Answer:
[tex]\underline{192}, 24, \underline{3}, \underline{\dfrac{3}{8}}, \dfrac{3}{64}[/tex]
[tex]\underline{\dfrac{1}8}, \dfrac{1}{4}, \dfrac{1}{2}, \underline{1}[/tex]
[tex]81, \underline{27, 9, 3, 1},\dfrac{1}{3}[/tex]
Step-by-step explanation:
Given the Geometric sequences:
1. ___, 24, ___, ___, 3/64
2. ___, 1/4, 1/2, ___
3. 81, ___, ___, ___, ___, 1/3
To find:
The values in the blanks of the given geometric sequences.
Solution:
First of all, let us learn about the [tex]n^{th}[/tex] term of a geometric sequence.
[tex]a_n=ar^{n-1}[/tex]
Where [tex]a[/tex] is the first term and
[tex]r[/tex] is the common ratio by which each term varies from the previous term.
Considering the first sequence, we are given the second and fifth terms of the sequences.
Applying the above formula:
[tex]ar = 24\\ar^4 = \dfrac{3}{64}[/tex]
Solving the above equation:
[tex]r = \dfrac{1}{8}[/tex]
Therefore, the sequence is:
[tex]\underline{192}, 24, \underline{3}, \underline{\dfrac{3}{8}}, \dfrac{3}{64}[/tex]
Considering the second given sequence:
[tex]ar = \dfrac{1}{4}\\ar^2 = \dfrac{1}{2}\\\text{Solving the above equations}, r = 2[/tex]
Therefore, the sequence is:
[tex]\underline{\dfrac{1}8}, \dfrac{1}{4}, \dfrac{1}{2}, \underline{1}[/tex]
Considering the third sequence:
[tex]a = 81\\ar^5=\dfrac{1}{3}\\\Rightarrow r = 3[/tex]
Therefore, the sequence is:
[tex]81, \underline{27, 9, 3, 1},\dfrac{1}{3}[/tex]
Need to know the three triangle measures of (2x-12) and (3x)
Answer:
32,52,96
Step-by-step explanation:
HELP PLEASE!!!!!!! ! ! !!
Population data from three towns is displayed in the tables below. Which town has growth that follows an exponential model?
Answer:
It would have to be D.
Step-by-step explanation:
None of the tables display an exponential growth of population.
x/12=-7 what's the answer? show work
Answer:
X = - 84
Step-by-step explanation:
A line is perpendicular to y = -x + 1
and intersects the point (-5,1).
What is the equation of this
perpendicular line?
Answer:
y = 5x + 26
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{1}{5}[/tex] x + 1 ← is in slope- intercept form
with slope m = - [tex]\frac{1}{5}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{5} }[/tex] = 5 , thus
y = 5x + c ← is the partial equation
To find c substitute (- 5, 1) into the partial equation
1 = - 25 + c ⇒ c = 1 + 25 = 26
y = 5x + 26 ← equation of perpendicular line
b) The adjoining cylindrical vessel is 70 CM high and the radius
of its base is 35cm. If it contains some water up to the height
of 20 cm, how much water is required to fill the vessel
completely
[tex]\large\boxed{\pink{\sf \leadsto The \ Volume \ of \ water \ needed \ to \ be \ filled \ is \ 192,500 cm^3}}[/tex]
Step-by-step explanation:Given that , cylindrical vessel is 70 cm high and the radius of its base is 35cm . it contains some water up to the height of 20 cm .
And we need to find the water required to fill it completely .
Figure :-
[tex]\setlength{\unitlength}{1 cm}\begin{picture}(12,12)\linethickness{0.4mm}\put(0,0){\line(0,1){5}} \put(3,0){\line(0,1){5}}\qbezier(0,5)(1.5,4)(3,5)\qbezier(0.001,0)(1.5,1)(3,0)\qbezier(0,5)(1.5,6)(3,5)\qbezier(0.001,0)( 1.5, - 1)(3,0)\put(3.5,2){\vector(0,-1){2}}\put(3.5,3){\vector(0,1){2}}\put(3.5,2.5){$\sf 70 cm $}\put(1.4,0){\line(1,0){1.6}} \put(1.4,0.2){$\sf 35cm$}\qbezier(0,2.5)(1.5,3.5)(3,2.5)\qbezier(0,2.5)(1.5, 1.8)(3,2.5)\put(-1,1){\vector(0,-1){1}}\put(-1,1.5){\vector(0,1){1}}\put(-1.3,1.2){$\sf 20cm $}\end{picture}[/tex]
Let us take the Volume of Cylinder be V and the volume of cylinder filled be v . Let the volume required to be filled be X .
From the figure it's clear that , Volume of water required to fill the cylindrical vessel completely will be :-
[tex]\tt:\implies v + x = V \:\: \bigg\lgroup \red{\bf As \ per \ our \ assumption }\bigg\rgroup \\\\\tt:\implies x = V - v \\\\\tt:\implies x = \pi r^2 H - \pi r^2 h \\\\\tt:\implies x = \pi r^2 ( H - h ) \\\\\tt:\implies x = \pi r^2 ( 70 cm - 20 cm ) \\\\\tt:\implies x = \dfrac{22}{7} \times (35 cm)^2 \times 50 cm \\\\\tt:\implies x = \dfrac{22\times 35 cm \times 35 cm }{7} \times 50 cm \\\\\underline{\boxed{\red{\tt \longmapsto Volume_{fill } = 192,500 cm^3}}}[/tex]
Hence the required volume of water to be filled is 192,500 cm³.Find the value of each variable
Answer:
x = 17[tex]\sqrt{3}[/tex]
y = 17
Step-by-step explanation:
You would need to use the following trigonometric functions cosine and sin. Sin is used for the y-variable to get the answer and cosine is used for the x-variable to get the answer. For this case, you would need to do 34 sin 30 for y and 34 cos 30 for x. You should get 17 for y and 17 root 3 for x when you put it in the calculator.
The value of each variable are,
x = 17√3
y = 17
We have to give that,
A triangle is shown in the image.
Now, from the triangle we get;
cos 30° = x/34
Solve for x,
√3/2 = x/34
Cross multiply,
34√3 = 2 × x
2x = 34√3
x = 17√3
And, We get;
⇒ sin 30° = y/34
⇒ 1/2 = y/34
Cross multiply,
⇒ 34 = 2y
⇒ y = 17
Hence, the value of each variable is,
x = 17√3
y = 17
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Write 230,000,000,000 in scientific notation.
Evaluate: 30 - 12÷3×2 =
Evaluate: |4 - 8(3 - 12)| - |5 - 11| =
Evaluate: -18 + 4(6 ÷ 2)2
Evaluate: 11 + sqrt(-4 + 6×4÷3)
Simplify: 12x3 - 3(2x3 + 4x -1) - 5x + 7
Simplify: (x4 / x3)3
Simplify: (3x2y-2)3 / (9xy3)3
Simplify: (2x-3y4)3(x3 + y)0 / (4xy-2)3
Write as a mathematical inequality:"9 is less than the product of M and N".
Find the slope of the line perpendicular to the line y = (1/3)x - 7
Answer:
1. 2.3 x 108
2. 22
3. 70
4. - 84
5. 13
6. 6 3 − 1 7 + 1 0
7. 3x
8. 3x^2y - 2/ xy^3
9. 0
10. mn - 9
11.
What percent of 18 is 24?
Plssss help me
Answer:
133%
Step-by-step explanation:
24 of 18 can be reduced by 6 in which is also known as 4 of 3. 4/3 is equivalent to 133%
Then solve the equation.
A copy center charges 40¢ for the first 3
copies and 7¢ for each additional copy.
How many copies can be made for 75¢?
Answer:
8
Step-by-step explanation:
Ok so 3 copies = 40 cents.
75 - 40 = 35.
We only have 35 cents left.
The highest number that can go in 35 with 7 is 5.
Oir original 3 copies + our 5 copies is 8
I did this in my head so sorry if I'm totally wrong.
what's the difference between whole numbers and integers
Answer:
Whole numbers cannot include negative numbers. Integers are whole number and they can have negative whole numbers.
Step-by-step explanation:
what would the coordinate of a be?
Answer:
A'(-9,-3)
Step-by-step explanation:
-3*3=-9
-1*3=-3
n is m % of what? Help Please!!!!
9514 1404 393
Answer:
what = 100n/m
Step-by-step explanation:
You are given ...
n = m% × what
You know that % is fully equivalent to /100, so this can be written as ...
n = (m/100) × what
If we want to find "what", we can multiply by the reciprocal of its coefficient. That is, multiplying by 100/m gives ...
(100/m)n = (100/m)(m/100)×what
what = 100n/m
_____
Example
13 = 20% of what . . . . . n = 13, m = 20
what = 100(13)/20 = 65
so, 13 = 20% of 65.
Which expression is equivalent to –8?
–2–3
(Negative one-half) Superscript negative 3
(one-half) Superscript negative 3
2–3
Answer:
2, - 3
Step-by-step explanation:
Expression equivalent to - 8
Answer:
d
Step-by-step explanation:
PLLLLLLSSSSSs helpppppppp
Answer:
x = 40
y = 62
Step-by-step explanation:
I figured out the answer by finding the x on the left triangle first by writing an equation:
(3x - 18) + (x + 7) + (x - 9) = 180
once I worked that I plugged in the number which was 40.
Then for the triangle to the right I also plugged in the numbers for x and got 118 degrees I took 180 and subtracted 118 to get my answer of 62 for y.
if the radius of a coin is 20cm ,find its surface area.
Answer:
It's surface area is 1257.14cm^2
Step-by-step explanation:
area=22/7×20cm×20cm
=3.14×20cm×20cm
=1257.14cm^2
anyone ?? i need helppp
Find the value of x. PLEASE HELP I GOT 13 MINS I’ll cashapp you comment cashtag when you find the answer
Answer:
x=5
Step-by-step explanation:
Select all of the values that are solutions of x2 + 20 = 12x.
X = -10
x = -2
x= 2
x = 10
RETRY
Answer:
the answer is : x=2 not 100% sure
What is the tangent ratio of angle x?
please help me on this >_
Answer: x=74°
180-133=47 and 47+59=106 so 180-106= 74°
Give the rule for translating a point 4 units left and 8 units up
Answer:
(x-4,y+8)
Step-by-step explanation:
Given
[tex]Point = (x,y)[/tex]
Required
Translate
4 units left8 units up8 units up
The general rule for up translation is;
[tex]f'(x,y) = f(x,y+h)[/tex]
Where h is the unit translated up
In this case:
[tex]h = 8[/tex]
So, we have:
[tex]f'(x,y) = f(x,y+8)[/tex]
4 units left
The general rule for up translation is;
[tex]f'(x,y) = f(x-b,y)[/tex]
Where b is the unit translated left
In this case:
[tex]b = 4[/tex]
So, we have:
[tex]f"(x,y) = f(x -4,y+8)[/tex]
Hence, the rule of translation is: (x-4,y+8)
Answer:
translation is
x-4,y+8
Step-by-step explanation:
The Jacksons
Eric and Amy Jackson wish to invest in a no-risk savings account. They currently have $55,000 in an account that has a 4.125% annual interest rate, compounded continuously. They have the following options:
a. keep their money in the account they already have
b. invest the money in an account that has 5% annual interest, compounded annually
c. invest the money in an account that has 4.5% annual interest, compounded quarterly
d. invest the money in an account that has 3.875% annual interest, compounded monthly
Write a function for each option, that represents the amount of money in the account after t years after the account is opened.
a. C(t) keep their money in the account they already have
b. A(t) invest the money in an account that has 5% annual interest, compounded annually
c. Q(t) invest the money in an account that has 4.5% annual interest, compounded quarterly
d. M(t) invest the money in an account that has 3.875% annual interest, compounded monthly
pls help!
for which of the following does f(-3)=0 select all that apply
A. f(x) = (x - 3)^2
B. f(x) = -x^2 – 3x
C. f(x) = -(x + 3)^2
D. f(x) = x^2 + 5x + 4
E. f(x) = 2x - 3(x + 1)
F. f(x) = -2(x - 2) + 3x
The function which has the value of 0 at x = -3 are C. f(x) = (x + 3)² and E. f(x) = 2x - 3(x + 1).
What is Function?
A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
A. f(x) = (x - 3)²
Substituting x = 3,
f(-3) = (-3 - 3)² = 36
B. f(x) = x² - 3x
f(-3) = (-3)² - (3 × -3) = 9 + 9 = 18
C. f(x) = (x + 3)²
f(-3) = (-3 + 3)² = 0
Here the function value is 0.
D. f(x) = x² + 5x + 4
f(-3) = 9 - 15 + 4 = -2
E. f(x) = 2x - 3(x + 1)
f(-3) = -6 - 3(-3 + 1) = 0
Here the function value is 0.
F. f(x) = -2(x - 2) + 3x
f(-3) = 1
Hence the required functions are C. f(x) = (x + 3)² and E. f(x) = 2x - 3(x + 1).
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what is the distance between the points (4, 6) and (-1, 8)?
Answer:
Step-by-step explanation:
Anton is constructing an angle congruent to ∠PQR. With his straightedge, he draws and labels AB−→. He places the compass point on point Q and draws an arc that intersects QP−→− and QR−→−. He labels the point where the arc intersects QP−→− as point S and the point where the arc intersects QR−→− as point T. What should Anton do next?
Answer: i just took the test yesterday and got it right
With the same compass opening, place the compass point on point A and draw a long arc through AB−→−.
hopefully this helps. i would have helped you sooner if i seen it before now
Place the compass point on point A and draw a long arc through AB using the same compass opening.
What is arc ?An "arc" is a smooth curve that connects two points. In general, an arc is a section of a circle. It is essentially a portion of a circle's circumference. An arc is a type of curve. An arc can be a portion of another curved shape, such as an ellipse, but it most commonly refers to a circle.
The arc of a circle is defined as a portion or segment of a circle's circumference. A chord of a circle is a straight line formed by connecting the two ends of an arc. A semicircular arc is one that is exactly half the length of a circle.
A chord of a circle is a straight line that can be drawn by connecting the two ends of an arc.
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A furniture store salesman had $15,200 in total monthly sales last month. He made $912 in commission from those sales.
What is the salesman's commission as a percent of his total monthly sales?
Enter your answer in the box.
Answer:
6%
Step-by-step explanation:
percent = part/whole * 100%
percent = 912/15,200 * 100%
percent = 6%
How do you solve 5d+5-3D=2+5d+3 and what’s the answer?
Answer:5/-3
Step-by-step explanation:
5=-3d
Joe and Alice are selling pies for a fundraiser. Jose sold 7 cherry pies and 2 apple pies
for $103. Alice sold 14 cherry ples and 12 apple pies for $366. What is the price for
a cherry pie?
Answer:
9.42857142857
Step-by-step explanation: Is a long decimal so you could just round it to 9.43
True or False?
The ratios 4/5 and 52/60 are proportional
Answer:
False
Step-by-step explanation:
Answer:
False.
Step-by-step explanation: