Step-by-step explanation:
the sum of an infinite geriatric series with |r| < 1 is
s = a1/ (1 - r)
in our case we have
a1 = 8
12 = 8/(1 - r)
12(1 - r) = 8
1 - r = 8/12 = 2/3
-r = -1/3
r = 1/3
so, the first 4 terms (I added a5 too, just in case your teacher meant the NEXT 4 terms) are
a1 = 8
a2 = a1 × 1/3 = 8/3
a3 = a2 × 1/3 = 8/9
a4 = a3 × 1/3 = 8/27
a5 = a4 × 1/3 = 8/81
...
Answer:
[tex]8,\quad \dfrac{8}{3},\quad \dfrac{8}{9},\quad\dfrac{8}{27}[/tex]
Step-by-step explanation:
Sum to infinity of a geometric series:
[tex]S_\infty=\dfrac{a}{1-r} \quad \textsf{for }|r| < 1[/tex]
Given:
[tex]a[/tex] = 8[tex]S_\infty[/tex] = 12Substitute given values into the formula and solve for [tex]r[/tex]:
[tex]\implies 12=\dfrac{8}{1-r}[/tex]
[tex]\implies 1-r=\dfrac{8}{12}[/tex]
[tex]\implies r=1-\dfrac{8}{12}[/tex]
[tex]\implies r=\dfrac{1}{3}[/tex]
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
(where a is the first term and r is the common ratio)
Substitute the found values of [tex]a[/tex] and [tex]r[/tex]:
[tex]\implies a_n=8\left(\dfrac{1}{3}\right)r^{n-1}[/tex]
The first 4 terms:
[tex]\implies a_1=8\left(\dfrac{1}{3}\right)r^0=8[/tex]
[tex]\implies a_2=8\left(\dfrac{1}{3}\right)r^1=\dfrac{8}{3}[/tex]
[tex]\implies a_3=8\left(\dfrac{1}{3}\right)r^2=\dfrac{8}{9}[/tex]
[tex]\implies a_4=8\left(\dfrac{1}{3}\right)r^3=\dfrac{8}{27}[/tex]
How to calculate the area of trapezium B using the scale factor
Answer:
612.5 cm²
Step-by-step explanation:
The ratio of areas of similar figures is the square of the scale factor. The scale factor is the ratio of corresponding side lengths. Here, we must find the scale factor.
__
missing side of AThe only given side of trapezium B corresponds to an unknown side of trapezium A. We can find the length of that unknown side using the area formula.
A = 1/2(b1 +b2)h . . . . . parallel sides b1, b2; height h
98 cm² = 1/2(16 cm +b2)(7 cm) . . . . use known values
28 cm = 16 cm +b2 . . . . . . . . . . divide by 3.5 cm
b2 = 12 cm . . . . . . . . . . . . . . subtract 16 cm
The top side of trapezium A is 12 cm long.
scale factorNow we have the lengths of corresponding (top) sides, so we can find the scale factor. It is their ratio. We choose to express it as (size of B)/(size of A).,
k = (30 cm)/(12 cm) = 2.5
area of BThe area of trapezium B will be that of trapezium A multiplied by the square of the scale factor:
area B = (k²)(area A) = (2.5²)(area A)
area B = 6.25×98 cm² = 612.5 cm²
The area of trapezium B is 612.5 cm².
An airplane flight has 374 seats. The probability that a person who buys a ticket actually goes on that flight is about 85%. If the airline wants to fill all the seats on the flight, how many tickets should it sell?
Taking into account the definition of ratio and proportion, the airline should sell 440 tickets.
What is ratio and proportionThe ratio is the comparison of two quantities and is measured from the division of two values.
The relationship of equality that exists between two ratios, that is, between two comparisons between two determined quantities, is known as a proportion. So if [tex]\frac{a}{b}[/tex] corresponds to the ratio, then [tex]\frac{a}{b}[/tex] = [tex]\frac{c}{d}[/tex] equals a proportion.
Amount of tickets soldAn airplane flight has 374 seats. The probability that a person who buys a ticket actually goes on that flight is about 85%. The airline wants to fill all the seats (100%) on the flight.
This can be represented by the proportion:
[tex]\frac{374}{85}[/tex] = [tex]\frac{amount of tickets}{100}[/tex]
Solving:
amount of tickets= 100×[tex]\frac{374}{85}[/tex]
amount of tickets= 440
Finally, the airline should sell 440 tickets.
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Each statement describes a transformation of the graph of y = ln x. Which statement correctly describes the graph of y = ln(x - 7) + 3?
The statement correctly describes the graph of y = ln(x - 7) + 3 is translated 3 units up as well as 7 units to the right.
what is the graph of logarithmic function?The graph of a logarithmic function has a vertical asymptote at x = 0. The graph of a logarithmic function will decrease from left to right
if 0 < b < 1. And if the base of the function is greater than 1, b > 1, then the graph will increase from left to right.
Given graph : y = ln(x), has a vertical and horizontal translation.
As we know, y = ln(x - h) + k | where h is the vertical shift, and k is the horizontal shift.
If ln(x - k), then the graph is translated right k units.If ln(x + k), then the graph is translated left k units.If ln(x) + h, then the graph is translated up h units.If ln(x) - h, then the graph is translated down h units.Therefore, comparing y = ln(x - 7) + 3 it with different function we can write the graph of y = ln(x - 7) + 3 is translated 3 units up as well as 7 units to the right.
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Combine like terms to simplify the expression:
-50 m+ 10-3 m+ (-13) =
[tex] - 50m + 10 - 3m + ( - 13) \\ - 50m + 10 - 3m - 13 \\ - 53m - 3[/tex]
Hope it helps
please give brainliest
JK ∥ NM. If JL = 32, LM = 20, and JK = 60, what is the length of NM
Answer:
NM= JL + LM + JK
NM= 32 + 20 + 60
NM= [112]
NM= 10,58
Step-by-step explanation:
Hope it helps!!
HELP WITH THE RIGHT ANSWER FOR BRAINLIEST!!!
Answer: this is the wrong answer
Step-by-step explanation:
What is the measure of x
Answer:
58 degrees
Step-by-step explanation:
XYZ is 90 degrees. XYO is 32 degrees. Angle x takes up the space leftover in the right angle, so simply subtract 32 from 90.
90-32= 58
Hope this help! (if it does pls consider giving me brainliest)
Find the solutions of each equation on the interval
(SHOW WORK)
im not in collage but I'll try ok so its most likely
Factor then solve to find the complex solutions.
x=2πn, for any integer n
if i was right could i get brainly?
Which function is being graphed below?
The absolute function will be f(x) = | x - 5 | - 4.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
The absolute function is given as
f(x) = | x - h | + k
Where h,k is the vertex of the absolute function.
f(x) = | x - 5 | - 4
Therefore the absolute function will be f(x) = | x - 5 | - 4.
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m || n, find the value of x.
m
n
(6x+16)⁰
(8x-18)°
Please help! I’ll give good review
Step-by-step explanation:
please mark me as brainlest
Which expression is not a polynomial?
Answer:
the first choice is not a polynomial because you can't divide by a variable.
Please help. Trigonometric ratios
Question 2.1.1
Answer: 5 unitsReason:
Use the distance formula to find the distance from the origin (0,0) to the terminal point (-3, 4)
[tex](x_1,y_1) = (0,0) \text{ and } (x_2, y_2) = (-3,4)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-(-3))^2 + (0-4)^2}\\\\d = \sqrt{(0+3)^2 + (0-4)^2}\\\\d = \sqrt{(3)^2 + (-4)^2}\\\\d = \sqrt{9 + 16}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]
The pythagorean theorem is a similarly related alternative path you can take.
This triangle is a 3-4-5 right triangle.
====================================================
Question 2.1.2
Answer: 1/5Reason:
r = distance from origin to terminal point
r = 5, calculated back in the previous problem above.
sin(alpha) = y/r = 4/5
cos(alpha) = x/r = -3/5
sin(alpha)+cos(alpha) = (4/5)+(-3/5) = 1/5
====================================================
Question 2.1.3
Answer: 1Reason:
Recall that tangent is the ratio of sine over cosine
tan = sin/cos
Therefore,
[tex]\tan(\alpha) *\frac{\cos(\alpha)}{\sin(\alpha)}\\\\\frac{\sin(\alpha)}{\cos(\alpha)}*\frac{\cos(\alpha)}{\sin(\alpha)}\\\\\frac{\sin(\alpha)*\cos(\alpha)}{\cos(\alpha)*\sin(\alpha)}\\\\1[/tex]
This assumes that neither sin(alpha) nor cos(alpha) are zero. Otherwise, we have a division by zero error.
What is the area of this rectangle? (4 points)
A rectangle completely covered in square units is partitioned into two rectangles. The first rectangle has a measurement of four centimeters along the top and seven centimeters along the side. The second rectangle has a measurement of two centimeters along the top and seven centimeters along the side.
Answer:
42 cm
Step-by-step explanation:
The first rectangle has a length of 4 and a Width of 7. the second rectangle has a length of 2 and a width of 7.
The formula for area of a rectangle is A=l*w
SO,
Rectangle 1: A= L*W
A=4*7
A=28
Rectangle 2:
A=L*W
A=2*7
A=14
Now, add both areas since they are both part of one whole recatngle.
28+14
= 42
Need help ASAP
Stuck on this question and need help
Answer:
Factory A = 1200
Factory B= 1350
Factory C= 1050
Factory D = 1100
Step-by-step explanation:
Factory B as the fastest rate of production
what percentage of 5/2 hours is 15 minutes?
Answer:
10 %
Step-by-step explanation:
15 mn = 1/4 h
We have :
[tex]\frac{\frac{1}{4} }{\frac{5}{2} } =\frac{1}{4} \times \frac{2}{5} =\frac{2}{20} =\frac{1}{10}=0.1[/tex]
Then the percentage that 15 mn represents of 5/2 h is :
0.1 × 100 = 10 %
Solve the system of equations by substitution.
-3x - 2y + 2z = 19
2x + y + 3z = -20
Z = -2
Answer:
Step-by-step explanation:
-3x - 2y + 2(-2) = 19
-3x -2y - 4 = 19
-3x - 2y = 23
2x + y - 6 = -20
2x + y = -14
-3x -2y = 23
2x + y = -14
-3x - 2y = 23
4x + 2y = -28
x = -5
-10 + y = -14
y = -4
x= -5, y = -4, z= -2
tn=2(n-1)
Given the formula for the nth term, state the first 5 terms of each sequence.
Answer:
0, 2, 4, 6, 8
Step-by-step explanation:
substitute 1 for n in first term, 2 for n in second term, 3 for n in third term, 4 for n in fourth term, 5 for n in fifth term
2 (1) -2 = 0 first term
2 (2)-2 = 2 second
2 (3)-2 = 4 third
2 (4)-2 =6 fourth
2 (5)-2 =8 fifth
Sketch the graph of y = –1.5(4)x. Then state the function’s domain and range.
The plot of the graph y = –1.5(4)^x is shown below of which its domain and range exist on all real values
Exponential equationThe standard exponential function is expressed as y = ab^x
where
a is the base valuex is the exponentThe exponential function shows an increase along the y-axis and towards the x-axis
According to the equation, we are to plot the graph y = –1.5(4)^x of which its domain and range exist on all real values
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Solve the proportion 60/n = 20/7
Answer:
The answer is zero there is no solving.
Step-by-step explanation:
cause you do
60/n=20/7, and then you move all the terms to the left
now it is: 60/2-(20/7)=0
the domain to this is n=0
add the numbers and variables together and get
60/n-(+20/7)=0 now get rid of the parentheses and now you got
60/n-20/7=0
and all that is 0
kinda hope this help lol
sanjana wrote the cross multiplication property for her proportion: xt=uy
Answer:
what does this mean. oh wAit iM dematerializinG mvxhkgd
hdgxmgxmgxkgzkgsktxktdktdktdktdtdkgd
Which of the following are solutions to the equation below?
Check all that apply. x^2 + 6x + 9= 20
What is answer? (-4589)+(+7658)=
Answer: Heyaa! ~
Your Answer is 3069
Step-by-step explanation:
(-4589)+(+7658)= 3069
Simplify the expression.Add together.
Hopefully this helps you! ~
rotation 180° about the origin
Answer:
The rule for a rotation by 180° about the origin is (x,y)→(−x,−y).
Step-by-step explanation:
The rotation of angle 180 degree about origin is described below.
Rotation 180° about the origin is a geometric transformation that involves rotating a figure or shape around the point (0,0),
Also known as the origin, by an angle of 180 degrees.
This means that every point on the shape is moved to an equal distance away from the origin but on the opposite side of the origin.
This transformation is a reflection where the shape is flipped along,
the x-axis or y-axis or both, depending on the shape's orientation.
The rotation 180° about the origin is a common transformation in various geometrical applications, such as computer graphics, engineering, and physics.
It is a simple transformation that can be easily represented and performed using matrices or complex numbers.
Therefore,
rotation 180° about the origin is a geometric transformation that is important in various applications and involves rotating a shape around the origin by an angle of 180 degrees, resulting in a reflection of the shape across the x or y-axis.
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What is the solution to √6x-3 = 2√x?
Answer:
the answer is B
Step-by-step explanation:
the answer is B if it correct can i have brainalliest
Which clock shows 11:22?
A.
A clock shows the hour hand slightly past 11 and the minute hand at one mark past the 3.
B.
A clock shows the hour hand slightly past 11 and the minute hand at 6.
C.
A clock shows the hour hand slightly past 11 and the minute hand at two marks past the 4.
D.
A clock shows the hour hand slightly past 11 and the minute hand at one mark past the 2.
Answer:
Option C
Step-by-step explanation:
A clock shows the hour hand slightly past 11 and the minute hand at two marks past the 4.
for each circle , work out
Answer:
Formulas
[tex]\textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}[/tex]
[tex]\textsf{Area of a semicircle}=\dfrac{1}{2}\pi r^2 \quad \textsf{(where r is the radius)}[/tex]
[tex]\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}[/tex]
[tex]\textsf{Radius of a circle}=\sf \dfrac{1}{2}d\quad\textsf{(where d is the diameter)}[/tex]
[tex]\textsf{Perimeter of a semicircle}=r(\pi +2) \quad \textsf{(where r is the radius)}[/tex]
Use the above formulas to calculate the various measurements, remembering to calculate the radius first when given the diameter.
Question 9a) Radius = 2.7 cm
[tex]\implies \textsf{Area}=\sf \pi (2.7)^2=22.9\:\:cm^2\:(1\:d.p.)[/tex]
[tex]\implies \textsf{Circumference}=\sf 2 \pi (2.7)=17.0\:\:cm\:(1\:d.p.)[/tex]
-----------------------------------------------------------------------
b) Diameter = 45 mm
[tex]\sf \implies Radius =\dfrac{45}{2}=22.5\:\:mm[/tex]
[tex]\implies \sf Area= \pi (22.5)^2=1590.4\:\:mm^2\:(1\:d.p.)[/tex]
[tex]\implies \sf Circumference= 2 \pi (22.5)=141.4\:\:mm\:(1\:d.p.)[/tex]
Question 10a) Radius = 8.5 cm
[tex]\implies \sf Area=\dfrac{1}{2}\pi (8.5)^2=113.5\:\:cm\:(1\:d.p.)[/tex]
[tex]\sf \implies Perimeter=8.5(\pi +2)=43.7\:\:cm\:(1\:d.p.)[/tex]
-----------------------------------------------------------------------
b) Radius = 24 mm
[tex]\implies \sf Area=\dfrac{1}{2}\pi (24)^2=904.8\:\:mm\:(1\:d.p.)[/tex]
[tex]\sf \implies Perimeter=24( \pi +2)=123.4\:\:cm\:(1\:d.p.)[/tex]
-----------------------------------------------------------------------
c) Diameter = 32 cm
[tex]\sf \implies Radius =\dfrac{32}{2}=16\:\:cm[/tex]
[tex]\implies \sf Area=\dfrac{1}{2}\pi (16)^2=402.1\:\:cm\:(1\:d.p.)[/tex]
[tex]\sf \implies Perimeter=16( \pi +2)=82.3\:\:cm\:(1\:d.p.)[/tex]
-----------------------------------------------------------------------
d) Diameter = 15 m
[tex]\sf \implies Radius =\dfrac{15}{2}=7.5\:\:m[/tex]
[tex]\implies \sf Area=\dfrac{1}{2}\pi (7.5)^2=88.4\:\:m\:(1\:d.p.)[/tex]
[tex]\sf \implies Perimeter=7.5( \pi +2)=38.6\:\:m\:(1\:d.p.)[/tex]
The angle measures of quadrilateral RSTU are shown.
m∠R = (2x)°
m∠S = (3x – 35)°
m∠T = (x + 35)°
The measure of angle U is unknown. Can quadrilateral RSTU be a parallelogram?
Yes, opposite angles R and T are congruent to each other if x = 35.
Yes, consecutive angles R and S are congruent to each other if x = 35.
No, if x = 35, all three given angles measure 70°. The fourth angle would measure 150°.
No, if x = 35, the three given angle measures make it impossible for the figure to be a quadrilateral.
The quadrilateral RSTU be a parallelogram if opposite angles R and T are congruent to each other if x = 35 option first is correct.
What is quadrilateral?It is defined as the four-sided polygon in geometry having four edges and four corners.
We have:
The angle measures of quadrilateral RSTU are shown.
m∠R = (2x)°
m∠S = (3x – 35)°
m∠T = (x + 35)°
If R and T are congruent:
2x = x + 35
x = 35 degree
Opposite angles R and T are congruent to each other if x = 35.
Thus, the quadrilateral RSTU be a parallelogram if opposite angles R and T are congruent to each other if x = 35 option first is correct.
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Answer:
It's c
Step-by-step explanation:
On edge 2023
Match each expression on the left with an equivalent expression on the right. Some answer choices on the right will not be used.
Answer:
The answer is below :
The graph of function g (x) predicts the profit of jimmy's famous Jer*y for a week. The x-axis represents the number of employees earning overtime for the week. The y-axis is the business's profit for the week in hundreds of dollars.
By identifying the maximums, we see that in each blank we need to write:
1) 2
2) 2
3) greater.
How to complete the given statement?
First, we need to find the maximum of the function g(x).
You can see that for x = 2 we have the maximum of the parabola, which gives y = 9.
Then the maximum profit is got when 2 employees earn overtime.
We also need to find the maximum for the table. Notice that the maximum value of the table also happens for x = 2, and this time the maximum is y = 16.
So we can see that the maximum of Cathy's cupcakes is larger than the maximum of Jimmy's.
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What is the volume of this rectangular
pyramid?
3 m
4 m
Submit
5 m
cubic meters
The volume of the given rectangular pyramid.
Solution:[tex]\large\boxed{Formula:V=\frac{1}{3}lbh}[/tex]
First, multiply the length (5), breadth (4) and height (3).
[tex]5×4×3[/tex]
[tex]= 60 \: cm [/tex]
Now, divide 60 by 3.
[tex]\frac{60}{3}[/tex]
[tex]\large\boxed{V= 20 \: {m}^{3}}[/tex]
Therefore, the volume of the given rectangular pyramid is 20 cubic meters.