Answer:
The sum of the series is Sₙ = n/2 [2·a + (n - 1)·d] where a = 8 and d = 8, therefore 8 + 16 + 24 + ... + 8·n = 4·n·(n + 1)
Step-by-step explanation:
The parameters given are;
8 + 16 + 24 + ... + 8·n = 4·n·(n + 1)
The given series of numbers can be checked to find;
16 - 8 = 24 - 16 = 8
Therefore, the series of numbers is an arithmetic progression with first term = 8, and common difference = 8, we have;
The sum of n terms of an arithmetic progression, Sₙ, is given as follows;
Sₙ = n/2 [2·a + (n - 1)·d]
Where;
a = The first term of the series of numbers = 8
d = The common difference = 8
∴ Sₙ = n/2 × [2×8 + (n - 1)×8] = n [2×8/2 + (n - 1)×8/2] = n × [8 + (n - 1)×4]
Sₙ = n × [8 + (n - 1)×4] = n × [8 + 4·n - 4] = n × [8 - 4 + 4·n] = n × [4 + 4·n]
Sₙ =n × [4 + 4·n] = 4 × n×(n + 1) = 4·n·(n + 1).
Consider the following points. (−4, −1) and (4, 2) Let Y'O' be the image of YO after a reflection across line . Suppose that ′ is located at (1, 4) and ′ is located at (−2, −4). Which of the following is true about line ?
The line was reflected about the line y = -x.
-----------------------------------------
This question is solved using reflection concepts.
There are various kinds of reflections, 90º clockwise about the origin, 90º counterclockwise, among other, and each of them has a rule.
-----------------------------------------
In this question:
Point (-4,-1) became (1,4).Point (4,2) became (-2,-4).From this, we have the following rule: (x,y) -> (-y,-x)
Checking the rules, it can be said that the line was reflected about the line y = -x.
A similar question can be found at https://brainly.com/question/16130908
I NEED HELP I GIVE 5 STARS PLEASE ;(
Translate each verbal expression to an algebraic expression.
1. 6 less than the product of a cubed number and 15
2. The sum of the product of 4 and a squared number and the quotient of 5 and 3.
Step-by-step explanation:
Let the number be x, thenx³×15-6
15x³-6
2. Let the number be y, then
(4×y)+(5/3)
4y+5/3
Z varies directly as x/y² and y varies inversely as x,if z=⅓ when x =2 and y=¼. Express (a). Y interms of x and (b). Z interms of x
Answer:
Baba
Step-by-step explanation:
Booey
a=v^2/r Solve the formula for r
Answer:
[tex]\Large \boxed{r =\frac{v^2 }{a}}[/tex]
Step-by-step explanation:
[tex]\displaystyle a=\frac{v^2 }{r}[/tex]
We need to rearrange and solve the formula for [tex]r[/tex].
Multiply both sides of the equation by [tex]r[/tex].
[tex]\displaystyle a \times r=\frac{v^2 }{r} \times r[/tex]
Simplify the equation.
[tex]ar=v^2[/tex]
Divide both sides of the equation by [tex]a[/tex].
[tex]\displaystyle \frac{ar}{a} =\frac{v^2 }{a}[/tex]
Simplify the equation.
[tex]\displaystyle r =\frac{v^2 }{a}[/tex]
I have underlined the volume of water needed (left) and the volume of chemicals needed (right). How much of the chemical would I need if I used 16 oz. of water?
HELP ME PLEASE.
find the perimeter,area and T.S.A of the following solids
Answer:
I think the perimeter is 50cm the solids is 600cm³
Step-by-step explanation:
Perimeter: (5×10)=50cm
Solids: divided with 2box(A box & B box)
Abox: 5cm x 5cm x 12cm
=300cm³
Bbox: 5cm x 12cm x 5cm
=300cm³
Solids:(Abox +Bbox) 300cm³ + 300cm³
=600cm³
I think, I'm sorry if it's wrong
please help me for the homework
Answer:
refer to the pic attached
what are the factors of 47 (cuz im STUPID and i dont feel like doing this cuz im working on geogrophy)
Hey there! I'm happy to help!
The factors are the numbers you multiply to get 47. And they can't be fractions or numbers with fractions. They have to be integers (numbers without fractions).
So far, we see that we can multiply 1 and 47 to get 47. To see if there are any more, we see what numbers 1-10 we can divide by.
We cannot divide by 2 because 47 is odd.
We cannot divide by 3 because it gives us 15.6666...
We can't divide by 4 because 47 is odd.
We can't divide by 5 because 47 does not have a 5 or 0 in the ones place.
We can't divide by 6 because 47 is odd.
We can't divide by 7 because it gives us 6.714285....
We can't divide by 8 because 47 is odd.
We can't divide by 9 because it gives us 5.2222
And we obviously can't divide it by 10.
Therefore, the factors of 47 are 1 and 47. A number whose only factors are 1 and itself is called a prime number.
I hope that this helps! Have a wonderful day! :D
Answer: 47 is a prime number
The exponent of prime number 47 is 1 . Adding 1 to that exponent we get (1+1)=2
Factor of 47: 1, 47
The base of a triangle is two times its height. If the area of the triangle is 36, then what is the height of the triangle?
We have:
h - height
b = 2h - base
A = 36 - area
so:
[tex]A=\frac{1}{2}\cdot b\cdot h\\\\A=\frac{1}{2}\cdot 2\cdot h \cdot h\\\\A=h^2\\\\36=h^2\quad|\sqrt{(\dots)}\\\\\boxed{h=6}[/tex]
Simplify 4^2+6(.5)-2^
Please show step by step :)
———————
Simplify 10- (15/5+4)
Please show step by step :)
Answer:
4^2 + 6(5)-2^3
16+30-8
38
My brain has stopped working, can you answer this?
Answer:
$40.00, $30.00, B
Step-by-step explanation:
We can first write an expression for the cost of each plan.
Given x amount of texts and y amount of minutes, plan A costs 15 cents per text sent (so given x amount of texts, plan A costs 15 * x for texts) and 10 cents per minute (so given y amount of minutes, plan A costs 10 * y for minutes). Adding these up, plan A costs 15 * x + 10 * y. Plugging Jaden's 200 texts in for x and 100 minutes in for y, we have
15 * x + 10 * y = 15 * 200 + 10 * 100 = 4000 cents. 100 cents = 1 dollar, and the conversion rate for cents to dollars is divide by 100, so we divide 4000 cents by 100 to get $40.00 as the cost for plan A
For plan B, the flat rate is 15 dollars. To convert from dollars to cents, we multiply by 100, so 15 * 100 = 1500 cents for the flat fee.
Texts cost 5 cents per text, so 5 * x is the cost for texts in cents for plan B. Similarly, 5 * y is the cost for minutes in cents for plan B. Adding these up, we get
1500 + 5 * x + 5 * y
combine like terms
1500 + 5 * (x+y)
plug 200 in for x and 100 in for y
1500 + 5 * (200+100)
1500 + 5 * (300)
1500 + 1500
3000
divide by 100 to convert to dollars
$30.00 is the cost for plan B
$30 < $40, so plan B will be cheaper for Jaden
3. a. Simplify (2x + y) (x-7)
b. Find the truth set of 2x-3 +3 = -1
Answer: b. X=-1/2
Step-by-step explanation:
2x-3+3=-1-3 and +3 cancel each other
2x=-1 both sides divided by 2
X=-1/2
Heyyy could someone please help me out?? Would appreciate it. Thanks in advance!!^^
Answer:
Below,...
Step-by-step explanation:
They are saying that if you add a odd number + a odd number than you'd get a even number,... odd + even = odd,... odd x even = even,... and so on,...
Hope it helps,... Chow!
What is the smallest number than can be subtracted from 438 to make it
exactly divisible by 5? Give a reason for your answer.
Answer:
3
Step-by-step explanation:
basically the largest number decided by 5 smaller than 438 is 435. so the answer is 3
Answer:
Any number divisible by 9 must have the sum of its digits divisible by 9. The sum of the digits of 456 is 15, so you need to subtract 6.
Find four rational number between 1/4 and 2/3.
Answer:
4/12, 5/12, 6/12, 7/12
Step-by-step explanation:
1/4 x 3/3 = 3/12
2/3 x 4/4 = 8/12
between 3/12 and 8/12
4/12, 5/12, 6/12, 7/12
you can simplify these if you wish
Hope that helped!!! k
5. Which property was used to simplify the expression?
a) distributive property
b) commutative property
c) associative property
d) inverse property
Answer:
a
Step-by-step explanation:
distributive property
What is the values of x and y
Answer:
If you have given an equation, you see the x and y in it. Just taking second equation and think any common factor between x's variable. With common factor, multiply both and you will find the value of y and put it in any equation, you will find the value of X.
Answer:
Hey there!
I can't see the full problem, but if when x=0.5, y=4, then when x=4, y=32, and when x=9, y=72. You multiply by a common multiple to get from x to y.
Hope this helps :)
The volume of a sphere whose diameter is 18 centimeters is π cubic centimeters. If its diameter were reduced by half, its volume would be of its original volume.
Answer:
3053.5517 cm^3 ; 1/8
Step-by-step explanation:
Given the following :
Volume (V) of sphere = (4/3)πr^3 where r = radius
Diameter of sphere = 18 ; radius(r) = diameter / 2 = 18/2 = 9cm
V = (4/3) × π × 9^3
V = 1.3333 × π × 729
V = 3053.5517 cm^3
When diameter(d) is reduced to half
d = d/2
Volume (V1) of sphere with diameter 'd' =
V1 = (4/3)π(d/2)^3
Volume (V2) of sphere with diameter 'd' reduced to half, d = d/2, d/2 * 1/2 = d/4
V2 = (4/3)π(d/4)^3
V1 / V2 = [(4/3)π(d/2)^3] / [(4/3)π(d/4)^3]
V1 / V2 = (d/2)^3 / (d/4)^3
V1 / V2 = [d^3 / 2^3] / [d^3 / 4^3]
V1 / V2 = 8 / 64
V1 / V2 = 1 / 8
Answer:
first blank is 972
second blank is 1/8
yup
Step-by-step explanation:
(08.02)How many solutions are there for the system of equations shown on the graph? No solution One solution Two solutions Infinitely many solutions
Answer: Infinitely many solutions
Step-by-step explanation:
There are many solutions because the lines lies on top of each other.
i dont know the exact answer but its not
One solution
Two solutions
so its most likely
Infinitely many solutions
Find y. A. 63–√ B. 33–√ C. 23√3 D. 3
This is a 30-60-90 triangle. The shortest leg (opposite the smallest angle) is half that of the hypotenuse, so y = 6/2 = 3.
Extra info: The long leg is sqrt(3) times the short leg, so x = y*sqrt(3) = x = 3*sqrt(3)
Answer:
D.) 3
Step-by-step explanation:
I got it correct on founders edtell
Can anyone help idk how to do it
Answer:
Carl can type 450 words in 5 minutes at that rate.
Step-by-step explanation:
Every two minutes, carl can type 180 words. To find out how many words he can type in 1 minute, all we have to to is divide 180 by 2 to get 90wpm (words per minute)
if we multiply 90wpm by 5 Minutes, we get 450 words per minute
Rodrigo and his cousin have 8 bags of marbles. Some of the bags contain 5 white marbles. The rest of the bags contain 7 pink marbles. They have 48 marbles in all. How many bags of each color marble do the cousins have?
Answer:
The cousins have 4 bags of white marbles and 4 bags of pink marbles.
Step-by-step explanation:
If x is the number of bags with white marbles and y is the number of bags with pink marbles, we can write the following system:
x + y = 8 -- Equation 1
5x + 7y = 48 -- Equation 2
5x + 5y = 40 -- Equation 3 (Multiply Equation 1 by 5)
2y = 8 -- (Subtract Equation 3 from 2)
y = 4 -- (Divide both sides by 2)
x + 4 = 8 -- (Substitute y = 4 into Equation 1)
x = 4 -- (Subtract 4 from both sides)
simple way to differentiate between speed and average speed.
Answer:
speed
1)the distance travelled by a body per unit time is known as speed.
2) speed is speed, or something how fast is going,
3) while velocity is speed how fast something is going in a specific direction.
average speed
1) average speed is the speed added up and divided by number of speed .
2)the average of all the instantaneous speed in a give time interval.
3) the average speed as the duration of the time interval approaches zero.
solve for x 7(x-3)+3(4-x)= -8
Answer:
Step-by-step explanation:
7x - 21 + 12 - 3x = -8
4x - 9 = -8
4x = 1
x = 1/4
Answer:
x= 0.25, or x=1/4
Step-by-step explanation:
First, use the distributive property and multiply 7 within the parenthesis:
7x -21
Next, use the distributive property again, and multiply 3 within the parenthesis:
12 -3x
Combine Like terms: 7x - 21 + 12 - 3x
4x - 9
Add 9 to both sides: 4x - 9 = -8
-8 + 9 = 1
Divide 4 by both sides: 4x = 1
1 / 4 = .25 or 1/4
Someone plz help me I’m stuck with this one T^T
Answer:
SID WILL FINISH FIRST
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] ÷ [tex]\frac{1}{6} =[/tex]
[tex]\frac{2}{3}[/tex] * [tex]\frac{6}{1} =[/tex] = 12/3 = 4
~~~~~~~~~~~~~~~~~~~
[tex]\frac{1}{3}[/tex] ÷ [tex]\frac{1}{9} =[/tex]
[tex]\frac{1}{3}[/tex] * [tex]\frac{9}{1} =[/tex] = 9/3 = 3
A football stadium splits ticket sales in ratio of 3 : 4 between the away team and the home team. The home team make £36,000. What is the total amount of ticket sales?
The ratio 3:4 means for every 3 pounds made in away team tickets versus home team tickets. Multiply both sides by 9000 to have that 4 turn into 36000. The ratio 3:4 will then turn into 27000:36000
With this new ratio, we see that the away team pulls in 27000 and the home team pulls in 36000. Add the two amounts to get the final answer
27000+36000 = 63000
------------
We could alternatively add 3 and 4 (from the ratio 3:4) to get 3+4 = 7. Then multiply by that same scale factor 9000 getting 9000*7 = 63000.
In a bag of M&MS there are 4 green, 6 yellow and 8 blue candies. What is the probability of drawing a blue then a green if you replace the candy after the draw?
Answer:
8/81
Step-by-step explanation:
8/18 x 4/18 = 32/324 = 8/81
The probability of drawing a blue and then a green and replacing the candy after the draw is 8/81.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of sample
It is given that in a bag of M&MS there are 4 green, 6 yellow, and 8 blue candies.
The probability for blue = 8/18
The probability for green = 4/18
The probabilities of drawing a blue then green if you replace the candy after the draw will be calculated as below:-
Probability = 8/18 x 4/18
Probability = 32/324
Divide the number 32 by 324 to get the probability.
Probability = 8/81
Therefore, the probability of drawing a blue and then a green and replacing the candy after the draw is 8/81.
To know more about probability follow
https://brainly.com/question/24756209
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Points A, B, and C are collinear. Point B is between point A and point C. Find the length of AB if AB=20+x, BC=2x+31, and AC=18. *
Answer:
ab=9
Step-by-step explanation:
AB=BC
2X+31=20+X
X=-11
ab= 20+(-11)
= 9
bc= 2(-11) +31
=9
ab+bc= ac
9+9=18
Solve for b. -11b+7 = 40 b=
Answer:
B= -3
Step-by-step explanation:
Move the terms that do not contain b to the right then solve. Hope this helps!
Answer:
[tex]\large \boxed{{b=-3}}[/tex]
Step-by-step explanation:
[tex]-11b +7=40[/tex]
Subtract 7 from both sides.
[tex]-11b +7-7=40-7[/tex]
[tex]-11b=33[/tex]
Divide both sides by -11.
[tex]\displaystyle \frac{-11b}{-11} =\frac{33}{-11}[/tex]
[tex]b=-3[/tex]