======================================================
Explanation:
To get the 6th term, we multiply the fifth term by the common ratio
6th term = (fifth term)*(common ratio)
6th term = 162*3
6th term = 486
The 7th term is found by tripling 486, and so on.
To get the fourth term, we go in reverse of this process. We'll divide 162 by 3 to get 162/3 = 54
The third term is then going to be 54/3 = 18
The second term is 18/3 = 6
The first term is 6/3 = 2
-----------------------
Here's another way we can solve this question.
The nth term of a geometric sequence is a*(r)^(n-1)
We know that the common ratio is 3, so r = 3.
The 5th term is 162, meaning plugging n = 5 into that expression above leads to 162, so,
a*(r)^(n-1)
a*(3)^(n-1)
a*(3)^(5-1) = 162
a*(3)^4 = 162
a*81 = 162
81a = 162
a = 162/81
a = 2 is the first term
-----------------------
The first five terms of the geometric sequence are:
2, 6, 18, 54, 162
Each time we go from left to right, we're multiplying by 3. Going in reverse (right to left), we divide by 3.
Multiplying by 1/3 is the same as dividing by 3.
Evan, James, and Burt are fishing in a lake that has 200 fish. They are going to be fishing for three hours. What is the probability that they each will catch 3 fish?
Answer:
The probability that they each will catch 3 fish is 0.000063956
Step-by-step explanation:
The hyper geometric distribution is used to solve this as it has a population, a sample , number of successes for both the population and sample.
Here
Population size= N =200
Sample size= n =9= (3*3)
Number of successes in population = k = 3 hours
Number of successes in sample = x= 3
Applying the hyper geometric distribution
P (x=3) = kCx *(N-k) C (n-x)/ N Cn
= 3 C 3 * 197 C 6/ 200 C 9
=0.000063956
The probability that they each will catch 3 fish is 0.000063956
Someone please help me ASAP! Worth 10 points
Answer:
(-1,-1)
Step-by-step explanation:
Step 1 identify coordinates of A
A is located at ( -3 , -3 )
Step 2 apply dilation by multiplying the x and y values of coordinate A by the scale factor
Given:
scale factor = 1/3
Coordinates of A: ( -3 , -3 )
* Multiply the x and y values by 1/3 *
( -3 * 1/3 , -3 * 1/3 ) -------> ( -1 , -1 )
The new coordinates would be (-1,-1)
multiply the coordinates of A by the scale factor given
Emily and Kylie are 140 miles apart, traveling towards each other. If Kylie travels 12 mph and Emily travels 8 mph how long until they meet?
Answer: 7 hr
Step-by-step explanation:
Given
Distance between Emily and Kylie is [tex]140\ \text{miles}[/tex]
Speed of Emily [tex]v_e=12\ mph[/tex]
Speed of Kylie [tex]v_k=8\ mph[/tex]
Distance traveled by Emily [tex]\Rightarrow d_e=12t[/tex]
Distance traveled by Kylie [tex]\Rightarrow d_k=8t[/tex]
[tex]\Rightarrow 12t+8t=140\\\Rightarrow 20t=140\\\Rightarrow t=7\ hr[/tex]
They will meet after 7 hour.
Darcy's harvests 8 3/4 acres of corn every 5/6 hours. How much corn can she collect in a hour. ? =Amount of acres of corn done in a hour.
Answer:
Step-by-step explanation:
Acres of corn harvested : time taken = 8 3/4 : 5/6
How much corn can she collect in a hour. ?
Let
x = Acres of corn harvested
Acres of corn harvested : time taken = x : 1
8 3/4 : 5/6 = x : 1
35/4 : 5/6 = x : 1
35/4 ÷ 5/6 = x/1
35/4 × 6/5 = x/1
35*6/4*5 = x/1
210/20 = x/1
210 * 1 = 20 * x
210 = 20x
x = 210/20
= 10 1/2 acres
x = Acres of corn harvested = 10 1/2 acres
Evaluate the function. f(x)=3x^2 −4x Find f(−1)
Answer:
7
Step-by-step explanation:
evaluate the function means substitute x=-1 and calculate
f(x) = 3x²-4x
f(-1) =f(x=-1) = 3(-1)²-4(-1) =3+4 =7, because (-1)²=1 and -4(-1) =4
find x
(4x - 3) – ( x + 5) = 3(10 - x)
please.....
Answer: 19/3
Step-by-step explanation:
[tex]4x+3-x-5=30-3x\\\\3x-8=30-3x\\\\6x-8=30\\\\6x=38\\\\x=\frac{19}{3}[/tex]
what is the y-coordinate of the red point?
The y-coordinate of the red point is -3.
Find the value of `x´ in the given parrallelogram.
Step-by-step explanation:
=> (3x-12) =(x+6)
or,3x - x = 6 + 12
or,2x = 18
or,x = 18/2
•: x=9#
Write the equation for a parabola with a focus at (6,-4) and a directrix at y= -7
Given:
The focus of the parabola is at (6,-4).
Directrix at y=-7.
To find:
The equation of the parabola.
Solution:
The general equation of a parabola is:
[tex]y=\dfrac{1}{4p}(x-h)^2+k[/tex] ...(i)
Where, (h,k) is vertex, (h,k+p) is the focus and y=k-p is the directrix.
The focus of the parabola is at (6,-4).
[tex](h,k+p)=(6,-4)[/tex]
On comparing both sides, we get
[tex]h=6[/tex]
[tex]k+p=-4[/tex] ...(ii)
Directrix at y=-7. So,
[tex]k-p=-7[/tex] ...(iii)
Adding (ii) and (iii), we get
[tex]2k=-11[/tex]
[tex]k=\dfrac{-11}{2}[/tex]
[tex]k=-5.5[/tex]
Putting [tex]k=-5.5[/tex] in (ii), we get
[tex]-5.5+p=-4[/tex]
[tex]p=-4+5.5[/tex]
[tex]p=1.5[/tex]
Putting [tex]h=6, k=-5.5,p=1.5[/tex] in (i), we get
[tex]y=\dfrac{1}{4(1.5)}(x-6)^2+(-5.5)[/tex]
[tex]y=\dfrac{1}{6}(x-6)^2-5.5[/tex]
Therefore, the equation of the parabola is [tex]y=\dfrac{1}{6}(x-6)^2-5.5[/tex].
To maintain a balanced diet, ensure that your food contains minimal amounts of certain ingredients. Which ingredient is missing in the sentence below?
One’s diet should include small amounts of fat, , and sugar.
Step-by-step explanation:
i think minerals and vitamins since they are micro nutrients
In a college of 400 students, 45% are girls. Of the boys, 30% are football
players. How many boys are football players?
What is the vertex of
y= 3/4x^2+3x+2
Answer:
The vertex is located at (-2,-1)
Step-by-step explanation:
is AC greater than, less than, or equal to BC? explain your reasoning
Answer:
AC is greater than BC
Step-by-step explanation:
First, we know that the angle of a straight line is 180°, so angle B as a whole is equal to 180 degrees. Therefore, angle YBC + angle ABC = 180 degrees. As angle YBC is a right angle, signified by the small square on the angle, it is 90 degrees. Therefore,
90 degrees + angle ABC = 180 degrees
subtract 90 degrees from both sides to isolate angle ABC
angle ABC = 90 degrees
Therefore, as angle ABC is equal to 90 degrees, and a right angle is 90 degrees, triangle ABC has a right angle, making it a right triangle.
In a right triangle, using the Pythagorean Theorem, the square of the side opposite the right angle is equal to the sum of the squares of the other side. Since side AC is opposite the right angle, we can say that
AC² = AB² + BC²
As the length of a side has to be greater than 0, we can say that
AC² = AB² + BC²
AB² > 0
AC² > BC²
square root both sides
AC > BC
Therefore, AC is greater than BC
Prove that the value of the expression: (3^5 - 3^4)(3^3 + 3^2) is divisible by 24. Answer format: The value of the expression is 24 • __
Step-by-step explanation:
(3^5 - 3^4) (3^3 + 3^2)
= (243 - 81) (27 + 9)
= (162) (36)
= 5832
24 = 8*3
since 832 is divisible by 8 and 5+8+3+2 = 18 is divisible by 3
5832 is therefore divisible by 24
check:
5832/24 = 243
Which ordered pair makes both inequalities true? y < 3x – 1 y > –x + 4 On a coordinate plane, 2 straight lines are shown. The first dashed line has a positive slope and goes through (0, negative 1) and (1, 2). Everything to the right of the line is shaded. The second solid line has a negative slope and goes through (0, 4) and (4, 0). Everything above the line is shaded.
Answer:
None of the options is true
Step-by-step explanation:
Given
[tex]y < 3x - 1[/tex]
[tex]y > -x + 4[/tex]
Required
Which makes the above inequality true
The missing options are:
[tex](4,0)\ (1,2)\ (0,4)\ (2,1)[/tex]
[tex](a)\ (x,y) = (4,0)[/tex]
Substitute values for x and y in the inequalities
[tex]y < 3x - 1[/tex]
[tex]0<3*4 - 1[/tex]
[tex]0<12 - 1[/tex]
[tex]0<11[/tex] ---- This is true
[tex]y > -x + 4[/tex]
[tex]0 > -4 + 4[/tex]
[tex]0 > 0[/tex] --- This is false
[tex](b)\ (x,y) = (1,2)[/tex]
Substitute values for x and y in the inequalities
[tex]y < 3x - 1[/tex]
[tex]2<3 * 1 - 1[/tex]
[tex]2<3 - 1[/tex]
[tex]2<2[/tex] --- This is false (no need to check the second inequality)
[tex](c)\ (x,y) = (0,4)[/tex]
Substitute values for x and y in the inequalities
[tex]y < 3x - 1[/tex]
[tex]4< 3*0-1[/tex]
[tex]4< 0-1[/tex]
[tex]4<-1[/tex] --- This is false (no need to check the second inequality)
[tex](d)\ (x,y) = (2,1)[/tex]
Substitute values for x and y in the inequalities
[tex]y < 3x - 1[/tex]
[tex]1<3*2-1[/tex]
[tex]1<6-1[/tex]
[tex]1<5[/tex] --- This is true
[tex]y > -x + 4[/tex]
[tex]1 > -2+4[/tex]
[tex]1 > 2[/tex] -- This is false
Hence, none of the options is true
Which number line represents the solutions to -2x = -6?
Answer:
3
Step-by-step explanation:
-2x = -6
or, x = -6 / -2
or, x = 3
a therate ticket cost £63 plus a booking fee of 3%
what is the total price of the ticket
Answer:
Total amount of ticket free = £64.89
Step-by-step explanation:
Given:
Cost of theater ticket = £63 plus
Booking fee of theater ticket = 3%
Find:
Total amount of ticket free
Comutation:
Total amount of ticket free = Cost of theater ticket + Booking fee of theater ticket
Total amount of ticket free = 63 + 3%
Total amount of ticket free = 63 + 1.89
Total amount of ticket free = 64.89
Total amount of ticket free = £64.89
52.3 X 16.0 please help me thank you so much !
Answer:
836.8
Step-by-step explanation:
Can someone help me with this math homework please!
Answer:
First dropbox: 7h + 43 = 64
Second dropbox: $3
Step-by-step explanation:
Here's what we know about the question so far:
$43 is the initial fee
The rototiller worked for 7 hours
$64 is the total cost (including initial fee)
h = hourly fee
The answer should be 7h + 43 = 64 because:
- It includes the initial fee of $43
- It sets the equation equal to $64, which is the total cost
- The hourly fee is being multiplied with 7 hours, which is correct since the h variable is hourly (not sure how to explain this part ;w; )
For the 2nd drop box, we will use basic algebra to solve for h:
7h + 43 = 64
(subtract both sides by 43)
7h = 21
(divide both sides by 7)
h = 3
There's your 2 answers!
Hope it helps (●'◡'●)
I have a lot of algebra problems. Someone help me even with this one please!
X -Y =44 will represent the number of glasses of ice tea .
What is an equation of the line that is parallel to y = 3x - 8 and passes
through the point (4,-5)?
Answer:
[tex]y=3x-17[/tex]
Step-by-step explanation:
Parallel equations always share a slope.
So since we know the slope and a point the equation needs to pass through we can plug in the values and replace -8 with [tex]b[/tex]
[tex]-5=3(4)+b[/tex]
simplify both sides
[tex]-5=12+b[/tex]
isolate the variable
[tex]-17=b[/tex]
plug [tex]b[/tex] back into the equation and you get
[tex]y=3x-17[/tex]
Answer:
y = 3 x + 11
Explanation:
Parallel lines have the same slopes.
The slope of the new line will have the same slope as the given line:
y = 3 x − 4
⇒ m = 3
One point on the line is given,
( − 2 5 ) .
This is ( x 1 y 1 )
The formula for slope is
m = ( change in y values/ change in x-values ) = y 2 − y 1/ x 2 − x 1
If you have the slope and one point , substitute them into a formula which is based on the formula for slope given above.
y − y 1 = m ( x − x 1 )
y − 5 = 3 ( x − ( − 2 ) )
y − 5 = 3 ( x + 2 )
Simplify to get the required equation of the line.
y = 3 x + 6 + 5
y = 3 x + 11
Step-by-step explanation:
10 points!!!!!:)
Describe the graph of the function.
[tex]y = \sqrt{x + 3} [/tex]
a). the graph is a radical function y=sqrt(x) shifted 3 units right.
b). the graph is a radical function y=sqrt(x) 3 units left.
c). the graph is of exponential growth.
d). the graph is an absolute value function with vertex (-3,0).
pls help me:).
Answer:
b) y=sqrt(x) shifted 3 units left
Step-by-step explanation:
3rd line in the attached table:
f(x+3) = sqrt(x+3) horizontal translation left 3 units
instructions: state what additional information is required in order to know that the triangle in the image below are congruent for the reason given.
Given: AAS
Answer:
QP ≈ HG
Common side between those angles are QP and HG
so, they should be congruent to prove AAS
Answered by GAUTHMATH
Factor using the perfect squares method:
x^2 - 3x + 16
Answer:
what are the answer choice?
Step-by-step explanation:
Please help me! ❤️ I got stuck on this and really need some help
Answer:
0,-4
-2.65,2.62
2.65,2.62
Step-by-step explanation:
[tex]0^2 = 0\\-2.65^2 =7.0225\\ 2.65^2 =7.0225[/tex]
[tex]y = x^2 - 4[/tex]
-4, 3.0225
[tex]-4^2 = 16\\3.0225^2=9.1355[/tex]
Which of the following is the equation of the quadratic function below?
Answer:
C y=x^2+2x+1
Step-by-step explanation:
Solve for e. 4/3 = -6e - 5/3
Answer:
e = -1/2
Step-by-step explanation:
To solve this problem, our first step is to add 5/3 to both sides of the equation. This gives us:
4/3 + 5/3 = -6e - 5/3 + 5/3
9/3 = -6e
We can simplify the left side of the equation by performing the division.
3 = -6e
Next, we can solve for e by dividing both sides of the equation by -6.
e = -1/2
Therefore, the correct answer is e = -1/2.
Hope this helps!
Answer:
The value of e is -1/2
Step-by-step explanation:
4/3 = - 6e - 5/3
Now, add 6e both side we get,
4/3 + 6e = + 6e - 6e - 5/3
4/3 + 6e = - 5/3
Now, subtract 4/3 from both side we get,
4/3 - 4/3 + 6e = -4/3 - 5/3
6e = -4/3 - 5/3
6e = -4 - 5/3
6e = -9/3
6e = -3
Now, divide 6 from both side we get,
6e/6 = -3/6
e = -1/2
Thus, The value of e is -1/2
-TheUnknownScientist
if$3=£2 and Rs. 325=$3, how many pound(£) will be equal to Rs. 39000
Answer:
Rupees 39,000 are
378.63 Pound sterling
Can someone help me with this math homework please!
Answer:
11.2
Step-by-step explanation:
[tex]p =\frac{160.16}{14.3}=\frac{160.16*10}{14.3*10}\\\\p = \frac{1601.6}{143}\\\\[/tex]
p = 11.2
Answer:
The person above me is correct I just did the work and I got the same answer as them :)
Step-by-step explanation:
What number, divided by 3/7 , will result in a value of 2 1/3?
