Final answer:
The remainder of 4^31 when divided by 10 is 4, determined by examining the repeating last-digit pattern of powers of 4.
Explanation:
To find the remainder of 4^31 when divided by 10, we can use the concept of powers and properties of numbers related to modulo arithmetic. Specifically, we look at the last digit pattern that emerges when calculating powers of 4, since the remainder when dividing by 10 depends solely on the final digit of the number.
The powers of 4 have a cycle: 4^1 ends with 4, 4^2 ends with 6, 4^3 ends with 4 again, and so on. This cycle repeats every two powers, so we only need to consider the power of 4 modulo 2 to determine the last digit of 4^31. Since 31 is an odd number, we know that 4^31 will end with a 4. Hence, the remainder of 4^31 divided by 10 is 4.
Which pairs of quadrilaterals can be shown to be congruent using rigid motions?
Select Congruent or Not Congruent for each pair of quadrilaterals.
Congruent Not Congruent
quadrilateral 1 and quadrilateral 2
quadrilateral 1 and quadrilateral 3
quadrilateral 1 and quadrilateral 4
quadrilateral 2 and quadrilateral 3
quadrilateral 2 and quadrilateral 4
quadrilateral 3 and quadrilateral 4
Answer:
quadrilateral 1 and quadrilateral 2 NOT CONGRUENT
quadrilateral 1 and quadrilateral 3 CONGRUENT
quadrilateral 1 and quadrilateral 4 CONGRUENT
quadrilateral 2 and quadrilateral 3 NOT CONGRUENT
quadrilateral 2 and quadrilateral 4 NOT CONGRUENT
quadrilateral 3 and quadrilateral 4 CONGRUENT
Step-by-step explanation:
quadrilateral 1 and quadrilateral 2 NOT CONGRUENT
quadrilateral 1 and quadrilateral 3 CONGRUENT:
rigid motion: reflection
axis of reflection: y=x
quadrilateral 1 and quadrilateral 4 CONGRUENT:
rigid motions: translation and reflection
axis of reflection y=0
quadrilateral 2 and quadrilateral 3 NOT CONGRUENT
quadrilateral 2 and quadrilateral 4 NOT CONGRUENT
quadrilateral 3 and quadrilateral 4 CONGRUENT:
rigid motions: translation and reflection
axis of reflection: x=0
The corresponding parts of congruent quadrilateral are congruent.
The true statements are:
Quadrilateral 1 and quadrilateral 2 Not Congruent Quadrilateral 1 and quadrilateral 3 Congruent Quadrilateral 1 and quadrilateral 4 Congruent Quadrilateral 2 and quadrilateral 3 Not Congruent Quadrilateral 2 and quadrilateral 4 Not Congruent Quadrilateral 3 and quadrilateral 4 Congruent
From the attached figure:
Quadrilaterals 1, 3 and 4 are congruentQuadrilateral 2 is not congruent to any of the other quadrilaterals.The above highlights mean that:
Statements 1, 4 and 5 are Not CongruentStatements 2, 3 and 6 are CongruentRead more about congruent quadrilaterals at:
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the class median is lower than the exam median ( the dark blue lines in the middle of the rectangles)
A local civic group is selling t-shirts to raise funds for Relay to Life. They plan to sell
2500 t-shirts for $10. They consider raising the t-shirt price in order to earn more
profit. For each $1 increase, they will sell 100 fewer t-shirts. Let x represent the
number of $1 increases.
a. Write a function,
Write a function, c(x), to represent the cost of one t-shirt based on the number
of increases.
b. Write a function, t(x), to represent the number of t-shirts sold based on the
number of increases.
c. Write a revenue function, r(x), for the t-shirt sell that could be used to maximize
a. Let us say that c(x) is the cost of one t shirt based on the number of increases therefore:
c = 10 + x
b. Say that t(x) is the number of t shirts sold based on the number of increases so:
t = 2500 – 100 x
b. The revenue is simply the product:
r(x) = (10 + x) (2500 – 100 x)
Combining:
r(x) = 25000 – 1000 x + 2500 x – 100 x^2
r(x) = 25000 + 1500 x – 100 x^2
Taking the 1st derivative and setting dr / dx = 0 to get the maxima:
dr / dx = 1500 – 200 x
1500 = 200 x
x = 7.5
t = 2500 – 100 x = 2500 – 100 (7.5) = 1750
Hence 1750 shirts should be sold.
-3(m-2n) = 5m
solve for m
Answer:
n=3n/4
Step-by-step explanation:
Write the ratio as a fraction in simplest form a/b. What is the ratio of baseballs to basketballs?
Answer: 5/8 im pretty sure i hope it helps :) i took it on freckle so i know but i think this is right
Really need help with this GeoMETry qUIz
The following is an incomplete paragraph proving that ∠WRS ≅ ∠VQT, given the information in the figure where segment UV is parallel to segment WZ. :
(picture attached)
According to the given information, segment UV is parallel to segment WZ while angles SQU and VQT are vertical angles. Angle VQT is congruent to angle SQU by the Vertical Angles Theorem. Because angles SQU and WRS are _____________ angles, they are congruent according to the ____________ Angles Postulate. Finally, angle VQT is congruent to angle WRS by the Transitive Property of Equality.
Which term accurately completes the proof?
1Same-side interior
2Corresponding
3Alternate interior
4Vertical
Find the absolute value and the opposite of the integer.
–989,006
You are the human resources manager for a new local bank. Create a customer service code of behavior for the bank’s employees. In the code, identify the top five areas that bank employees should focus on to meet the needs of their customers. For each area, list three behaviors or practices employees should demonstrate to keep the bank’s customers satisfied.
The top five areas that bank employees should focus on for customer satisfaction include professionalism, focus and productivity, commitment to service, respect for authority, and continuous learning and improvement. For each area, employees are expected to adhere to specific behaviors and practices.
Explanation:As a human resources manager for a banking institution, creating a customer service code of behavior is an essential task. Notably, there are five areas employees should focus on to meet their customers' needs. They include:
Professionalism: Employees should demonstrate punctuality, maintain a professional appearance, and treat everyone with respect. Focus and Productivity: Avoid personal distractions, complete tasks on time, and demonstrate support for the company's goals. Commitment to Service: Display a positive attitude, express enthusiasm, and be committed to providing excellent customer service. Respect for Authority: Employees should respect from their supervisors and managers. Continuous Learning and Improvement: Employees should actively seek to understand their roles and their manager's expectations, adopt effective time management and conflict resolution strategies, identify and respect their rights and responsibilities, and continuously strive for growth and improvement.
These practices and behaviors are expected to provide satisfactory services to the bank's customers and help maintain a productive work environment.
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The pitch of the roof is the number of feet the roof rises for each 12 feet horizontally. If a roof has a pitch of 8. What is its slope expressed as a positive number? What does the slope mean in this story?
The slope of the roof, expressed as a positive number, is 0.67. This represents the steepness of a roof, with a higher number indicating a steeper roof. The figure is calculated using the rise over run ratio.
Explanation:The pitch of a roof is a number that expresses how much the roof's height changes for every 12 feet you move along horizontally. If a roof has a pitch of 8, it means that for every 12 feet you move horizontally, the height of the roof increases by 8 feet. This gives us a rise/run ratio, which is how slope is defined in mathematical terms.
In this case, the rise is 8 feet, and the run is 12 feet. So, the slope would be 8/12, or 0.67 when expressed as a positive decimal number.
The slope here represents the steepness of the roof. A higher slope means a steeper roof and vice versa. By expressing the slope as a number, we can get an idea of how steep the roof is without having to see it in person.
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What is the area of a rectangle with vertices at (−3, −1) , (1, 3) , (3, 1) , and (−1, −3) ? Enter your answer in the box. Do not round any side lengths. ___units²
The area of the rectangle is 8 units².
Explanation:To find the area of a rectangle, we can use the formula A = length * width. In this case, we can use the coordinates of the vertices to determine the length and width of the rectangle.
Using the distance formula, we can find the length between the points (-3, -1) and (1, 3) to be 4 units, and the width between the points (1, 3) and (3, 1) to be 2 units.
Therefore, the area of the rectangle is 4 * 2 = 8 units².
Brandon has 7/1/2gallon of paint. He plans on using 1/1/2 gallon on each room. How many rooms will he be able to paint.
If a polygon POLYG is oriented clockwise, what is the orientation of a reflection image P’O’L’Y’G’?
I made a clay snake 9 5/8 inches long, but a section 1 7/8 inches long broke off. How long is the snake now?
A car travels 95 miles on 5 gallons of gas. give the ratio of miles to gallons as a rate in miles per gallon.
In a triangle, the measure of the first angle is three timesthree times the measure of the second angle. the measure of the third angle is 80 degrees80° more than the measure of the second angle. use the fact that the sum of the measures of the three angles of a triangle is 180degrees° to find the measure of each angle.
A car travels 416 miles in 8 hours and at this rate how many miles will the car travel in 22 hours
To find out how many miles the car will travel in 22 hours, we calculate the unit rate by dividing 416 miles by 8 hours to get 52 miles per hour and then multiply this unit rate by 22 hours to get 1144 miles
The question involves calculating the distance a car will travel at a given rate over a different period of time. This is a basic rate problem in math, often approached by finding the unit rate and then scaling it to the desired time.
Step 1: Identify the rate of travel. The car travels 416 miles in 8 hours.
Step 2: Find the unit rate by dividing the distance by the time. Unit rate = 416 miles / 8 hours = 52 miles per hour.
Step 3: Calculate the distance the car will travel in 22 hours using the unit rate. Distance = 52 miles/hour * 22 hours = 1144 miles.
So, at this rate, the car will travel 1144 miles in 22 hours
The price of a bookcase, including 8% sales tax, is $378. What is the price of the bookcase, before sales tax?
A hockey team played 81 games in a season. they won one fewer games than three times the number of ties, and lost eight fewer games than they won. how many games did they win? lose? tie?
Final answer:
The hockey team won 38 games, lost 30 games, and tied 13 games in the season.
Explanation:
Let's define the variables for the different outcomes in the hockey team's season:
T = number of games tiedW = number of games won = 3T - 1L = number of games lost = W - 8The total number of games is the sum of wins, losses, and ties, and we know this number is 81. This gives us the equation:
W + L + T = 81
Substituting W and L gives:
(3T - 1) + (3T - 1 - 8) + T = 81
Combining like terms and solving for T:
7T - 10 = 81
7T = 91
T = 13 (number of ties)
We then calculate W and L as:
W = 3T - 1 = 3(13) - 1 = 38 (number of wins)
L = W - 8 = 38 - 8 = 30 (number of losses)
The steps to do it. It says "solve for x. Each figure is a parallelogram. Show your work.
The value of x is 4.
To solve for x, we'll use the property of parallelograms that opposite angles are supplementary.
Given that one angle is [tex]\(140^\circ\)[/tex], we can set up the equation:
140 + 10x = 180
Now let's solve for x:
10x = 180 - 140
10x = 40
[tex]x = \frac{40}{10}[/tex]
x = 4
Therefore, the value of x is 4. Adjacent angles in a parallelogram are indeed supplementary.
y is 5 less than the product of 4 and x
Answer: heres all the answers for the practice
1.A c=8+n/2
2.C y=4x-5
3.D 3/5 b-7=a
4.C w=2.5 + h/3
5.B e=8.7n
6.B a=8- 1/6 b
7.C h=40+21t
8.D 99 square cm
9.A 8 square ft
10.A -435.5m
hope i helped
Step-by-step explanation:
Consider the equation below. f(x) = 4x3 + 6x2 − 24x + 3 (a) find the intervals on which f is increasing. (enter your answer using interval notation.)
The function f(x) = 4x^3 + 6x^2 - 24x + 3 is increasing on the interval (-2/3, 1.5), where the derivative of the function is positive.
Explanation:To find the intervals on which the function f(x) = 4x^3 + 6x^2 − 24x + 3 is increasing, we first need to calculate its derivative, which will give us the slope of the tangent line to the function at any point x. The function is increasing wherever its derivative is positive.
The derivative of f with respect to x is:
f'(x) = 12x^2 + 12x - 24.
To find where the function is increasing, set the derivative greater than zero:
12x^2 + 12x - 24 > 0
Solve this inequality to find the intervals for x. Factoring the quadratic, we get:
(2x - 3)(6x + 4) > 0
The zeros of this equation are x = 1.5 and x = -2/3. These values divide the real number line into intervals. Test a value from each interval to see where the function is increasing:
If x < -2/3, for example x = -1, the derivative becomes negative, indicating the function is decreasing.If -2/3 < x < 1.5, for example x = 0, the derivative is positive, indicating the function is increasing.If x > 1.5, for example x = 2, the derivative is again negative, indicating the function is decreasing.Thus, the function f(x) is increasing in the interval (-2/3, 1.5).
Suppose you drop a ball from a window 10 meters above the ground. The ball bounces to 80% of its previous height with each bounce. What is the total number of meters (rounded to the nearest tenth) the ball travels between the time it is dropped and the 10th bounce?
79.3 meters
73.2 meters
89.3 meters
77.5 meters
m + 2m - 6 = -12 + 2m
solve for m
The solution of m is -6 for the equation m + 2m - 6 = -12 + 2m
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is m + 2m - 6 = -12 + 2m
m plus two times of m minus six equal to minus twelve plus two mines of m.
Plus and minus are the operators of the equation.
Take all the variables on one side and constants on other side.
3m-2m=-12+6
Add the like terms
m=-6
Hence, the solution of m is -6 for the equation m + 2m - 6 = -12 + 2m
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Find the GCF of the given polynomial.
16a⁴b⁴ + 32a³b⁵ - 48a²b⁶
Three friends were born in consecutive years. The some of their birth years is 5982.find the year in which each person was born
Answer:
The birth years of first person is 1993.
The birth years of second person is 1994.
The birth years of third person is 1995.
Step-by-step explanation:
Three friends were born in consecutive years
Let the birth years of first person be x,
Let the birth years of second person be (x+1)
Let the birth years of third person be(x+2)
The sum of their birth years is 5982.
[tex]x+(x+1)=(x+2)=5982[/tex]
Solving the given equation for x:
[tex]3x+3=5982[/tex]
[tex]x=\frac{5982-3}{3}=1993[/tex]
The birth years of first person = x = 1993
The birth years of second person = (x+1) = 1993+ 1 = 1994
The birth years of third person = (x+2) = 1993+2 = 1995
A car travels 100 meters in 5 seconds. What is the speed of the car/7281023/14f0e74f?utm_source=registration
please help me with my math homework??
Find the value of x, please
4 inside angles = 360 degrees
131 + 75 + 105 = 311
360 - 311 = 49
x^2 = 49
x = sqrt(49) = 7
x = 7
the steps to solve it
Pqr is a right angle. If pq=8 what is equivalent
A rectangle has a length of n units its width is 6 unit less its length what is the area of the rectangle
Answer:
Step-by-step explanation: