Answer:
To graph an arithmetic sequence, you can start by plotting the first few terms of the sequence on the coordinate plane. The x-axis represents the term number, and the y-axis represents the value of the term.
In this case, we are given that the fourth term is 20 and the common difference is -1/5 times the first term. Let's say the first term is x. Then, the second term is x - (1/5)x = 4/5x, the third term is 4/5x - (1/5)x = 3/5x, and the fourth term is 3/5x - (1/5)x = 2/5x.
Therefore, the first four terms of the sequence are x, 4/5x, 3/5x, and 2/5x. If we plot these terms on the coordinate plane, we get the following graph:
(0, x)
(1, 4/5x)
(2, 3/5x)
(3, 2/5x)
This graph represents the first four terms of the arithmetic sequence. To find the fifth term, we can use the formula for the nth term of an arithmetic sequence: a_n = a_1 + (n - 1)d, where a_1 is the first term, d is the common difference, and n is the term number.
For this sequence, the fifth term is x + (-1/5)x = 4/5x. To find the sixth term, we can use the same formula: a_6 = x + (-1/5)x = 3/5x.
By continuing this process, we can plot the rest of the terms of the arithmetic sequence on the coordinate plane.
Step-by-step explanation:
Which of the following equations expresses the
relationship between x and y in the table below?
A y = 10x + 1
B. y = 2x - 1
C. y = -x + 45
D. y = -3x + 53
E. y = -7x + 81
Answer:
D
Step-by-step explanation:
ummm.....
please answer in full process question
In the given figure l ||m and p || q. Find the measure of angles √1,2,3,4
Answer:
The Measure of angle 1 is 68
The Measure of angle 2 is 112
The Measure of angle 3 is 68
The Measure of angle 4 is 112
Step-by-step explanation:
In a tournament, a professional golfer knows that she is 200 yards from the hole. A spectator is watching her play and is 140 yards away from the golfer.
Triangle with vertices labeled golfer and spectator and hole, with the distance from the golfer to the spectator measuring 140 yards and the distance from the golfer to the hole measuring 200 yards and the vertex of the spectator measuring 120 degrees
If the spectator has an angle of 120° between the golfer and the hole, what is the angle that the golfer has between the spectator and the hole?
60.0°
59.6°
37.3°
22.7°
The angle that the golfer has between the spectator and the hole is 60°. Therefore, option A is the correct answer.
What is sine rule?Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.
The formula for sine rule is sinA/a=sinB/b=sinC/c
Given that, in a tournament, a professional golfer knows that she is 200 yards from the hole. A spectator is watching her play and is 140 yards away from the golfer.
Let the angle that the golfer has between the spectator and the hole be x
Here, sin 120°/200 =sin x/140
0.8660/200 =sin x/140
0.00433 = sin x/140
sin x=0.866
x=60°
Therefore, option A is the correct answer.
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Hi hi! The answer would be 22.7°, I took the test a while ago.
help! what is
737 is it
natural number
real number
rational number
irrational number
integer
PLS HELP NO LINKS I BEEN ON THIS QUESTION FOR 3 HOURS
Answer:
oof...so sorry bro...
Step-by-step explanation:
9- left side of 10
-4 - right side of -5
2 - two points to the right of zero
so sorry if i am wrong..
mr.jim would like to plant carrots all around base of the fence surrounding his square feet. the area of his garden is 100 sq feet. in feet what is tje perimeter
A cone has a radius of 7cm and a height of 12 cm. Find the volume
Answer:
615.75m cubed
Step-by-step explanation:
f(x)=x/x-9 g(x)= -8/x What's 1. f(g) 2. g(f) 3. f(f) 4. g(g)
The function f(g) is 8/(8+9x) and the function g(f) is -8x/(x-9).
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given functions are f(x)=x/(x-9) and g(x)= -8/x.
1) f(g)
Here, f(-8/x)= -8/x ÷ (-8/x -9)
= -8/x ÷ (-8-9x)/x
= -8/x × x/(-8-9x)
= 8/(8+9x)
2) g(f)
Now, -8/x/(x-9)
-8x/(x-9)
3) f(f)
Here, f(f) = x/(x-9) ÷ (x/(x-9) -9)
= x/(x-9) ÷ ((x-9x+81)/(x-9))
= x/(x-9) × (x-9)/(-8x+81)
= x/(-8x+81)
4) g(g)
Now, -8/(-8/x)
= 64/x
Therefore, the function f(g) is 8/(8+9x).
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Answer both questions
Answer:
First Question - 74.25
Second Question - 23.92
Hope this helps you out
Rewrite the function f(x)=-4(x-4)^2+26 in the form f(x)=ax^2+bx+c
(2x + 3)" and solve for x
Answer:
2x−3=x
Move all terms containing x
to the left side of the equation.
Subtract x
from both sides of the equation.
2x−3−x=0
Subtract x
from 2x
x−3=0
Add 3
to both sides of the equation.
x=3
Help please thank you guys! Really appreciate it
Answer:
1
Explanation:
Radius = C/2π
C is 6.28 and 2*pi is also 6.28
So 6.28/6.28 = 1.
Answer: the answer is 1
Step-by-step explanation:
A train travels 2,000 miles in 40 hours ,going the same distance each hour .how many miles does the train travel each hour
Answer:
50
Step-by-step explanation:
2000/40=50
Answer:
The train travels 50 miles per hour
Step-by-step explanation:
You can solve this by dividing 2,000 by 40.
Complete the table as you answer the multiple choice questions below.
Complete the table with values 3, 2, 24 and 10 respectively
How to complete the table?
The constant of proportionality is the ratio of the y value to the x value i.e.
constant of proportionality (k) = y/x
The table can be completed by determining the constant of proportionality. That is:
k = y/x
where y = hours and x = magnets
k = 4/12 = 1/3
when y = 1:
1/3 = 1/x
x = 3
when x = 6:
1/3 = y/6
y = 2
when y = 8:
1/3 = 8/x
x = 24
when x = 30:
1/3 = y/30
x = 10
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Sara had 222 dollars to spend on 9 books after buying then she had 15 dollars how much did each book cost
Answer:
Each book cost 222 - 15 = 207 / 9 = 22.88 dollars.
The perimeter of a rectangle is twice the sum of its lenght and its width. The perimeter is 34 meters and its lenght is 2 meters more than twice its width.
Answer:
The width of the rectangle is 5 meters, while the length of the rectangle is 12 meters.
Step-by-step explanation:
Given that the perimeter of a rectangle is twice the sum of its lenght and its width, and the perimeter is 34 meters and its lenght is 2 meters more than twice its width, to determine the length and width of the rectangle the following calculation must be done:
(2X + 2 + X) x 2 = 34
(3X + 2) x 2 = 34
6X + 4 = 34
6X = 34 - 4
X = 30/6
X = 5
(2x5 + 2 + 5) x 2 = 34
(10 + 2 + 5) x 2 = 34
17 x 2 = 34
34 = 34
Therefore, the width of the rectangle is 5 meters, while the length of the rectangle is 12 meters.
Help asap 6th grade math
Answer:
I believe the answer is D.
[tex]\huge\boxed{Answer\hookleftarrow}[/tex]
D
[tex]\huge\boxed{Explanation\hookleftarrow}[/tex]
Mark as Brainliest
type an (x,y) ordered pair to put a point on this line.
The ordered pair (x, y) for the given line can be obtained from the graph as (-4, 1).
What is the equation for a straight line?A straight line can be written in the form of an equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
The graph of the line is given.
In order to find the coordinate of a point do as follows,
Draw a perpendicular line from any point on the line to the x-axis.
The intersection of this line with the x-axis will give the x-coordinate.
Similarly, find the y-coordinate by drawing a perpendicular line to the y-axis.
Applying the above procedure, a point is obtained as (-4, 1).
Hence, the ordered pair for the line shown in the graph is (-4, 1).
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A diver made 6 dives in 30 days. At this rate how many dives did the diver make in 50 days?
HELP IM GIVING BRAINLIEST!!!! :))
given: p is the midpoint of AN prove: AG=NI (direct proof)
As a result, AG = NI according to the ASA congruency, where p is the midpoint between AN and AG=NI.
what is triangle ?Given that it has three sides and three vertices, a triangle is a polygon. It is one of the fundamental geometric shapes. Triangle ABC is the term used to refer to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon because it has three sides and three corners. The points at which the three sides of the triangle converge are referred to as its corners. Three triangle angles can be multiplied to get 180 degrees.
given
p is the midpoint of GI
GP = PI , PN = AP ( as mid point )
∠APG = ∠IPN ( as vertical opp. angle )
∠A = ∠N ( given )
so by ASA congruency ΔAPG = ΔIPN
As a result, AG = NI according to the ASA congruency, where p is the midpoint between AN and AG=NI.
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This is worth half of my grade
Answer:
[tex]y = 8 - 8\sin(2x) [/tex]
Identify the domain and range of each function
Answer: A) Domain: All real numbers , Range: All real numbers
Step-by-step explanation: Since the line of the graph continued to infinity, the answer for both domain (goes from Left to right) and range (goes up to down) would be all real numbers
m∠1 = (4x + 9)° and m∠2 = (x − 14)° in the given figure. Find x.
An image of two parallel lines and two transversals.
Question 13 options:
7
19
8
37
Answer:
[tex]x = 19[/tex]
Step-by-step explanation:
Given
[tex]\angle 1 = 4x + 9[/tex]
[tex]\angle 2 = x - 14[/tex]
See attachment
Required
Find x
From the attached image, we have:
[tex]\angle 1 +\angle 2 = 90[/tex]
Because the sum of both angle corresponds to the right angle between n and m
So, we have:
[tex]4x + 9 + x - 14 = 90[/tex]
Collect like terms
[tex]4x + x = 90 - 9 +14[/tex]
[tex]5x = 95[/tex]
Divide by 5
[tex]x = 95/5[/tex]
[tex]x = 19[/tex]
PLEASE HELP ITS DUE TOMORROW maths
Answer:
Average speed: 698 kmh^-1
Step-by-step explanation:
In 1440 earth days, there are 34560 hours (1440 × 24)
Solving for the average speed, km/h
[tex]\frac{24~130000km}{3450hr}[/tex] ≈ [tex]698.21 km[/tex]
so, the average speed is [tex]698 kmh^{-1}[/tex]
[tex]---------[/tex]
hope it helps..
have a great day!!
The table shows the educational attainment of the population of Mars, ages 25 and over, expressed in millions. Find the probability that a randomly selected martian,
aged 25 and over has not completed four years (or more) of college.
Years of High School Years of College
Less than 4 4 only Some (less than 4)
Total
Male
27
Female
19
23
Total
27
51
48
11
16
4 or more
25
25
24
88
82
170
44
==========================================================
Explanation:
There are 170 million martians surveyed, note the "170" in the bottom right hand corner.
Of this total, there are 48 million who have completed 4 (or more) years of college. Refer to the bottom of the "4 or more" column.
This must mean that 170 - 48 = 122 million martians have not completed 4 or more years of college. This figure of 122 is effectively the sum of nearly everything in the bottom row, except for the 48 and the 170. In other words, 27+51+44 = 122.
We divide the values 122 over 170, and reduce fully, to get the answer we're after.
122/170 = (2*61)/(2*85) = 61/85
This can be thought of as "if we had 85 million people total, then 61 million of them did not complete 4 or more years of college".
Side note: 61/85 = 0.7176 = 71.76% approximately
The probability that a randomly selected martian, has not completed four years (or more) of college is P = 0.72.
How to find the probability?
We want to find the probability that a randomly selected martian over the age 25, is not completed over 4 years of studies.
In the table, we can see that we have a total of 170 Martians.
Of these 170, only 48 have completed more than 4 years of college.
Then: 170 - 48 = 122 have not completed 4 years or more.
Then the probability that a randomly selected martian has not completed 4 years or more of college is:
P = 122/170 = 0.72
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Convert the polar equation to rectangular form [tex]r=5cot(\theta)csc(\theta\))[/tex]
Answer:
[tex]\displaystyle x=\frac{1}{5}y^2[/tex]
Step-by-step explanation:
[tex]\displaystyle r=5\cot(\theta)\csc(\theta)\\\\r=5\biggr(\frac{\cos(\theta)}{\sin(\theta)}\biggr)\biggr(\frac{1}{\sin(\theta)}\biggr)\\\\r=\frac{5\cos(\theta)}{\sin^2(\theta)}\\\\r^2=\frac{5r\cos(\theta)}{\sin^2\theta}\\\\r^2\sin^2(\theta)=5r\cos(\theta)\\\\(r\sin(\theta))^2=5x\\\\y^2=5x\\\\x=\frac{1}{5}y^2[/tex]
Simplify the expression
-4|2.5-6|
Answer: -14
Step-by-step explanation:
any help? please make sure it's correct thank you
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 6
Step-by-step explanation:
The slope will be perpendicular to equation through A and B because of the 90 degree angle at B.
Lines that are perpendicular have opposite reciprocal slopes.
The slope of the line we know is 2 (The slope is the number before the x). The opposite reciprocal is -[tex]\frac{1}{2}[/tex].
Now that we have the slope we need a point on the line. They give us that point at (0,6) We will use the y value of 6 and the x value of 0 from the point given to find the y-intercept.
slope (m) = - [tex]\frac{1}{2}[/tex]
y = 6
x = 0
We will substitute all of this information into y = mx + b to solve for b (y-intercept)
y = mx + b
6 = - [tex]\frac{1}{2}[/tex] (0) + b
6 = b
Now that we have the slope (- [tex]\frac{1}{2}[/tex]) and the y-intercept (6) we can write the equation
y = - [tex]\frac{1}{2}[/tex] x + 6
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 6
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 = 2x + 1 ← is in slope- intercept form
with slope m = 2
BC is perpendicular to AB
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{BC}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]
the line BC has point C at (0, 6 ) ⇒ c = 6
y = - [tex]\frac{1}{2}[/tex] x + 6 ← equation of line BC
At a local shop Sissi spends one third of her money on milk and two fifths of her money on bread and a one ninth on a lolipop
(A) what fraction of Sissi's money did she spend in the local shop?
(B) what fraction of Sissi's money does she have left?
Answer:
the answer for a is 38 over 45 that is the total fraction of her money that she spent in the local shop for b the answer is 7/45
This came about as for a when we added the total number of expenditures that CeCe had made that is 1/3 + 2/5 + 1/9 and that is 38/45 so that is the fraction of money that she said that she spent in the local shop.
as for b it said what fraction of sissies money does she have left and we know that the total fraction is 38 over 45 and we are going to subtract it from 1.
and that will give us 7/45
The volume of a rectangular box is x^3+x^2-4x-4 cubic inches. If the length of the box is x+1 inches and the width is x-2 inches, what is the height , in inches, off the box in terms of x
The volume of a rectangular box can be found by multiplying the length, width, and height of the box together. So if the volume of the box is x³+x²-4x-4 cubic inches, the length is x+1 inches, and the width is x-2 inches, we can set up the equation h = (x³+x²-4x-4) ÷ (x²-x-2).
The formula for the volume of a rectangular box is V = l × w × h, where l is the length, w is the width, and h is the height of the box. This formula can also be written as V = l×w×h.
In the question you provided, the volume of the rectangular box is given as x³+x²-4x-4 cubic inches, and the length and width are given as x+1 inches and x-2 inches, respectively. With this information, we can set up an equation using the formula for the volume of a rectangular box:
(x+1)(x-2)(h) = x³+x²-4x-4
where h is the height of the box in inches. To solve for h, we can divide both sides of the equation by (x+1)(x-2) to get:
h = (x³+x²-4x-4) ÷ (x+1)(x-2)
And Now we can simplify the expression using standard algebraic operations.
h = (x³+x²-4x-4) ÷ (x²-x-2)
You can now substitute any value of x to find the height of the box.
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