[tex]a(n) = 3 + 2n[/tex] for [tex]n \ge 0[/tex] functions generate the arithmetic sequence.
What is arithmetic sequence?It is a "sequence where the differences between every two successive terms are the same" (or) In an arithmetic sequence, "every term is obtained by adding a fixed number (positive or negative or zero) to its previous term".
The first term of an arithmetic sequence is a, its common difference is d, n is the number of terms.
Arithmetic sequence formula is given as, [tex]a_{n} =a+(n-1)d[/tex].
Given arithmetic sequence
[tex]3, 5, 7, 9,.....[/tex]
n is an integer
[tex]a = 3[/tex]
By considering the above arithmetic sequence, we can say that each term in the sequence is in the form of 3 + 2n, where , n ≥ 0.
So, the correct option is A
[tex]a(n) = 3 + 2n[/tex] for [tex]n \ge 0[/tex]
Thus, [tex]a(n) = 3 + 2n[/tex] for [tex]n \ge 0[/tex] functions generate the arithmetic sequence.
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7x+8y= 8
Slope
Y intercept
Answer:
Slope = -7/8
Y-intercept = (0, 1)
Step-by-step explanation:
Answer:
[tex]slope = - \frac{7}{8} [/tex]
y- intercept= 1
Step-by-step explanation:
Rearrange the equation such that it is in the form of y=mx+c. This form is known as the slope-intercept form, and m is the gradient while c is the y-intercept.
7x +8y= 8
8y= -7x +8
Divide by 8 on both sides:
[tex]y = - \frac{7}{8} x + 1[/tex]
Thus, the slope is [tex] - \frac{7}{8} [/tex] and the y-intercept is 1.
Another way to find the y-intercept is to substitute x= 0 into the equation since the y-intercept occurs at x= 0.
7x +8y= 8
When x= 0,
7(0) +8y= 8
8y= 8
y= 8 ÷8
y= 1
Thus, the y-intercept occurs at y= 1 or the coordinate (0, 1).
Note: slope and gradient have the same meaning and can be used interchangeably
Which two teams have the same ratio of wins to losses?
Answer:
Lightning and Eagles
Step-by-step explanation:
14:7 can be rewritten as 2:1 (Factor out 7)
12:6 can be rewitten as 2:1 (Factor out 6)
Both are 2:1
-- Gage Millar, Algebra 2 Tutor
Answer:
D.
Step-by-step explanation:
when you simplify 14:7 you get 2:1 and if you do the same to eagles(12:6) you will get the Same answer( 2:1 )as lightning
The angle of elevation to the top of the Empire State Building in New York is found to be 11° from the ground at a distance of 5281 feet from the base of the building. Using this information, find the height of the Empire State Building in feet. Use the dimensions given in the diagram to give an equation and solve. Round two decimal places.
Answer:
The height of the building is of 1026.52 feet.
Step-by-step explanation:
This situation is modeled by a right triangle, in which the length of the opposite side to the angle of 11º is the height of the building, while the length of the adjacent side is of 5281 feet.
Tangent:
In a right triangle, the tangent of an angle is the length of the opposite side divided by the length of the adjacent side.
In this question:
[tex]\tan{(11)} = \frac{x}{5281}[/tex]
[tex]x = 5281*\tan{(11)}[/tex]
Using a calculator, we have that the tangent of 11 degrees is: 0.1944. Thus:
[tex]x = 5281*\tan{(11)} = 5281*0.1944 = 1026.52[/tex]
The height of the building is of 1026.52 feet.
x = 15, x = 5; (0.75)
Answer:
12
Step-by-step explanation:
12 is 75 of 15 %^%^%^%^^^___<<<7<
In ΔOPQ, the measure of ∠Q=90°, the measure of ∠O=26°, and QO = 4.9 feet. Find the length of PQ to the nearest tenth of a foot.
The length of PQ is ____ ft.
Given:
In ΔOPQ, m∠Q=90°, m∠O=26°, and QO = 4.9 feet.
To find:
The measure of side PQ.
Solution:
In ΔOPQ,
[tex]m\angle O+m\angle P+m\angle Q=180^\circ[/tex] [Angle sum property]
[tex]26^\circ+m\angle P+90^\circ=180^\circ[/tex]
[tex]m\angle P+116^\circ=180^\circ[/tex]
[tex]m\angle P=180^\circ -116^\circ[/tex]
[tex]m\angle P=64^\circ[/tex]
According to Law of Sines, we get
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
Using the Law of Sines, we get
[tex]\dfrac{p}{\sin P}=\dfrac{o}{\sin O}[/tex]
[tex]\dfrac{QO}{\sin P}=\dfrac{PQ}{\sin O}[/tex]
Substituting the given values, we get
[tex]\dfrac{4.9}{\sin (64^\circ)}=\dfrac{PQ}{\sin (26^\circ)}[/tex]
[tex]\dfrac{4.9}{0.89879}=\dfrac{PQ}{0.43837}[/tex]
[tex]\dfrac{4.9}{0.89879}\times 0.43837=PQ[/tex]
[tex]2.38989=PQ[/tex]
Approximate the value to the nearest tenth of a foot.
[tex]PQ\approx 2.4[/tex]
Therefore, the length of PQ is 2.4 ft.
Which describes the relationship between EG and DF 2 Select all that apply.
ty
F
E
21
ס
o
2
4
A
perpendicular
B bisect each other
C. parallel
D. congruent
Answer:
A perpendicular
B bisect each other
D. congruent
Step-by-step explanation:
Given
Attached quadrilateral
Required
Relationship between EG and DF
First, we have that: DEFG is a square
EG and DF are diagonals
Using the property of diagonals of a square, we have:
EG and DF to be perpendicular
EG and DF to be congruent
EG and DF to be bisect each other
Plz help me
Use the discriminant to determine The number of solutions to the quadratic equation -x^2+10x-2=0
Answer:
x=-5
Step-by-step explanation:
i just solved the problem
Answer:
=5±√23
Step-by-step explanation:
-10+2√23
= -------------
-2
-10-2 √23
= -------------
-2
What are fees paid to the lender before it releases a check for the home
purchase called?
A. Nonrecurring fees
B. Home fees
C. Recurring fees
D. Closing costs
SUBMIT
I own 1 mini fish and 2 giant fish each giantfish weighs 3 times as much as minfish. If my mini fish eats my two giantfish, then how many times more weight will my mini fish have now than before
Answer: 6 pounds
Step-by-step explanation:
Answer:
The mini fish would weigh 6 times its original amount hypothetically but if we were talking realistically then you would need more information to figure that out. But even then there's no way of determining the specific weight.
Step-by-step explanation:
An office upgrades its internet speed from 10^4 bits per second to 10^8 bits per second. How many times greater is the new internet speed?
How much paint will you need to paint all sides of the box shown below? show work and use volume or surface area formula.
Answer: 100
Explanation: triangle area is l x h ÷ 2 rectangle area is l x h. 4 x 3 =12÷2 +12÷2 =12 11x4x2= 88 88+ 12=100.
What is 3(4x−8) in simplified form?
7x−11
12x−8
12x + 24
12x−24
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\boxed{\mathsf{3(4x - 8)}}\\\huge\text{DISTRIBUTE 3 WITHIN the PARENTHESES}\\\huge\boxed{\mathsf{= 3(4x) + 3(-8)}}\\\huge\boxed{\mathsf{= 12x - 24}}\\\\\huge\boxed{\textsf{Answer: Option D. \bf 12x - 24}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Find the surface area of the rectangular prism
Using the picture above Find the measure of arc EF
Given:
Measure of arc CG is 125 degrees.
The measure of angle CDG is 85 degrees.
To find:
The measure of arc EF.
Solution:
Intersecting chords theorem: If two chords intersect each other inside the circle, then the measure of angle on the intersection is half of the sum of intercepted arcs.
Using the intersecting chords theorem, we get
[tex]m\angle CDG=\dfrac{1}{2}(m(arcCG)+m(arcEF))[/tex]
Let x degrees be the measure of arc EF.
Substituting the given values, we get
[tex]85^\circ=\dfrac{1}{2}(125^\circ+x)[/tex]
[tex]2\times 85^\circ=125^\circ+x[/tex]
[tex]170^\circ -125^\circ=x[/tex]
[tex]45^\circ=x[/tex]
Therefore, the measure of arc EF is [tex]45^\circ[/tex].
The owner of a home cleaning company provides her customers with?
A) Promotion
B) Services
C) Brand Name
D) Places
Answer:
Step-by-step explanation:
services
If 2/3x -1 = 4, then x=
Answer:
15/2
Step-by-step explanation:
2/3x-1=4
2/3x=4+1
2/3x=5
x=5/(2/3)
x=(5/1)(3/2)
x=15/2
I am a 3-digit number divisible by 7, but not 2. The sum of my digits is 4. Hint it is not 121
Answer:
301
Step-by-step explanation:
3 + 0 + 1 = 4
301 / 7 = 43
301 / 2 = 105.5
Answer:
301
Step-by-step explanation:
301 divided by 7 = 43
301 is not divisible by 2
3 + 1 + 0 = 4
Hope this helps :)
A marathon had 567 runners registered. Of these runners, about 0.7% completed the race in under 2 h 12 min. How many runners completed the race in this time?
Answer:
3
Step-by-step explanation:
can you please explain how i can work through these problems?
A soccer ball is kicked from the top of a 64 ft building into the air at an initial speed of 48 ft/sec. Its flight as a functions of time can be modeled by: h(t)=−16t2+48t+64. After how many seconds, will the soccer ball hit the ground (h=0)?
Answer:
t = 4 seconds
Step-by-step explanation:
The height of a soccer ball as a function of time is given by :
[tex]h(t)=-16t^2+48t+64[/tex]
We need to find the time when the ball hit the ground i.e. h = 0
Put h = 0 in above equation. So,
[tex]-16t^2+48t+64=0\\\\16(-t^2+3t+4)=0\\\\-t^2+3t+4=0[/tex]
It is a quadratic equation such that,
t = -1 s and t = 4 s
Neglecting -1 s, the ball will hit the ground after 4 seconds.
Convert the time. Enter your answer in the box.
4 minutes 53 seconds =
seconds
Answer:
293 seconds
Step-by-step explanation:
60*4=240
240+53=293
Can somebody help me seriously
Answer: b
Step-by-step explanation:
I don't know but i am right
how do i do this? i don’t know how
The 3 inside angles of a triangle need to equal 180 degrees.
Add the 3 together to equal 180:
X + 2x + x+ 14 = 180
Combine like terms:
4x + 14 = 180
Subtract 14 from both sides:
4x = 166
Divide both sides by 4
X = 41.5
Answer:
Fraction form: x = 83/2
Decimal form: x = 41.5
Step-by-step explanation:
The 3 angles inside the triangle will always add up to 180 degrees.
So that gives us the equation:
x + 14 + x + 2x = 180
Combine like terms:
4x + 14 = 180
Subtract on both sides:
4x = 166
Divide:
41.5
you roll a six sided die two times. What is the probability of rolling a 4 then rolling a 2?
Answer: 1/36
Step-by-step explanation:
Rolling a 4: 1/6 (one favorable outcome, six possible outcomes)
Rolling a 2: 1/6 (one favorable outcome, six possible outcomes)
1/6*1/6 = 1/36
The diameter of a pipe is 6 cm. If the pipe is 26 cm long, what is its volume?
Use the value 3.14 for π , and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
i think this question answer is 734.76cm^3
Marie grew 10 plants with 2 seed packets. How many seed packets does Marie need to have a total of 15 plants in her backyard? Solve using unit rates
Answer:
he need 3 seeds to plant a 15 plant
Chandra needs to make 3 gallons of punch. How many cups of frozen strawberries are needed? Use the drown-down menus to complete the answer.
The number of cups of frozen strawberries that are needed to make 3 gallons of punch is equal to 48 cups.
How to calculate the cups of frozen strawberries needed?In this exercise, you're required to determine the number of cups of frozen strawberries that are needed to make 3 gallons of punch. Thus, we would apply direct proportion.
Note: There are 16 cups of frozen strawberries in a gallon.
By direct proportion:
16 cups = 1 gallon
X cups = 3 gallons
Cross-multiplying, we have:
X = 16 × 3
X = 48 cups of frozen strawberries.
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PLEASE HELP ALL LINKS GIVEN WILL BE REPORTED
Answer:
- 13
Step-by-step explanation:
[tex]log \frac{ {a}^{6} {b}^{6} }{ {c}^{7} } \\ \\ = log( {a}^{6} {b}^{6} ) - log {c}^{7} \\ \\ = 6log \: a + 6log \: b - 7log \: c \\ \\ = 6(2) + 6( - 3) - 7(1) \\ \\ = 12 - 18 - 7 \\ \\ \therefore \: log \frac{ {a}^{6} {b}^{6} }{ {c}^{7} } = - 13[/tex]
Can someone answer this please
Answer:
<COB = 50°
Step-by-step explanation:
We can say that m<AOC + m<COD + m<DOB = 180° because the three mentioned angles form a straight line. We can substitute to get:
3x + 94 + x + 18 + 2x - 4 = 180
Then, we can combine like terms:
6x + 108 = 180
6x = 72
x = 12
We can see that m<COB is the sum of m<COD and m<DOB. We can wrote an equation to model the situation:
m<COB = m<COD + m<DOB
m<COB = x + 18 + 2x - 4
m<COB = 3x + 14
We have the value of x, so we can substitute that in:
<COB = 3(12) + 14
<COB = 36 + 14
<COB = 50°
Due to budget cuts the Fire Department only has one ladder which is 35 feet long. While rescuing a damsel from a burning house the ladder must be 12 feet from the base of the house. How high up the house can the ladder reach?
a. Draw a diagram that models the situation. Be sure to label it.
b. Write an equation that models the situation and solve it.
Answer:
good luck always brings luck the answer is 12
Step-by-step explanation: