Answer:
0, 5, 10, 15, 20
0, 5, 40, 405, 5,120
Step-by-step explanation:
One rule can be "add 5 to the previous term to get the next term."
0, 5, 10, 15, 20
Second rule:
For each term number 1, 2, 3, ..., n,
each term = 5(n - 1)^n
0, 5, 40, 405, 5,120
The next three terms for the rule Tn = a + (n-1)d will be 10,15 and 20
The next three terms for rule 5(n-1)ⁿ will be 40, 405 and 5120.
Sequences are numbers arranged in a specific pattern.
Given the sequence 0, 5...
This sequence can be an arithmetic sequence with nth term expressed as:
Tn = a + (n-1)da is the first term = 0
n is the number of terms
d is the common difference = 5 - 0 5
If n = 3
T3 = 0 + (3-1)*5
T3 = 2 * 5
T3 = 10
If n = 4
T4 = 0 + (4-1)*5
T4 = 3 * 5
T4 = 15
If n = 5
T5 = 0 + (5-1)*5
T5 = 4 * 5
T5 = 20
Hence the next three terms for the rule will be 10,15 and 20
Also, we can also use the recursive rule f(n) = 5(n-1)ⁿ
If n = 3
f(3) = 5(3-1)³
f(3) = 5(2)³
f(3) = 5 * 8
f(3) = 40
If n = 4
f(4) = 5(4-1)⁴
f(4) = 5(3)⁴
f(4) = 5 * 81
f(4) = 405
If n = 5
f(5) = 5(5-1)⁵
f(5) = 5(4)⁵
f(5) = 5 * 81
f(5) = 1024 * 5
f(5) = 5120
Hence the next three terms for the rule will be 40, 405, and 5120.
Learn more here: https://brainly.com/question/16151695
which of the binomials below is a factor of this trinomial x2+6x-40
Answer:
x2 - 16x + 28 = (x - 2)(x - 14)
Step-by-step explanation:
Even though you don't mention any factors below, it is easy to tell that the above-given two factors must be the ones you are looking for.
When the input is 1, what is the output of the function? That is, find the value of g(1).
Answer:
g(1) = 1
Step-by-step explanation:
In this situation, one is given a graph of the function (g(x)), and one is asked to evaluate the function (g(x)) for (1). An easy way to do so is to find (x = 1) on the coordinate plane, then draw a vertical line at this point. Note the place where (x = 1) intersects the graph of (g(x)). The (y-coordinate) of this intersection point is the output of the function (g(x)).
The line (x = 1) intersects the function (g(x)) at the point (1, 1). Thus (g(1) = 1).
What is 15+(-11) simpyfied
Hi there!
»»————- ★ ————-««
I believe your answer is:
4
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the Answer...}}\\\\15+(-11)\\----------------\\\rightarrow 15 +1(-11)\\\\\rightarrow 15 - 11\\\\\rightarrow \boxed{4}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
your answer will obviously be 4
Find the approximate side length of a square game board with an area of 194 in2.
Answer:
root 194=13.928 inches
In the parallelogram below,
z = [ ? ]°
124°
2z+16°
Helpp!
2z+16+124=180
2z=180-16-124
2z=40
z=40/2
Z=20°
I hope I helped you ^_^
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
The students in Shawn's class got to choose whether to visit the zoo or the aquarium. 3 students went to the zoo and 15 students went to the aquarium. What is the ratio of the number of students who went to the zoo to the number of students who did not go to the zoo?
A. 1:6
B. 1:1
C. 1:3
D. 1:5
Answer:
either it's 1:3 or 1:6
Step-by-step explanation:
3 students went to the zoo, and 15 students went to the aquarium.
15 plus 3 is 18.
3/18 then reduces to 1/6
therefore it is:
1:6
(before, I got my answer deleted so, maybe it is 1:3, but I solved it and got 1:6)
A tank initially has 300 gallons of a solution that contains 50 lb. of dissolved salt. A brine solution with a concentration of 2lb of salt/gallon is admitted into the tank at a rate of 6 gallons per minute. The well-stirred solution is drained at the same rate. How long will it take for the tank to have 100 lb. of dissolved salt
Let s(t) be the amount of salt in the tank at time t. Then s(0) = 50 lb.
Salt flows into the tank at a rate of
(2 gal/min) (6 lb/gal) = 12 lb/min
and flows out at a rate of
(2 gal/min) (s(t)/300 lb/gal) = s(t)/150 lb/min
so that the net rate at which salt is exchanged through the tank is
ds(t)/dt = 12 - s(t)/150 … (lb/min)
Solve for s(t). The DE is separable, so we have
ds/dt = 12 - s/150
150 ds/dt = 1800 - s
150/(1800 - s) ds = dt
Integrate both sides to get
-150 ln|1800 - s| = t + C
Solve for s :
ln|1800 - s| = -t/150 + C
1800 - s = exp(-t/150 + C )
1800 - s = C exp(-t/150)
s = 1800 - C exp(-t/150)
Now given that s(0) = 50, we solve for C :
50 = 1800 - C exp(-0/150)
50 = 1800 - C
C = 1750
Then the amount of salt in the tank at any time t ≥ 0 is
s(t) = 1800 - 1750 exp(-t/150)
To find the time it takes for the tank to hold 100 lb of salt, solve for t in
100 = 1800 - 1750 exp(-t/150)
1700 = 1750 exp(-t/150)
34/35 = exp(-t/150)
ln(34/35) = -t/150
t = -150 ln(34/35) ≈ 4.348
So it would take approximately 4.348 minutes.
By the way, we didn't have to solve for s(t), we could have instead stopped with
-150 ln|1800 - s| = t + C
Solve for C - this C is not the same as the one we found using the other method. s(0) = 50, so
-150 ln|1800 - 50| = 0 + C
C = -150 ln|1750|
==> t = 150 ln(1750) - 150 ln|1800 - s|
Then s(t) = 100 lb when
t = 150 ln(1750) - 150 ln(1700)
t = 150 ln(1750/1700)
t = 150 ln(35/34)
t ≈ 4.348
Help I don’t get this
Directions: Write rack of the following statements using a symbolic language.
2. A number is four times larger than the square of half the number.
3. Steven has some money. If he spends $9.00, then he will have of the amount he started with.
4
The sum of a number squared and three less than twice the number is 129.
5. Miriam read a book with an unknown number of pages. The first week, she read five less than of the pages. The
second week, she read 171 more pages and finished the book. Write an equation that represents the total number
of pages in the book
Answer:
2.)4n>(n/2)^2
3. (The problem isn't clear)
4.)n^2+2n-3=129
5.)n-5=171
Step-by-step explanation:
2.)
4n(four times the number) >(larger than) (n/2)^2 (half the number squared)
4.)
Sum=addition
n^2 (number squared) +2n (twice the number)-3=129
5.)
N(unknown number of pages) -5(amount of pages already read)= 171(the number of pages it took her to finish)
Once upon a time, there was a former whose family raised pigs and chickens. One morning, the farmer's wife looked into the barnyard and told her husband that she counted 24 heads and 80 feet. How many chickens are in the yard? How many pigs are in the yard?
Using a system of equations, it is found that:
There are 8 chickens in the yard.There are 16 pigs in the yard.-----------------------------------------
This question is solved using a system of equations. I am going to say that:
x is the number of chickens.y is the number of pigs.-----------------------------------------
A chicken has 1 head, as do a pig.There are 24 heads.Thus:
[tex]x + y = 24 \rightarrow y = 24 - x[/tex]
-----------------------------------------
A chicken has 2 feet.A pig has 4 feet.In total, there are 80 feet.Thus:
[tex]2x + 4y = 80[/tex]
-----------------------------------------
Number of chicken:
Since [tex]y = 24 - x[/tex]
[tex]2x + 4y = 80[/tex]
[tex]2x + 4(24 - x) = 80[/tex]
[tex]2x + 96 - 4x = 80[/tex]
[tex]2x = 16[/tex]
[tex]x = \frac{16}{2}[/tex]
[tex]x = 8[/tex]
There are 8 chickens in the yard.
-----------------------------------------
Number of pigs:
[tex]y = 24 - x = 24 - 8 = 16[/tex]
There are 16 pigs in the yard.
A similar problem is given at https://brainly.com/question/24104709
If YWZ=17, what is WXY?
34
56
17
73
Answer:
73
Step-by-step explanation:
17×2=34
180-34=146
146/2=73
=73
Identify the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler's formula.
The Euler's formula relates the vertices, faces and the edges of a polyhedron.
The correct option is (e) [tex]V = 6[/tex] [tex]E = 10[/tex] [tex]F = 6[/tex] [tex]6- 10 + 6 = 2[/tex]
First, we count the number of faces. This is the flat parts of the shape.
The attached shape has 6 flat surfaces.
So:
[tex]F = 6[/tex]
Next, we count the number of edges. This is where two faces meet.
The attached shape has 10 edges;
So:
[tex]E = 10[/tex]
Lastly, we count the number of vertices. This is where two edges meet.
The attached shape has 6 vertices.
So:
[tex]V = 6[/tex]
Using Euler's formula, we have:
[tex]V - E + F = 2[/tex]
Substitute values for V, E and F
[tex]6- 10 + 6 = 2[/tex]
[tex]2 = 2[/tex]
Hence, the polyhedron has 6 vertices, 10 edges and 6 faces
Read more vertices, edges, and faces at:
https://brainly.com/question/23347978
Number of subsets of B={p,q,r}
Answer:
Step-by-step explanation:
B = {p , q , r}
Number of subsets = [tex]2^{n}[/tex]
Her, n is the number of elements in the set.
Number of subsets = 2³ = 8
Answer:
Sorry I don't know the answer
Find the measure of the missing arc KN labeled on the graph. Show ll your work that leads the final answer. *
Answer:
Arc KN = 201°
Step-by-step explanation:
Recall: According to the tangent-secant exterior angle theorem, the measure of the vertex angle formed at an external point where a tangent and a secant meet outside a circle is ½ of the difference between the intercepted major and minor arcs.
Applying this to the problem given, we have:
m<L = ½(Arc KN - Arc KM)
m<L = 70° (given)
Arc KN = ?
Arc KM = 61°
Substitute
70° = ½(Arc KN - 61°)
2*70° = Arc KN - 61°
140° = Arc KN - 61°
140° + 61° = Arc KN
201° = Arc KN
Arc KN = 201°
Determine the values of n and m so that the following system have infinite number of solutions
Answer:
n = 3
m = -1/2
Step-by-step explanation:
Multiply the second equation by 4
4(n - 2)x + y = 4(n + m) Y is now correct.
4(n - 2) = 4 Remove the brackets
4n - 8 = 4 Add 8 to both sides
4n = 8 + 4 Combine
4n = 12 Divide by 4
n = 3 x is now correct
4(n - 2) = 4
4(3 -2) = 4
4 = 4
Now you have to worry about m
4(n + m) = 10
n = 3
4(3 + m) = 10 Divide by 4
m + 3 = 10/4
m + 3 = 2.5 Subtract 3 from both sides.
m = 2.5 - 3
m = - 1/2
Please help. I don't understand anything.
Answer:
A
Step-by-step explanation:
The area of figure=Area of rectangle+Area of triangle
Area of figure=(x+2)(x-3)+1/2*(x)*(x+2)
Area of figure=x^2-x-6+0.5*x^2+x
Area of figure=(3/2)x^2-6
Answer:
A, M(x)=3/2 (x^2-6)
Step-by-step explanation:
Let's calculate the area of the figure 1st,
Area of figure=Area of triangle+Area of rectangle
=1/2 b*h + l*b = 1/2 (x+2)x + (x+2)(x-3)
=(x^2+2x)/2+x^2 - x - 6 =(x^2+2x+2x^2 - 2x -12)/2
=3x^2-12/2=3/2(x^2-6)
In the options,
M(x)=3/2 (x^2-6) is given, so it best represents the area.
solve for each of the following equations. /2x+3/=10
Answer:
/2x+3/=10
2x+3=10 or 2x+3=-10
2x=10-3 or 2x=-10-3
2x=7 or 2x=-13
X=7÷2 or X=-13÷2
X=3.5 or X=-6.5
When you subtract two positive integers is the result always a positive integer
Sai vì số Nguyên dương nhỏ trừ số nguyên dương lớn bằng số nguyên âm
will mark brainliest!!
picture included ^^^^
please and THANK YOU
^^!!
Answer:
shift the graph up 1 unit
Step-by-step explanation:
d is the vertical shift
+1 means we shift the graph up 1 unit
Find the volume of each figure. Round your answers to the nearest tenth, if necessary
Answer:
437.9
Step-by-step explanation:
Volume is pi*r^2*h=pi*(49)*9=437.9
A lake near the Arctic Circle is covered by a thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a rate of 0.20 meters per week. After 7 weeks, the sheet is only 2.42 meters thick. Let y represent the ice sheet's thickness (in meters) after x weeks.
Complete the equation for the relationship between the thickness and number of weeks.
Answer:
Step-by-step explanation:
We know that the thickness of the lake decreases at a rate of 0.2 meters per week, so we can write:
S(t)=-0.2t+4
we also know that after 7 weeks, the sheet is only 2.42 meters thick, which means we can write:
S(7)=2.42
S(7)=-0.2*7+X
S(7)=-1.4+X
2.42=-1.4+X
X=3.82
So, the function is: S(t)=--0.2*t+3.82
Answer:
y = 3.8 - 0.2x
Step-by-step explanation:
Khan Academy
What is the measure of each intercepted arc for each inscribed angle of a regular hexagon inscribed in a circle?
Answer:
Step-by-step explanation:
The inscribed angles are made up of the remote interior angles of this hexagon, of which each of them measures 120 degrees. That means that if this is measure of the inscribed angle, the arc this angle intercepts is twice the degree measure of the inscribed angle. The arcs then will all measure 240 degrees.
HELP ASAP PLEASE!!!!!
what is the factorization of the polynomial below -x^2-2x+48
I HOPE IT WILL HELP YOU. I DID HOW I KNOW .
Hello! Hello ! guys. or any genius of math. can you help me on this math problems. this question is out of my answer.
could you help me.
if your answer is correct there is a big changes to get brain list answer and 2 followers from my two accounts.
don't need to follow back.
Answer:
we have to convert that question centimeters to meters
Step-by-step explanation:
I think all are going to be less as you change all of them.
!20 Point! Please help me find the surface area!
PLEASE, forgive me but I answered this and hopefully what I see is correct. I’m really sorry if this weren’t the real measurements!
Answer:
192 square inches
Step-by-step explanation:
Surface area questions often include the net for easy answering. All you do is just find the area of each face and add them all up:
As you can see, all triangles in this net of a pyramid are the same, so once we find the area of one triangle, we’ll just multiply by 4:
FIND AREA OF ONE TRIANGLE (1/2 x b x h)
1/2 x 8 x 12 = 48 square inches
MULTIPLY BY 4 for SURFACE AREA:
48 x 4 = 192
so the SA is 192 square inches!
brainliest?
Answer:
The base is 12 the height is 8.
Using the formula of finding the area of a triangle: BH x 1/2
8 x 12 x 1/2 = 48 Area of one triangle.
Since there are 4 equilateral triangles we multiply the area of one triangle 4 times since they are all equal.
48 x 4 = 192 in2 is your surface area
(haven't done this in quite a while so make sure to check other answers for more reassurance)
The pizza restaurant down the street wants to advertise on its marquee sign the number of ways you can order a $10 pizza. The restaurant offers 18 toppings and for $10 you can order up to 4 toppings, meaning you can either order 1, 2, 3, or 4 toppings and you can’t order any toppings twice. Use this information to answer the following questions:
a. Is this a permutation problem, a combination problem, or a problem using both elements?
b. Determine how many ways you can order a pizza from the restaurant. Explain what strategies you used.
c. If there were no restriction on the number of toppings you could choose, how would that change the answer?
Answer:
Step-by-step explanation:
I need help!!
Find the height of this cone using the Pythagorean Theorem.
Answer:
h = 4sqr(3)
Step-by-step explanation:
r = d/2
d = 8
r = 8/2
r = 4
a = 4
c = 8
b = h = ?
a^2 + h^2 = c^2
4^2 + h^2 = 8^2
16 + h^2 = 64
h^2 = 64 - 16
h^2 = 48
sqrt(h^2) = sqrt(16*3)
h = 4 sqrt3)
Answer:
48
Step-by-step explanation:
A length on a map is 7.5 inches. The scale is 1inch & 5 miles. What is the actual distance?
Answer: Actual distance = 37.5 miles
Step-by-step explanation:
Let x be the actual distance
Given information
Length on map = 7.5 inches
Scale = 1 inch : 5 miles
Set up proportion
[tex]\frac{7.5}{x} =\frac{1}{5}[/tex]
Cross multiply to convert out of fraction form
[tex]7.5*5=1*x[/tex]
[tex]\boxed{x=37.5}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Find 3rd and 5th form by using nth term formula tn=a+(n-1)d when tn=a+(n-1)d when a=2 and d=3.
Answer:
t3 = 8, t5 = 14
Step-by-step explanation:
t3 = 2 + (3-1) × 3
t3 = 2 + (2) × 3
t3 = 2 + 6
t3 = 8
t5 = 2 + (5-1) × 3
t5 = 2 + (4) × 3
t5 = 2 + 12
t5 = 14
Find the volume of this sphere please help
Answer:
Volume = 108 ft³
Step-by-step explanation:
Volume of a sphere is given by the expression,
V = [tex]\frac{4}{3}\pi r^{3}[/tex]
Here, r = Radius of the sphere
From the picture attached,
Radius of the sphere = 3 ft
By substituting the value of r in the expression,
Volume = [tex]\frac{4}{3}\pi (3)^{3}[/tex]
= 36π
= 36×3
= 108 ft³
Find the coordinates of the image of M (−3, −4) after the translation (x, y) → (x + 4, y).
Answer:
(1,-4)
Step-by-step explanation:
We add 4 to the x-coordinate, so -3+4=1.
