Given:
First five consecutive positive integers.
To find:
The sum of the first 5 consecutive positive integers.
Sum of the first n consecutive whole numbers.
Solution:
First five consecutive positive integers are 1, 2, 3, 4 and 5.
Sum of these numbers is
[tex]1+2+3+4+5=15[/tex]
Therefore, the sum of the first 5 consecutive positive integers is 15.
First n consecutive whole numbers are 0, 1, 2, 3,..., (n-1). These numbers are in AP.
Here, first term is 0 and common difference is 1.
Sum of n terms of an AP is
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
where, a is first term and d is common difference.
Substitute a=0 and d=1 in the above formula.
[tex]S_n=\dfrac{n}{2}[2(0)+(n-1)(1)][/tex]
[tex]S_n=\dfrac{n}{2}[n-1][/tex]
Sum of first 5 consecutive positive integers is equal to the sum of first 6 consecutive whole number because in whole numbers 0 is extra number.
For n=6,
[tex]S_6=\dfrac{6}{2}[6-1][/tex]
[tex]S_6=3(5)[/tex]
[tex]S_6=15[/tex]
The sum of the first 5 consecutive positive integers is 15.
So, the sum of (n-1) consecutive positive integers is
[tex]S_n=\dfrac{n}{2}[n-1][/tex]
Help please!!!
Question 6
5 pts
Factor the variable expression:
36X + 8X
0419x-4)
4X (9+2)
9(4X+2x)
8(X+X)
Answer:
4x (9+2)
Step-by-step explanation:
36x+8x
36 and 8 can be divided by 4 and they both have an x
[tex]36x + 8x = 4x(9 + 2)[/tex]
[tex]44x = 36x + 8 x[/tex]
[tex]44x = 44x[/tex]
The Answer is
[tex] \green {\boxed{4x(9+2)}}[/tex]
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Which method represents a correct way to solve the equation?
-x+(-3+x)2 = 6
Multiply -3 by 2.
Multiply x by 2.
Combine like terms.
Subtract 6 from both sides.
Use the quadratic formula to solve for x.
OA.
Square -3.
Square x.
Subtract -7x from both sides.
OB. Subtract 9 from both sides.
Take the square root of both sides.
Square -3.
Square x.
Combine like terms
OC. Subtract 6 from both sides.
Use the quadratic formula to solve for x.
OD
Square the quantity (-3 + x).
Combine like terms.
Subtract 6 from both sides.
Use the quadratic formula to solve for x.
Answer:
Multiply -3 by 2.
Multiply x by 2.
Combine like terms.
Subtract 6 from both sides.
Use the quadratic formula to solve for x.
Step-by-step explanation:
Given:
-x (-3 + x )2 = 6
-x (-3 + x )2 = 6
-x (-6 + 2x) = 6
-6x + 2x^2 = 6
2x^2 - 6x - 6 = 6 - 6
2x^2 - 6x - 6 = 0
Multiply -3 by 2.
Multiply x by 2.
Combine like terms.
Subtract 6 from both sides.
Use the quadratic formula to solve for x.
Hector is dividing students into groups for a nature hike. He wants to divide the boys and girls so that each group has the same number of both boys and girls. There are 21 boys and 56 girls signed up for the hike. Into how many groups can the students be divided? How many boys and how many girls will be in each group?
Answer: The students can be divided into 7 groups.
Each group will have 3 boys and 8 girls.
Step-by-step explanation:
There are 21 boys and 56 girls.
To divide them so that each group has the same number of both boys and girls.
We find GCD(21,56).
21 = 3 x 7
56 = 2 x 2 x 2 x 7
GCD (21,56) = 7
So, the students can be divided into 7 groups.
Number of girls in each group = [tex]\dfrac{56}{7}=8[/tex]
Number of boys in each group = [tex]\dfrac{21}{7}=3[/tex]
So, each group will have 3 boys and 8 girls.
what is (3,0) reflected on the y-axis
Reflecting across the y axis, the x value becomes opposite and the y value remains the same.
(3,0) becomes (-3,0)
Answer:
(-3, 0)
Step-by-step explanation:
There is the same amount of units from either side of the y-axis to the points.
Leo the Rabbit
Leo the Rabbit is climbing up a flight of 10 steps. Leo can only hop up 1 or 2 steps each time he hops. He never hops down, only up. How many different ways can Leo hop up the flight of 10 steps? Provide evidence to justify your thinking.
Can someone provide an answer and explain. Thanks
Answer:
2?
Step-by-step explanation: because he can hop them one step at a time or two steps at a time
Make s the subject of the formula
T^2=2p+as
Step-by-step explanation:
Original formula: T^2 = 2p + as
T^2 - 2p = as
s = (T^2 - 2p) / a
In a certain fraction, the denominator is 4 larger than the numerator. If 2 is added to both the numerator and the denominator,the result is 3\5. Find the original fraction. PLS ANSWER
Step-by-step explanation:
Here you go, I tried my best
cheers
The original fraction is [tex]\frac{4}{8}[/tex]
Let the numerator = a
Let the denominator = b
Denominator is 4 larger than the numerator: b = a + 4
2 is added to both the numerator and the denominator: (a + 4 +2) and a + 2
The algebraic equation from the given statement is formed as follows;
[tex]\frac{a+ 2}{a+4+2 } = \frac{3}{5} \\\\\frac{a+ 2}{a + 6} =\frac{3}{5} \\\\5(a + 2) = 3(a + 6)\\\\5a + 10 = 3a + 18\\\\5a - 3a = 18 -10\\\\2a = 8\\\\a =4[/tex]
The original fraction is calculated as follows;
[tex]\frac{a }{a +4} = \frac{4}{4+ 4} = \frac{4}{8}[/tex]
Thus, the original fraction is [tex]\frac{4}{8}[/tex]
Learn more here: https://brainly.com/question/16889590
Find the slope from the table
Answer:-4/1
Step-by-step explanation:
Write four different equations that have –3 as the solution
1 + -4
2 + -5
3 + -6
4 + -7
Answer:
5 + -8
6 + -9
7 + -10
8 + -11
Step-by-step explanation:
7) Write an equation in point-slope form of the line
through point J(-2,10) with slope - 2
Answer:
y=-2x+6
Step-by-step explanation:
y=mx+b
10=(-2)(-2)+b
10=4+b
10-4=b
6=b
Y=9x+2x please help, i don't know how to
do this stuff
Answer: I hope you understand, just mutiply whatever x is by 11 to get Y
Step-by-step explanation:
x = unknown number
9x+2x= 11x
Y=11x
PLEASE HELP FAST. WILL MARK AS BRAINLIEST IF GIVEN GOOD ANSWER
Answer:y=9
Step-by-step explanation:
what is the point if (2,0) gets rotated 180° clockwise
Answer:
The point is (0,-2)
If a = 8 in and b = 15 in what is the length of leg c in a right triangle using the
pythagorean theorem?
See attachment for math work and answer.
13 PLS TELL ME THE EQUATION AND HOW TO SOLVE IT WITH THE ANSWER
Answer:
b
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
This triangle should be 180 degrees.
So you should add 80 and 45 and subtract it from 180 to get x.
Point S is the _ of UT?
Answer:
VStep-by-step explanation:
SV is correct because it is the same
length of UT. You can check by using
your fingers to check the length of
UT then turn the picture around to
see if it is equal.
Hope this helps! <3
Answer:
S is the midpoint of UT
Step-by-step explanation:
US = ST -----> from the picture
So, S is the mid point
Point B is located at (0, 2) and is translated to point B' with coordinates (1, -1), which translation did point B undergo? One unit right and three units down One unit right and one unit down Two units right and two units down Three units left and one unit up
Answer:
One unit right and three units down
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, dilation, rotation or translation.
If a point X(x,y) is translated a units right and b units up, its new location is at X'(x + a, y + b) while if a point is translated a units left and b units down, its location is X'(x - a, y - b).
Since point B is located at (0, 2) and translates to B' with coordinates (1, -1), the translation is given as (x + 1, y - 3) that is 1 unit right and 3 unit down.
M to the power of 5 n to the power of 3 divided by m to the power of 2 n to the power of -4
please solve fast I will mark the first answer as brainliest and give with step by step explanation
Question 3 of 10
What is the slope of the line given by the equation below?
y + 2 = -3(x-5)
A. -5
B. 3
C. -3
D. 2
What is a good problem to use for an inequality equation? using ax + b > c. Including the solution.
Answer:
A "solution'' of an inequality is a number which when substituted for the variable makes the inequality a true statement. When we substitute 8 for x, the inequality becomes 8-2 > 5. Thus, x=8 is a solution of the inequality.Step-by-step explanation:
Answer:
the person above me is correct
Shark boi U~U
Please send an answer quick I really need it the picture is above.
Answer:
-132
Step-by-step explanation:
When you plug in -8 to every x you get -2(8)^2+2(8)-20 which gives you -132.
Is (1,1) a solution to this system of inequalities
Help me please need help
Answer:
w = 10
Step-by-step explanation:
I did the math and and I got 10
Hope it helps!! :D
Answer:
w = 10?
Step-by-step explanation:
Can someone answer this?
Answer:
y = 1500 + 800x
Step-by-step explanation:
This is the answer because Elisa charges 1500 dollars no matter what. That value is not dependant on anything. Every hour she is with the client is 800 dollars. That is why it is represented as 800x. X being the amount of hours. You add the two together to find how much Elisa's services cost.
2. A train starts its journey with 240 passengers.
144 of the passengers are adults and the rest are children.
(a) Write the ratio Adults: Children in its lowest terms.
[2]
(b) At the first stop, 37 % of the adults and of the children get off the train.
20 adults and x children get onto the train.
The total number of passengers on the train is now 200.
(i)
How
many children got off the train?
(ii)
How
many adults got off the train?
[1]
(iii) How many adults passengers are on the train as it sets off again? [1]
(iv) What is the value of x?
[1]
Answer:
i=52
ii=32
iii=54
iv=92
Step-by-step explanation:
Comment if you need explanation
Answer:
A. 3:2
B. 31 children
(i). 35 children
(ii) 53 adults
(iii) 111 adults 89 children
(iv) The value of x is 35.
Step-by-step explanation:
What is the slope of this graph?
4
−14
−4
14
Answer:
-4
Step-by-step explanation:
i took the quiz on k12 :)
In the book,the distance between two planets is given as 4.07×10^¹² kilometres. The speed of light is 1.1×10^⁹ kilometres per hour. Calculate the time taken for light to travel from one of these planets to the other. Give your answer in days and hours.
Answer:
3700hours
154days
Step-by-step explanation:
Speed can be defined as the distance cover per time, it can be expressed as
Speed= distance/ time........eqn(1)
Given:
distance between two planets= 4.07×10^¹²
speed of light = 1.1×10^⁹ kilometres per hour
Time= ??
Then substitute the values into equation (1) we have
Speed= distance/ time
1.1×10^⁹ kilometres per hour= 4.07×10^¹²kilometre/ time
Cross multiply, we have
Time= (4.07×10^¹²kilometre) /(1.1×10^⁹ kilometres per hour)
Time= 3700hours.
To convert to day, we know that
60 minute= 1hour
24hour=1day
Time= (3700hour×1day)/24hour
Time= 154days approximately.
Hence, the time taken for light to travel from one of these planets to the other is 154days or 3700hours
Whats the answer? I will give brainliest if correct♡︎ꨄシ
Answer:
b isnt a fuction
Step-by-step explanation:
Answer:B
Step-by-step explanation:
For each value of x, determine whether it is a solution to x - 42 = 7.
Answer:
67- No 46-No 49-Yes 47-No
Step-by-step explanation:
Hope this helps!
Answer:
67...No
46...No
49...Yes
47...No
Step-by-step explanation:
x - 42 = 7
Add 42 to both sides
x = 49
PLEASE HELP, GIVING BRAINLIEST!!!
These triangles are congruent by _____.
A. SAS
B. AAS
C. SSS
D. Not enough information
E. None of these
Answer:
I think it might be C...