Answer:
[tex]a_{n}[/tex] = 3n - 1
Step-by-step explanation:
There is a common difference d between consecutive terms, that is
d = 5 - 2 = 8 - 5 = 11 - 8 = 14 - 11 = 3
This indicates the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 2 and d = 3 , thus
[tex]a_{n}[/tex] = 2 + 3(n - 1) = 2 + 3n - 3 = 3n - 1
The expression for the nth term of the series is [tex]a_n = 3n-1[/tex].
Given that,
Sequence; 2, 5, 8, 11, 14.
We have to find, the expression in terms of n for the nth term of the following given sequences?
According to the question,
The nth of the arithmetic sequence is,
[tex]\rm a_n = a+ d(n-1)[/tex]
Where a is the first term of the sequence,
d is the common difference between the terms,
n is the number of terms.
Then,
The given sequence is 2, 5, 8, 11, 14.
Here, the common difference between the terms is 3.
And the first term of the sequence is 2.
Substitute all the values in the formula,
Therefore,
The nth term of the given terms is,
[tex]\rm a_n = a+ d(n-1)\\\\a_n = 2+ 3(n-1)\\\\a_n + 2+3n-1\\\\a_n = 3n-1[/tex]
Hence, The required expression for the nth term of the series is [tex]a_n = 3n-1[/tex].
For more details refer to the link given below.
https://brainly.com/question/17043393
John would like to go on a ski trip with his friends. In order to go on the trip, John needs to save more
than $350 dollars. Write an inequality that describes, M, the money that John needs to save.
Answer:
$350 < M
Step-by-step explanation:
Simplify 12 square root of 7
Answer:
Step-by-step explanation:
[tex]12\sqrt{7}\\=31.74901[/tex]
Caylee caylee build a rectangular prism using 18 cubes that are each measure 1 cm on each side. What could be the dimensions of her rectangular prism
Answer:
2cm by 3cm by 3cm.
Step-by-step explanation:
So, we are given the following data or parameters or information which is going to help us in solving this particular Question or problem;
=> We have a built rectangular prism.
=> The rectangular prism was built by using 18 cubes.
=> Each of the 18 cubes measure 1 cm on each side.
So, the dimensions of Carley's rectangular prism is given below as the multiples of 18 since each of the 18 cubes measure 1 cm on each side.
That's 2 cm × 3 cm × 3cm. Therefore, the length will be 2cm, breadth will be 3cm and height will be 3cm.
1) 2x – y = 1
2x +2y = 10
2) 5x – y =15
x + y = -3
please do both of these with explanation!!
Answer:
1) (2, 3)
2) (2, -5).
Step-by-step explanation:
2x – y = 1
2x +2y = 10 Subtract to eliminate the 2x:
2x - 2x - y - 2y = 1 - 10
-3y = -9
y = 3.
Plug this into the first equation:
2x - 3 = 1
2x = 4
x = 2.
2)
5x – y =15
x + y = -3 Adding to eliminate y:
5x + x - y + y = 15 + -3
6x = 12
x = 2
Plug this into the first equation:
5(2) - y = 15
-y = 15 - 10 = 5
y = -5.
Factor-8x^3-2x^2-12x-3 by grouping
Answer:
[tex]=-\left(4x+1\right)\left(2x^2+3\right)[/tex]
Step-by-step explanation:
[tex]-8x^3-2x^2-12x-3\\\mathrm{Factor\:out\:common\:term\:}-1\\=-\left(8x^3+2x^2+12x+3\right)\\\mathrm{Factor}\:8x^3+2x^2+12x+3:\quad \left(4x+1\right)\left(2x^2+3\right)\\8x^3+2x^2+12x+3\\=\left(8x^3+2x^2\right)+\left(12x+3\right)\\\mathrm{Factor\:out\:}3\mathrm{\:from\:}12x+3\mathrm{:\quad }3\left(4x+1\right)\\12x+3\\\mathrm{Rewrite\:}12\mathrm{\:as\:}3\cdot \:4\\=3\cdot \:4x+3\\\mathrm{Factor\:out\:common\:term\:}3\\=3\left(4x+1\right)[/tex]
[tex]\mathrm{Factor\:out\:}2x^2\mathrm{\:from\:}8x^3+2x^2\mathrm{:\quad }2x^2\left(4x+1\right)\\8x^3+2x^2\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\x^3=xx^2\\=8xx^2+2x^2\\\mathrm{Rewrite\:}8\mathrm{\:as\:}2\cdot \:4\\=2\cdot \:4xx^2+2x^2\\\mathrm{Factor\:out\:common\:term\:}2x^2\\=2x^2\left(4x+1\right)\\=3\left(4x+1\right)+2x^2\left(4x+1\right)\\\mathrm{Factor\:out\:common\:term\:}4x+1\\=\left(4x+1\right)\left(2x^2+3\right)\\=-\left(4x+1\right)\left(2x^2+3\right)[/tex]
as an estimation we are told 5 miles is 8km convert 84km to miles
Step-by-step explanation:
84 km to miles is 52.195 miles
Can someone answer this question please please help me I really need it if it’s correct I will mark you brainliest .
Answer:
work is shown and pictured
A multi level parking lot has 6 levels and there are total of 1,327 parking spots. There are 162 parking spots on the first level. The rest of the parking spots are distributed equally on the other 5 levels. How many parking spots are there on the top level? *
Answer:
233 parking spots
Step-by-step explanation:
1327 - 162 = 1165
1165 ÷ 5 = 233
what is the output value for the following function if the input value is 1?
y=3x + 1
Answer:
The output value is 4
Step-by-step explanation:
The output value is the y value, so y=3(1)+1
y=3+1
y=4
What is the correct formula for calculating a 3 x 3 determinant?
To work out the determinant of a 3×3 matrix:
Multiply a by the determinant of the 2×2 matrix that is not in a's row or column
Likewise for b, and for c
sum them up, but remember the minus in front of the b
_____________________________________________________
Hope this helps, stay safe, have a good day :D
Answer: it’s C
Step-by-step explanation:
just took the assignment
Please answer correctly !!!!!! Will mark brainliest answer !!!!!!!!
Answer:
-6 =x
Step-by-step explanation:
g(x) = -3x -8
g(x) = 10
10 = -3x-8
Add 8 to each side
10+8 = -3x-8+8
18 = -3x
Divide by -3
18/-3 = -3x/-3
-6 =x
Pick out the definition of the word.
Irregular
A
not normal
B
not registered
C
not unusual
Answer: Not normal
Step-by-step explanation:
Regular (in math) refers to an integer that is a whole number or the integers that make up a whole number.
If it’s irregular then it’s not a normal integer like a whole number.
CAN SOMEONE PLEASE HELP(IM BAD AT MATH)
Answer:
C
Step-by-step explanation:
like I said, find the square area and subtract the triangles.
28 x 28= 784
Find the dimensions of the triangles. Since the surrounding shape is a square, the legs should be equal in length.
28-11.6=16.4
16.4/2=8.2
8.2 is the leg's length.
8.2*8.2*1/2*4=134.48
Subtract it to the square's area. 784-134.48= 649.52
Now round!
You get C
Find the equation of the exponential function represented by the table below:
X
0
1
2
3
Y
4
16
64
256
Y= ?
Answer:
y = [tex]4^{x+1[/tex]
Given that D is the midpoint of AB and B is the midpoint of AC, which statement must be true? A line has points A, D, B, K, C. AD = One-thirdAC AC = 4DB AB + DC = AC BK = KC
Answer:
AC = 4DB
Step-by-step explanation:
see attachment
Given that B is the midpoint of AC, this means that AB≅BC.
Also, D is the midpoint of AB, therefore AD≅DB.
This shows that AD is 1/4 of the length of AC, since it is 1/2 of the length (1/2 x 1/2 = 1/4). DB is the same length, since it is congruent to AD.
Thus, AC = 4DB.
Answer:
B. AC = 4DB
May I have brainliest please? :)
(algebra) i think of a number add 3 to it and multiply the result by seven what is the answer
Answer:
[tex]7x+21[/tex]
Step-by-step explanation:
Let the number be [tex]x[/tex].
[tex]x+3[/tex]
[tex]7(x+3)[/tex]
Expand the brackets.
[tex]7x+21[/tex]
Find the range of the graphed function
Answer:
-9 ≤ y ≤ 5
Step-by-step explanation:
The range is all the values of y. In this case, the values of y are any number in between -9 and 5. So -9 ≤ y ≤ 5.
Answer:
x ≥ 0
Step-by-step explanation:
Please please please answer this if you do this i will give you brain list I’ll give a thank you and I’ll rate you five star. It’s due soon so pls answer FAST!!
Answer:
b) 30^2 + b^2 = 40^2
Step-by-step explanation:
This is cuz the diagonal is the hypotenuse of the diagonal formed so it'll be c^ 2
c ^ 2 always is on the right hand side of the equation.
In this case since 40^2 is c^2 is should be on the right side of the equation.
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
What are the zeros of the function g(x)=2(x+2)(x-9) located at
Answer:
x = - 2, x = 9
Step-by-step explanation:
Given
g(x) = 2(x + 2)(x - 9)
To find the zeros let g(x) = 0, that is
2(x + 2)(x - 9) = 0
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 9 = 0 ⇒ x = 9
The zeros of the function g(x)=2(x+2)(x-9) are -2 and 9.
What is the zeros and y-intercept of a function?Zeros is the Intersection points of the considered function's curve on input axis(usually represented by values of x)
y-intercept = Intersection points of the considered function's curve on output axis. On x-axis, value of y-coordinate is 0, On y-axis, value of x-coordinate is 0.
Thus, if function is y=f(x) then putting y = 0 gives zeros of the function.
And putting x = 0 gives the y-intercept of the function. (if any, for both cases).
Given the function as;
g(x) = 2(x + 2)(x - 9)
To find the zeros let g(x) = 0, that is;
2(x + 2)(x - 9) = 0
Then Equate each factor to zero and solve for x;
x + 2 = 0 ⇒ x = - 2
x - 9 = 0 ⇒ x = 9
Hence, the zeros of the function g(x)=2(x+2)(x-9) are -2 and 9.
Learn more about function here:
https://brainly.com/question/2253924
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What is the length of the hypotenuse of the triangle when x=13
Answer:
90.80
Step-by-step explanation:
6x+4
= (6)(13)+4
= 78+4
=82
3x
=(3)(13)
= 39
So we know the sides are 39 and 82
Pythagoras theorem in triangles
= a2+b2= c2
Now, we know the value of a and B but not c (the hypotenuse)
Therefore,
c2 = (39)^2 + (82)^2
= 1521+ 6724
= 8245
so, c = √8245
= 90.80 unitd
Help im lazy im looking for h
Answer: h = -13
Step-by-step explanation: To get the answer for h all we have to do is....
78 ÷ -6 = -13
Let's check our work....
-6 x -13 = 78
I hope this helps!
Answer:
h= -13
Step-by-step explanation:
To solve the equation, we want to find out what h is. In order to do this, we have to get h by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.
-6h=78
h is being multiplied by -6. The opposite of multiplication is division. Divide both sides by -6.
-6h/-6=78/-6
h=78/-6
h= -13
Let's check our solution. Substitute -13 back in for h in the original equation.
-6h=78
-6(-13)=78
Multiply
78=78
Since both sides of the equation are the same, we know that the correct answer is h= -13.
How do you solve the inequality 2x − 3 < −5
Answer:
x=< -1
Step-by-step explanation:
move the constant to the right-hand side and change its sign. 2x<-5+3
Calculate the sum
2x<-2
Divide both sides of the inequality by 2
x <-1
Ashley is on her way home in her car. She has driven 18 miles so far, which is two-thirds of the way home. What is the total length of her drive?
____ Miles
Answer:
27 miles
Step-by-step explanation:
2/3rds of the way home is 18 miles
2/3 d = 18
Multiply each side by 3/2
3/2 * 2/3 = 18 *3/2
d = 27
The distance is 27 miles
What is 12 1/4`÷7/8
Answer:
14
Divide
12 and 1 over 412
1
4
÷ 7 over 8
7
8
= 392 over 28
392
28
Step 1 of 2: Divide, sub-step a: Convert mixed number to improper fraction.
Convert mixed number to improper fraction
12 and 1 over 412
1
4
= ( 12 × 4 ) over 4
12 × 4
4
+ 1 over 4
1
4
= ( 48 + 1 ) over 4
48 + 1
4
= 49 over 4
49
4
Step 1 of 2: Divide, sub-step b: Divide.
Divide
49 over 4
49
4
÷ 7 over 8
7
8
= 49 over 4
49
4
× 8 over 7
8
7
= ( 49 × 8 ) over ( 4 × 7 )
49 × 8
4 × 7
= 392 over 28
392
28
To divide fractions, invert the second one (turn it upside-down), then multiply the numerators and denominators.Divide
12 and 1 over 412
1
4
÷ 7 over 8
7
8
= 392 over 28
392
28
Step 1 of 2: Divide, sub-step a: Convert mixed number to improper fraction.
Convert mixed number to improper fraction
12 and 1 over 412
1
4
= ( 12 × 4 ) over 4
12 × 4
4
+ 1 over 4
1
4
= ( 48 + 1 ) over 4
48 + 1
4
= 49 over 4
49
4
Step 1 of 2: Divide, sub-step b: Divide.
Divide
49 over 4
49
4
÷ 7 over 8
7
8
= 49 over 4
49
4
× 8 over 7
8
7
= ( 49 × 8 ) over ( 4 × 7 )
49 × 8
4 × 7
= 392 over 28
392
28
To divide fractions, invert the second one (turn it upside-down), then multiply the numerators and denominators.
A^5 divided a^3 simplified
Answer:
[tex] {a}^{2} [/tex]
Step-by-step explanation:
[tex] \: \: \: \: \: \: \: \frac{ {a}^{5} }{ {a}^{3} } \\ = {a}^{5 - 3} \\ = {a}^{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Hey!!
The answer is a^2
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
The right trapezoid below has been decomposed into a rectangle and a right triangle.Find it's area two ways: By summing the areas of the rectangle and triangle.
Answer:
103.5 m²
Step-by-step explanation:
To find the area of a right trapezoid, you can decompose it into a rectangle and a triangle. The sum of the area of the rectangle and the triangle gives the area of the trapezoid.
For the right trapezoid attached below, the area can be gotten by:
Area of rectangle = length × breadth = 9 × 8 = 72 m²
Area of triangle = 1/2(base × height) = 0.5 × 7 × 9 = 31.5 m²
Area of trapezoid = Area of rectangle + Area of triangle = 72 m² + 31.5 m² = 103.5 m²
One of the base for a trapezoid is 5in the other is unknown the height is 3in the area is 18in what is the other base.
Answer:
7 inches
Step-by-step explanation:
formula for a trepezoid is 1/2(a+b)*h
1/2(5+x)X3=18 (now make x the subject)
(5+x)X3=36
5+x=12
x=7
so the other base is 7in
One cubic centimeter of sand weighs 1.9 grams. Find the amount of sand that the sandcastle bucket can hold.
Answer:
2160
Step-by-step explanation:
1872(volume of the cube)+288(volume of the square pyramid)=
2160
v of cube= lwh
v of square pyramid= a² times h/3
please mark brainliest!
You roll a twelve-sided die (having values one through twelve on its faces). What is the probability that the value of the roll will be a composite number?
show work pls!
Step-by-step explanation:
If a die is rolled once, determine the probability of rolling a 4: Rolling a 4 is an event with 1 favorable outcome (a roll of 4) and the total number of possible outcomes is 6 (a roll of 1, 2, 3, 4, 5, or 6). Thus, the probability of rolling a 4 is .
If a die is rolled once, determine the probability of rolling at least a 4: Rolling at least 4 is an event with 3 favorable outcomes (a roll of 4, 5, or 6) and the total number of possible outcomes is again 6. Thus, the probability of rolling at least a 4 is = .