Answer:
d=1, r=4/3
Step-by-step explanation:
For aritmetic sequence
a1=9
a1+3d=a4 9+3d=a4.
a1+7d=a8 9+7d=a8.
For geometric sequence
b1*r=b2
b2=a4, b1=a1=9
9*r=a4
b3= b1*r^2
b3=a8
a8=9*r^2
So 9+3d=a4
9+3d=9r
9+7d= a8=9r^2
So we have a system of equations
9+3d=9r
9+7d=9r^2
Multiply 9+3d=9r by -7 It is equal to -63-21d=-63r
And multiply 9+7d=9r^2 by 3. It is equal to 27+21d=27r^2
Then add them
-63-21d+ (27+21d)= -63r+27r^2
-36+63r-27r^2=0 /9
-4+7r-3r^2=0
3r^2-7r+4=0
r=1 r=4/3
If r=1 9+3d=9
d=0 (It is not right, d isn't equal to 0)
If r=4/3
9+3d= 9*4/3
9+3d=12
d=1
The value of the common difference, d is 9
The value of the common ratio r is 2
Arithmetic and Geometric SequencesThe nth term of an arithmetic sequence is:
[tex]T_n=a+(n-1)d[/tex]
The first, fourth, and eighth terms are therefore:
a, a + 3d, a + 7d
The nth term of a geometric sequence is:
[tex]T_n=ar^{n-1}[/tex]
The first three terms of the arithmetic sequence are:
[tex]a, ar^2, ar^3[/tex]
For both sequences, the first term is 9
That is, a = 9
[tex]a+3d=ar^2\\\\9+3d=9r^2..............(1)\\\\a+7d=ar^3\\\\9+7d=9r^3..........(2)[/tex]
Make d the subject of the formula in equation (1) and substitute to equation (2)
[tex]d=\frac{9r^2-9}{3} \\\\d=3r^2-3[/tex]
Substitute equation (3) into equation (2)
[tex]9+7(3r^2-3)=9r^3\\\\9+21r^2-21=9r^3\\\\21r^2-9r^3=12\\\\7r^2-3r^3=4\\\\r=1, \frac{-2}{3}, 2[/tex]
Substitute r = 2 into (1)
[tex]9+3d=9(2^2)\\\\d = 9[/tex]
The value of the common difference, d is 9
The value of the common ratio r is 2
Learn more on sequences here: https://brainly.com/question/6561461
A
B
C
D
PICK ONE
Correct answer will get you brainiest
Answer:
¾
Explanation:
A number is said to be rational if it can be expressed in the form p/q, where q is not 0.
In the given options, only ¾ fulfills this criteria.
Answer:
it's answer is c.......
5x + 4x2 - 9x + 8x2
Answer:
12x^2-4x
Step-by-step explanation:
5x + 4x^2 - 9x + 8x^2
Combine like terms
4x^2+8x^2+5x-9x
12x^2-4x
[tex]\begin{cases}\bf \large{\purple{ \implies}} \tt \: 5x \: + \: 4 {x}^{2} \: - \: 9x \: + \: 8 {x}^{2} \\ \\ \bf \large{\purple{ \implies}} \tt \: 4 {x}^{2} \: + \: 8 {x}^{2} \: + \: 5x \: - 9x \\ \\ \bf \large{\purple{ \implies}} \tt \: 12 {x}^{2} \: - \: 4x \end{cases}[/tex]
What point is the intersection of the graphs of the lines 2x - y = 3 and x+y = 3?
Answer: (2, 1)
======================================================
Explanation:
Let's add the equations straight down
The x terms add up to 2x+x = 3xThe y terms add to -y+y = 0y = 0, so the y terms go awayThe right hand sides add to 3+3 = 6After those three things happen, we're left with 3x = 6 which solves to x = 2 after dividing both sides by 3.
Now let's use this x value to find y
2x-y = 3
2(2)-y = 3
4-y = 3
-y = 3-4
-y = -1
y = 1
Or we could use the other equation
x+y = 3
2+y = 3
y = 3-2
y = 1
which gets us there in fewer steps.
So that's how we get to the final answer of (x,y) = (2,1)
The graph is shown below.
Suppose a function f has an inverse. If f(2)=6 and f(3)=7, find: f^-1 (f(3))
9514 1404 393
Answer:
3
Step-by-step explanation:
The definition of an inverse function is ...
f^-1(f(x)) = x
Then ...
f^-1(f(3)) = 3
How would you write 845 as a multiplication expressions
A.
8x5
B.
8x8x8x8x8
O c. 5x5x5x5x5x5x5x5
Answer:
13x13x5
Step-by-step explanation:
We can write 845 as
845 = 13 x 13 x 5
because
845 = (13x13) x5 = 169 x5 = 845
so the expression is
13 x 13 x 5
Suppose that F(x) = x^3 and G(X) = -3x^3. Which statement best compares the
graph of G(x) with the graph of F(x)?
A. The graph of G(x) is the graph of F(x) flipped over the y-axis and
compressed vertically.
B. The graph of G(x) is the graph of F(x) flipped over the x-axis and
compressed vertically.
C. The graph of G(X) is the graph of F(x) flipped over the x-axis and
stretched vertically.
D. The graph of G(x) is the graph of F(x) flipped over the yaxis and
stretched vertically.
Answer:
D. The graph of G(x) is the graph of F(x) flipped over the y-axis and
stretched vertically.
Step-by-step explanation:
since there is a negative, there must be a reflection. the reflection is over the y-axis because it is outside the x-value (-F(x) not F(-x))
the same goes for the vertical stretch. we know it is a vertical stretch because the 3 is outside the x-value (3F(x) not F(3x))
help me pleaseeeeee!!!!!!
Step-by-step explanation:
AC = 20
AB = 18
BC² = 20²+ 18² -2•20•18•cos(52°)
BC² = 280.72
BC = √280.72
BC ≈ 16.75
Angle C:
18² = 20² + 16.75² -2•20•16.75•cos(C)
324 = 400 + 280.72 -670•cos(C)
cos(C) = -356.72/-670
cos(C) ≈ 0.53
acos(0.53) = C
C = 57.8°
Angle B:
180-52-57.8 = 70.2°
I need help with this ASAP!
Find the area of the sector.
Answer:
B
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
The area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{255}{360}[/tex]
= π × 4² × [tex]\frac{17}{24}[/tex]
= 16π × [tex]\frac{17}{24}[/tex]
= [tex]\frac{16\pi (17)}{24}[/tex]
= [tex]\frac{272\pi }{24}[/tex]
= [tex]\frac{34\pi }{3}[/tex] mi² → C
The three seventh grade classes at Sunview Middle School collected the most boxtops for a school funderaiser, and so they won a $600 prize to share among them. Mr. Aceves' class collected 3.750 box tops, Mrs Baca's class collected 2,301, and Mr. Canyon's class collected 1,855. A. What fraction of total box tops did each class collect? B. How much money should each class receive to reflect their fraction of the total?
Answers and step-by-step explanation:
First, we add up all the totals for the box tops. This would be 3,750+2,301+1855 which totals to 7,906. Then, we take each individual box top value and divide it by 7,906 to get the fractions. For Mr. Aceves' class, the percentage is 47%, for Mrs. Baca's class, the percentage is 29% and finally for Mr. Canyon's class, the percentage is roughly 24%. This would mean that Mr. Aceves' class should get $282, Mrs. Baca's class should get roughly $174, and Mr. Canyon's class should receive $144.
Hope this helped!!
Hong buys candy that costs $5 per pound. He will buy at least 7 lbs of candy. What are the possible amounts he will spend on candy? Use c for the amount (in dollars) Hong will spend on candy. Write your answer as an inequality solved for c.
Step-by-step explanation:
if he buys 7 pounds, it will cost 7×5 = $35
he might buy more than that (and it will then also cost more than that) , but not less than that.
so,
c >= $35
Don’t know. Someone help a person!Ty
Answer:
3rd option
Step-by-step explanation:
8x³ - 27y³ ← is a difference of cubes and factors in general as
a³ - b³ = (a - b)(a² + ab + b²)
8x³ - 27y³
= (2x)³ - (3y)³
= (2x - 3y)((2x)² + 2x(3y) + (3y)²) , that is
= (2x - 3y)(4x² + 6xy + 9y²)
Kylie is comparing the cost of two housekeeping companies, DoItRight and CleanIt. The table describes the costs for DoItRight.
Hours, x 1.5 3 3.5 4.5
Total Cost, f(x) $26 $44 $50 $62
The cost of CleanIt Housekeeping is represented by g(x) = 10x + 16, where x represents the number of hours and g(x) represents the total cost in dollars.
Determine which company has the greater initial cost. Plot a point on the graph to represent the initial cost of that company.
Answer:
First, find the cost function of DoItRight Housekeeping:
Slope(m) = cost per hour = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{44-26}{3-1.5}=\frac{18}{1.5}=12[/tex]The y-intercept(b), representing the initial cost, can be calculated by substituting in values to the function:
[tex]f(x)=12x+b\\26=12(1.5)+b\\b=26-18=8[/tex]
Therefore, the function for two companies are:
The function for DoItRight is [tex]f(x)=12x+8[/tex]The function for CleanIt is [tex]g(x)=10x+16[/tex]When comparing the two functions, it's shown how CleanIt has a greater y-intercept than DoltRight, meaning that CleanIt has a greater initial cost than DotRight. The y-intercept is when the graph intercepts the y-axis, therefore, the coordinates there would be (0, y-value), which, in this case for CleanIt company, will be (0, 16). While CleanIt has a greater y-intercept(initial cost), DoItRight has a greater slope, meaning they cost more per hour.
Solve the following inequality algebraically:
-2 < x/3 +1 <5
Answer:−9<x<12
Step-by-step explanation:
−2< x 3 +1<5
−2< 1 3 x+1<5(Simplify all parts of the inequality)
−2+−1< 1 3 x+1+−1<5+−1(Add -1 to all parts)
−3< 1 3 x<4
−3/( 1/ 3) <(1/3x)/1/3 < (4)/1/3 (Divide all parts by \,{1}/{3}\,)
−9<x<12
Algebra Piecewise functions!!!
Can someone help with number 1? I got some of it but I don’t know what to do next!
Answer:
f(7) = 16
Step-by-step explanation:
f(7)
Let x = 7
We use the first part of the function since 7 > 4
3(7) -5
21 -5
16
f(7) = 16
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
x = 7
Brainliest, please!
Step-by-step explanation:
90 + 33 + (6x + 15) = 180
6x + 138 = 180
6x = 42
x = 7
James defines an angle as "a figure consisting of two rays." His statement is not precise enough because he should specify that
the rays must be collinear
the rays must form a right angle
the rays must have a common endpoint
the rays must continue in one direction forever
Statement: If two noncollinear rays join at a common endpoint, then an angle is created. Which geometry term does the statement represent?
Defined term
Postulate
Theorem
Undefined term
James should define that the rays must be collinear. the two rays coming from the same point will form collinear rays which will form an angle at end point.
The statement of james should be precise in order to clearly explain the angle formation.
The two non collinear rays will form an angle at end point where they meet with each other.
The defined vertex will form the appropriate angle. there should be defined term for the non collinear rays.
Learn more at https://brainly.com/question/24373158
1: The rays must have a common endpoint
2: Defined term
I took the test and got both right :))
Do radical expressions with the same degree and the _____ are called like terms.
Answer:
The answer is A - Radicand.
Hope that helps!
you need to fence off two rectangular lots. the larger of two lots is 45 feet long and 22 feet wide, while the smaller lot is 24 feet long and 16 feet wide. How much fencing in feet will you need to fully enclose both lots?
==============================================================
Explanation:
I'll assume that both lots are not adjacent. So we have two separate rectangles that aren't touching.
We use the rectangle perimeter formula
P = 2(L+W)
where L is the length and W is the width. For the first rectangle, we have L = 45 and W = 22, so
P = 2(L+W)
P = 2(45+22)
P = 2(67)
P = 134
You need 134 feet of fencing for the 45 ft by 22 ft rectangle.
Repeat for the other rectangle
P = 2(L+W)
P = 2(24+16)
P = 2(40)
P = 80
You need 80 feet of fencing for the 24 ft by 16 ft rectangular lot.
Overall, you need 134+80 = 214 feet of fencing
------------------------
Extra info (optional section):
Now if the two lots are touching in some way, then you won't need as much fencing. This is because the two lots will share the bit of fencing between them. This might apply to a portion of one side, or the entire side, of either rectangle. It depends how the lots are laid out.
The assumption that the lots aren't adjacent considers the worst case scenario, aka the situation where you'll need the most fencing (hence the largest cost). This will allow you to prepare for the worst and not be caught off guard. All of this assumes there is no waste, and that there are no gaps or overlaps. If there is expected to be some inefficiency of waste (which is fairly realistic in my opinion) then it's probably a good idea to slightly overshoot this target.
Find x (Round to the nearest tenth). PLS HURRY
Answer:
x = 28.4°
Step-by-step explanation:
The cos(x) = 15/17 ≈ 0.88
The acos(0.88) = 28.4°
A pendulum's height is modeled by the function h(t) = 4 cos(pi/4*t) + 8 where h is the
measure of the pendulum's height in feet and t is the number of seconds since the
maximum height. How many seconds does it take the pendulum to complete one
full swing?
===========================================================
Explanation:
The general cosine template is
y = A*cos(B(t - C)) + D
where in this case
A = 4B = pi/4C = 0D = 8We only really need to worry about the B value. To get the period T, we do the following
T = 2pi/B
T = (2pi)/(pi/4)
T = 2pi * (4/pi)
T = 8
Note how the pi terms canceled. The period is 8 seconds, which is the length of one full cycle. This is the time it takes for the pendulum to do one full swing (eg: start at the right, swing to the left all the way, then swing back to the right again).
The result of 8 we got has nothing to do with the D = 8 value (this D value could be any other number and T = 8 would still be the case as long as B doesn't change of course).
Joshua is trying to find the product of 38 × 12. Which expression shows how Joshua could use place value to break up this problem and solve it?
(32 + 6) × (10 + 2)
(30 + 8) × (10 + 2)
(31 + 7) × (11 + 1)
(30 + 8) × (11 + 1)
Answer:
B did it on edg
Step-by-step explanation:
The expression that shows how Joshua could use place value to break up this problem and solve it is:
(30 + 8) x (10 + 2)
Option B is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
38 x 12
This can be written in place value as,
38 = 3 tens and 8 ones
12 = 1 tens and 2 ones
So,
38 = 30 + 8
12 = 10 + 2
Thus,
The expression used is (30 + 8) x (10 + 2)
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
arshad's father bought x sweets .(x-4)were eaten by children and 20 were left.how many sweets did his father bring
Answer:
24
Step-by-step explanation:
20+4
simple
x-4=20
x=20+4
x=24
mark me as brainliest
Answer:
24 sweets
Step-by-step explanation:
Remaining sweets = 20
x - 4 = 20
Add 4 to both sides.
x = 20 +4
x = 24
What is the GCF of 12a^4b^2 - 3a^2b^5 ??
hope it helps~
A triangle has sides measuring 6, 8, and 10 cm. Using a dilation factor of 0.75, what would the measurements of a second triangle be?
Answer:
The Measurement of the second triangle would be 4.5, 6, 7.5. and the dilation type is reduction.
Step-by-step explanation: The sizes you have will be multiplied by the dilation factor 0.75.
6*0.75=4.5, 8*0.75=6, 10*0.75=7.5.
Have a good day.
The dilated form of the sides of the triangle is 4.5,6, and 7.5.
What is dilation?Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased. The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.
Given that a triangle has sides measuring 6, 8, and 10 cm. Using a dilation factor of 0.75.
The measurement of the second triangle would be 4.5, 6, and 7.5. and the dilation type is reduction.
The sizes you have will be multiplied by the dilation factor of 0.75.
6 x 0.75=4.5,
8 x 0.75=6,
10 x 0.75=7.5.
Therefore, the dilated form of the sides of the triangle is 4.5,6, and 7.5.
To know more about dilation follow
https://brainly.com/question/3457976
#SPJ2
Solve for X. Geometry
Answer:
11
Step-by-step explanation:
6+(2x+28)=x+23=-11 -> Answer can't be negative -> 11
c. The sum of two number is 59. If the Smaller number is less than the bigger one by 7,find the number.
Step-by-step explanation:
Hi there!
According to the question;
The sum of two number is 59. And the Smaller number is less than the bigger one by 7,
Let the bigger number be "X" then smaller number will be x-7.
Then;
x + (x-7) = 59
2x = 59+7
X = 66/2
Therefore, the bigger number (X) is 33 and smaller number (x-7) is 26.
Hope it helps!
f) 60 students in a hostel have food enough for 30 days. If 20 more students join the hostel after 10 days, how long will the remaining food last?
Answer:
Hello,
10 days
Step-by-step explanation:
60 étudiants dans un foyer ont assez de nourriture pour 30 jours. Si 20 étudiants supplémentaires rejoignent l'auberge après 10 jours, combien de temps durera la nourriture restante ?
Let say A the quantity of food
60 students in a hostel have food enough for 30 days ==> A=k*60*30
==> k=A/1800
Let say x the duration of the food.
60 students for x days + 20 students for (x-10) days =A
[tex]k*60*x+k*20*(x-10)=A\\[/tex]
[tex]\dfrac{A*60*x}{1800} +\dfrac{A*20*(x-10)}{1800} =A\\\\60x+20x-200=1800\\\\80x=1600\\\\x=20\\[/tex]
Duration for the 80 students: 20-10=10days
inverse functions
Given that f(X)=2x-3 and g(X)=3x+1÷x+2
Answer:
765(7-()83)₹8_!_?84?8₹92092)8₹+!_()
Which expression is equivalent to 8f+5f?
The answer is
8f+5f
=13f
