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:
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what would an equation be for 6 bags of flyers each bag containing 12 flyers
Answer:
6x12
Step-by-step explanation:
Answer:
6 multiplied by 12
Step-by-step explanation:
you have 6 bags, each bag contains 12 flyers
help meh pleaseeeeeeeeeee
Answer:
-2/1
Step-by-step explanation:
-2/1 starting point -1
a 4.5 pound of apples costs $22.50. how many pounds for a dollar?
Answer:
.2 lbs
Step-by-step explanation:
4.5/22.5
0.2 pounds as 4.5 / 22.5 = 0.2
Of the 50 students in the cafeteria, 7 have red hair. Suppose there are 750 students in the school. Write a proportion that could be used to predict the number of students who have red hair. Use x to represent the number of students who have red hair.
Given:
Of the 50 students in the cafeteria, 7 have red hair.
Total number of students = 750
To find:
The proportion that could be used to predict the number of students who have red hair.
Solution:
Let x represent the number of students who have red hair.
The ratio of student having red hair to the total number of students are
[tex]Ratio_1=\dfrac{7}{50}[/tex]
[tex]Ratio_2=\dfrac{x}{750}[/tex]
The number of students having red hair is proportional to the total number of students. So, the above ratios are equal.
[tex]\dfrac{x}{750}=\dfrac{7}{50}[/tex]
Multiply both sides by 750.
[tex]\dfrac{x}{750}\times 750=\dfrac{7}{50}\times 750[/tex]
[tex]x=7\times 15[/tex]
[tex]x=105[/tex]
Therefore, the required equation is [tex]\dfrac{x}{750}=\dfrac{7}{50}[/tex] and the number of students who have red hair is 105.
The lines AB and CD are perpendicular to each other. If the slope of line AB is 2/3 then what is the slope of line CD
Answer:
-3/2
Step-by-step explanation:
you can find the perpendicular slope by putting the slope in 1/-m. M is the current slope you have or really you can flip it and change the signs so for example, 1/-(2/3) = -3/2
The slope of line CD is = -3/2
What are Perpendicular lines?A perpendicular is a straight line that makes an angle of 90° with another line.
Given that the lines AB and CD are perpendicular to each other, the slope of line AB is 2/3.
Slope of perpendicular lines are negative reciprocal of each other, so,
Hence, The slope of line CD is = -3/2
For more references on Perpendicular lines, click;
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10 Nessa takes her friends out to lunch and the total cost of the meal is $88.71. The
restaurant then added a 20% tip to the cost of the meal. Not including the sales or
meals tax, what was the total cost of the lunch with the tip?
Does the following table show a proportional relationship between the variables ggg and hhh?
ggg 333 666 999
hhh 999 363636 818181
Answer:
the answer is no
Step-by-step explanation:
khan said so
Answer:
No
Step-by-step explanation:
All three ratios aren't the same number when simplified
A restaurant serves sandwiches and salads. They sold 14 sandwiches and 14 salads for a total of $280 for lunch. In the evening, 42 sandwiches and 154 salads were sold for a total of $1400. How much does each sandwich cost?
Answer:
33.3
Step-by-step explanation:
1400 divided by 42
Answer:
$33.30
Step-by-step explanation:
1400 divided by 43 = 33.3
If the place these marbles in a bag close your eyes and choose a marble what is the probability that it will be pink?
Answer:
3/14
Step-by-step explanation:
There are 14 marbles, 5 are yellow, 6 are blue, and 3 are pink. You have a 5/14 chance to get a yellow marble, a 6/14 chance to get a blue marble, and a 3/14 chance to get a pink marble.
I hope that this helps :)
Answer:
3/7
Step-by-step explanation:
the answer is
How many solutions does the following equation have? -7x + 3 = 2x + 2 - 9x *
1 point
No solution
One solution x = 5
Infinite solutions
One solution x = 7
Answer:
no solutions because you would get an outcome of a not real world problem
Harper and her children went into a bakery and will buy cupcakes and brownies.
Each cupcake costs $4.25 and each brownie costs $2.75. Harper has a total of $40 to
spend on cupcakes and brownies. Write an inequality that would represent the
possible values for the number of cupcakes purchased, c, and the number of brownies
purchased, b.
Answer:
4.25c+2.75b_<40
Step-by-step explanation:
Can someone help me please
Answer:
The answer is A.
Step-by-step explanation:
2x2x2= 8 but one of them fell off.
At school 2 out of every 5 students in the sixth grade are members of the band which ratio represents the number of 6th graders that are not members of the band
Answer:3:5
Step-by-step explanation:
Answer:
3/5
Step-by-step explanation:
had that answer
4. x+ 4 + 7 = 3
How do I solve the absolute value ?
Answer:
-2
Step-by-step explanation:
4x +4 +7 =3
or, 4x = 3 - 11
or, x = (-8) / 4
since,
X = -2
If l is parallel to m, find the value of each missing variable
Answer:
x = 18
y = 5
Step-by-step explanation:
From the figure attached,
'l' and 'm' are the parallel lines and two transversal lines are intersecting these parallel lines at points A, B and C.
Since, m∠ABC + (7x - 23)° = 180° [Supplementary angles]
m∠ABC = 180° - (7x - 23)°
m∠BCA = (11y - 1)° [Vertical angles]
m∠BAC = 49°
In ΔABC,
m∠ABC + m∠BAC + m∠CAB = 180°
180° - (7x - 23)° + 49° + (11y - 1) = 180°
-7x + 11y = -71
7x - 11y = 71 ------(1)
Since, sum of consecutive angles is 180°
Therefore, m(∠ABC) + (3x + 49)° = 180°
180° - (7x - 23)° + (3x + 49)° = 180°
-4x = -72
x = 18
From equation (1),
7(18) - 11y = 71
11y = 55
y = 5
Why do you think the military police (MPs) confronted the men at the reservoir shack? Do you think the MPs did the right thing? Do you think Kaz and his men did the right thing? Explain.
Farewell To Manzanar, Chapter 6-11. IF U GET IT RIGHT U GET BRAINLIEST, 5 STARS AND THANKS
Answer:
ywes
Step-by-step explanation:
Last week, the value of an investment changed at a rate of –$0.80 each hour.
After how many hours was the total change in value –$3.60?
Answer:
4 hours
Step-by-step explanation:
3.6 / .8
x = -7y; 2x - 8y = 22
Answer:
(7; -1)
Step-by-step explanation:
Hi there!
Here is a solution:
If x=-7y then -14y-8y=22 => y=-1 and x=7
Hope this helps)
Have a nice day!
can you help me please
Answer: i think it would be 5
[tex]\sqrt{x} \left \{ {{y=2} \atop {x=2}} \right. \lim_{n \to \infty} a_n \int\limits^a_b {x} \, dx \\[/tex]
Evaluate x ÷ y for x = 3 and y = 12.
Answer:
1/4 or 0.25
Step-by-step explanation:
Lets plug x and y into the equation. We now have 3/12, which would be equal to 1/4 or 0.25
1 The formula for the area of a triangle is
A = 1/2 bh
where b is the base of the triangle and h is the height of the triangle.
What is the length of the base if the area is 22 cm2 and the height 2 is 8 cm?
Answer:
The formula of area of triangle= ½ base×height
Answer:
5.5cm
Step-by-step explanation:
22= (1/2)(8)(b)
22=(4)(b)
22/4= 5.5
b=5.5
which equation represents a line that passes through 4 6) and is parallel to the line whose equation is 3x - 4y= 6
TIMED TEST WILL GIVE BRAINLIEST
Parallel means their slopes should equal to each other.
Thus we need to find the slope of the given line ,
Let's do it.....
[tex]3x - 4y = 6[/tex]
Subtract sides -3x
[tex] - 3x + 3x - 4y = - 3x + 6[/tex]
[tex] - 4y = - 3x + 6[/tex]
Divided sides by -4
[tex] \frac{ - 4}{ - 4}y = \frac{ - 3}{ - 4}x + \frac{6}{ - 4} \\ [/tex]
[tex]y = \frac{3}{4}x - \frac{3}{2} \\ [/tex]
This is the slope-intercept of the line.
We know that the coefficient of the x in slope-intercept form , is the slope of the line.
Thus the slope of the equation which we want is :
[tex]slope = \frac{3}{4} \\ [/tex]
_________________________________
We have following equation to find the point-slope form of the linear functions.
[tex]y - y(given \: point) = slope \times (x - x(g \: p) \: ) \\ [/tex]
Now just need to put the slope and the given point in the above equation.
[tex]y - 6 = \frac{3}{4} \times (x - 4) \\ [/tex]
Multiply sides by 4
[tex]4(y - 6) = 3(x - 4)[/tex]
[tex]4y - 24 = 3x - 12[/tex]
Plus sides 24
[tex]4y - 24 + 24 = 3x - 12 + 24[/tex]
[tex]4y = 3x + 12[/tex]
Subtract sides -3x
[tex]4y - 3x = 3x - 3x + 12[/tex]
[tex]4y - 3x = 12[/tex]
And we're done....♥️♥️♥️♥️♥️
how do you do this? help me (show work) thank you
Answer:
7.5 < x < 8
Step-by-step explanation:
since the domain of a function is the value it can take as an argument except 0, then f(x) = 7.7.
Ten is at least the product of a number h and 5.
Answer:
Ten is at least the product of a number h and 5. h = 2
Step-by-step explanation:
Divide 10 by 5 and you get 2.
Check; 5 x 2 = 10
find the equation of the line that passes through a and b
Lines l and m are intersected by transversal t. l ∥ m.
If m∠4 = 105, what is m∠5?
Answer:
m<5 is 105
Step-by-step explanation:
<5 and <4 are alternate interior angles meaning they are congruent to each other.
1. The length of a rectangular parking lot is 8m longer than its width. The area of
the parking lot is 560m2. What is the length of the parking lot? How about its
width?
Answer:
Length = 20
Breadth = 12
Step-by-step explanation:
What are the transformations to the graph compared to the parent function y=√(x)?
Pls help me. I need help
Answer:
x= horizontal y=verticalCompare -25 and 25 help meeee
Answer:
-25 is less than 25
-25<25
Step-by-step explanation:
any negnegative number will always be less than a whole number.
please tell me if i answered this wronf or if you need more help!! :)