Answer:
The correct answer is = 15.
Step-by-step explanation:
Formula:
The sum of the first n terms of an arithmetic progression with first term a and constant difference d is
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d[/tex]
using this formula in this problem
Solution:
The sum of the first ten terms is
[tex]S_{10}=\dfrac{10}{2}[2a+(10-1)d[/tex]
[tex]S_{10}=5(2a+9d)[/tex]
The sum of the 20th, 21st, and 22nd terms is three times the 21st term:
[tex]3a_{21}=3(a+(21-1)d)[/tex]
[tex]3a_{21}=3(a+20d)[/tex]
[tex]3a_{21}=3a+60d[/tex]
The problem then tells us
[tex]S_{10}=3a_{21}[/tex]
[tex]10a+45d=3a+60d[/tex]
[tex]7a=15d[/tex]
there are only positive integers and the first term a is less than 20 as given. Since 7 and 15 have no common factor, the only explanation of the requirements is a = 15 and d = 7. So the progression is
then, 15, 22, 29, 36, ...
The problem says to find the number of terms n for which the sum is 960:
putting value in the formula
[tex]30n+7n^{2}-7n=1920\\7n^{2}+23n-1920=0[/tex]
solving quadratic will give n = 15
thus, the correct answer is 15.
Samuel had 12 red marbles , 15 blue marbles , and 13 green marbles . Which fraction represents the number of red marbles he has
Answer:
12/40 or simplified it would be 3/10
Step-by-step explanation:
What is the reciprocal of 0.025 (not -0.025)
Answer:
1000/25 or 40
Step-by-step explanation:
~ A reciprocal is the fraction's reverse
For example 2/3=3/2
.025 is also 25/1000
The reverse of 25/1000 is 1000/25
Simplified into 40 wholes
1000/25 is the reciprocal of 0.025
What is Fraction?A fraction represents a part of a whole.
Given,
Decimal value is 0.025
Zero point zero two five.
Firstly let us convert this to the fraction form.
When twenty five is divided by thousand we get 0.025
25/1000=0.025
So the fraction is 25/1000.
Now we need to find the reciprocal of fraction 25/1000.
Reciprocal means the numerator changes to denominator and denominator changes to numerator.
So 25/1000 reciprocal is 1000/25
Hence, 1000/25 is the reciprocal of 0.025
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What is the
range of the function in the graph?
Answer:
Step-by-step explanation:
A resposta é a letra a
solve: x^2-x-12÷x+5 ≥ 0
Answer:
Step-by-step explanation:
x3−x2+5x−12
x
≥0
Let's find the critical points of the inequality.
x3−x2+5x−12
x
=0
x3−x2+5x−12=0(Multiply both sides by x)
(Use cubic formula)
x=1.836169
Check possible critical points.
x=1.836169(Works in original equation)
Critical points:
x=1.836169(Makes both sides equal)
x=0(Makes left denominator equal to 0)
Check intervals in between critical points. (Test values in the intervals to see if they work.)
x<0(Works in original inequality)
0<x≤1.836169(Doesn't work in original inequality)
x≥1.836169(Works in original inequality)
Answer:
x<0 or x≥1.836169
A motorboat travels 189 kilometers in 3 hours going upstream and 475 kilometers in 5 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Answer:
boat speed 79 kph
stream speed 16kph
Step-by-step explanation:
Let v be the still water velocity
Let s be the stream velocity
3(v - s) = 189
3v - 3s = 189
v - s = 63
v = 63 + s
5(v + s) = 475
5v + 5s = 475
5(63 + s) + 5s = 475
315 + 5s + 5s = 475
10s = 160
s = 16 km/hr
v = 63 + 16
v = 79 km/hr
A sports stadium has a capacity of 42,000. On a
particular night, 35,000 spectators attend an event. At
the end of the event, spectators leave the stadium at a rate
of 320 spectators every minute. If m represents the
number of minutes after spectators begin to leave the
stadium, which of the following inequalities describes
the times when there are still spectators in the stadium?
A) 42,000 - 35,000m < 320
B) 35,000 - 320m > 0
C) 35,000 + 320m < 42,000
D) 320m < 87,000
Answer:
B
Step-by-step explanation:
The inequality will be 35000-320m>0
Compare 8/3 and 19/8.
Answer:
8/3 > 19/8
Step-by-step explanation:
Get a common denominator
8/3 *8/8 = 64/24
19/8 *3/3 =57/24
Comparing the numerators
64>57
8/3 > 19/8
Find the missing side of the triangle
Answer:
approximately 12.7
Step-by-step explanation:
using phythagoras rule,
hyp²=opp²+ adj²
15²=x² + 8²
225=x² + 64
x²=225 - 64
x²= 161
x=12.7
OR
sin ø= 8/15
sin ø=0.53333333
ø=sin(inverse) of 0.53333333
ø=0.563⁰
therefore angle opposite 8 is 0.563
tan 0.563= 8/x
x tan 0.563=8
x= 8/tan 0.563
x= 12.7
Show Work! A warehouse worker shipped 289 boxes of notebooks. Each box contained 36 notebooks. What was the total number of notebooks shipped?
(A) 2, 601
(B) 9, 404
(C) 10, 404
(D) 10, 413
Answer:
(c) 10, 404.
Step-by-step explanation:
Step 1.
To multiply 289 by 36, set them up as shown by arranging the two numbers in columns. We usually put the number with the smaller number of digits at the bottom.
Step 2.
Firstly, work out 6 × 289. The smaller figures in green are the tens figures carried over. Working from right to left:
6 × 9 = 54
Put the 4 in the appropriate column and carry the 5.
6 × 8 + 5(carried) = 53
Put the 3 in the appropriate column and carry the 5.
6 × 2 + 5(carried) = 17
Put the 7 in the appropriate column and carry the 1.
Step 3.
Lastly, work out 30 × 289.
This can be written as 3 × 289 × 10.
Because we are multiplying by 10, we place 1 zero to the right and then work out 3 × 289.
3 × 9 = 27
Put the 7 in the appropriate column and carry the 2.
3 × 8 + 2(carried) = 26
Put the 6 in the appropriate column and carry the 2.
3 × 2 + 2(carried) = 8
Step 4. Finally, the 2 rows are added together starting at the right. The smaller figures in green are the tens figures carried over.
0 + 4 = 4
7 + 3 = 10
Put the 0 in the appropriate column and carry the 1.
6 + 7 + 1(carried) = 14
Put the 4 in the appropriate column and carry the 1.
8 + 1 + 1(carried) = 10
Put the 0 in the appropriate column and carry the 1.
1 (carried) = 1
So: 289 × 36 = 10404
Mathematics done on paper should look something like this; ( Did the best I can on PC)
2 8 9
................. 3....6....×
1 7 3 4
1 5 5
8 6 7 0
....... 2......2.........
1 0 4 0 4
1 1 1
Hope this helped!
Need answers in 2 minutes ASAP
Kane's Furniture Store advertised a table at 9% discount. The original selling price was $109, and the sale price was $100. Was the sale price consistent with the ad? Explain.
Answer:
No, the sale price wasn't consistent with the ad
Step-by-step explanation:
The original selling price is 109. 9% of 109 is 9.81. So the sale price should be 99.19.
Brenna went to the mall with her mom. They started shopping at 4:47 P.M. First, they spent 26 minutes in the shoe store. Then they spent 1 hour and 13 minutes shopping for a dress for Brenna. Finally, they spent 1 hour and 2 minutes eating dinner at the food court. What time was it when Brenna and her mom finished eating dinner?
Brenna and her mom finished eating dinner at 7:28 PM
They started shopping at 4:47 PM, and spent 26 minutes in the shoe store.
4:47 + 26 = 5:13 PM
They spent another 1 hour and 13 minutes shopping for a dress.
5:13 + 1 hr 13 min = 6:26 PM
Finally, they spent 1 hour and 2 minutes eating dinner at the food court.
6:26 + 1 hr 2 min = 7:28 PM
Hope this helps :)
Please help will give brainliest
Complete the equation describing how
x and y are related.
X
0
1
2
3
4
у
-6
-10
-14
- 18
-22
y = [ ? ]x + [ ]
Enter the answer that belongs in [?].
Answer:
-6
Step-by-step explanation:
The equation is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The y intercept is the value when x = 0
The y value is -6 when the x value is 0
y = -4x+ (-6)
solve for x please help (show work!)
Answer:
x = 1/2 or 0.5
Step-by-step explanation:
8(-2x + 1) = 0
Distribute the 8 by multiplying 8 by what's inside of the parenthesis (-2x and 1)
8 * -2x = -16x
8 * 1 = 8
We now have
-16x + 8 = 0
Subtract 8 from both sides
-16x + 8 - 8 = 0 - 8
-16x = -8
Divide both sides by -16
-16x/-16 = -8/-16
x = 1/2
8( -2x + 1 ) = 0
S O L U T I O N :8( -2x + 1 ) = 0Simplify the left hand side
-16x + 8 = 0Transposing -16x to the other side
8 = 16xCross multiplying we get
x = 8/16x = ½x = 0.5Hence the value of x is 0.5 or ½
A line passes through the point (12,-4) and is perpendicular to the line with the equation y=6x +3
Answer:
y= -(1/6)x -2
Step-by-step explanation:
We know:
y= mx +b is the general equation of the line
Was given:
y= 6x +3, has the slope m=6
Find the equation of the line
y= -(1/6)x + b, perpendicular lines have their slope negative reciprocal m=-1/6
Find the y-intercept that is b
for point (x=12, y= -4) the equation of our line becomes
-4 = -(1/6)(12) + b, multiply a fraction and a number (a/b)*c = ab/c
-4 = -12/6 +b, simplify the fraction
-4 = -2 + b , add 2 to both sides
-4+2 = -2+2 +b , solve for b
-2 = b
The equation of the line that passes through the point (12,-4) and is perpendicular to the line with the equation y=6x +3 is :
y= -(1/6)x -2
If JKL = TUV which of the following can you not conclude as being true
Answer:
Step-by-step explanation:
D
Answer:
∠J ≅ ∠V
Step-by-step explanation: I took the same test (:
Please Help Polygons
Step-by-step explanation:
5.25....................
I need help with 4 x (7 - 3) please show your work
Answer: 16
Step-by-step explanation:
Take ( 7 - 3 ) and subtract 3 from 7, which gives you 4, then take 4 and multiply it by 4, ( 4x4 ) which gives you 16.
Answer:
16
Step-by-step explanation:
4 * (7 - 3)
Parentheses first
4*(4)
Then multiply
16
the sum of 2 numbers is 18 and there difference is 6
Answer:
The two numbers are 6 and 12.
Step-by-step explanation:
So, let's start off, with x+y = 18 and x-y = 6.
Algebraically, we can add the above two equation sets, and we find out that 2x = 24, so x = 12. And then, it says the other number must be 6.
You start with a number that when added to the second number you will get 18 and when you subtract the second number from the first you will get 6. The difference between the above two results is 12.
So that difference of 12 is twice the second number; that means the second number is 6. And then using either of the given pieces of information, you can find that the first number is 12.
------------------------------------------------------
In conclusion:
6 + 12 = 18
12 - 18 = 6
solve 8x=5x+3 pls pls pls
Answer:
x = 1
Step-by-step explanation:
8x = 5x + 3
Subtract 5x from both sides
8x - 5x = 5x - 5x + 3
Simplify
3x = 3
Divide both sides by 3
3x/3 = 3/3
Simplify
x = 1
What is the size of each piece in square units?
What is the area of the shaded rectangle in square units?
Answer Asapp plezz
Answer:
8 pieces are shaded
Size of one square is (1/3)*(1/5)=1/15
The area of shaded region is basically (2/3)*(4/5)=8/15
The Size of one square is 1/15. The area of the shaded region rectangle is 8/15.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
From the given figure we can see that 8 pieces of the square makes a shaded region.
The area of a square = side x side
[tex]= \dfrac{1}{3}\times\dfrac{1}{5}\\\\=\dfrac{1}{15}[/tex]
Therefore, the Size of one square is 1/15.
The area of the shaded region rectangle = length × Width
[tex]= \dfrac{2}{3}\times\dfrac{4}{5}\\\\=\dfrac{8}{15}[/tex]
Learn more about the area;
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Find each question solutions.Please
Answer:
Dependent variable = Total daily cost
Independent variable = number of items manufactured
2500 ;
9750
Step-by-step explanation:
Given the cost function in. A manufacturing company :
C(x) = 7.25x + 2500 ; Where
C(x) = total daily cost
x = number of items manufactured
The Independent variable is the variable whose value causes a change in the measured variable, this is the number of items manufactured, and the variable which charges as the predictor variable charges is the dependent variable (Total daily cost).
2.)
C(0) ;
C(x) = 7.25x + 2500
Put x = 0
C(0) = 7.25(0) + 2500
Cost = 2500
This is the total daily cost even if no items are produced, this is probably the fixed cost of daily production.
3.)
C(1000)
C(x) = 7.25x + 2500
Put x = 1000
C(0) = 7.25(1000) + 2500
Cost = 7250 + 2500
Cost = 9750
This is the total cost including variable cost of producing 1000 items.
Se o preço de 8 potes de nutella é 288 reais, qual e o preço se 5 potes de Nutella
What is the missing digit?
820,107
– 65□,084
167,023
Please help it’s due today
Answer:
67 degrees
Step-by-step explanation:
23 + 90 = 113
180 - 113 = 67
5 pencils for 15 dollers how much for each pencil
5 pencils = 15 dollors
1 pencil = 15/5 dollors
therefore 1 pencil = 3 dollors...
Answer:
Each pencil would cost $3.00
Step-by-step explanation:
If 5 costs $15, to find the cost of one you divide 15 by 5
15 ÷ 5 = 3
Three numbers form an arithmetic sequence whose
common difference is 3. If the first number is
increased by 1, the second increased by 6, and
the third increased by 19, the resulting three
numbers form a geometric sequence. Determine
the original three numbers.
Let x be the first number in the sequence. Then the first three numbers are
{x, x + 3, x + 6}
The next sentence says that the sequence
{x + 1, x + 9, x + 25}
is geometric, which means there is some fixed number r for which
x + 9 = r (x + 1)
x + 25 = r (x + 9)
Solve for r :
r = (x + 9)/(x + 1) = (x + 25)/(x + 9)
Solve for x :
(x + 9)² = (x + 25) (x + 1)
x ² + 18x + 81 = x ² + 26x + 25
8x = 56
x = 7
Then the three numbers are
{7, 10, 13}
If X = 4 and y = -2, the value of 1/2 xy^2 is
Answer:
[tex]8[/tex]
Step-by-step explanation:
Note that 1/2 xy^2 is, by order of operations, read as [tex]\frac12xy^2[/tex]. If this is not what was intended in the question then please amend it according order of operations.
Plugging the values [tex]x=4[/tex] and [tex]y=-2[/tex] gives
[tex]\frac12xy^2=\frac12(4)(-2)^2=\frac12(4)(4)=\frac12(16)=8[/tex]
domain of function y=|x|
Answer:
All real number
Step-by-step explanation:
The graph of y = x is shown to the right. We can see that it is defined for all x-values because the line will continue to infinity. Thus, the domain of y = x is all real numbers.
Hope this help <3
Find the remainder when f(x) = x^3- 6x^2 +3x -1 divided by 2x-3
Answer:
Remainder is -53/8
Step-by-step explanation:
the divisor is (2x - 3):
make x the subject:
[tex]2x - 3 = 0 \\ 2x = 3 \\ x = \frac{3}{2} [/tex]
substitute for x in the function:
[tex]f(x) = {x}^{3} - 6 {x}^{2} + 3x - 1 \\ f( \frac{3}{2} ) = {( \frac{3}{2}) }^{3} - 6 {( \frac{3}{2}) }^{2} + 3( \frac{3}{2} ) - 1 \\ \\ f( \frac{3}{2} ) = \frac{ - 53}{8} [/tex]