Find three consecutive odd integers such that the sum of the smallest and 7 times the largest is 68

Mathematics

2 answers:

Yuki888 [10]3 years ago

6 0

If you are trying to find the equation to this problem, I am pretty sure that it is 2x + x + 4 = 25.

Please mark as brainliest

scZoUnD [109]3 years ago

3 0

First we must assign variables to the integers.

x = smallest
y = middle
z = largest

x + 7z = 68 ← This equation represents the given information

We can assume that "z" is less than 11 because 7*11 = 77, which is greater than 68.

Our possible consecutive odd integers could be:

a) 1, 3, 5
b) 3, 5, 7
c) 5,7, 9

Lets to plug in the "x" and "z" values

a) 1 + 7(5) = 1+ 35 = 36 This is incorrect, because 36 ≠ 68

b) 3 + 7(7) = 3 + 49 = 52 This is incorrect as well, because 52 ≠ 68

That leaves our final choice. Let's check to be certain

c) 5 + 7(9) = 5 + 63 = 68

5, 7, 9 is the 3 consecutive integers such that the sum of the smallest and 7 times the largest is 68.

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A lab technician has to fill the tank given below. Find it’s volume .

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Answer:

The volume of the cylinder shown in the figure is 628 cube meters

Step-by-step explanation:

Given figure is about cylinder

The height of the cylinder = h = 8 meters

The radius of the base of cylinder = r = 5 meters

Now, let The volume of cylinder = V m³

So, The volume of cylinder is given as V = $\pi$ ×r²×h

where r is the radius of its base

And h is the height of cylinder

The value of $\pi$ = 3.14

So, V = $\pi$ × r² × h

Or, V = 3.14 × (5)² × 8

Or, V = 3.14 × 25 × 8

or, V = 628 m³

So, The volume of cylinder = V = 628 m³

Hence The volume of the cylinder shown in the figure is 628 cube meters Answer

6 0

3 years ago

The varsity basketball team started selling T-shirts online in 1994. The number of T-shirts sold online, s, is modeled by the gr

-Dominant- [34]

(PART-A): s-intercept in this case represents the y-intercept of the graph, whereas the t-intercept in this case represents the x-intercept of the graph.

Always remember that y-intercept represents the value of y where the curve (or line) crosses the y-axis, and x-intercept represents the value of x where the curve (or line) crosses the x-axis.

In the graph attached with the question, at point (0,6) the curve crosses the y-axis. Therefore, the y-intercept (s-intercept) in this case is 6. It means that in year 2000 (t=0), 6 hundred shirts were sold.

However, there is no point on the graph where the curve crosses the x-axis, meaning there is no x-intercept (t-intercept). It means that there is not a single year when the number of shirts sold is 0.

(PART B): As you can see in the graph (attached with the question) that the f(t) is increasing (exponentially) with the increase in t. Therefore, we can safely say that as t increases without bound, the f(t) increases (also). In this context, it means that the sale of shirts increases as the years go by. Hence, the correct blank is "increases."

(PART C): The average rate of change is actually the slope. To find the slope, we can use the following formula:

slope = $\frac{y_2 - y_1}{x_2 - x_1}$ --- (X)

Given points: (5, 12.5) and (7, 22). Plug the values in equation (X),

slope = $\frac{22-12.5}{7-5} = 4.75$

Hence, the average rate of change for the function between t=5 and t=7 is 4.75 (answer).

(PART D): This part is bit tricky. Therefore, read the explanation carefully!

You can see in the graph that number of Shirts sold is in hundreds. It means that 1 unit (of y-axis in a graph) represents 100 shirts. Therefore, as in the question it is mentioned that there are 1000 T-shirts sold, it will become 10 units (since 10*100 = 1000). So, the function g(t) will become the following:

$g(t) = f(t) + 10$ --- (Y)

Why did I add f(t)? Because in the question, the word "and" is underlined. It means that g(t) represents not only 1000 T-shirts (10*100 = 1000) sold at the basketball games each year, but it also has the number of T-shirts sold ONLINE, which is f(t).

Now insert f(t) in (Y) and solve:

$g(t) = f(t) + 10\\g(t) = (1.5)^t + 5+ 10\\g(t) = (1.5)^t + 15$