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1 year ago

The number 2^1993 + 3^1993 is a multiple of 5. What is the units digit of the quotient (2^1993 + 3^1993)/5?

Mathematics

1 answer:

Ad libitum [116K]1 year ago

3 0

Answer: The unit digit of the quotient is 1.

Step-by-step explanation:

Since the number 2^1993 + 3^1993 is a multiple of 5, this means that no matter the value of the answer to the equation, the last digit will be 5 (we call the last digit of any number its "unit digit").

Since the unit digit of 2^1993 + 3^1993 is 5, if the unit digit is divided by 5 i.e 5/5, it will give us 1.

We will only consider the last digits of the multiple of 5 as our numerator

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I really need points plsss

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1 year ago

4x+3 =23 2x - 10 = -32 - 4x + 1 = -27 6x - 2 = -20

Scrat [10]

Answer:

1)x = 5

2)× = -11

3)x = 7

4)x = 3.66

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2 years ago

The distance to the surface of the water in a well can sometimes be found by dropping an object into the well and measuring the

Harman [31]

THE QUESTION IS NOT PROPERLY WRITTEN

The distance to the surface of the water in a well can sometimes be found by dropping an object into the well and measuring the time elapsed until a sound is heard. If t1 is the time (in seconds) it takes for the object to strike the water, then t1 obeys the equation s = 16t1², where s is the distance (in feet) Solving for t1, we have t1 = √s/4. Let t2 be the time it takes for the sound of the impact to reach your ears. Since sound waves travel at a speed of approximately 1100 feet per second, the time to travel the distance s is t2 = s/1100. Now t1 +t2 is the total time that elapses from the moment that the object is dropped to the moment that a sound is heard. We have the equation; Total elapsed time √s/4 + s/1100.

Find the distance to the water’s surface if the total time elapsed from dropping a rock to hearing it hit water is 4 seconds.

Answer:

229.94 feet

Step-by-step explanation:

Given

t1 = √s/4

t2 = s/1100

From the question, we understand that

t1 + t2 = 4 seconds

Let y = √s

So,

t1 + t2 = 4 becomes

√s/4 + s/1100 = 4

y/4 + y²/1100 = 4 ------ Solve the fractions

(275y + y²)/1100 = 4

275y + y² = 4 * 1100

275y + y² = 4400 ------- Rearrange

y² + 275y - 4400 = 0 (Quadratic Equation)

The standard form of a quadratic equation is ax² + bx + c = 0

Where x =

frac{-b+-\sqrt{bx^{2} - 4ac } }{2a}

Here a = 1, b = 275 and c = -4400

So,

y = (-275+- √(275² - 4*1*-4400))/2

y = (-275+- √75625 + 17600))/2

y = (-275+- √(93225))/2

y = (-275 +- 305.328)/2

y = (-275 + 305.328)/2 or (-275-305.328)/2

y = 30.328/2 or -580.328/2

y = 15.164 or -290.164 -------Negative is not applicable

So, y = 15.164

But y = √s

So, s = y²

S = 15.164²

s = 229.94 ft

6 0

2 years ago

Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2 and the profit

Ann [662]

Let
x--------> the number of sandwich lunch specials sold
y-------> the number of wrap lunch specials sold

we know that
2x+3y=1470

Part 1) Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.

we know that
the equation to slope-intercept form is of the form
y=mx+b
so
2x+3y=1470------> solve for y
3y=1470-2x-----> divide by 3 both sides
y=(-2/3)x+1470/3
y=(-2/3)x+490

the slope m=-2/3
the y-intercept is 490

Part 2) Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences.

the slope is -2/3 and the y-intercept is 490

Plot the point (0,490)------> the y-intercept.
With the slope count 3 squares to the right and 2 squares down and plot that point, which is (0+3,490-2)--------> (3,488)
Draw a line through the two points

Part 3) Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.

In function notation, the equation is:
f(x)=(-2/3)x+490
The graph of this function represents how the value of the function varies as the value of x varies. Looking back at the question context, this graph specifically represents how many wraps could have been sold at each number of sandwich sales, in order to maintain the same profit of $1470.

Part 4) Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology

using a graph tool
see the attached figure

Part 5) Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different

we have that
2x+3y=1593
3y=1593-2x--------> y=(-2/3)x+531
slope=(-2/3)
y intercept=531
therefore
similarities : same slope
differences : y intercepts are different.
This is basically telling me that the lines are parallel lines because they have the same slope.

6) Below is a graph that represents the total profits for a third month. Write the equation of the line that represents this graph. Show your work or explain how you determined the equations

Select two points on the line and write down their coordinates

Let
A( 0,300) B (450,0)
a) find the slope
m=(y2-y1)/(x2-x1)----> m=(0-300)/(450-0)----> m=-2/3
b) with the slope m=(-2/3) and the point A (0,300)
y-y1=m*(x-x1)-----> y-300=(-2/3)*(x-0)----> y=(-2/3)x+300

the answer Part 6) is
y=(-2/3)x+300

7 0

2 years ago

Name the value of each 2 in 222,222?

Eva8 [605]

Hundred thousand,ten thousand,hundred,ten,ones

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1 year ago