Answer:
Step-by-step explanation:There are formulas to work this out, but you can also suss out an answer by a liberal application of critical thinking.
Okay, you want to add 51 + 52 + 53 + … + 99 + 100, right? (The … represents all the numbers in between, in case you were wondering.)
Well, that’s a total of 50 numbers. And if you know anything about addition, you know that it doesn’t matter what order you add them.
So you could also say 51 + 100 + 52 + 99 + 53 + 98 + … and so on.
Let’s see what happens. 51 + 100 = 151. So far so good.
Then, 52 + 99 also equals 151. And 53 + 98 also equals 151. Since there are 50 numbers, that’s 25 pairs that are going to add up to 151.
151 + 151 + 151 + 151 + … (21 more instances of 151).
So we can simplify our workload a bit. Instead of adding up all the numbers by hand, we can just multiply 151 by 25.
151 x 25 = 3775
From that, we can work out a generic formula that will allow you to add any sequence of numbers…without actually adding.
Let a be the first number in the sequence, and let n be the last number in the sequence. The number of numbers is (n - a) + 1. (You have to add 1, because if you just subtract, it’s like you’re losing the lowest number in the sequence).
So…you get the sum by adding the first and last number in the sequence, and then multiplying that result by half of the total number of numbers.
(a+n)((n−a)+12)
an−a2+a+n2−an+n2
−a2+a+n2+n2
−a(a−1)+n(n+1)2
Let’s check to see if it works!
−51(51–1)+100(100+1)2
−51(50)+100(101)2
−2550+10,1002
75502
3775
Note that if the starting number were 1, the formula would simplify to n(n+1)2
Following are the calculation to the sum of integers:
Given:
33 to 47
To find:
Sum of integers=?
Solution:
Given numbers:
33 to 47
[tex]\to \bold{33,34,35,36,37,38,39,40,41,42,43,44,45,46,47}[/tex]
Using formula:
[tex]\bold{S = \frac{n(a + l)}{2}}[/tex]
[tex]n=15\\\\a=33\\\\l=47 \\\\ \bold{S = \frac{15(33 + 47)}{2}}\\\\[/tex]
[tex]\bold{= \frac{15(80)}{2}}\\\\\bold{= \frac{1200}{2}}\\\\\bold{= 600}[/tex]
Therefore, the sum of the integers "600".
Learn more:
brainly.com/question/18365093
5,2,-1,-4,-7 arithmetic
Can someone help me?
Answer:
x = 10
Step-by-step explanation:
50 + 4x = 90
4x = 40
x=10
Complete the statements below that show y = 8x2 + 32x + 17 being converted to vertex form.
Factor out the leading coefficient.
y = 8(x2 + 4x) + 17
Form a perfect-square trinomial.
Answer:
y = 8(x + 2)^2 + -15
Step-by-step explanation:
Factor out the leading coefficient.
y = 8(x2 + 4x) + 17
Form a perfect-square trinomial.
y = 8(x2 + 4x + 4) + 17 + -32
Write in vertex form.
y = 8(x + 2)^2 + -15
Answer:
4, -32
Step-by-step explanation:
solve each equation for x:
-5(3x + 4) = 25
4(x + 2) - 3(2x - 4) = 10
-4x - 3 = -1
Answer:
1. x = -3
2. x = 5
3. Exact Form: x = −1/2
Decimal Form: x = −0.5
Step-by-step explanation:
Answer:
1. -3
2. 2/3
3. 1/2
Roxy is multiplying 18 by 43.
Use the drop-down menu to complete the statement.
1
4
1
The product × will be
.
8
3
8
Answer:
774,
Step-by-step explanation:
You have $300 to spend on school clothes shirts cost $15 and pants $20
Answer
19 pants and 6 shirts
combining like terms: -7x+x HELP ASAP
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
When you combine like terms you see the ones that are similar then you add or subtract, depends on what the signs are. For this one -7x is similar to x so in this case you would add x to the -7x which will give you -6x.
-8≤8+y for the solution?
Answer:
- 16 ≤ y
Step-by-step explanation:
- 8 ≤ 8 + y
- 8 -8
- 16 ≤ y
Answer:
Y>-16
The > is a greater than or equal to i just can’t put it in since I’m on my phone
Step-by-step explanation:
If you’re solving for y that should be the answer
Solve the equation for b. Use lowercase letters and no spaces when typing in the equation. a+b/3= C type your answer...
6. 108 is how many times as large as 2. 103?
Answer:
54 times larger than 2
Step-by-step explanation:
108 divided by 2 is 54
Which quadrant contains the point named by (2,5)
Answer:
Quadrant 4
Step-by-step explanation:
I may or may not be dumb in the brain... I'll give brainliest to whoever answers first and correctly.
Answer:
23 degrees
Step-by-step explanation:
6x + 42 = 180
x = 23
Answer:
23 Degrees
Step-by-step explanation:
6x + 42 = 180
-42. -42
6x = 138
/6. /6
× = 23
what ordered pair is the solution
james painted 3/4 of his bedroom wall in 2/3 of an hour. How much of the wall could he paint in ONE full hour? (WRITE YOUR ANSWER AS A SIMPLIFIED IMPROPER FRACTION) Use either strategy to solve.
Answer:3/3 i think
Step-by-step explanation:
Answer:
Step-by-step explanation:
First, we need to find the common denominator between 3/4 and 2/3. The least common factor of these fractions is 12. Now we can turn 3/4 into 9/12, and 2/3 into 8/12, simply by multiplying. To figure out what one third is, we can divide by 2 to get 4/6 and 3/6... And now I'm lost (* ̄∀ ̄) *embarrassed face lol*
Determine whether the equation below has a one solutions, no solutions, or an
infinite number of solutions. Afterwards, determine two values of x that support your
conclusion.
2 – 3 = -3 + 2
Answer:
one solution
Step-by-step explanation:
what is -6 divided by (-3) • (-5)
Answer:
d
Step-by-step explanation:
A right rectangular prism is packed with cubes of side length fraction 1 over 8 inch. If the prism is packed with 16 cubes along the length, 8 cubes along the width, and 6 cubes along the height, what is the volume of the prism?
Answer:
768
Step-by-step explanation:
16x8x6=768 because volume equals length times width times height ! :)
is 3/17 rational or irrational
Answer:
A rational number is a number that can be put in the form p / q where p and q are integers.
3 and 17 are integers
3 / 17 is rational
Identify the like term(s) in the following expression...
-11d-12z-5+9m+8d+2z
A) +8d and 11d, +2z and -12z
B) -11d and +8d, +2z and -12z
C) -11d and +8d, +2z and 12z
D) -11d and +8d, +2z and -12z, +9m
Answer:
If Im correct B). is the correct answer
B) -11d and +8d, +2z and -12z
POSSIBLE PO In a bag there are 10 red marbles, 5 green marbles, and 5 blue marbles. Wh at is the ratio IN FRACTION FORM of RED marbles to the total?
Answer:
10/20 = 1/2
There are a total of 20 marbles, and ten of those are red = 10/20
Which, is half of the total.
A rectangle has coordinates A(-4,3). B(0,0), C(6,8) and D(2,11)
Answer:
what is the question
Step-by-step explanation:
Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes.
y= 1/3 x− 2/3
Answer:
y-intercept = (0,-2/3)
x-intercept = (2,0)
Step-by-step explanation:
*X-intercept touches the x-axis & y-intercept touches the y-axis*
You can identify the y-intercept by looking at the equation.
The slope is 1/3x and the y-intercept is -2/3.
I'm not sure how to solve for the x-intercept, but you can make a graph with the y-intercept and the slope points. By doing this you should be able to find the x-intercept.
Hope this helped!!! :)
PS: Check out the Desmos Graphing Calculator
This website helps a lot with these types of problems. You can type the equation, and it will show you a graph. If you look at the graph, you'll be able to determine the slope, the x-intercept, and the y-intercept.
At the beginning of the school year, Jamie had $500 in her savings account. She wants to have at least $200 left in the account at the end of the school year. Each week, she withdraws $30 for spending money. To determine how many weeks she can spend $30, Jamie wrote and solved this inequality. 500 − 30x ≥ 200 −500 −500 −30x ≥ −300 x ≥ 10 Review Jamie's work. What was her error?
Answer:
Step-by-step explanation:
Given the inequality solved by H=Jamie expressed as:
500 − 30x ≥ 200
We need to calculate the range of x of the inequality to determine the number of weeks she can spend $30 as shown:
500 − 30x ≥ 200
Subtract 500 from both sides
500 − 30x - 500≥ 200 - 500
− 30x ≥ -300
Divide both sides by -30
− 30x/-30 ≥ -300/-30
x ≤ 10 (note that the inequality sign changes after dividing both sides by a negative sign)
Jamie's error was that she didn't change the sense of inequality after dividing both sides by -30 hence rendering her solution incorrect
Hence the number of weeks is less than or equal to 10.
Answer:
Answer is B
Step-by-step explanation:
Jamie should have reversed the inequality when using the division property of inequality. is the right answer hope it helps
-10+1= plssssss help meeeeeee
Answer:
-9
Step-by-step explanation:
-10 - (-1) = -9
A rectangular garden has length and width as given by the expressions below.
Length: 4 - 7(3x + 4y)
Width: 3x(-2y)
Write a simplified expression for the perimeter of the rectangle.
if x=-2, y=-6 and z=4, Find the value of 4xy 3marks
Answer:
Step-by-step explanation:
4xy=4*(-2)*(-6)
4xy=48
If the selling prices of 20 pens are equal to the cost price of 25 pens, what is the gain percentage?
[tex]\huge\bold\red{Answer:-}[/tex]
No(0)Let the cost price of the 20 pens be ₹100.
Cost of each pen=₹100/20=₹5
Selling price of each 25 pens sold=₹100/25=₹4.
%LOSS:
If cost of each pen. = 5=100%
..selling price of each pen. = 4= ?%.
Cross multiply:5? =400
?=80%
So,%loss= 100%-80%=20%
FOLLOW ME ♥️At the start of the football game, there were 840 fans in the stadium. It began to rain during halftime, so 10% of the fans went home.
During the 3rd quarter of the game, the visiting team scored five touchdowns, so 25% of the remaining fans went home.
How many fans were in the stadium after the 3rd quarter?
Phil would like to make a profit of $250 this summer mowing his grandfather’s lawn. If he plans to mow 20 times and estimates that his fuel costs will be $30 for the entiresummer,which equation could be used to determine how much should he charge for each mowing?
Answer:
which principle prevents a brach from abusing its power
Step-by-step explanation:
which principle prevents a brach from abusing its power
Answer:
20x - 30 = 250
Step-by-step explanation:
20x - 30 = 250
20x = 280
x = 14
Two pulleys, one with radius r 1r1 and the other with radius r 2r2, are connected by a belt. The pulley with radius r 1r1 rotates at omega 1ω1 revolutions per minute, whereas the pulley with radius r 2r2 rotates at omega 2ω2 revolutions per minute. Show that StartFraction r 1 Over r 2 EndFraction equals StartFraction omega 2 Over omega 1 EndFraction r1 r2
Answer:
r1/r2 = 2ω2/ω1
Step-by-step explanation:
The velocity of each pulley is expressed as v = ωr where;
v is the linear velocity of the pulley
ω is the angular velocity of the pulley
r is the radius of the pulley.
For the two pulleys, the velocity I'd both pulleys are the same.
v1 = v2
v1 is the linear velocity of first pulley
v2 is the linear velocity of the second pulley.
v1 = ω1r1
v2 = 2ω2(r2)
r1 and r2 is the radius of pulley 1 and pulley 2 respectively.
Since v1 = v2
ω1r1 = 2ω2(r2)
Divide both sides by r2
ω1r1/r2 = 2ω2(r2)/r2
ω1r1/r2 = 2ω2
Divide both sides by ω1
ω1r1/r2/ω1= 2ω2/ω1
r1/r2 = 2ω2/ω1