The sum of the series [tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)[/tex] is 44.
Step-by-step explanation:
The given series is [tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44[/tex]
To find the sum of the series, we need to substitute the values for k in the series.
[tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=\left[2(1)^{2}-4\right]+\left[2(2)^{2}-4\right]+\left[2(3)^{2}-4\right]+\left[2(4)^{2}-4\right][/tex]
Now, simplifying the square terms, we get,
[tex][2(1)-4]+[2(4)-4]+[2(9)-4]+[2(16)-4][/tex]
Multiplying the terms,
[tex][2-4]+[8-4]+[18-4]+[32-4][/tex]
Subtracting the values within the bracket term, we get,
[tex]-2+4+14+28[/tex]
Now, adding all the terms, we get the sum of the series,
[tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44[/tex]
Thus, the sum of the series is [tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44[/tex]
Hes right its 44
444444444444444444444
-4x + y = 4
2x + 2y =13
Answer: What exactly are you asking??
Step-by-step explanation:
Problem 1 Answer: x = -1 + 0.25y
Show Work:
1) Solving
-4x + y = 4
2) Solving for variable 'x'.
3) Move all terms containing x to the left, all other terms to the right.
4) Add '-1y' to each side of the equation.
-4x + y + -1y = 4 + -1y
5) Combine like terms: y + -1y = 0
-4x + 0 = 4 + -1y
-4x = 4 + -1y
6) Divide each side by '-4'.
x = -1 + 0.25y
7) Simplifying
x = -1 + 0.25y
Problem 2 Answer: x = 6.5 + -1y
Show Work:
1) Solving
2x + 2y = 13
2) Solving for variable 'x'.
3) Move all terms containing x to the left, all other terms to the right.
4) Add '-2y' to each side of the equation.
2x + 2y + -2y = 13 + -2y
5) Combine like terms: 2y + -2y = 0
2x + 0 = 13 + -2y
2x = 13 + -2y
6) Divide each side by '2'.
x = 6.5 + -1y
7) Simplifying
x = 6.5 + -1y
please help!! Kurt's car gets 23 miles to a gallon of gasoline. He filled up his car's gas tank with g gallons. Write an expression that shows how far Kurt can drive on a tank of gasoline.
Expression that shows distance Kurt can drive on a tank of gasoline is 23g miles
Solution:
Given that, Kurt's car gets 23 miles to a gallon of gasoline
He filled up his car's gas tank with g gallons
To find: Expression that shows distance Kurt can drive on a tank of gasoline
From given,
1 gallon of gasoline = 23 miles
Kurt fills up his car with "g" gallons
Therefore, for "g" gallons,
[tex]1 \times g \text{ gallons of gasoline } = 23 \times g \text{ miles }\\\\g \text{ gallons of gasoline } = 23g \text{ miles }[/tex]
Thus the distance Kurt can cover with "g" gallons is:
[tex]distance = 23g\ miles[/tex]
Thus with "g" gallons of gasoline, Kurt can drive 23g miles
Are 4x and 15 + x equivalent expressions
Final answer:
The expressions 4x and 15 + x are not equivalent as they yield different results for the same value of x.
Explanation:
The expressions 4x and 15 + x are not equivalent. Equivalence between two expressions means that for any value of the variable(s) involved, the expressions yield the same result. To determine if these expressions are equivalent, you can compare them for different values of x. For instance, if x is 1, 4x yields 4, whereas 15 + x yields 16, which are not the same. Thus, we can say that the expressions 4x and 15 + x are not equivalent as they produce different results for the same values of x.
-5(-× -6) =31
Solve the equation
Answer: I believe the answer to this question is: X= 1/5.
Select the correct answer.
Which group settled in America to escape religious persecution?
O
A.
Puritans
O
B.
Quakers
O
c.
Baptists
O D. Methodists
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Answer:
A. Puritans
Remember, King James was Catholic (brought up presbyetirian) and later enforced Anglican
A) Puritans settled in America to escape religious persecution.
what is emigration?Emigration is the act of leaving one's country or region to live in another. It is a type of migration, which refers to the movement of people from one place to another. Emigration is different from immigration, which is the process of entering a new country or region to live there permanently.
The Puritans were a group of English Protestants in the 16th and 17th centuries who sought to "purify" the Church of England from what they saw as Roman Catholic practices.
They faced persecution and discrimination in England, which led many of them to emigrate to America in search of religious freedom.
The most well-known group of Puritan emigrants to America were the Pilgrims, who established the Plymouth Colony in Massachusetts in 1620.
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Complete question:
Which group settled in America to escape religious persecution?
A.) Puritans
B.) Quakers
C.) Baptists
D.) Methodists
Which system of equations could be graphed to solve the equation below?
log (2 x + 1) = 3 x minus 2
(Image Attached Below)
Answer:
[tex]\left\{\begin{array}{l}y_1=\log (2x+1)\\ \\y_2=3x-2\end{array}\right.[/tex]
Step-by-step explanation:
Given the equation
[tex]\log (2x+1)=3x-2[/tex]
This equation consists of two parts. In the left part, there is a logarithmic function [tex]y=log (2x+1)[/tex]
In the right part, there is a linear function [tex]y=3x-2[/tex]
To solve the equation graphically, you have to plot the graphs of these two functions and find the point of intersection of these graphs.
Hence, appropriate system is
[tex]\left\{\begin{array}{l}y_1=\log (2x+1)\\ \\y_2=3x-2\end{array}\right.[/tex]
200 children attended the school play. of total attendance, 40% were boys. How many girls attended the school play
Answer:120 girls
Step-by-step explanation:
40% equals 80 boys, so 200 people less 80 is equal 120, therefore are 120 girls!
The number of girls is 120.
What are percentages?Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. It is used to measure frequency.
Percentage of girls = 100 = 40 = 60%
Number of girls = 60% x 200
= 120
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If f(x) = 2x^2+1 and g(x) =x^2-7 find (f+g)(x)
Answer:f=−
7
x
2
+1−2g−x
Step-by-step explanation:
1 Subtract {x}^{2}x
2
from both sides.
2{x}^{2}+1-g-x-{x}^{2}=-7f+g2x
2
+1−g−x−x
2
=−7f+g
2 Simplify 2{x}^{2}+1-g-x-{x}^{2}2x
2
+1−g−x−x
2
to {x}^{2}+1-g-xx
2
+1−g−x.
{x}^{2}+1-g-x=-7f+gx
2
+1−g−x=−7f+g
3 Subtract gg from both sides.
{x}^{2}+1-g-x-g=-7fx
2
+1−g−x−g=−7f
4 Simplify {x}^{2}+1-g-x-gx
2
+1−g−x−g to {x}^{2}+1-2g-xx
2
+1−2g−x.
{x}^{2}+1-2g-x=-7fx
2
+1−2g−x=−7f
5 Divide both sides by -7−7.
-\frac{{x}^{2}+1-2g-x}{7}=f−
7
x
2
+1−2g−x
=f
6 Switch sides.
f=-\frac{{x}^{2}+1-2g-x}{7}f=−
7
x
2
+1−2g−x
Solve the equation -1/4x=7
Answer:
-1/4 x = 7
x4 x4
-x = 28
x = -28
Step-by-step explanation:
Answer: -1/4*-28=7
x=-28
Step-by-step explanation:
First, do -1/4 and you should get-0.25 as your answer .
Next, do 7/-0.25
Last, check your answer and to do so simply multiply -1/4*-28 and you should get 7 as your final answer.
10. * MULTIPLE CHOICE Which ordered pair is a solution of 6x + 3y = 18?
A (-2,-10) 6 (-2, 10) © (2, 10)
(10,-2)
Answer:
(-2,10)
Step-by-step explanation:
6x-2= -12
3y = 3×10 =30
30+(-12)=18
Evaluate the expression if b = 3.
12 (63 -1)
6=3
2
1/2(3^3-1)
1/2(27-1)
1/2(26)
13
Answer:
13
Step-by-step explanation:
Replace b with 3, then multiply 3^3 get the answer then subtract by 1, last multiply what u got from the paranthesis by 1/2
A new car is purchased for 24000 dollars. The value of the car depreciates at 6.75% per year. To the nearest year, how long will it be until the value of the car is 15500 dollars?
Final answer:
To the nearest year, it will take about 6 years for the value of the car to reach $15,500.
Explanation:
To find how long it will take for the value of a car to depreciate to $15,500, we can set up an equation using the formula for exponential decay: V = P[tex](1 - r)^t[/tex], where V is the final value, P is the initial value, r is the depreciation rate, and t is the time in years.
Plugging in the given values, we have 15500 = 24000[tex](1 - 0.0675)^t[/tex]. To solve for t, we can take the logarithm of both sides:
log(15500) = log(24000[tex](1 - 0.0675)^t)[/tex]
t * log(1 - 0.0675) = log(15500/24000)
t = log(15500/24000) / log(1 - 0.0675)
Using a calculator, we find that t is approximately 5.54 years. Rounding to the nearest year, it will take about 6 years for the value of the car to reach $15,500.
Which equation represents the line that passes through points (0,6) and (2,0)?
A) y= -1/3x + 2
B) y= -1/3x + 6
C) y= -3x +2
D) y= -3x + 6
( yes, im that dumb, sorry )
Answer:
D) y= -3x + 6
Step-by-step explanation:
y = mx + p
m = slope = (0-6)/(2-0) = -6/2 = -3
p = y-intercept = 6 ,because the line passes through points (0,6)
Answer:
D) y= -3x + 6
A fraction f multiplied by 4 equals 1/2
Answer:
f = 1/8
Step-by-step explanation:
f x 4 = 1/2
f = 1/8 ( multiplying both sides by 1/4 )
The fraction f that gives 1/2 when multiplied by 4 is 1/8.
That is, f = 1/8
A fraction f multiplied by 4 equals 1/2
This can be written mathematically as:
[tex]f \times 4 = \frac{1}{2}[/tex]
This can be re-written as:
[tex]4f=\frac{1}{2}[/tex]
Divide both sides by 4
[tex]\frac{4f}{4} =\frac{1}{2} \div 4\\\\f= \frac{1}{2} \times \frac{1}{4}\\\\f=\frac{1}{8}[/tex]
The fraction f that gives 1/2 when multiplied by 4 is 1/8.
That is, f = 1/8
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Ms. Ellis expected 50 families to attend parent teacher conference but 60 families attended. What is the percent error?
Answer:
20%.
Step-by-step explanation:
That is (60 - 50) / 50
= 10/50
= 1/5
To convert to a percent we multiply by 100:
= 20%.
I think it will be 10% because you invited 50 right? And 60 atended or was it 60 and 50 atended? Well either way I think it’s 10%
John is selling tickets to an event. Attendees can either buy a general admission ticket, x, or a VIP ticket, y. The general admission tickets are $70 and the VIP tickets are $80. If he knows he sold a total of 29 tickets and made $2,130, how many of each type did he sell?
Step-by-step explanation:
x+y=29...because x and y means how many tickets they have
and if normal 1 ticket is 70...then x number of tickets are $70x.
and
1 VIP ticket is 80...then y number of tickets are $80y..got that?...sum of all earned by selling tickets equal to $2130
so...
70x+80y=2130
so...equations are
x+y=29
70x+80y=2130
solve these equations.i did the hard part...you will get the answer...if u dont know hot to solve this comment me...
78 divided by 2789 how would I do this in long division form
If b equals 8 and h equals 6 what does bh/2 equal
Answer:
if b = 8
and h = 6
and if im understanding correctly it is asking B*H/2 that would be 8*6 which is 48 then divided by 2 would be 24
Step-by-step explanation:
Final answer:
Using the formula A = bh/2 for the area of a triangle, with b as 8 and h as 6, we find that the area A equals 24 square units.
Explanation:
To solve the given problem, we need to apply the formula for the area of a triangle, which is A = bh/2, where 'b' is the base of the triangle and 'h' is the height. Given that b equals 8 and h equals 6, we can substitute these values into the formula to find the area.
A = bh/2
A = (8)(6)/2
A = 48/2
A = 24
Therefore, the area of the triangle when b is 8 and h is 6 is 24 square units.
Suppose your parents invest $20,000 in an account paying 5% interest compounded annually. What will the balance be after 10 yr?
Answer:
$32,577.89
Step-by-step explanation:
Use the formula for amount after compound interest. A = P(1 + i)ⁿ
'P' is the principal, meaning starting amount. P = $20,000
'i' is the interest per compounding period in decimal form. Since the compounding period is annual, just like the interest rate is given as, i = 0.05. If the compounding period was not annual: then i = r/c (annual interest rate divided by number of compounding periods in a year).
'n' is the number of compounding periods, or the number of times the interest increases. n = 10. Calculate 'n' using n = tc (number of years times number of compounding periods in a year). Since c=1, n = t. ('t' is the number of years).
'A' is the amount after 'n' years. We need to find A.
Use all of the numbers that we know for the variables, replace the variables with the numbers in the formula. Solve for 'A'.
A = P(1 + i)ⁿ
A = $20,000(1 + 0.05)¹⁰ Add inside brackets first
A = $20,000(1.05)¹⁰ Do (1.05)¹⁰ then multiply by 20,000
A = $32,577.89 Answer
Therefore the balance will be $32,577.89 after 10 years.
Write an equation from the following points (plug in the numbers you would use for "m" and "b"):
(3, 9) and (6, 13)
Answer:
[tex]y =\fracc{4}{3}x+5[/tex]
m=4/3 and b=5
Step-by-step explanation:
We want to find the equation of the line passing through (3,9) and (6,13).
We determine the slope using:
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
Let:
[tex](x_1=3,y_1=9), (x_2=6,y_2=13)[/tex]
We substitute the points to get:
[tex]m = \frac{13 - 9}{6 - 3} = \frac{4}{3} [/tex]
We now use the formula:
[tex]y-y_1=m(x-x_1)[/tex]
We substitute to get:
[tex]y - 9 = \frac{4}{3} (x - 3)[/tex]
Multiply through by 3 to get;
[tex]3y - 27 = 4(x - 3)[/tex]
We expand further to get:
[tex]3y - 27 = 4x - 12[/tex]
This implies that:
[tex]4x - 3y = - 15[/tex]
We solve for y to get:
[tex]y =\fracc{4}{3}x+5[/tex]
Therefore m=4/3 and b=5
The equation v=-2000+20000 describes the value in dollars of a certain model of car after it is t years old. If a car is worth $10,000, substitute 10,000 into the equation to find the age of the car.
I'm assuming the equation is:
v = -2000t + 20,000 because the value of a car decreases with time
v = worth of the car
t = number of years
Since you know the value of v = 10,000, substitute or plug in 10,000 for v in order to find t
v = -2000t + 20,000 Substitute 10,000 into v [To find t, you need to get the variable by itself to one side of the equation.]
10,000 = -2000t + 20,000 Subtract 20,000 on both sides
-10,000 = -2000t Divide -2000 on both sides to get t by itself [negative divided by a negative results in a positive]
5 = t
Dave ordered dinner for a party of 10 people. Three people ordered the $4.75 chicken dinner, two people ordered the $4.95 fish dinner, and five had the beef dinner at a cost of $6.75 each. what was the average cost of each dinner at Dave's party?
Answer:
The average cost of each dinner at Dave's party is $5.79.
Step-by-step explanation:
Given:
Dave ordered dinner for a party of 10 people.
Three people ordered the $4.75 chicken dinner, two people ordered the $4.95 fish dinner, and five had the beef dinner at a cost of $6.75 each.
Now, to find the average cost of each dinner at Dave's party.
So, we get the total amount for the dinner:
Three people ordered the $4.75 chicken dinner.
[tex]4.75\times 3=14.25[/tex]
Two people ordered the $4.95 fish dinner.
[tex]4.95\times 2=9.90[/tex]
Five had the beef dinner at a cost of $6.75.
[tex]6.75\times 5=33.75[/tex]
Total amount of dinner = [tex]14.25+9.90+33.75=\$57.90.[/tex]
Now, to get the average cost of each dinner of 10 people we divide the total amount of dinner by 10:
[tex]57.90\div 10[/tex]
[tex]=\$5.79.[/tex]
Therefore, the average cost of each dinner at Dave's party is $5.79.
Final answer:
To find the average cost per dinner at Dave's party, calculate the total cost of each type of dinner and sum them up to get the total cost. Then, divide the total cost by the number of guests to obtain the average cost. The average cost per dinner is $5.79.
Explanation:
To calculate the average cost of each dinner at Dave's party, first calculate the total cost of all dinners combined by multiplying the number of each type of dinner by its price and then adding up the totals:
Chicken dinner cost: 3 dinners × $4.75 = $14.25
Fish dinner cost: 2 dinners × $4.95 = $9.90
Beef dinner cost: 5 dinners × $6.75 = $33.75
Next, add all the costs together to get the total cost of the dinners:
Total cost = $14.25 + $9.90 + $33.75 = $57.90
Now, divide the total cost by the number of guests to find the average cost per dinner:
Average cost = Total cost ÷ number of guests
Average cost = $57.90 ÷ 10 = $5.79
So, the average cost per dinner at Dave's party is $5.79.
Nate scored 5 more than twice the number of points as jake scored. write an expression that represents the relationship of the number of points Nate scored in terms of the number of points jake scored,p. help pls
Answer:
2p+5=n
(p = Jake's points) (n = Nate's points)
The relationship between Nate's and Jake's scores can be expressed by the expression N = 2p + 5.
Explanation:The relationship between the number of points Nate scored (represented by N) and the number of points Jake scored (represented by p) can be expressed as:
N = 2p + 5
This expression represents that Nate's score is equal to twice the number of points Jake scored, plus 5.
A rectangular yard measuring 35ft and 45ft is bordered (and surrounded) by a fence. Inside, a walk that is 4ft wide goes all the way along the fence find the area of this walk
First, calculate the area of the rectangular yard.
A = L x W where A equals area, L equals length, and W equals width.
According to your stated problem:
A = 31 x 49
A = 1519 square feet <-------Area of Rectangular yard.
Two cars are 190 miles apart and travel toward each other along the same road. They meet in 2 hours. One car travels 5 miles per hour faster than the other car. What is the average speed of each car?
The speed of slower car is 45 mph and faster car is 50 mph.
Step-by-step explanation:
Given,
Distance covered by both cars = 190 miles
Time taken by both of them = 2 hours
Let,
x be the speed of slower car.
Speed of faster car = x+5
Combined speed = x+x+5 = 2x+5
We know that;
Distance = Speed * Time
[tex]190=(2x+5)*2\\190=4x+10\\4x=190-10\\4x=180\\[/tex]
Dividing both sides by 4
[tex]\frac{4x}{4}=\frac{180}{4}\\x=45[/tex]
Speed of slower car = 45 miles per hour
Speed of faster car = 45+5 = 50 miles per hour
The speed of slower car is 45 mph and faster car is 50 mph.
Keywords: speed, distance
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The problem given is a relative speed problem in mathematics. By solving the equation, we find that the slower car travels at 45 mph and the faster car travels at 50 mph.
Explanation:This is a
problem of relative speed
in
mathematics
. Let's consider the speed of the slower car as 'x' miles per hour. The faster car is travelling 'x+5' miles per hour. Since they are moving towards each other, the sum of their speeds equals the total distance divided by the total time, that is (x + (x + 5)) = 190/2. Simplifying the equation, we get 2x + 5 = 95. Solving further, we get x = 45 miles per hour. Therefore, the slower car is travelling at 45 mph and the faster car is travelling at 50 mph.
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1. Megan is using an equilateral triangle as part of a design on a sweatshirt. Each side of the triangle
is 12 inches long. Megan is sewing a line of sequins from the midpoint of one side of this triangle to
the opposite vertex. Approximately how long will the line of sequins be?
A.
B.
C.
D.
13.4 in.
10.4 in.
8.5 in.
5.2 in.
Answer:
B 10.4
Step-by-step explanation:
10
2
5
2
6
7
9
2
3
Calculate the mean,
median and mode of the
following set of numbers.
Answer:
Step-by-step explanation:
Mean= 10+2+5+2+6+7+9+2+3/9
=46/9 = 5.11
Arrange in Ascending order:
2,2,2,3,5,6,7,9,10
Mode = 2 ( that occurs most number of times)
Median = 5 ( median is the middle term)
simplify this expression
2[(13-1)^2+2]
Answer:
292
Step-by-step explanation:
2(12^2+2)
2(144+2)
2(146)
292
Answer:
292
Step-by-step explanation:
13-1=12
12×12=144
144+2=146
146×2= 292
Julia is allowed to watch no more than 5 hours of television a week. So far this week, she has watched 1.5 hours. Write and solve an inequality to show how many hours of television Julia can still watch this week.
Answer:
The inequality to show how many hours of television Julia can still watch this week can be given as:
⇒ [tex]x+1.5\leq 5[/tex]
where [tex]x[/tex] represents he number of hours of television that Julia can still watch this week
On solving for [tex]x[/tex], we get
[tex]x\leq3.5[/tex]
Thus, Julia can still watch no more than 3.5 hours of television this week.
Step-by-step explanation:
Given:
Julia is allowed to watch television no more than 5 hours a week.
She has already watched 1.5 hours
To write and solve an inequality to show how many hours of television Julia can still watch this week.
Solution:
Let the number of hours of television that Julia can still watch this week be = [tex]x[/tex]
Number of hours already watched = 1.5
Total number of hours of watching television this week would be given as:
⇒ [tex]x+1.5[/tex]
It is given that Julia is allowed to watch no more than 5 hours of television in a week.
Thus, the inequality can be given as:
⇒ [tex]x+1.5\leq 5[/tex]
Solving for [tex]x[/tex]
Subtracting both sides by 1.5
[tex]x+1.5-1.5\leq 5-1.5[/tex]
[tex]x\leq3.5[/tex]
Thus, Julia can still watch no more than 3.5 hours of television this week.
2. Find the missing side length of the right triangle
shown below.
26 cm
10 cm
A. 18 cm
B. 20 cm
C. 22 cm
D. 24 cm
Using the Pythagorean Theorem with a hypotenuse of 26 cm and one side of 10 cm, the length of the other side is found to be 24 cm. Thus, the correct answer is (D) 24 cm.
In a right-angled triangle, you can use the Pythagorean Theorem to find the length of the missing side.
The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse c is equal to the sum of the squares of the lengths of the other two sides a and b:
[tex]\[c^2 = a^2 + b^2\][/tex]
Given that the hypotenuse c is 26 cm and one side a is 10 cm:
[tex]\[26^2 = 10^2 + b^2\]\[676 = 100 + b^2\]\[b^2 = 576\]\[b = 24\][/tex]
Therefore, the length of the other side is 24 cm, and the correct answer is (D) 24 cm.
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The complete question is:
The hypotenuse of a right triangle is 26 cm long. If one of the remaining two sides is 10 cm long. Find the length of the other side.
A. 18 cm
B. 20 cm
C. 22 cm
D. 24 cm