[tex]n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_7=\stackrel{7^{th}\ term}{192}\\ 7=\textit{term position}\\ a_1=\textit{first term}\\ r=\stackrel{\textit{common ratio}}{2} \end{cases} \qquad \qquad a_7=a_1\cdot 2^{7-1} \\\\\\ 192=a_1\cdot 2^6 \implies 192=64a_1\implies \cfrac{192}{64}=a_1\implies \boxed{3=a_1}[/tex]
In the function y=f(x), y varies inversely with the square of x and when x=4, y=1/2. Find y when x=1.
ok so
y= 4/3x2
Y varies inversely with square of x means
y = k (1/x²) where k is the constant
plug in y =1/3 and x = - 2 in the above equation.
1/3=k (1/{-2}²)
1/3=k (1/4)
multiply with 4 to both sides.
4/3 =k
therefore,
y=4/3 (1/x²) = 4/3x²
plz help me plz need your help plz help
Step-by-step explanation:
a+b^2 =a^2+b^2+2ab
-2ab and+2ab cut
What is 919,827 rounded to the nearest hundred
Answer:
919,800
Step-by-step explanation:
To round up, the tens place would have to be either 5 or higher. Since the number in the tens place is 2, which is under 5, it will stay the same.
Help help help help help help help help
Answer:
7
Step-by-step explanation:
15-8 is 7
16-8 is 7
17-10 is 7
18-11 is 7
this fits the eqation.
hope this helps you
Give the slope of each of the following lines Name a point on each line
y+2=2/3 (x-4)
Answer:
See answer below
Step-by-step explanation:
y + 2 = 2/3(x - 4)
y + 2 = 2/3x - 8/3
y = 2/3x - 8/3 - 2
y = 2/3x - 2 2/3 - 2
y = 2/3x - 4 2/3 or y = 2/3x - 14/3
Slope = 2/3
The value of the slope of the line is 2/3.
Used the concept of the equation that states,
The equation of a line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Given that;
The equation of the line,
y + 2 = 2/3 (x - 4)
Now comparing the given equation of the line with the equation of a line in point-slope form,
y + 2 = 2/3 (x - 4)
y - (- 2) = 2/3 (x - 4)
Therefore, the slope of the line is 2/3
To learn more about the equation of line visit:
https://brainly.com/question/18831322
#SPJ3
2
Select the correct answer.
Which statement is true about this equation?
-412p+5) + Bp=-11
A. The equation has one solution, p=2.
B. The equation has one solution, p=-2.
C. The equation has no solution.
D. The equation has infinitely many solutions.
Step-by-step explanation:
The equation has infinite solution p=2 that's tour variable
name the parts mentioned in the figure below
please answer this
Answer:
O - point
CD- chord
AB- diametre
I dont know PO sorry
Answer:
O is the center.
AB is the diameter.
OP is a radius.
CD is a tangent.
By the way the combination of letters is the two points that it relates too.
Step-by-step explanation:
hope this helps. . .<3
I need help really bad! I have literally no clue what the answer is to this question
Answer: C is the answer
Answer:
The second answer: {(-1, 4),(2, 7),(3,7)} because every x value has one y value
Caroline opens a savings account at her local
bank. She plans to put of her net paycheck
10
in her savings account every week. In June, her
paychecks are $164.69, $177.86, $187.74,
and $163.04. How much money did Caroline
put in her savings account in June?
Answer:
So she has $50–$43.85 = $6.15 in her pocket and $25 in her savings account
Step-by-step explanation:
If z varies directly as x and inversely as y and is equal to 4 when x and y have the values 12 and 8 respectively, what is the value of z when x is equal to 6/7 and y is equal to 5/28?
Answer:
[tex]z = \frac{2}{7} [/tex] when x= [tex] \frac{6}{7} [/tex],
z= 179.2 when y= [tex] \frac{5}{28} [/tex]
Step-by-step explanation:
Let's start by writing out the two general equations for z.
Since z varies directly with x,
z= kx, where k is a constant.
Since z varies inversely with y,
[tex]z = \frac{k}{y} [/tex], where k is a constant.
When x= 12, z= 4,
4= k(12)
12k= 4
k= 4 ÷12
k= ⅓
∴ z= ⅓x
When x=[tex] \frac{6}{7} [/tex],
[tex]z = \frac{1}{3} ( \frac{6}{7} )[/tex]
[tex]z = \frac{2}{7} [/tex]
When y= 8, z= 4,
[tex]4 = \frac{k}{8} [/tex]
k= 4(8)
k= 32
[tex]∴z = \frac{32}{y} [/tex]
When y= [tex] \frac{5}{28} [/tex],
[tex]z = 32 \div \frac{5}{28} [/tex]
[tex]z = 32 \times \frac{28}{5} [/tex]
z= 179.2
Clare had t books. After she bought 8 more books, she had 24 books. Write and solve an equation to find the number of books Clare started with
Answer:
24-8=t
Step-by-step explanation:
I cant really explain much...
but, Hope it helps
plz mark brainiest if it does
Function or non functional? Pls help ty :3
can someone please help me get the answer for this!! PLEASE. I'll give u 45 points
Answer:
8
Step-by-step explanation:
7) What symbol should be used to show the relationship of 101.768 101.867 between the numbers?
The symbol that can be used to show the relationship of 101.768 -----
101.867 between the numbers is < (less than)
The question is what symbol should be used to show the relationship
between 101.768 and 101.867.
Both numbers are decimal numbers.
101.768 is not equal to 101.867.
Instead, 101.768 is less than 101.867.
Therefore, the symbol that can be used to show the relationship of 101.768 ---
-- 101.867 between the numbers are as follows:
101.768 < 101.867
read more: https://brainly.com/question/21507430?referrer=searchResults
Zack buys some potatoes from a store. The potatoes cost $7.68 for 3 pounds. He wants to buy more vegetables, but at the same price per pound as the potatoes. Which of the following vegetables could Zack buy?
Answer:
23.04 i think pls mark brainliest
Step-by-step explanation:
can you answer these fractions
[tex] \frac{2}{5} + \frac{3}{2} [/tex]
I need help please I don't not understand this is getting on my nerves.
I will give you all my point
Answer:
24,748
Step-by-step explanation:
538
x 46
3228
21520
24748
2 - 2x 4x + 12
------- = ---------
4 3
[tex]\tt\frac { 2 - 2 x } { 4 } = \frac { 4 x + 12 } { 3 }[/tex]
[tex]\tt3\left(2-2x\right)=4\left(4x+12\right) [/tex]
[tex]\tt6-6x=16x+48 [/tex]
[tex]\tt6-6x-16x=48 [/tex]
[tex]\tt6-22x=48 [/tex]
[tex]\tt-22x=42 [/tex]
[tex]\tt\:x=\frac{42}{-22} [/tex]
[tex]\boxed{\tt\:x = -\frac{21}{11} = -1\frac{10}{11} \approx -1.90}[/tex]
Method used :-
◇ ✖ Cross multiplication ❌
________
Hope it helps ⚜
Step-by-step explanation:
Given equation is [{(2-2x)/4} = {(4x+12)/3]
On applying cross multiplication then
Since, (a/b) = (c/d)
⇛ab = bc
Where, a = (2-2x), b = (4), c = (4x+12) and d = (3).
Now,
⇛3(2-2x) = 4(4x+12)
Multiply the number outside the bracket with numbers and variables in the bracket.
⇛6 - 6x = 16x + 48
Shift the variable value on LHS and constant on RHS.
⇛-6x - 16x = 48-6
Subtract the values on LHS and RHS.
⇛-22x = 42
Shift the value (-22) from LHS to RHS.
⇛x = 42/-22
Write the obtained answer in lowest form by cancelling method.
⇛x = (42÷2)/(-22÷2)
Therefore, x = 21/-11 = -(21/11)
Answer: Hence the value of x for the given problem is -21/11.
VERIFICATION:
If x = -21/11 then the equation is
[{(2-2x)/4} = {(4x+12)/3]
Substitute the value x = -21/11 in expression, then
⇛[{2-2(-21/11)}/4 = {4(-21/11)+12}/3]
Multiply (-2) from (-21) to get 42 on LHS.
⇛[{2(42/11)}/4 = {4(-21/11)+12}/3]
Again multiply 4 from (-21) to get 81 on RHS.
⇛[{2(42/11)}/4 = {(-81/11) + 12}/3]
Take the LCM of the denominator 1 and 11 is 11 on LHS
⇛[{(2*11 + 42*1)/11}/4 = {(-81*1 + 12*11)/11}/3]
Multiply the numerator on both LHS and RHS.
⇛[{(22+42)/11}/4 = {(-81 + 132)/11}/3]
Add the numerator numbers on both LHS and RHS
⇛[{(64/11)}/4 = [{(48/11)}/3]
Now, conver the division fraction in multiply fraction on both LHS and RHS.
⇛[{(64/11) * 4} = {(48/11) * 3}]
Now, write the numbers in Lower form by cancelling method, on both LHS and RHS.
⇛(16/11) = (16/11)
LHS = RHS
Please let me know if you have any other questions.
Evaluate (32 – 1)when z = 6
Answer:
17
Step-by-step explanation:
(3z - 1) when z = 6
Let's plug in 6 into the equation (3(6)-1)
Now we multiply the parenthesis (18-1)
Now we subtract (17)
So the answer is 17!
A water tank has volume of 300 m3. If the length and width of the tank is 5 m and 300 cm, find the height of the tank.
Answer:
volume=300m3
length=5m
width=300cm=300/100=3m
To find: height of tank .
so,
volume=l×b×h
300=5×3×h
300/15=h
finally,h=20m
Explain why the order in an ordered pair is important
Step-by-step explanation:
An ordered pair is the x-coordinate and the y-coordinate of a point. The order is important because, without a set order, there would be no way to know which was the x and which was the y.
The x-coordinate always comes first, before the y-coordinate.
(x, y)
Step-by-step explanation:
The order in an ordered pair is important because it indicates the location of the given point in a coordinate plane.
In an ordered pair, (x, y):
The first number, (x ) represents the first coordinate. It provides the location of the point relative to the horizontal axis of the coordinate plane.The second number, (y ) represents the second coordinate. It provides the location of the point relative to the vertical axis of the coordinate plane.We cannot switch the values of the first and second coordinates; otherwise, the ordered pair will provide a different location on the coordinate plane.
For instance, if we're given the point, (3, 2), this means that x = 3, and y = 2. This is not the same as (2, 3), as the coordinates imply that x = 2, and y = 3.
Please see the attached screenshot where it shows how these two points have varying locations.
3. The graph of F(x), shown below,
resembles the graph of G(X)=x2, but
it has been changed somewhat.
Which of the following could be the
equation of F(x)?
1
16
FOX0 = ?
G00= x
5
Answer Choices:
F(X)=-X²+2
F(x)= 3x2 +2
F(x)=2x2 - 2
F(x) = (2x + 2)2
The equation of f(x) from the graph if, G(x) = x², is F(x) = 2x² + 3, so option A is correct.
What is a graph?A graph is a structure made up of a collection of things, where some object pairs are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
here, we have,
Given:
G(x) = x²,
As you can see from the graph, the vertex of the parabola is (0, 3),
Write the equation of a parabola as shown below,
y = a(x - 0)² + 3
y = ax² + 3
Here a is the slope of the parabola,
slope = 4 / 2 (from the graph),
slope = 2
Thus, the equation will be,
y = 2x² + 3 or F(x) = 2x² + 3
To know more about Graph:
brainly.com/question/10712002
#SPJ7
Where does -3/7 belong on the Venn diagram
A) integers
B) natural numbers
C)rational numbers
D) irrational numbers
Answer:
rational
Step-by-step explanation:
what is pulmonary function
Answer:
pulmonary function is the blood or gas flow from or to the lungs
Step-by-step explanation:
the lungs take in oxygen and take out c02
The lungs' main role is to bring in air from the atmosphere and pass oxygen into the bloodstream. From there, it circulates to the rest of the body. Help is required from structures outside of the lungs in order to breathe properly.
−3 ≤ n < 2
−2 < m < 4
n and m are integers.
Given that n = m, write down all the possible values of n.
_1,0,1 are possible value of n
Felicia bought 20.8 gallons of gasoline. There are approximately 3.8 liters in 1 gallon.
Answer:
79.04 liters
Step-by-step explanation:
20.8 x 3.8 = 79.04
A model rocket is launched with an initial upward velocity of 125/fts. The rocket's height h (in feet) after t seconds is given by the following.
h=125t- -16t^2
Answer:
H = V0 t + 1/2 g t^2 is the equation in question with V0 and g in different directions, they have different signs
draw a number line and locate all the integers between -3 and 3
Answer:
sry I just wanted the points I'm in middle school so I don't know this stuff either but can you give free brainlyest I'm soo close to my next rank I'd really appreciate it if you would
50 points! Help (Vectors)
[tex]2v - 3u\\\\=2<3,7> - 3<-5,4>\\\\=<6,14>-<-15,12>\\\\=<6+15, 14-12>\\\\=<21,2>[/tex]
Answer:
Step-by-step explanation:
In an auditorium,10,200 people were seated in 12 rows. Find number of people in each row. ____________
Answer:
850 people
Step-by-step explanation:
10,200 people in 12 rows
÷ 12 on both sides:
[tex]\frac{10200}{12}[/tex] people in [tex]\frac{12}{12}[/tex] rows
[tex]850[/tex] people in [tex]1[/tex] row.