can divide 25 million by 2.95 x 10^6:

Average number of people per square mile = 25,000,000 / 2.95 x 10^6

Simplifying this expression, we get:

Average number of people per square mile ≈ 8.47

Therefore, the approximate average number of people per square mile in Australia is approximately 8.47.

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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]