Answers
[tex]\displaystyle\\\sum_{n=3}^5(-2x-4n)=-2x-4\cdot3+(-2x)-4\cdot4+(-2x)-4\cdot5\\\sum_{n=3}^5(-2x-4n)=-6x-12-16-20\\\sum_{n=3}^5(-2x-4n)=-6x-48[/tex]
Related Questions
Please help, question above
Answers
Answer:
4^ (r-s)
Step-by-step explanation:
When the bases are the same, and we are dividing, we subtract the exponents
x^a ÷ x^b = x^ (a-b)
4^r ÷ 4^s = 4^ (r-s)
The first 5 terms of a number pattern are shown below.
4, 9, 14, 19, 24
Which expression is equivalent to the value of the nth term in the pattern?
Answers
[tex]\bf 4~~,~~\stackrel{4+5}{9}~~,~~\stackrel{9+5}{14}~~,~~\stackrel{14+5}{19}~~,~~\stackrel{19+5}{24}\qquad \impliedby \stackrel{\textit{common difference}}{d=5} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=4\\ d=5 \end{cases} \\\\\\ a_n=4+(n-1)5\implies a_n=4+5n-5\implies a_n=5n-1[/tex]
You use technology ans find a sum of 6.712E-8. Write this sum in standard form
Answers
Answer:
[tex]0.000\,000\,067\,12[/tex]
Step-by-step explanation:
The exponent of -8 tells you the most significant digit (6) goes in the 8th position to the right of the decimal point.
With some spaces to help in counting decimal places, the number is written ...
[tex]0.000\,000\,067\,12[/tex]
A rock is tossed at an initial velocity of 60 m/s at an angle of 10° with the ground. After 0.9 second, how far has the rock traveled horizontally and vertically?
Answers
Step-by-step explanation:
In the x direction:
x = x₀ + v₀ₓ t + ½ at²
x = (0 m) + (60 m/s cos 10°) (0.9 s) + ½ (0 m/s²) (0.9 s)²
x ≈ 53 m
In the y direction:
y = y₀ + v₀ᵧ t + ½ gt²
y = (0 m) + (60 m/s sin 10°) (0.9 s) + ½ (-9.8 m/s²) (0.9 s)²
y ≈ 5.4 m
Answer:
53.2 m horizontally and 5.4 m vertically
Step-by-step explanation:
How many blue counters must be added so that the ratio of yellow counters to total counters is 1 to 6
Answers
Answer:
5
Step-by-step explanation:
if the ratio is 1:6, and its yellow to total, that means that you would need to subract 1 from 6 to get the number to blue counters needed to get the correct ratio
Answer:5
Step-by-step explanation:
. Find the rate of change for the situation. You run 3 miles in one hour and 6 miles in two hours. 2 hours 3 miles 3 miles per hour 2 miles per hour
Answers
Answer:
3 miles per hour
Step-by-step explanation:
because he runs 3 mile per hour , for another one hour 3 miles therefore it will be 3 miles per hour
Ms. Kiyama is fed up with all the legos around her living room so she decides to do something about it. She starts by getting rid of 23 of them because they are cracked. She then takes what is left and splits them evenly between the living room, James’ room, and Christopher’s room. When grandma comes over and sees how they can’t complete their creations with the legos in each room, she doubles each set for Valentine’s Day, so that each room contains 78 legos. How many legos were there to start?
Answers
Answer: 140
Step-by-step explanation:
Begin by dividing 78 by 2 to go back to the original amount before the grandmother doubled them. Then multiply by 3 (each room). Finally, add the 23 that were thrown away at the beginning.
Initially, there were 140 legos. Each room had 39 legos before grandmother doubled them to 78, so multiplying 39 by the 3 rooms gives 117 legos, plus 23 removed cracked legos equals 140 original legos.
The student is trying to calculate the original number of legos Ms. Kiyama had before any were removed or added. We know that each room ended up with 78 legos, and this number was obtained after grandmother doubled the amount in each room. Therefore, before being doubled, there would have been 78 / 2 = 39 legos in each room. Since these legos were distributed equally among three rooms, we'll multiply 39 legos by 3 rooms to find the total number of legos before they were doubled, which is 39 * 3 = 117 legos.
However, we must not forget that Ms. Kiyama initially got rid of 23 cracked legos. To find the original number, we need to add those 23 legos back to our total. So we take the 117 legos and add the 23 that were removed, giving us 117 + 23 = 140 legos. Therefore, Ms. Kiyama started with 140 legos.
Graph the function y=|x+1-4
Answers
Answer: see graph
Step-by-step explanation:
I am assuming the question should read: y = |x + 1| - 4
You can graph this using transformations or by creating a table.
Transformations:
The parent function is y = |x|
The transformation is moving the graph 1 unit to the left and 4 units down - the vertex is moved from the origin to (-1, -4)
Table:
Choose x-values and solve for y
[tex]\begin{array}{c|c||c}\underline{\quad x\quad }&\underline{\quad y=|x+1|-4\quad }&\underline{Coordinate}\\-1&y=|-1+1|-4&(-1,-4)\\0&y=|0+1|-4&(0,-3)\\1&y=|1+1|-4&(1,-2)\end{array}[/tex]
In 1980 the population of detroit michigan was approximately 1,200,000.If the population decreased at an annual rate of 14.6% over the next vacate , what was the population of detriot in 1990, 10 years later
Answers
Answer:
247,605
Step-by-step explanation:
Each year, the population is multiplied by a factor of (1 -14.6%) = 0.854. Multiplying by that factor for 10 years gives the value ...
1,200,000×0.854^10 ≈ 247,605
The population in 1990 is predicted to be 247,605.
Julie has $80 in her savings account and plans to save $x each month for 8 months. The expression $8x + $80 represents the total amount in the account after 8 months. Factor this expression.
Answers
Answer:
8(x+10)
Step-by-step explanation:
8x + $80
We can factor out an 8 from each term
8(x+10)
You deposit $750.00 in an account that earns 5% simple interest. How much interest will your money earn in 6 months? Select the best answer from the choices provided. A. $18.75 B. $37.50 C. $712.50 D. $787.50
Answers
Answer:
7%
Step-by-step explanation:
I = PRT
I = 787.50
P = 750
T = 15
now we sub and find R (the rate)
787.50 = (750)(r)(15)
787.50 = 11250r
787.50 / 11250 = r
0.07 = r
0.07 x 100 = 7% = R
answer is 7%
State the vertical asymptote of the rational function. f(x) = quantity x minus nine times quantity x plus seven divided by quantity x squared minus four.
Answers
The vertical asymptotes for the rational function f(x) = (x - 9)(x + 7) / (x² - 4) are at x = 2 and x = -2.
Explanation:The rational function provided is f(x) = (x - 9)(x + 7) / (x² - 4). The denominator of this rational function is a difference of squares, which can be further factored into (x - 2)(x + 2). Therefore, the equation for the denominator becomes 0 when x = 2 or x = -2. These values of x are undefined for the original rational function and hence, they are vertical asymptotes. Thus, the vertical asymptotes for the given rational function are x = 2 and x = -2.
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Which points lie on the graph of f(x) = - Square root -X ? (–9, 3) (–4, –2) (–1, 1) (0, 0) (1, 1) (2, –4) (9, 3)
Answers
Answer:
(0, 0) and (-4, -2)
Step-by-step explanation:
See the graph. Only two of the listed points are on the curve.
What would a monthly payment be on a purchase of a $11,000 car at 5.9% for 4 years?
A) $257.83
B) $252.50
C) -$257.83
D) $250.00
Answers
Answer:
A) $257.83
Step-by-step explanation:
A spreadsheet or financial calculator will tell you the monthly payment on $11,000 at 5.9% annual rate for 4 years is ...
$257.83
Identify the reflection of the figure with vertices E(8,4), F(-16,-8), and G(24,-16) across the y-axis.
E (2, 1), F (−4, −2), G (6, −4)
E (−8, 4), F (16, −8), G (−24, −16)
E (−8, −4), F (16, 8), G (−24, 16)
E (4, 8), F (−8, 16), G (16, −24)
Answers
Answer:
[tex]\boxed{\text{E$'$(-8, 4), F$'$(16,-8), G$'$(-24,-16)}}[/tex]
Step-by-step explanation:
When you reflect a point (x, y) in the y-axis, the y-coordinate remains the same, but the x-coordinate gets the opposite sign. Thus,
E (8,4) ⟶ E' (-8,4)
F (-16,-8) ⟶ F' (16,-8)
G (24,-16) ⟶ G' (-24,-16)
[tex]\text{The reflected figure has coordinates } \boxed{\textbf{E$'$(-8, 4), F$'$(16,-8), G$'$(-24,-16)}}[/tex]
The figure EFG and its reflection E'F'G' are shown in the diagram below.
If angle EAC is congruent to angle ECA, name the congruent segments.
A. AE, EC
B. EC, CA
C. AE, AC
D. AE, EC, AC
Answers
Answer:
A. AE, EC
Step-by-step explanation:
Because you know that the bottom two angles are congruent, you can conclude that this is an isosceles triangle. This means that the sides are congruent.
Rob is a geologist. He is surveying a conical crater that was created by a meteor impact. From one end to another, the crater forms a V shape. The deepest part of the crater is 400 feet deep. The depth of the crater varies at a rate of 0.25 foot with the horizontal distance from the west end of the crater. The equation that models the depth of the crater, d, in feet, with respect to the horizontal distance in feet from the west end of the crater, h, is d = . The depth of the crater is 250 feet at horizontal distances of and feet from the west end.
Answers
Answer:
equation: d(h) = 0.25|h -1600| -400depth is 250 ft at 1000 ft and 2200 ft from the west edgeStep-by-step explanation:
The crater shape can be modeled by an absolute value function with a slope of 0.25. The vertex of the function will not be at (0, 0) but will be at (1600, -400). The usual methods of translating functions apply. Horizontal displacement of the vertex is subtracted from the independent variable; vertical displacement is added to the function value.
d(h) = 0.25×|h -1600| -400
We know the horizontal displacement is 1600 ft, because the depth changes at a rate of 1/4 foot for each horizontal foot. A depth change of 400 feet will require 1600 horizontal feet to accomplish.
__
At a depth of 250 ft, the distance from the west edge can be found from ...
-250 = 0.25|h -1600| -400
150 = 0.25|h -1600| . . . . . . . . add 400
600 = |h -1600| . . . . . . . . . . . multiply by 4
This resolves to two equations:
-600 = h -1600 ⇒ h = 1000600 = h -1600 ⇒ h = 2200The depth is 250 ft at distances of 1000 ft and 2200 ft from the west edge.
_____
Comment on the equation
We have chosen to make depths be negative numbers. If you want the equation to give positive numbers for depth, multiply it by -1:
d = 400 -0.25×|h -1600|
Answer:
0.25|x-1,600|-400 / 1,000 / 2,200
Step-by-step explanation:
Use the x-intercept method to find all real solutions of the equation. -9x^3-7x^2-96x+36=3x^3+x^2-3x+8
Answers
Answer:
x ≈ 0.290640965127
Step-by-step explanation:
By subtracting the right side of the equation, we get a function that is zero at a real solution for x. The only x-intercept is at approximately 0.290640965127.
___
The graph shows the x-intercept to be 0.2906. The value above was obtained by Newton's method iteration. The roots of this cubic will all be irrational.
Need help with a math question PLEASE HELP NEED ANSWER SOON
Answers
Try a smaller example with 2 or 3 if that helps next time
Answer:
720
Step-by-step explanation:
So there are 6 slots and 6 commercials so.
There are 6 outcomes which means.
we can use this formula
(p-1)(p-2)(p-3)..etc.
So
We have (6-1)(6-2)(6-3)(6-4)(6-5)(6-6)
6,5,4,3,2,1,0 and zero is 0!=1
So now we multiply
6*5*4*3*2*1*1=720
Hopefully this helps!
HELP ASAP!! A truck starts from a warehouse, which is 8 miles south and 3 miles west of the town center. The truck travels 3 miles north, makes a right turn, and then travels for 4 miles. What is the truck’s final position? What single translation vector moves the truck from its starting position to its final position?
Answers
The answer, I think, is (1, -5);(4,3).
Answer:
1, −5); (4, 3)
Step-by-step explanation:
The starting point coordinates and the changes in x or y of each movement are given.
Draw the given information in the coordinate plane to better visualize it. The truck starting coordinates are (−3, −8).
To find the vector that gives the translation (−3, −8)→(1, −5), subtract the x and y coordinates of the starting point from the x and y coordinates of the end point. The vector is: ⟨1 − (−3), −5 − (−8)⟩ = ⟨4,3⟩.
Therefore, the truck’s final position is (1, −5) and ⟨4, 3⟩ is the single translation vector that moves the truck from its starting position to its final position.
A girl scout sells 3 boxes of cookies during week 1. She has a goal to sell twice as many cookies each week as she did the week before. If she succeeds in doing this during weeks 2, 3, 4, and 5, how many boxes will she sell all together? a0
Answers
Answer
93 boxes
Step-by-step explanation:
Week one= 3 boxes
Week two= 2×3=6 boxes
Week three= 2×6=12 boxes
Week four= 2×12=24 boxes
Week five= 2×24=48 boxes
Total number of boxes sold is the sum for boxes sold in week 1,2,3,4 and 5
[tex]T=3+6+12+24+48=93[/tex]
Answer:
Step-by-step explanation:
Week one= 3 boxes
Week two= 2×3=6 boxes
Week three= 2×6=12 boxes
Week four= 2×12=24 boxes
Week five= 2×24=48 boxes
Total number of boxes sold is the sum for boxes sold in week 1,2,3,4 and 5
T=3+6+12+24+48=93
Amy was thinking of a number then divides by 2 then adds 11 and the answer was 12 what was the original number?
Answers
Answer:
2
Step-by-step explanation:
Let x be the original number.
x/2 +11=12
Now solve for x
x=2
Answer:
The number was 2
Step-by-step explanation:
To solve this you would just have to work backwards using the inverses of operations previously used
First you would subtract 11 from 12:
12-11=1
Then you would multiply by 2:
1 x 2=2
Among 100 students who enrolled in both Math 101 and English 101, 30% of the students scored an A in Math 101, 35% of the students scored an A in English 101, and 20% of the students scored an A in both Math 101 and English 101. What percentage of the students scored an A in neither Math 101 nor English 101?
Answers
Answer:
The percentage of the students scored an A in neither Math 101 nor English 101 is 55%
Step-by-step explanation:
* Lets study the meaning of or , and on probability
- The use of the word or means that you are calculating the probability
that either event A or event B happened
- Both events do not have to happen
- The use the word and, means that both event A and B have to happen
* The addition rules are:
# P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen
at the same time)
# P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they
have at least one outcome in common)
- The union is written as A∪B or “A or B”.
- The Both is written as A∩B or “A and B”
* Lets solve the question
- There are 100 student enrolled in both math and English Exams
- 30% of them scored an A in Math
- 35% of them scored an A in English
- 20% of them scored an A in both
- To find the neither lets find either and then subtracted from the total
∵ P(A or B) = P(A) + P(B) - P(A and B)
∵ P(Math) = 30%
∵ P(English) = 35%
∵ P(Math ∩ English) = 20%
∴ P(Math ∪ English) = 30% + 35% - 20% = 45%
- To find the neither subtract either from the total
∵ The total of students who enrolled is 100
∴ The percentage of the students who enrolled is 100%
∴ The percentage of the students scored an A in neither Math nor
English = 100% - 45% = 55%
* The percentage of the students scored an A in neither Math 101 nor
English 101 is 55%
To find the percentage of students who scored an A in neither Math 101 nor English 101, subtract the percentage of students who scored an A in both subjects from the total percentage of students who scored an A in either subject.
Explanation:To find the percentage of students who scored an A in neither Math 101 nor English 101, we need to subtract the percentage of students who scored an A in both subjects from the total percentage of students who scored an A in either Math 101 or English 101.
Given that 30% of the students scored an A in Math 101, 35% of the students scored an A in English 101, and 20% of the students scored an A in both subjects, we can calculate the percentage of students who scored an A in neither subject as follows:
Percentage of students who scored an A in neither subject = 100% - (Percentage of students who scored an A in Math 101 + Percentage of students who scored an A in English 101 - Percentage of students who scored an A in both subjects)
= 100% - (30% + 35% - 20%)
= 100% - 45%
= 55%
At the start of the first down, the football was 25 yards from the Captains' end zone. During three downs, the ball moved 6
yards closer to their end zone, then 10 yards farther from it, and then 8 yards closer to it. How many yards from their end
zone was the ball at the end of the third down?
Answers
First down = 25 yards.
Ball moved 6 yards closer = 25 - 6 or 19 yards.
Then 10 yards away = 19 + 10 or 29 yards.
Then 8 yards closer = 29 - 8 or 21 yards.
The ball at the end of the third down will be 21 yard rom Captain's end zone .
What are addition and subtraction?Addition and subtraction are the simple mathematical operations, that are used for adding values to get total and reducing or removing value.
We have,
At first down the football = 25 yards
Now,
According to the question,
During three downs,
So,
For first down of three downs moves closer = 25 - 6 = 19 yards,
Now,
For second down of three downs moves farther = 19 + 20 = 29 yards
Now,
For third down of three downs moves closer = 29 - 8 = 21 yards
So,
21 yards away from the Captains' end zone.
Hence, we can say that the ball at the end of the third down will be 21 yard rom Captain's end zone .
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Find the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2.
A. y2 = 2x
B .y = one divided by twox2
C .y2 = 8x
D. y = one divided by eightx2
Answers
Answer:
D. y = one divided by eightx2
Step-by-step explanation:
The standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2 is y = one divided by eightx2.