Answer:
[tex]a_n=-3a_{n-1}[/tex] where [tex]a_1=2[/tex]
Step-by-step explanation:
Recursive means you want to define a sequence in terms of other terms of your sequence.
The common ratio is what term divided by previous term equals.
The common ratio here is -6/2=18/-6=-54/18=-3.
Or in terms of the nth and previous term we could say:
[tex]\frac{a_n}{a_{n-1}}=r[/tex]
where r is -3
[tex]\frac{a_n}{a_{n-1}}=-3[/tex]
Multiply both sides by the a_(n-1).
[tex]a_n=-3a_{n-1}[/tex] where [tex]a_1=2[/tex]
Answer:
see explanation
Step-by-step explanation:
A recursive rule allows us to obtain any term in the sequence from the previous term.
These are the terms of a geometric sequence with common ratio r
r = - 6 ÷ 2 = 18 ÷ - 6 = - 54 ÷ 18 = - 3
Thus to obtain a term in the sequence multiply the previous term by - 3
[tex]a_{n+1}[/tex] = - 3 [tex]a_{n}[/tex] with a₁ = 2
PLEASE HELP FAST!!!!
A man goes fishing in a river and wants to know how long it will take him to get 10km upstream
to his favourite fishing location. The speed of the current is 3 km/hr and it takes his boat twice
as long to go 3km upstream as is does to go 4km downstream. How long will it take his boat to
get to his fishing spot?
Answer:
Time = 25/9 hr
Step-by-step explanation:
Let speed of boat in still water is x km/hr
then, speed in downstream equals to "x + 3"km/hr
and speed in upstream equals to "x - 3" km/hr
We also know that time taken to travel 3km in upstream is twice as time taken to travel 4km in downstream.
so, using time = distance/speed
3/x- 3 = 2 × (4/x + 3)
3x + 9 = 8x -24
5x = 33
x = 33/5 km/hr
Net speed in upstream = 33/5 - 3 = 18/5 km/hr
So, Time taken to travel 10km upstream = distance /speed
= (10 × 5) / 18 = 25/9 hr
Time = 25/9 hr
The boat speed in still water is determined to be 6.6 km/hr, and it will take around 2.78 hours to travel 10 km upstream.
To determine how long it will take the man to travel 10 km upstream to his favorite fishing location, let's first define the boat speed in still water as v km/hr.
From the problem, we know:
The speed of the current is 3 km/hr.
It takes twice as long to travel 3 km upstream as it does to travel 4 km downstream.
The speed of the boat upstream relative to the shore is v - 3 km/hr, and downstream it is:
→ v + 3 km/hr.
Let t be the time it takes to travel 4 km downstream. Then time to travel 3 km upstream is 2t.
We can set up the following equations using distance = speed x time:
→ For downstream: 4 = (v + 3)t
→ For upstream: 3 = (v - 3)2t
Solve these equations:
→ From 4 = (v + 3)t, we have t = 4/(v + 3)
Substitute t in 3 = (v - 3)2t: 3 = (v - 3)2(4/(v + 3))
→ Simplify: 3(v + 3) = 8(v - 3)
→ Expand and solve for v: 3v + 9 = 8v - 24
→ 33 = 5v
→ v = 33/5
= 6.6 km/hr
Now that we know the speed of the boat in still water is 6.6 km/hr, we can determine the time it takes to travel 10 km upstream:
→ The effective speed upstream is:
= 6.6 - 3
= 3.6 km/hr.
→ Time required to travel 10 km upstream is:
= 10 / 3.6
≈ 2.78 hours.
Which description does NOT guarantee that a quadrilateral is a kite?
A two distinct pairs of congruent adjacent sides
B perpendicular diagonals
C perpendicular diagonals, exactly one of which bisects the other
D one diagonal bisects opposite angles and the other diagonal does not
Answer:
D one diagonal bisects opposite angles and the other diagonal does not
Option D, 'one diagonal bisects opposite angles and the other diagonal does not,' does NOT guarantee that a quadrilateral is a kite.
To determine if a quadrilateral is a kite or not based on its properties.
A quadrilateral is a kite if and only if its diagonals are perpendicular and exactly one of them bisects the other diagonal. Let's analyze the given options:
If a quadrilateral has two distinct pairs of congruent adjacent sides, it is not necessarily a kite.If a quadrilateral has perpendicular diagonals, it is one condition for it to be a kite, so this option could guarantee a kite.If a quadrilateral has perpendicular diagonals, exactly one of which bisects the other, it guarantees a kite.If one diagonal bisects opposite angles and the other diagonal does not, it is not sufficient to guarantee a kite.Therefore, option D, 'one diagonal bisects opposite angles and the other diagonal does not,' does NOT guarantee that a quadrilateral is a kite.
What is the median of the following data set?
{5, 2, 9, 7, 4}
5
7
8
9
Answer:
a
Step-by-step explanation:
What is the measure of angle x, in degrees
Option C ,
40 degrees
Because angle Z was 70 (isosceles triangle)
Then 180-140=40 degrees
Carrie has 300 marbles 25 of the marbles are green 15% of the marbles are red and the rest of the marbles are blue how many blue marbles does he have
Answer:
230.
Step-by-step explanation:
[tex] \: \: \: \: 300 - 25 - \frac{15}{100} \times 300 = \\ = 275 - 45 = \\ = 230[/tex]
Hope this helps!
Answer:
230 blue marbles
Step-by-step explanation:
In order to answer this question, we need to find how many marbles are red.
We know that 25 marbles are green
15% of the marbles are red.
There are a total of 300 marbles.
We would multiply 300 by 0.15 to find how many marbles are red.
[tex]300*0.15=45[/tex]
45 marbles are red.
In the question, it says the rest of the marbles are blue.
This means that we would subtract 300 by 25 and 45 to find how many marbles are blue.
[tex]300-25-45=230[/tex]
This means that 230 marbles are blue.
I hope this helps!Best regards,MasterInvestor
When is a rhombus a rectangle?
À. When its sides are parallel
B. When its angles are convex angles
C. When its angles are right angles
D. When its sides are congruent
Answer:
c. when all angles are right angles
Step-by-step explanation:
joseph had started saving quarters,dimes,nickel and penny but is unable to give the
exact change for a hamburger costing $3.50.What the greatest amount of money he could have in coins.
Answer:
$3.49
12 quarters,4 dimes,1 nickle, 4 pennies
Step-by-step explanation:
First remember that;
Quarter=25 pennies
Dime=10 pennies
Nickel =4 pennies
I cent =0.01$
Given the amount as $3.50
Assume you use 4 quarters, this means a whole dollar, so it will be;
1 dollar = 4quarters
3 dollars=?
cross multiply
3×4=12 quarters
The remaining $0.49
Here identify 40 cents, which is 40 pennies
But 10 pennies=1 dime
so 40 pennies=?
cross-multiply
(40×1)÷10=4 dimes
and a nickel for 4 pennies.
Eighty percent of the students in a class (group A) share 40% of the candy equally. The remaining 20% of the students (group B) share the other 60% of the candy equally. The ratio of the amount of candy a student in group A has to the amount of candy a student in group B has is equal to what common fraction?
Answer:
1/6
Step-by-step explanation:
There is x candy in total and y students in total.
Group A consists of 0.8y students, and group B consists of 0.2y students.
Group A gets 40% of x, or 0.4x. Each student in group A gets 0.4x/(0.8y) = 0.5x/y candy per person.
Group B gets 60% of x, or 0.6x. Each student in group B gets 0.6x/(0.2y) = 3x/y candy per person.
The ratio of candy each student in group A has to the amount of candy each student in group B has is:
(0.5x/y)/(3x/y) = 0.5/3 = 1/6
The ratio of the amount of candy a student in group A has to the amount of candy a student in group B has is equal to 1/6
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Eighty percent of the students in a class (group A) share 40% of the candy equally.
The remaining 20% of the students (group B) share the other 60% of the candy equally.
We need to find the common fraction between Group A and group B if ratio of the amount of candy a student in group A has to the amount of candy a student in group B has is equal
Let the total number of candy's are x
The total number of students are y.
The number of students in group A=0.8y
The number of students in group B=0.2y
Group A gets 40% of x, or 0.4x.
Each student in group A gets 0.4x/(0.8y) = 0.5x/y candy per person.
Group B gets 60% of x, or 0.6x. Each student in group B gets 0.6x/(0.2y) = 3x/y candy per person.
The ratio of candy each student in group A has to the amount of candy each student in group B has is:
(0.5x/y)/(3x/y) = 0.5/3 = 1/6
Hence, the ratio of the amount of candy a student in group A has to the amount of candy a student in group B has is equal to 1/6
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What is the value of y in this simplified expression?
k + m 10
Answer:
y=5
x=7
Step-by-step explanation:
When given an expression in the form a⁻ᵇ the expression is the same as 1/aᵇ where a and b are integers.
Solving the question by giving the equivalents of the expression:
Therefore (-j)⁻⁷ is the same as 1/j⁷
The value of x=7
k⁻⁵+m⁻¹⁰=1/k⁵+1/m¹⁰
Therefore the value of y is 5.
Question 1:
For this case we have that by definition of properties of powers it is fulfilled that:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
So, if we have the following expression:
[tex](-j) ^ {- 7}[/tex]
We can rewrite it as:
[tex]\frac {1} {(- j) ^ 7}[/tex]
So we have to:
[tex]x = 7[/tex]
ANswer:
[tex]x = 7[/tex]
Question 2:
For this case we have that by definition of properties of powers it is fulfilled that:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
If we have the following expression:
[tex]k^{-5}+m^{-10}[/tex]
We can rewrite it as:
[tex]\frac {1} {k ^ 5} + \frac {1} {m ^ {10}}[/tex]
So we have[tex]y = 5[/tex]
Answer:
[tex]y = 5[/tex]
Graph the pair of equations on the same axes and state whether they are parallel, perpendicular, or neither.
Answer:
Parallel
Step-by-step explanation:
Instead of putting this and slope intercept form. I'm going determine the
x-intercept and the y-intercept of both.
The x-intercept can be found by setting y to 0 and solving for x.
The y-intercept can be found by setting x to 0 and solving for y.
So let's look at 3x-2y=5.
x-intercept?
Set y=0.
3x-2(0)=5
3x =5
x =5/3
y=intercept?
Set x=0.
3(0)-2y=5
-2y=5
y=-5/2
So we are going to graph (5/3,0) and (0,-5/2) and connect it with a straightedge.
Now for 6y-9x=6.
x-intercept?
Set y=0.
6(0)-9x=6
-9x=6
x=-6/9
x=-2/3
y-intercept?
Set x=0.
6y-9(0)=6
6y =6
y =1
So we are going to graph (-2/3,0) and (0,1) and connect it what a straightedge.
After graphing the lines by hand you can actually do an algebraic check to see if they are parallel (same slopes), perpendicular (opposite reciprocal slopes), or neither.
Let's find the slope by lining up the points and subtracting then putting 2nd difference over 1st difference.
So the points on line 1 are: (5/3,0) and (0,-5/2)
(5/3 , 0 )
- (0 ,-5/2)
-----------------
5/3 5/2
The slope is (5/2)/(5/3)=(5/2)*(3/5)=3/2.
The points on line 2 are: (-2/3,0) and (0,1)
(-2/3 , 0)
- ( 0 , 1)
-----------------
-2/3 -1
The slope is -1/(-2/3)=-1*(-3/2)=3/2.
The slopes are the same so they are parallel. The line lines are definitely not the same; if you multiply the top equation by -3 you get -9x+6y=-15 which means the equations are not the same. Also they had different x- and y-intercepts. So these lines are parallel.
This is what we should see in our picture too.
The lines 3x - 2y = 5 and 6y - 9x = 6 are parallel lines
How to find if the lines are parallelThe lines 3x - 2y = 5 and 6y - 9x = 6 are parallel lines if their their slopes are equal
Lets rewrite the equation to be in slope intercept form: y = mx + b. where m is the slope
3x - 2y = 5
2y = 3x - 5
y = 3x/2 - 5/2. slope is 3/2
6y - 9x = 6
6y = 9x + 6
y = 3x/2 + 1. slope is 3/2
Comparing the equations with equal slope of 3/2, and from the graph shows that they are parallel lines
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Which of the following options is a polynomial with a root 2i and exactly 2
real roots?
Answer:
B. [tex]f(x)=x^4-x^3+2x^2-4x-8[/tex]
Step-by-step explanation:
If [tex]2i[/tex] is a root of f(x), then the complex conjugate [tex]-2i[/tex] is also a solution. If f(x) should have exactly 2 real roots, then by the Fundamental Theorem of Algebra, the minimum degree of f(x) is 4.
Hence the first and last options are eliminated.
By the Remainder Theorem, [tex]f(2i)=0[/tex].
Let us check for options B and C.
For option B.
[tex]f(x)=x^4-x^3+2x^2-4x-8[/tex]
[tex]\implies f(2i)=(2i)^4-(2i)^3+2(2i)^2-4(2i)-8[/tex]
[tex]\implies f(2i)=16i^4-8i^3+8i^2-8i-8[/tex]
[tex]\implies f(2i)=16+8i-8-8i-8=0[/tex]
For option C
[tex]f(x)=x^4-x^3-6x^2+4x+8[/tex]
[tex]\implies f(2i)=(2i)^4-(2i)^3-6(2i)^2+4(2i)+8[/tex]
[tex]\implies f(2i)=16i^4-8i^3-24i^2+8i+8[/tex]
[tex]\implies f(2i)=-16+8i+24+8i+8\ne0[/tex]
Therefore the correct choice is B.
x to the 2nd power + 3=12
Answer:
x = ±3
Step-by-step explanation:
x^2 +3 = 12
Subtract 3 from each side
x^2 +3-3 = 12-3
x^2 = 9
Take the square root of each side
sqrt(x^2) =±sqrt(9)
x = ±3
WILL MARK BRAINLIEST
PLEASE
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a restraunt owner is going to panel a square portions of the restaurants ceiling. The portion to be paneled has an area of 185 ft^2. The owner plans to use square tin ceiling panels with a side length of 2 ft. What is the first steps in finding ouw whether the owner will be able to use a whole number of panels?
Answer: Dividing 185 by 4 is the first step in finding out whether the owner will be able to use a whole number of panels. Hope this helps!
Step-by-step explanation:
The owner will not be able to use a whole number of panels btw
What is the area of the composite figure O120 O100 O110 O90
Total area is 110 square meter
Answer:
140
Step-by-step explanation:
Built in 1599, the Globe Theatre was home to William Shakespeare and his performing company, The Lord Chamberlain’s Men. It was a circular amphitheater that stood 3-stories tall and had a diameter of 100 feet. What formula can you use to calculate the distance around the theatre?
Answer:
C = pi * d formula
C = 314 ft
Step-by-step explanation:
To find the distance around the theatre, we want to use circumference.
C= 2 * pi *r where r is the radius
or
C = pi * d where d is the diameter
C = pi *100
C = 100pi
Using 3.14 as an approximation for pi
C = 3.14*100
C = 314 ft
Which of the following is not a whole number followed by its square?
A. 11, 121
B. 13, 169
C. 15, 205
D. 8, 64
E. 2, 4
Answer:
C 15, 205.
Step-by-step explanation:
That would be C because 15^2 = 225. The others are all correct.
The whole number not followed by its square is (c) 15, 205
How to determine the whole number?The square of a number x can be represented as:
y = x^2
Using the above equation, we have:
121 = 11^2 --- true
169 = 13^2 --- true
205 = 15^2 --- false
64 = 8^2 --- true
4 = 2^2 --- true
Hence, the whole number not followed by its square is (c) 15, 205
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The blue segment below is a diameter of O. What is the length of the radius of the circle?
Answer:
c 5.1
Step-by-step explanation:
The diameter of the circle is 102.
The radius is half of the diameter
r =d/2
r =10.2 /2 =5.1
A hunter shot 7 ducks. The hunter's dog recovered 5/7 of
the ducks. How many ducks were recovered?
Answer:
5
Step-by-step explanation:
7 ducks=7/7 ducks
7/7-?=5/7
7/7-2/7=5/7
5/7=5 ducks
which of the following is the quotient of the rational expressions shown below x-2/x+3 divided by 2/x
Answer:
2x^2+4x/3x-3
Step-by-step explanation:
ape.x
The quotient of (x-2)/(x+3) divided by 2/x is (x² - 2x)/(2x + 6), which corresponds to option D. This is achieved by multiplying the first fraction by the reciprocal of the second fraction and then simplifying.
To find the quotient of (x-2)/(x+3) divided by 2/x, we'll follow these steps:
Rewrite the division of fractions as multiplication by the reciprocal. This means:(x-2)/(x+3) ÷ (2/x) = (x-2)/(x+3) * (x/2)Multiply the numerators and multiply the denominators:((x-2) * x) / ((x+3) * 2) = (x(x-2)) / (2(x+3))Simplify the expression:(x² - 2x) / (2x + 6)Looking at the given options, the correct answer is: (x² - 2x) / (2x + 6) (Option D)
The complete question is
which of the following is the quotient of the rational expressions shown below x-2/x+3 divided by 2/x
A. (2x - 4)/(x ^ 2 + 3x)
B. (2x - 2)/(x ^ 2 + 3x)
C. x/(2x + 3)
D. (x² - 2x)/(2x + 6)
find the distance between the points (-3,2) and (0,3).
Answer:
The distance between (-3, 2) and (0,3) is √10.
Step-by-step explanation:
As we go from (-3,2) to (0,3), x increases by 3 and y increases by 1.
Think of a triangle with base 3 and height 1. Use the Pythagorean Theorem to find the length of the hypotenuse, which represents the distance between the points (-3, 2) and (0, 3):
distance = √(3² + 1²) = √10
The distance between (-3, 2) and (0,3) is √10.
For this case we have that by definition, the distance between two points is given by:
[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]
We have the following points:
[tex](x_ {1}, y_ {1}): (- 3,2)\\(x_ {2}, y_ {2}) :( 0,3)[/tex]
Substituting:
[tex]d = \sqrt {(0 - (- 3)) ^ 2+ (3-2) ^ 2}\\d = \sqrt {(3) ^ 2 + (1) ^ 2}\\d = \sqrt {9 + 1}\\d = \sqrt {10}[/tex]
Answer:
The distance between the points is [tex]\sqrt {10}[/tex]
5/7 = y/6
Solve the following proportion for y
Round your answer to the nearest tenth
Answer:
The value of y = 4.3
Step-by-step explanation:
It is given that,
5/7 = y/6
To find the value of y
We have, 5/7 = y/6
(5 * 6) = (y * 7)
y * 7 = 5 * 6
y = (5 * 6)/7
= 30/7
= 4.29
≈ 4.3
Therefore the correct answer, the value of y = 4.3
308% is what percent of 530?
Answer:
58%
Step-by-step explanation:
you write it as
308= ? (because you dont know what percent of 530 is yet) x 530
so it should look like 308=?x530
then divide on both sides and then turn your answer into a percentage.
If the point (a,3) lies on the graph of the equation 5x + y = 8, then a= 1 -1 -7
Answer:
a=1
Step-by-step explanation:
Let's find out!
So we have the point (x,y)=(a,3) is on the equation 5x+y=8.
Let's replace x with a and y with 3. This gives us:
5x+y=8
5a+3=8
Subtract 3 on both sides:
5a =5
Divide both sides by 5:
a =5/5
a =1
So the point has to be (1,3)
What is the answer to 6x2-54x/x-9*7x/6x
Answer:
[tex]\large\boxed{\dfrac{6x^2-54x}{x-9}\cdot\dfrac{7x}{6x}=7x}[/tex]
Step-by-step explanation:
[tex]\dfrac{6x^2-54x}{x-9}=\dfrac{6x(x-9)}{x-9}=6x\qquad\text{canceled}\ (x-9)\\\\\dfrac{7x}{6x}=\dfrac{7}{6}\qquad\text{canceled}\ x\\\\\dfrac{6x^2-54x}{x-9}\cdot\dfrac{7x}{6x}=6x\cdot\dfrac{7}{6}=7x\qquad\text{canceled 6}[/tex]
Is ABC a right triangle? How do you know?
Answer:
Option A There is not enough information to determine
Step-by-step explanation:
we know that
If two lines are perpendicular, then the product of their slopes is equal to -1
You must calculate the slope of the AB segment and the BC segment, however the coordinates of the vertices are not known.
therefore
There is not enough information to determine
Complete the table Y=6x-4
Answer:
With Two points is enough to describe this graph
[tex]\left[\begin{array}{ccc}\frac{4}{6} &0\\0&-4\\\end{array}\right][/tex]
Step-by-step explanation:
Interception with Y axis (y=0), thus we have the following equation:
[tex]0=6*x+4[/tex]
[tex]x=4/6[/tex]
The point for this is (4/6 , 0)
Interception with x axis (x=0), thus we have the following equation:
[tex]Y=4*0-4[/tex]
[tex]y=-4[/tex]
The point for this is (0, -4)
Find the area of the shaded region if the dimensions of the unshaded region are 20ft x 35ft.
Answer:
The correct answer option is A. 1397.46 ft^2.
Step-by-step explanation:
We are to find the area of the shaded region. For that, we will divide the figure into smaller shapes, find their areas separately and then add them up.
From the given figure, we can see that there are two semi circles )or say one whole circle if we combine them) at the ends while 2 rectangles at the top and bottom.
Radius of circle = [tex]\frac{20+7+7}{2} [/tex] = 17
Area of circle = [tex]\pi r^2 = \pi \times 17^2[/tex] = 907.92 square ft
Area of rectangles = [tex]2(l \times w) = 2(35 \times 7)[/tex] = 490 square ft
Area of shaded region = 907.9 + 490 = 1397.46 ft^2
Answer:
A.) 1,397.46 ft²
Step-by-step explanation:
I got it correct on founders edtell
Find the range of the following set of data.
23,50, 49, 48, 49, 32, 37, 40, 41, 42, 41, 41, 43
Answer:
27
Step-by-step explanation:
The range is the greatest value subtract the smallest value
greatest value = 50 and smallest value = 23, so
range = 50 - 23 = 27
Answer:
27
Step-by-step explanation:
23,32,37,40,41,41,41,42,43,48,49,49,50.
Range=50-23=27
Where is the opposite of −10 located on a number line? A) to the left of 0 B) to the right of 0 C) to the right of 12 D) to the left of −10
Answer:
B. to the right of 0
Step-by-step explanation:
the opposite of -10 would be 10 and out of all the answer choices the number 10 only fits into B.
Answer:
B to the right of zero why? ITS COMMON SENSE!
Step-by-step explanation:
Scientists released 6 rabbits into a new habitat in year 0. Each year, there were four times as
many rabbits as the year before. How many rabbits were there after x years? Write a function
to represent this scenario.
The function that represents the given scenario is; f(x) = 6(4)ˣ
How to create an exponential growth function?We know the general formula for this population function is;
f(x) = abˣ
where;
a is initial population
b is the common ratio
x is number of years
We are given;
a = 6
b = 4
Thus;
f(x) = 6(4)ˣ
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