Answer:
a. a₁=7, b. a_n=7n+1, c. a₂₀=141Step-by-step explanation:
a.
[tex]a_1=S_1=3\cdot1^2+4\cdot1=3+4=7[/tex]
b.
[tex]a_1+a_2=S_2\\\\a_1+a_1+d=3\cdot2^2+4\cdot2\\\\7+7+d=3\cdot4+8\\\\14+d=12+8\\\\d=6\\\\\\a_n=a_1+d(n-1)\\\\a_n=7+6(n-1)\\\\a_n=7+6n-6\\\\\underline{a_n=7n+1}[/tex]
c.
[tex]a_{20}=7\cdot20+1=141[/tex]
Godric has 11 bills in his wallet. Each bill is either a $5 dollar or a $20 dollar.Godric has a total of $115 in his wallet.
A) Could Godric have five $20 bills given the information you know?Explain
B) Let n be the number of five dollar bills that Godric has. Set up an equation using n that models this situation and solve it for n
Answer:
A) Godric can have maximum of four $20 bills.
Therefore Godric can not have five $20 bills.
B) Equation is:
[tex]5n+20(11-n)=115[/tex]
[tex]n=7[/tex]
Step-by-step explanation:
Let the number of $5 bills with Godric = [tex]n[/tex]
Total number of bills = 11
Therefore, number of $20 bills = (11 - [tex]n[/tex])
Total amount of money in form of $5 bills = $[tex]5n[/tex]
Total amount of money in form of $20 bills = $[tex]20(11-n)[/tex]
Total money with Godric is $115.
[tex]\therefore 5n+20(11-n)=115\\\Rightarrow -15n=115-220\\\Rightarrow n=7[/tex]
Number of $5 bills present with Godric = 7
Number of $20 bills present with Godric = 11 - 7 = 4
A) Godric can have maximum of four $20 bills.
Therefore Godric can not have five $20 bills.
B) Equation is:
[tex]5n+20(11-n)=115[/tex]
Solution is [tex]n=7[/tex]
David watches Maria and Alma race electric trains around a track. Maria's train goes around the track in 10 seconds. Alma's train goes around the track in 12 seconds.
How long will it take for both trains to cross the finish line together the first time?
A
30 seconds
B
60 seconds
C
72 seconds
D
120 seconds
Answer:
60 seconds.
Step-by-step explanation:
We have been given that Maria train can go around the track in 10 seconds. Alma train can go around the track in 12 seconds.
To find the number of seconds after which both trains will cross the finish line together the first time we will find LCM of 10 and 12. LCM will give us the smallest positive integer that is divisible by both 10 and 12.
Multiples of 10 are: 10, 20, 30, 40, 50, 60, 70,...
Multiples of 12 are: 12, 24, 36, 48, 60, 72, 84,..
We can see that least common multiple of 10 and 12 is 60, therefore, it will take 60 seconds for both trains to cross the finish line together the first time.
find the absolute value
Answer:
3
Step-by-step explanation:
What is the remainder when (x4 + 36) is divided by (x2 – 8)?
Answer:
x^5/y for x
Step-by-step explanation:
Answer:
The answer is C 100
Step-by-step explanation:
Solve the problem please
Answer:
The correct answer would be 3x/5y
Step-by-step explanation:
You are substracting, and the denominator is the same for both 5x/5y and 2x/5y, so it will remain the same (5y). This only leaves you needing to substract 5x-2x, which equals 3.
5x/5y-2x/5y= 3x/5y
Step-by-step explanation:
[tex]\frac{5x}{5y}-\frac{2x}{5y}\\ \frac{5x -2x}{5y}\\ \frac{(5-2)x}{5y} \\ \frac{3x}{5y}[/tex]
Answer:[tex]\frac{3x}{5y} \\[/tex]
20)
Which square root is NOT a whole number?
A)
144
B)
156
C)
169
D)
196
Answer:
196
Step-by-step explanation:
196 does not have a whole number square
What is the slope of the line that passes through the points (1,-1) (-2,8)
Answer:
m=-3
Step-by-step explanation:
look at the picture
thx guys
what is the distance of the line segment between the endpoints (-6,5),(4,-5)
Find the slope of the line that is parallel to y = -x = 1
A. -1
B. 5/4
C.1
D.-5/4
Answer: A) -1
Step-by-step explanation: Parallel slopes are always the same, therefore a slope that is -1 is parallel to another slope that is equal to -1.
Find the product... Please and thank you.
(x+7) (x+5)
Answer:
x+12x+35
Step-by-step explanation:
use the FOIL method!
kelly is going to buy 12 items from Pablo's Food Truck. 1/6 of the items are tacos, 25% are empanadas, 1/3 are tamales and the rest are burritos. How many burritos did kelly buy?
Answer: 3 burritos
Step-by-step explanation:
Fraction of tacos = 1/6
Fraction of empanadas = 25% = 1/4
Fraction of tamales = 1/3
Fraction of burritos = 1 - (1/6 + 1/4 + 1/3)
It should be noted that the lowest common multiple for 6, 4 and 3 is 12.
Fraction of burritos = 1 - (1/6 + 1/4 + 1/3)
= 1 - (2/12 + 3/12 + 4/12)
= 1 - 9/12
= 3/12 or 1/4
The number of burritos bought by Kelly will now be:
= 1/4 × 12
= 3 burritos
An ice cream shop sells ice cream by the scoop. A
single scoop of ice cream costs $3. Each additional
scoop costs $1.25 and and each additional topping
costs $0.50.
Write an equation that represents the cost of ice cream.
Specify what each variable represents.
Complete the missing values in the table.
Answer:
The answer is 3+ 1.25s+ .5t= c
in which:
s is the number of scoops
t is each topping
c is the total cost
Printing Brochures The trade show is less than three weeks away. Your manager wants to be sure you have plenty of color brochures in time for the show. She said there will be nearly 4100 attendees, and that the brochures should cost no more than $1900. You were told to call Sofia for help ordering the brochures.
Step 1: Understand the Problem
What do you know?
11. List three criteria for the print order that you know are important to your manager. (6 points: 2 points for each piece of information)
Answer:
1. No extra fees unless we need out order sooner (2 weeks for an extra $50)
2 .orders of 1000 or more are 40 cents a piece orders of fewer thank 1000 are 60 cents a piece
3. The brochure will arrive in three weeks so we need to pay an extra $50 to get them before the show
Step-by-step explanation:
I’ve done this already but if you need me to explain lmk:)
What is the solution to the equation
7(3-x)=-7(x+3)-4
Answer:
No solution
Step-by-step explanation:
21−7x=−7x−21−4
21−7x=−7x−25
21=−25
No solution
i need help Nika baked three loaves of zucchini bread. Each cake needed StartFraction 17 over 4 EndFraction cups of flour. Which expression shows the best estimate of the number of cups of flour that Nika used?
4 + 4 + 4 = 12
5 + 5 + 5 = 15
4 + 4 + 4 = 16
17 + 17 + 17 = 51
Answer:
B..
lol
Step-by-step explanation:
After striking a pair of arcs from each endpoint of a line segment, what is the next step in constructing the segment's perpendicular bisector? Use a protractor to draw a 90°. Angle on the line segment. Use a protractor to draw a 90°. Angle on the line segment. , Use a straight edge to draw a horizontal line midway between the arcs. Use a straight edge to draw a horizontal line midway between the arcs. , Use a straight edge to draw a vertical line between the points where each pair of arcs intersect. Use a straight edge to draw a vertical line between the points where each pair of arcs intersect. Without using a straight edge, draw a vertical line through through the point where both arcs intersect.
Answer:
The answer is "Option C".
Step-by-step explanation:
The numbering of the choice was missing, which is defined in the attached file. please find it.
by using the straight corner to create a vertical line between both the places where every pair of orbits cross and the next step, throughout the perpendicular bisector construction of the segment after hitting a pair of arcs of each endpoint of the reference line.
ASAP!!! BRAINLIEST!!
PLS HELP!!! SHOW ALL WORK +STEPS!! Thx!
Equation: y = 2x + 4
72 = 2x + 4
68 = 2x
x = 34
Hope this helps! :)
Slope of the line: rise/run = 4/2 = 2
y-intercept = 4
Plug into y = mx+b
y = 2x + 4
Plug 72 for y
72 = 2x + 4
=34
Using the factor theorem, which of the following is a factor of the polynomial below?
x^3 + 12x^2 + 9x - 22
A. X-3
B. X+2
C. X+1
D. X-2
Answer:
B.X+2
Step-by-step explanation:
-2^3+12X-2^2+9X-2-22
-8+48-18-22
40-40=0
The following is a factor of the polynomial is x+2.
What is Factor theorem?Factor theorem is a special kind of the polynomial remainder theorem that links the factors of a polynomial and its zeros.
The factor theorem removes all the known zeros from a given polynomial equation and leaves all the unknown zeros. The resultant polynomial has a lower degree in which the zeros can be easily found.
As per the factor theorem, (y – a) can be considered as a factor of the polynomial g(y) of degree n ≥ 1, if and only if g(a) = 0. Here, a is any real number. The formula of the factor theorem is g(y) = (y – a) q(y). It is important to note that all the following statements apply for any polynomial g(y):
(y – a) is a factor of g(y).g(a) = 0.The remainder becomes zero when g(y) is divided by (y – a).The solution to g(y) = 0 is a and the zero of the function g(y) is a.Given:
f(x)=x³ + 12x² + 9x - 22
To the above equation (x + 2) is a factor of x³ + 12x² + 9x - 22.
As,
f(-2)= (-2)³ + 12(-2)² + 9(-2) - 22
f(x)= -8 + 48 -18 -22
f(x)= 40 -40
f(x) = 0
Hence, the factor of x+2
Learn more about factor theorem here:
https://brainly.com/question/26113096
#SPJ2
FIRST TO ANSWER GETS BRAINLIEST! (if the answer is correct)
UPS charges $7 for the first pound, and $0.20 for each additional pound. FedEx charges $5 for the first pound and $0.30 for each additional pound. How many pounds, p, will it take for UPS and FedEx to cost the same?
Answer:
It takes 31 Pounds for UPS and FedEx to cost the same?
Step-by-step explanation:
The equation for the cost of a UPS shipping:
7 + .20x
to check the answer, you can do : 7 + (.20 x 31)
= $14.00
The cost for the cost of the PedEx shipping is:
5 + .30x
to check the answer, you can do : 5x + (.30 x 31)
= $14.00
Pete owes his brother $35 from five weeks of borrowing money.
a. What is the mean amount Pete borrowed from his brother each week?
b. If Pete continues to borrow his money, how much money will he owe after three more weeks?
Answer:
The Answer for a is $175
Step-by-step explanation:
Thats all I know sorry
Help meeeeeeeeeeeeeeeeeeeeeee !!!!!
Answer:
i think it is the 2nd one and the 5th one.
Step-by-step explanation:
hope this helped!
p.s it would be cool if you gave me brainliest
For every 1/150 square mile Xavier mows, Boa mows 1/120square miles. How many square miles does Xavier mow for every 1 square mile?
A. 3/5
B. 4/5
C. 5/4
D 15/17
Answer:
4/5
Step-by-step explanation:
step 1: Divide 1/150 by 1/120. (You should get 0.8)
step 2: convert 0.8 into a fraction over 10. (8/10)
step 3: simplify that fraction by dividing 8/10 by 2, which will give you your final answer, 4/5.
The required square miles that Xavier mow 4 / 5. Option B is correct.
Given that,
For every 1/150 square mile Xavier mows, Boa mows 1/120square miles, how many square miles does Xavier mow for every 1 square mile is to be determined.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Ration of Xavier to Boa = 1 / 150 / 1 / 120
= 120 / 150
= 12 / 15
= 4 / 5
Thus, the required square miles that Xavier mow 4 / 5. Option B is correct.
Learn more about ratios here:
brainly.com/question/13419413
#SPJ2
1. How do the areas of the two shapes compare?
Answer:
we cant really answer cause we cant see the 2 squares
Step-by-step explanation:
sing the expression x + 3, write one equation that has one solution, one equation that has no solution, and one equation that has infinitely many solutions. Explain
Answer: one solution x + 3 = 5 x = 2 no other other value for x is possible
No solution: (x + 3) = 2(x +3)
Infinitely many solutions: x+3 = 3 + x
Step-by-step explanation:
why (x + 3) = 2(x +3) has no solution. Can you solve?
x+3=2x+6 -x=3 x=-3 substute -3 for x
(-3)+ 3)= 2[(-3) +3]
-3+3 = -6 +3
0 = -3 False!
x+3 = 3 + x has infinitely many solutions. Substitute any number for x, and the equation is true (5)+3=3+(5) 8=8 . 11111+3 =3+11111 11114=11114
An equation can either have: one solution, no solution, or infinitely many solutions. Some equations that can be derived from [tex]x + 3[/tex] and their solution type are:
[tex]x + 3 = 2x[/tex] has one solution[tex]x + 3 = x[/tex] has no solution[tex]x + 3 = 2(0.5x + 1.5)[/tex] has one solutionGiven that:
[tex]Expression = x + 3[/tex]
Equation with one solution
For an equation to have one solution. then the equation is consistent and dependent.
For instance:
[tex]x + 3 = 2x[/tex]
Collect like terms to solve for x
[tex]2x -x = 3[/tex]
[tex]x =3[/tex]
This means that [tex]x =3[/tex] is the only solution to [tex]x + 3 = 2x[/tex].
Hence, [tex]x + 3 = 2x[/tex] has one solution
Equation with no solution
For an equation to have no solution. then both sides of the equation are not equal
For instance:
[tex]x + 3 = x[/tex]
Collect like terms to solve for x
[tex]x- x = 3[/tex]
[tex]0 = 3[/tex]
Because 0 is not equal to 3, then [tex]x + 3 = x[/tex] has no solution
Equation with infinitely many solutions
For an equation to have infinitely many solutions. then both sides of the equation must be the same thing
For instance:
[tex]x + 3 = 2(0.5x + 1.5)[/tex]
Open the bracket
[tex]x + 3 = x + 3[/tex]
Collect like terms
[tex]x - x = 3 - 3[/tex]
[tex]0 = 0[/tex]
Because both sides are the same (i.e. 0), then [tex]x + 3 = 2(0.5x + 1.5)[/tex] has infinitely many solutions
Read more about equation solutions at:
https://brainly.com/question/10628783
what is the answer for x/1.2=-7
Answer:
x = -8.4
Step-by-step explanation:
You do the inverse operations:
The inverse of division is multiplication, so:
x/1.2 = -7 (x 1.2) - multiply by 1.2
x = -8.4
help me im dummmy head
Answer:
(-2, 3) And you're not a dummy!
Step-by-step explanation:
x + 3(3) = 7 (multiply 3 times 3)
x + 9 = 7 ( subtract 9 on both sides)
x = -2
It already gave you y
y = 3
HOPE THIS HELPED!!
How many x-intercepts and y-intercepts can a linear function have?
A sea turtle is 3 feet below the surface of the sea. If its position can be recorded as - 3 feet, what would the position 0 represent in this situation? (4 points) A the surface of the sea.B the distance above the surface of the sea.C the distance below the surface of the sea. D the height of the turtle
Answer:
A.
Step-by-step explanation:
Calculate the density of benzene if 0.10L has a mass of 36.4g.
Answer:
[tex]d=0.364\ g/cm^3[/tex]
Step-by-step explanation:
It is given that,
Mass of benzene, m = 0.1 L
Mass, m = 36.4 g
We know that, 1 L = 1000 cm³
0.1 L = 100 cm³
The density of an object is equal to its mass divided by its volume. So,
[tex]\rho=\dfrac{m}{V}\\\\=\dfrac{36.4\ g}{100\ cm^3}\\\\=0.364\ g/cm^3[/tex]
So, the density of benzene is [tex]0.364\ g/cm^3[/tex].
