The explicit formula that is equivalent to aₙ = -6aₙ₋₁ is; aₙ = 1(-6)ⁿ⁻¹
What is the explicit formula?We are given;
a₁ = 1
aₙ = -6aₙ₋₁
Thus, for second term;
a₂ = -6a₁
a₂ = -6
For the third term;
a₃ = -6a₂
a₃ = 36
The resulting sequence is 1, -6, 36,......
The sequence is a geometric sequence with;
a = 1
r = -6
The explicit rule will be aₙ = 1(-6)ⁿ⁻¹
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A spherical ball for a machine was made with a radius of 2 centimeters. if the ball has a mass of 278.1 grams, which material was used to make the ball?
The spherical ball for the machine with a radius of 2 centimeters, has a mass of 278.1 grams and will have a density of 8.29 grams per cm³, which is identical to the density of Terbium's 8.23 grams per cm³.
Thus, we can say that Terbium is the material used to make the spherical ball.
The density of an object is given as the ratio of its mass and its volume.
Density = Mass/Volume.
In the question, we are informed that a spherical ball for a machine was made with a radius of 2 centimeters.
Thus, the volume of the spherical ball, using the formula for the volume of a sphere, V = (4/3)πr³, where r is its radius, can be calculated as:
V = (4/3)π(2)³ cm³ = 32π/3 cm³ = 33.51032 cm³.
The mass of the ball is given to be 278.1 grams.
Thus, its density = 278.1/33.51032 grams per cm³ = 8.2989355 grams per cm³.
We know that the density of Terbium is 8.23 grams per cm³.
Thus, the spherical ball for the machine with a radius of 2 centimeters, has a mass of 278.1 grams, will have a density of 8.29 grams per cm³, which is identical to the density of Terbium's 8.23 grams per cm³.
Thus, we can say that Terbium is the material used to make the spherical ball.
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Answer: copper
Step-by-step explanation:
please help please and thank you
Answer:
B or the second option
Step-by-step explanation:
We can label the diagram parts A-E to fully represent the situation in the question.
A: Julie's ascent up the mountain (moving/increasing)
B: Julie drinking hot chocolate (stationary/constant)
C: Julie's descent down the mountain (moving/decreasing)
D: Julie rests (stationary/constant)
E: Julie's final descent down the mountain (moving/decreasing)
Many states use a sequence of three letters followed by a sequence of three digits as their standard license-plate pattern. Given that each three-letter three-digit arrangement is equally likely, what is the probability that a ran- domly chosen license plate contains at least one palindrome (a three-letter arrangement or a three-digit arrangement that reads the same left-to-right as it does right-to-left)?
Answer:
Step-by-step explanation:
There are 26 letters, so there are 26
3
possible 3-letter sequences.
the number of these which are palindromes can be computed as follows:
26 choices for the first letter
26 choices for the second letter
1 choice for the third letter ( it has to agree with the first)
number of ways =26
2
Probability of a letter palindrome =26
2
/26
3
=1/26
there are 10 digits, so there are 10
3
sequences of digits.
Reasoning as above, the number of digit-palindromes is (10)(10)(1)=10
2
so the probability of a digit-palindrome is 10
2
/10
3
=1/10
The events
D - digit palindrome
L - letter palindrome
are independent but not mutually exclusive.
So, P(LorD)=P(L)+P(D)−P(LandD)
P(LorD)=P(L)+P(D)−P(L)P(D)
=1/26+1/10−(1/26)(1/10)
=10/260+26/260−1/260
=35/360=7/52
please help
are these functions or not?
Answer:
1. Function
2. Not a function
3. Function
4. Not a function
Step-by-step explanation:
A function just means that for each input it outputs only 1 output. This output isn't necessarily unique. So for example if you're just given: f(2) = 3 and f(1) = 3, this is a function since each input only outputs 1 value, even though the output isn't unique, but if you're given: f(3) = 2, f(2) = 1, f(3) = 3. that's not a function since f(3) outputs both 2 and 3.
Anyways now that you hopefully understand this, let's look at each image.
Relation 1: (Function)
So for each input (the domain) it's only pointing to one output (range), even if multiple input (the domain) are pointing to the same output (the range), it's still a function.
Relation 2: (Not a function)
This is not a function, since if you look at the input 7 (the range), you'll see it outputs two things (range). It outputs -6 and -7. So this is not a function
Relation 3: (Function)
This is a function since each x-value (input) has only one y-value (output). So it's a function
Relation 4: (Not a functio)
This is not a function, since there are multiply coordinates with the same x-coordinate (input) and different y-coordinates (output). The x-coordinate 2 has the output b, y, and m, and since no value is given for these variables, it can be assumed they're different values, thus it's not a function.
which coordinate pair is a solution of the linear equation below -3x+4y=19
The coordinate pair that is a solution of the linear equation -3x+4y=19 is (0, 19)
How to determine the ordered pair?The linear equation is given as:
-3x + 4y= 19
Set x = 0
So, we have:
-3(0) + 4y = 19
Evaluate
4y = 19
Divide by 4
y = 19/4
Hence, the coordinate pair that is a solution of the linear equation -3x+4y=19 is (0, 19)
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Bryan is asked to write an inequality to represent the graph.
A number line going from negative 16 to negative 10. An open circle is at negative 14. Everything to the right of the circle is shaded.
He writes Negative 14 less-than-or-equal-to x.
Which error did Bryan make?
Bryan must write the inequality with the variable on the left side of the relation symbol.
Bryan chose a relation symbol that does not point in the same direction as the ray.
Bryan included –14 in his solution set.
Bryan used the wrong number in his inequality.
The error that Bryan has done in this inequality is that he included –14 in his solution set.
How to point out the mistake madeWhat Bryan has to do would be to write this inequality in such a way that the variable would appear on the left.
But the symbol that he has chosen does not move in this same direction as the graph.
The -14 should not be inclusive in the graph because it is not a part of the graph solution.
He used the wrong number in this inequality.
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Answer:
its c
Step-by-step explanation:
on edge
Help me pls my mom wants me to finish soon
Answer:
B
Step-by-step explanation:
Place the indicated product in the proper location on the grid. (x + 2)(x - 2)
The product of the polynomials, (x + 2)(x - 2) = x² - 4.
How to Find the Product of Polynomials?Given the following expression, (x + 2)(x - 2), to find the product, apply the distributive property as shown below:
(x + 2)(x - 2)
x(x - 2) + 2(x - 2)
x² - 2x + 2x - 4
Combine like terms together
x² - 4
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very hard problem someone help
Answer:
Everything in the box currently is correct but the bottom two numbers are just -3 and -4
Step-by-step explanation:
Please help quickly if you can ! :)
Answer:
y=49x
Step-by-step explanation:
As you can see from the graph, the distance from home increases by 49 miles per hour driven.
Therefore the distance driven for any given time in hours is 49x
Therefore y = 49x
what is the value of x and y
Answer:
x = 15° , y = 125°
I hope this helps u
22
Select the correct answer.
Consider functions fand g.
f(x) = ^x4 + 9x^2 - 3
g(x) = (1/2) ^x-2
Using a table of values, what are the approximate solutions to the equation f(x) = g() to the nearest quarter of a unit?
OA -0.5 and
OB.
I-0.25 and
OC
OD. I
0.5
1.5
-0.25 and ≈ 2.5
I ~ -1 and I ~ 0.75
Reset
Next
The approximate solution of the system of equations is x = 0.75
How to determine the approximate solutions?The functions are given as:
f(x) = x^4 + 9x^2 - 3
g(x) = (1/2)^x - 2
Calculate the values of the function from -1 to 1
x f(x) g(x)
-1 7 8
-0.75 2.38 6.72
-0.5 -0.69 5.66
-0.25 -2.43 4.76
0 -3 4
0.25 2.43 3.36
0.5 -0.69 2.83
0.75 2.38 2.38
1 7 2
From the above table, we have:
f(0.75) = g(0.75) = 2.38
Hence, the approximate solution of the system of equations is x = 0.75
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For the following exercises, evaluate the function at the indicated values:
f(−3); f (2); f(−a); −f(a); f (a + h).
6 f (x) = 2∣3 x − 1∣
Answer:
The evaluated function for the indicated values is given below.
The value of f(-3) is 20 .
The value of f(2) is 10 .
The value of f(-a) is [tex]$2|-3 a-1|$[/tex].
The value of -f(a) is [tex]$-2|3 a-1|$[/tex].
The value of f(a+h) is [tex]$2|3 a+3 h-1|$[/tex].
Step-by-step explanation:
A function [tex]$f(x)=2|3 x-1|$[/tex] is given.
It is required to evaluate the function at [tex]$f(-3) ; f(2) ; f(-a) ;-f(a) ; f(a+h)$[/tex].
To evaluate the function, substitute the indicated values in the given function to determine the output values and simplify the expression.
Step 1 of 5
The given function is [tex]$f(x)=2|3 x-1|$[/tex].
To evaluate the function at f(-3), substitute -3 in the given function [tex]f(x)=2|3 x-1|$\\ $f(-3)=2|3(-3)-1|$\\ $f(-3)=2|-9-1|$\\ $f(-3)=2|-10|$\\ $f(-3)=2(10)$\\ $f(-3)=20$[/tex]
Step 2 of 5
To evaluate the function at $f(2)$, substitute 2 in the given function.
[tex]f(x)=2|3 x-1|$\\ $f(2)=2|3(2)-1|$\\ $f(2)=2|6-1|$\\ $f(2)=2(5)$\\ $f(2)=10$[/tex]
Step 3 of 5
To evaluate the function at f(-a), substitute -a in the given function.
[tex]$$\begin{aligned}&f(x)=2|3 x-1| \\&f(-a)=2|3(-a)-1| \\&f(-a)=2|-3 a-1|\end{aligned}$$[/tex]
Step 4 of 5
To evaluate the function at -f(a), substitute a in the given function.
[tex]f(x)=2|3 x-1|$\\ $-f(a)=-2|3(a)-1|$\\ $-f(a)=-2|3 a-1|$[/tex]
Step 5 of 5
To evaluate the function at f(a+h), substitute a+h in the given function. [tex]$f(x)=2|3 x-1|$[/tex]
[tex]$$\begin{aligned}&f(a+h)=2|3(a+h)-1| \\&f(a+h)=2|3 a+3 h-1|\end{aligned}$$[/tex]
Question is in the picture, please help me out!!
The arithmetic sequences are as follow:
What is Arithmetic Sequence?An arithmetic sequence in algebra is a sequence of numbers where the difference between every two consecutive terms is the same.
1) t(n) = 5n + 4
t(1) = 9, t(2) = 14, t(3) = 19
So,
9,14,19,...
d= 14-9 = 5
d= 19-14 =5
Hence, it is an AP
2) 1, 2, 4, 8 , 16
Hence, it is not an AP
3) 3, 6, 9 ,...
It is an AP
4)It is given that it is an AP
5) tn = 2*3^n
t1= 6, t2= 18, t3= 54
So, 6, 18, 54,...
Hence, it is not an AP
6) 3 , 1, 1/3,...
It is not an AP
7) t(n+1)= 6*t(n)
t(1) = -1
t(2)=-6
t(3)= -36
Hence, it is not an AP
8) -3, 1, 5, 9
Hence, it is an AP.
9) 1, 4, 9,...
Hence, it not an AP
10) 2,1,0,1,2,...
It is not an AP
11) t(n)= -2n-5
t(1)= -7, t(2)= -9, t(3)= -11
Hence, it is an AP
12) tn= (1/2)^n
t1= 1/2, t2= 1/4, t3= 1/8
It is not an AP
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Help please I'll mark you as brainlist if the answer is correct
if (x + q) is a factor of two polynomials x2 + px + q and x2 + mx + n, then prove that a = n-q m-p
Answer:
factor polynomial is x+q so x=-q
putting the value of x in both equations
eqn 1)a^2+p(-a)+q=0
a^2 -ap+q=0
eqn 2)a^2+m(-a)+n=0
a^2-am+n=0
Since both are equal to zero,we can write:
a^2-ap+q=a^2-am+n
-ap+am=n-q
a(-p+m)=n-q
a=(n-q)/(m-p)
Explanation:
Since (x + a) is a factor of the two polynomials, when x = -a, the polynomials should both equal 0 (this is known as the factor theorem).
• First equation:
[tex]x^{2} + px + q[/tex]
When x = -a:
[tex](-a)^{2} + p(-a) + q = 0\\\\a^{2} -pa + q = 0[/tex]
• Second equation:
[tex]x^{2} + mx + n[/tex]
When x = -a:
[tex](-a)^{2} + m(-a) + n = 0\\\\a^{2} -ma + n = 0[/tex]
• As both equations equal 0, we can equate them:
[tex]a^{2} -pa + q = a^{2} -ma + n \\\\-pa + ma = n - q\\\\a(m - p) =n -q\\\\a = (n - q)/ (m - n)[/tex][proven]
A rectangular tank has its width exactly half its length. That the height of the tank is 3M and the length is 8m. What is the volume of the tank in M3?
Answer:
Volume = 96m^3
Step-by-step explanation:
If the length of the tank is 8 meters, then the width must be 4 meters, because the question said the width was half the length. Since the height, 3 meters, was also given, we can find the volume.
Vol = L × w × h
We multiply together the length, width and height.
Vol = 8 × 4 × 3
= 96
The volume is 96 meters^3
in triangle abc and triangle def angle a=angle d and angle b= angle e and ab=ef. will the 2 triangles be congruent ? justify your answer
Answer:
Step-by-step explanation:
no, you don't have the measure of at least one side, so having the same angles is similar but not congruent
What is the answer to the question down below
The equation which could be used to find the value of x is; (x+10) +(x-6) = 10.
Which equation can best be used to find the value of x?According to the task content, it follows that the lines WX and WY both amount to the line XY which joins points X and Y.
Hence, it follows that the equation which can be used to find the value of x is; (x+10) +(x-6) = 10.
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please help how do i this?
The order of the numbers from the greatest to the least is
|-20| > |12.3| > |8| > |-6| > |-4| > |2 3/10|
Magnitude of numbersFrom the question, we are to order the given numbers from the greatest to the least in magnitude
The given numbers are
|-20|, |-4|, |-6|, |8|, |2 3/10|, |12.3|
Since the modulo sign is included, the negative signs do not take effect.
Hence, the order of the numbers from the greatest to the least is
|-20| > |12.3| > |8| > |-6| > |-4| > |2 3/10|
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How is the relationship between the length and area of the rectangle different from other kinds of relationships we've seen before ?
The area of a rectangle = Length × Breadth
The area of a rectangle is the product of the breadth and length of a rectangle. A = L * W, where A is the area, L is the length, W is the width or breadth.We must determine the product of a rectangle's length and breadth in order to get its area.Area of a rectangle is equal to length times width.For instance, if a rectangle has a length of 50 cm and a width of 7 cm, its area is equal to 350 square cm (50 × 7 square cm).Every angle of a rectangle measures 90°. Opposite sides are equal and parallel. It has 2 diagonals of equal length.Learn more about Rectangle
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Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
7 is multipled by the difference of a number and 1.
The algebraic expression of the given sentence is: 7(x - 1).
How to Write an Algebraic Expression?Let the unknown number be represented as x.
The word "difference" means subtraction which is "-". Multiplied means times.
We would have the following:
"Difference of x and 1" is: x - 1
x - 1 multiplied by 7 would be: 7(x - 1)
Therefore, the algebraic expression is: 7(x - 1).
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¿Cual es el volumen del cilindro si su area lateral es 55,8cm2?
Based on the lateral area of the cylinder, the volume of the cylinder can be calculated to be 139.5 cm³.
What is the volume of the cylinder?When given the lateral surface area of a cylinder, you can find the volume as:
= Area of lateral surface x (radius / 2)
Solving gives:
= 55.8 x (5 / 2)
= 55.8 x 2.5
= 139.5 cm³.
Missing part of the question:
Radius of the cylinder is 5cm.
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Cual es el resultado de f(x)=−7x−1
The function of the linear equation shows that the slope(m) = -7, the x-intercepts is (-1/7,0), and the y-intercepts is (0,-1)
What is the function of f(x) of a linear equation?The function of a linear equation takes the form y = ax + b. In this situation, the values of y can be determined when x = 0, and the values of x can be determined when y = 0
From the given information:
y = f(x) = -7x - 1
We can determine the:
Slope (m)x-intercepts, andy-intercepts.y = -7x - 1
Slope (m) = -7
Set the values of y = 0 to determine the x-intercepts.
0 = -7x - 1
7x = - 1
x = -1/7
x-intercepts = (-1/7, 0)
Set the values of x = 0 to find the y-intercepts.
y = -7(0) - 1
y = - 1
y-intercepts = (-1, 0)
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A cheerleading team plans to sell t-shirts as a fundraiser. The team's
goal is to make a profit of at least $1248. The profit on each t-shirt sold
is $6.50. The team's goal is written as the inequality shown below.
6.50t ≥1248 where t=number of t-shirts sold
Which graph represents the solution to this inequality?
Answer:
You didn't include any choices.....see below
Step-by-step explanation:
Which statement is not true about the data shown by the box plot below?
a.The range is 67.
b. The data point 5 lies outside the range of the data.
c. Three fourths of the data is less than 68.
d. Half the data lies between 51 and 68.
based on the options given, one thing that isn't true of the box plot is that d. Half the data lies between 51 and 68.
what is false about the box plot?the box plot has a range of 67:
= 90 - 23
= 67
the data point 5 lies outside the data set.
3/4 of the data is less than 68 which is the 3rd quartile.
this means that the false statement is that half of the data is between 57 and 68.
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PLS HELPPPP MEEEEE EASY POINTS
Reflecting over y=x maps (x,y) onto (y,x).
So, the answer is A. (-8, 3).
Answer:
Step-by-step explanation:
32.For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.
32. (2, 4) and (4, 10)
Answer:
The required linear equation satisfying the given points (2,4) and (4,10) is y=3x-2
Step-by-step explanation:
Two points are given in question, (2,4) and (4,10).
It is required to find out a linear equation satisfying the points (2,4) and (4,10).
To find it out, find the slope of a line passing through these two given points. Then consider one of the points to give the linear equation of the line in the
[tex]$$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$$[/tex]
Step 1 of 3
The slope of a line passing through the points (2,4) and (4,10) is given by
[tex]$$\begin{aligned}m &=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\m &=\frac{10-4}{4-2} \\m &=\frac{6}{2} \\m &=3\end{aligned}$$[/tex]
Step 2 of 3
Now use the slope m=3 and use one of the two given points and write the equation in point-slope form:
[tex]$$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$$\\ $$(y-4)=3(x-2)$$[/tex]
Distribute 3 ,
[tex]$$\begin{aligned}&y-4=3 x-3 \times 2 \\&y-4=3 x-6\end{aligned}$$[/tex]
Step 3 of 3
This linear function can be written in the slope-intercept form by adding 4 on both sides,
[tex]$$\begin{aligned}&y-4+4=3 x-6+4 \\&y=3 x-2\end{aligned}$$[/tex]
So, this is the required linear equation.
Mason and Laney run laps. The ratio of the number of laps Mason ran to the number Laney ran was 2:3.
If Laney ran 930 meters, how far did Mason run? Draw a tape diagram to determine how you fou your answer.
Using proportions, it is found that Mason ran 620 meters.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Considering the ratio, the rule of three is given as follows:
2 laps for Mason - 3 laps for Laney.
n meters for Mason - 930 meters for Mason.
Applying cross multiplication:
3n = 930 x 2
n = 930 x 2/3
n = 620
Mason ran 620 meters.
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GIVING BRAINLEST!
A cup of apple juice requires spoons of sugar. If David prepares 18 cups of juice, then how much
spoons of sugar is required?
90
72
8
2
Answer:
I think it is 72
Step-by-step explanation:
but the question doesn't make sense because it should tell the number of spoons per 1 cup of sugar, perhaps it was a copy-paste mistake?
What is the asymptote of the function g(x) = 5•2^3x + 4 shown on the graph?
A: y=4
B: y=5
C: y=0
D: y = 3