Mr. Scott likes to pose interesting problems to his Mathematics classes. Today,
he started with the expression 6^2020 + 7^2020. He stated that the expression was
not equivalent to 13^2020 and that he was not interested in the actual sum. His
question to his class and to you is, “What are the final two digits of the sum?
Answer:
The last two digits of 6²⁰²⁰ + 7²⁰²⁰ is 7, 7
Step-by-step explanation:
The given question is to find the value of the sum of two numbers 6²⁰²⁰ + 7²⁰²⁰, where, 6²⁰²⁰ + 7²⁰²⁰ ≠ 13²⁰²⁰
We have;
The last two digits of the powers of 6 are;
6¹ = 6, last two digits = 06
6² = 36, last two digits = 36
6³ = 216, last two digits = 16
6⁴ = 1,296, last two digits = 96
6⁵ = 7,776, last two digits = 76
6⁶ = 46,456, last two digits = 56
6⁷ = 279,936, last two digits = 36
6⁸ = 1,679,616, last two digits = 16
6⁹ = 10,077,696, last two digits = 96
6¹⁰ = 60,466,176, last two digits = 76
6¹¹ = 362,767,056, last two digits = 56
Therefore, the last two digits repeat itself every 5 times
For 6²⁰²⁰, the last two digits will be for the 2020/5 = 404 complete times, which will be 76
The last two digits of the powers of 7 are;
7¹ = 7, last two digits = 07
7² = 49, last two digits = 49
7³ = 343, last two digits = 43
7⁴ = 2,401, last two digits = 01
7⁵ = 16,807, last two digits = 07
7⁶ = 117,649, last two digits = 49
7⁷ = 823,543, last two digits = 43
7⁸ = 5,764,801, last two digits = 01
Therefore, the last two digits repeat itself every 4 times
For 7²⁰²⁰, the last two digits will be for the 2020/4 = 505 complete times, which will be 01
Therefore, the last two digits of 6²⁰²⁰ + 7²⁰²⁰ is 76 + 01 = 77, which is 7, 7
A regular decagon is rotated n degrees about its center, carrying the decagon onto itself. The value of n could be:
1. 10 degrees
2. 150 degrees
3. 225 degrees
4. 252 degrees
Answer:
252°
Step-by-step explanation:
Given
Shape: Decagon
Required
Determine the value of n
A Decagon has 10 sides and a complete rotation takes 360°
First, we need to calculate the angle of each rotation as follows.
Each Rotation = ⅒ * 360°
Each Rotation = 360°
Next, we determine the possible values of n.
The statement is represented as "possible values of n" because n can assume infinite number of values.
However, n must be a multiple of 36
From the list of given options.
10, 150 and 225 are not multiples of 36
Only 252 happens to be a multiple of 36 from the list of given options.
Hence, option D answers the question [base on the given options]
A decagon is a ten-sided polygon.
The value of n could be 252 degree.
Since, A Decagon has 10 sides
The angle made in one complete rotation is 360 degree.
Now find angle made in each rotation is,
[tex]=\frac{360}{10}=36degree[/tex]
Now, we have to find possible values of n.
Since, n must be a multiple of 36
Apply hit and trial from given option.
We observe that from given options, only 252 degree is multiple of 36.
Therefore, value of n could be 252 degree.
Hence, option 4 is correct.
Learn more:
https://brainly.com/question/9549251
how many times bigger is 2 times 10 to the 10th power than 150 million
Answer: 2 x 10^10 =20000000000
and 150,000,000 is 150 million so you subtract and you get
19,850,000,000
Step-by-step explanation:
what is halfway between 5.3 and 5.4
Answer:
5.35
Step-by-step explanation:
5.31 5.32 5.33 5.34 5.35
i need help. it’s due tonight.thank you
Answer:28
Step-by-step explanation:
The vehicle's fuel efficiency is at least 35 miles per gallon.
Use f to represent the vehicle's fuel efficiency (in miles per gallon).
Answer:
f ≥ 35
Step-by-step explanation:
Took the test on Aleks, it was right! :)
I need help solving and checking the answer before my test tomorrow. ♀️im gonna fail so if you know anything please solve it and show how to check the answer
Step-by-step explanation:
-3+5=-10
−3x+5−5=−10−5
−3x=−15
−3x÷−3=−15÷-3
x=5
(-2 4/5)(1 4/5)
=-14/5×19/5
=-14×9/5×5
=-126/25
=-5 1/25
Answer:
3. x = 5
4. -5 1/25
Step-by-step explanation:
Question 3 Solving:
your equation is -3x + 5 = -10
subtract 5 from both sides to get the term with x alone: -3x = -15
divide both sides by -3 to isolate x (remember that a minus divided by minus is plus): x = 5
To check:
plug in 5 to x and see if you get -10 on both sides
-3(5) + 5 = -10
first multiply -3 and 5:
-15 + 5 = -10
then add 5 to -15:
-10 = -10
if the number are equal then you solved the equation correctly
Question 4:
multiply the whole number by the denominator, then add the numerator to the product, and that number will be your new numerator ( make sure to leave the negative sign out of this computation)
so multiply 2 and 5 to get 10, then add 4 to get 14
your new fraction is -14/5
practice doing the same thing to the other mixed fraction
you should get a new fraction of 9/5
multiply the numerators and denominators
so multiply -14 and 9, and multiply 5 and 5
you now have -126/25
divide 126 by 25 to get your whole number of the mixed fraction
you should have -5 ?/25
to find the numerator, multiply your whole number by your denominator (25 x 5 = 125), then subtract this from your numerator of the improper fraction
126-125 = 1
now you have an answer of -5 1/25
Solve for t in the equation
Answer:
t=1/5=0.2
Step-by-step explanation:
(5t+3)/4=1
5t+3=4
5t=1
t=1/5=0.2
Answer:
1/5
Step-by-step explanation:
5t+3/4=1
5t+3=1*4
5t+3=4
5t=4-3
5t=1
t=1/5
I need helppppppppp!!!!
Based on what you see here, what is the domain of this function?*
Your answer
This is a required question
Answer:
Domain seems to be all real numbers.
Step-by-step explanation:
HELP PLEASE ILL GIVE U 50 POINTS
Answer:
6x^2+2x
Step-by-step explanation:
Answer:
area of rectangle=2x×(3x+1)=6x²+2x
evaluate (73)^2 using the identity (a+b)^2=a2+2ab+b^2
73^2 = 5329
There's no identity that can be used.
PLS GIVE BRAINLIEST
A builder made a scale drawing of a rectangular room. The drawing has a length of 12 ½ cenmeters and a width of 7 ¾ cenmeters. The actual room will have a length of 56 ¼ meters. What will be the area of the actual room?
Answer:
18 / 6 = 3
The scale is 1:3
3 * 4.5 = 13.5
13.5 * 18 = 243 square feet
The answer is 243 square feet.
Step-by-step explanation:
Hope this helped!
An antelope can run 152.5 miles in 2.5 hours. The average speed of the antelope 62 mi/hr
True
False
Answer:
Step-by-step explanation:
152.2 miles /2.5 hours= 60.88 mph so false.
check by 62 mph * 2.5 hours = 155 miles or more then what the antelope actually ran.
What is the image of (2,3)(2,3) after a reflection over the line y=-xy=−x?
Answer:
After the reflection over the line y = -x, the image of the point is: (-3,-2)
Step-by-step explanation:
When a given point is reflected over a line the point only changes place but the distance between the point and the line remains same.
Let (x,y) be a point on the plane
and
y = -x be a line on the plane
When a point is reflected over a line y = -x , the coordinates of the point are exchanged which means x becomes y and y becomes x and both are negated
So (x,y) will become (-y,-x)
Given point is:
(2,3)
After the reflection over the line y = -x, the image of the point is: (-3,-2)
Is 1.6 or 1.25 bigger
Identify the hypotenuse.
A. MN
B. LN
Answer:
The hypotenuse is line segment MN.
Step-by-step explanation:
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The angle 90 degrees (also represented by the red line on angle L) always always is opposite to the hypotenuse. Since angle L is 90 degrees, it is opposite of the hypotenuse, which is MN.
*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^
#teamtrees #WAP (Water And Plant)
5 out of 12 issues it publishes each year. Write and solve a proportion to determine how many times a photo of a main dish will be on the front cover during the next 5 years?
Answer:
25 times
Step-by-step explanation:
If the magazine(we are assuming it's a magazine as we are not told) publishes 5 out of 12 issues of a photo of main dish each year then out of every 12 issues each year it only publishes 5 photos of main dish
The proportion is therefore 5/12
In five years there will be 12*5=60 issues of a photo of a main dish and 5*5=25 published photos of a main dish.
Therefore a photo of a main dish will be on the cover 25 times out of 60 issues in five years
To check if we are correct, we check the proportion to see if it still evaluates to 5/12
25/60= 5/12 when reduced to lowest terms
ab (3a-5b) equals to?
Answer:
3a^2b-5ab^2
Step-by-step explanation:
Answer:
3a²b-5ab²
Step-by-step explanation:
Distribution method:
ab (3a-5b) = 3a²b-5ab²
hcf and lcm of 120 and 180, shown your work
The HCM and LCM of 120 and 180 are 360.
What is HCF and LCM?The Highest Common Factor (HCF) of two or more given numbers is the largest number that divides each of the given numbers without leaving any remainder. The Least Common Multiple (LCM) of two or more numbers is the smallest of the common multiples of those numbers.
Given are two numbers as -
120 and 180
We can write 120 and 180 as -
120 = 2 x 2 x 2 x 3 x 5
180 = 2 x 2 x 3 x 3 x 5
HCF of 120 and 180 will be equal to = 2 x 2 x 3 x 5 = 60
Now, we can find LCM using the formula -
LCM(a, b) = (a x b)/HCF(a, b)
LCM(a, b) = (120 x 180)/60
LCM(a, b) = 2 x 180 = 360
Therefore, the HCM and LCM of 120 and 180 are 360.
To solve more questions on HCF and LCM, visit the link below-
https://brainly.com/question/20739723
#SPJ2
2x+7=19 solving two-step equations
Answer:
x=6
Step-by-step explanation:
divide each term by 2 then simplify
Answer:
6
Step-by-step explanation:
First what you do is you subtract 7 from both sides to get 2x by itself.
2x + 7 - 7 = 19 - 7
2x = 12
Then you divide 2 from both sides to get x by itself.
2x/2 = 12/2
x = 6
Your answer is then x = 6.
Help me pls
Steve earns $1575 a month.
Below is his monthly budget:
.3/5 of his budget is for rent and utilities
.1/3 of his income is for food and other expenses
. The rest will go into Steve's savings account
How much money will Steve put into his savings account each month?
The tables below represent different ratios of teaspoons of sugar to ounces of iced tea. Which table represents the greatest ratio of sugar-to-iced tea?
Answer:
Option (C)
Step-by-step explanation:
Option A.
Ratio of table spoons of sugar to ounces of iced tea = [tex]\frac{\text{Amount of sugar (in oz)}}{\text{Amount of ice tea (in oz)}}[/tex]
From the table attached,
Ratio = [tex]\frac{6}{24}[/tex]
= 1 : 4
Option B.
Ratio of sugar to ounces of iced tea = [tex]\frac{3}{18}[/tex]
= 1 : 6
Option C.
Ratio of sugar to ounces of iced tea = [tex]\frac{1}{3}[/tex]
= 1 : 3
Option D.
Ratio of sugar to ounces of iced tea = [tex]\frac{7}{24}[/tex]
= 7 : 24
≈ 1 : 3.43
Since, highest ratio means biggest fraction (with least denominator).
From the given options, biggest fraction is [tex]\frac{1}{3}[/tex].
Therefore, highest ratio of amount of sugar in (tsp) to number of ounces of ice tea is in Option (C).
apply appropriate methods in solving rationalequations and inequalities.
Task 2
If two figures are similar, then they are congruent.
Check all that apply
true in all cases
true in some cases
true in no cases
Answer:
pqoejbbbsvbhxncbqbqheeirowoqpnabzvxjsmqkw
Kevin ate 3 apples. This represents 20% of the bag of apples. How many apples were originally in the bag?
Yoo how yall doinnnnn
Answer:
pretty good tired of the virus stuff but good
Step-by-step explanation:
Answer:
Im great... how bout you?
Step-by-step explanation:
Which of the following can be used to represent 2x5 using repeated addition? Select all that apply.
5+5+5+5+5
5+5
2+2+2 + 2 + 2
2+2
Answer:
5+5
Step-by-step explanation:
5+5 and 2+2+2+2+2
two fives equal ten and five twos equal ten.
12x² + 8x = 0
What are the zeroes?
Answer:
The zeros are at 0 and -2/3
18. 4x +3=15+2x
Can someone help me solve this number and also 19,20,21,22,23,24,25
Answer:
[tex]{:}\longrightarrow[/tex][tex]\sf 4x+3=15+2x [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 4x-2x=15-3 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 2x=12 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac{12}{2}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x=6 [/tex]
__________________21-
[tex]{:}\longrightarrow[/tex][tex]\sf 3a-2=5+5a-7[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 3a-2=5a-2 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 3a-5a=-2+2 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf -2a=0 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf a={\dfrac {1}{-2}}[/tex]
_________________22-
[tex]{:}\longrightarrow[/tex][tex]\sf 11x-18=2+6x+1+2x [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 11x-18=8x+3 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 11x-8x=3+18 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 3x=21 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac {21}{3}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x=7[/tex]
_________________23-
[tex]{:}\longrightarrow[/tex][tex]\sf e+3+e=40-(-2)+5e [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 2e+3=42+5e [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 2e-5e=42-3 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf -3e=39 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf e={\dfrac {39}{-3}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf e=-13 [/tex]