Answer:
First term: a
Second term: a+d
Third term:a+2d
Step-by-step explanation:
An expression that can model the first three terms of any arithmetic sequence in terms of just a and d is aₙ = a + (n - 1)d.
What is an arithmetic sequence?An ordered group of numbers with a shared difference between each succeeding term is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 8, 13, 18, and 23 is 5. An arithmetic progression is another name for an arithmetic sequence.
How to solve this problem?Let the a be the initial term of a sequence and d be the common difference, then the nth term of any arithmetic sequence can be written as aₙ = a + (n - 1)d.
If we want first three terms of any arithmetic sequence, then we have to put n = 1, 2, 3 in the above expression.
So, for n = 1, a₁ = a + (1 - 1)d = a + 0d = a
for n = 2, a₂ = a + (2 - 1)d = a + d
for n = 3, a₃ = a + (3 - 1)d = a + 2d
Therefore, an expression that can model the first three terms of any arithmetic sequence in terms of just a and d is aₙ = a + (n - 1)d.
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plzz help if right i give brainliest
Answer:
b. (x+6)(x-6)
Step-by-step explanation:
x^2-36 So to get to this answer you can do two things
1. Guess and check
2. Factor it out (which is what I like to do)
In order to get x^2 you need 2xs that are positive which knocks out c and d
Then to get to -36, you need to multiply a positive 6 and a negative 6
(This was poorly explained but if you need anymore help just lmk)
GUYS PLEASE HELP!!A gardener plans to construct a triangular garden using logs for the edges. She has logs that measure
5 meters and 3 meters. Which of the following lengths could be used for the third side of the garden?
A 2 meters
B 6meters
C 8meters
D 9meters
Answer:
6 meters
Step-by-step explanation:
The sum of the lengths of any two sides of a triangle is always greater than the length of the third side. And this MUST be true for all the combinations
The only length where this is true is 6
3+5 is greater than 6
2+6 is greater than 5
5+6 is greater than 3
Please Help Me!! Will Give Brainliest!!!
What is the probability that the dice shows a 2?
Answer:
1/6
Step-by-step explanation:
the probability of rolling a 2 is 1/6
SOMEONE PLS HELP ME FIND THE AREA OF THIS COMPOSITE FIGURE. ILL GIVE BRAINLIEST!
Ms. Sze is grading math tests. A student’s work on a problem is given
below
Answer:
No the student is not correct because the answer is 0.4761. All the student did was wrong was the adding up the zeros.
Step-by-step explanation:
what is this help me out pls
Answer:
That would be -2n - 1.
Answer:
-2n - 1
Step-by-step explanation:
You have to combine like term which would be 4n,n,and 7n.
Since n doesn't have a variable just add a one in front. So now the equation would be
1n+4n-7n That equation equals -2n
Now just add the remaining number
So that makes the answer -2n -1
please show all work
Answer:
[tex]x=21.6[/tex]
Step-by-step explanation:
Use the Pythagorean theorem to solve this problem. The Pythagorean theorem states the following,
[tex]a^2 + b^c = c^2[/tex]
Where (a) and (b) are the legs or the sides adjacent to the right angle, and (c) is the hypotenuse or the side opposite the right angle.
Use the Pythagorean theorem in the right triangle with legs (15) and (18),
[tex](15)^2+(18)^2=c^2\\\\225 + 324=c^2\\\\549=c^2\\\\\sqrt{549}=c[/tex]
Use the Pythagorean theorem again in the right triangle with the legs (18) and (x)
[tex](x)^2+(18)^2=c^2\\\\\sqrt{x^2+324}=c[/tex]
Use the Pythagorean theorem one final time in the larger triangle,
[tex](\sqrt{x^2+324})^2+(\sqrt{549})^2=(x+15)^2\\[/tex]
Simplify, remember that anything to the power (2) is equal to the base (number under the exponent) times itself,
[tex]x^2+324+549=x^2+30x+225[/tex]
[tex]x^2+873=x^2+30x+225[/tex]
Inverse operations,
[tex]x^2+873=x^2+30x+225\\-x^2\\\\873=30x+225\\-225\\\\648=30x\\/30\\\\\frac{648}{30}=x\\\\21.6=x[/tex]
I REALLY NEED HELP ASAP
Answer:
I'm pretty sure it's C
Step-by-step explanation:
because that equation simplifyed = -7/8x-8
The average rainfall of a prairie land is:
Answer:
Heres the link - https://brainly.com/question/19882225?referrer=searchResults
Step-by-step explanation:
find the 12th term of the geometric sequence 5,20,80
Answer:
20971520
Step-by-step explanation:
Thank me later
Which of these expressions would be the best estimate of the quotient 15 1/2 ÷ 3 2/3?
A. 15÷3
B. 15÷4
C. 16÷3
D. 16÷4
Answer:
D
Step-by-step explanation:
Because 15 1/2 ÷ 3 2/3 equals 4.22727272727 and 15 divided by 3 is 5, 15 divided b 4 = 3.75 16 divided by 3 is 5.33333333333 and 16 divided by 4 equals 4 so thats the closest answer
Hope this helps
Which two consecutive integers does -√138 lie between?
A:11 and 12
B:12 and 13
C:-11 and -12
D:-12 and -13
Answer:
C:-11 and -12
[tex] - \sqrt{138} \\ = - 11.747 \\ - 11 < x < - 12[/tex]
You throw two dice. What is the probability of rolling a sum of 6 given that you rolled a sum that is greater than 4?Ill give BRAINLEST to best answer with explanation
Answer:
8/12
Step-by-step explanation:
if you have 2 dice and roll them t the same time you have 11 possible outcomes. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. If you roll something higher then a 4 then you get left with 5, 6, 7, 8, 9, 10, 11, 12. If you count them there is 8 different outcomes you can get out of the 2 dice since the highest you can roll is a 12.
A glider plane travels 120 miles in 2 hours. At that rate, how many hours will it take the plane to travel 300 miles?
10 hours
2 1/2 hours
5 hours
1 1/4
The answer is C.........
What is the area of the trapezoid below
Answer:
[tex]Area: 29 cm^{2}[/tex]
Step-by-step explanation:
[tex]Aear=(8.5+6)(\frac{4}{5} )[/tex]
[tex]Area=14.5 (2)[/tex]
[tex]Area=29[/tex]
----------------------
hope it helps...
have a great day!!
Can someone plz help me with this one problem!!?
Answer:
1
Step-by-step explanation:
Ok so since two of the sides are 1, that means 2 to make it 3 you need to label the other side 1.
Tran is using a coordinate plane to design a treasure hunt for his students. The hunt begins at the flagpole at the origin. The first clue is hidden 5 units north of the flagpole. The second clue is located 6 units east of the flagpole. The final clue is located 5 units south of the flagpole. Plot the locations of the flagpole and the 3 clues on the coordinate plane and show the path students will follow from the flagpole to all three clues. . Each unit represents 50 feet. What is the shortest combined distance along the path from the flagpole to Clue 1 to Clue 2 and to Clue 3?
Answer:
The shortest combined distance along the path from the flagpole to Clue 1 to Clue 2 and to Clue 3 is approximately 1,031.025 feet
Step-by-step explanation:
The given coordinates of the clues for the treasure hunt are
The location of the first clue = 5 units north of the flag pole
The coordinates is (0, 5)
The location of the second clue = 6 units east of the flag pole
The coordinates is (6, 0)
The location of the final clue = 5 units south of the flag pole
The coordinates is (0, -5)
The flagpole is at the origin
The coordinates of the flagpole is (0, 0)
Each unit on the graph = 50 feet
From the drawing of the treasure hunt created with Microsoft Excel, the shortest distances between the clues are as follows;
The shortest distance between 2 points is a straight line
Therefore
The shortest length from the flagpole to Clue 1 = 5 - 0 = 5 units
The actual distance from the flagpole to Clue 1 = 5 units × 50 feet/unit = 250 feet
The length from Clue 1 to Clue 2= √(6² + 5²) = √(61) units
The actual distance from Clue 1 to Clue 2 = √(61) units × 50 feet/unit = 50·√61 feet
By similarity, the actual distance from Clue 2 to Clue 3 = 50·√61
The combined shortest distance along the path from the flagpole to Clue 1 to Clue 2 and to Clue 3 = (250 + 50·√61 + 50·√61) feet ≈ 1,031.025 feet
help please. A bottle contains 30 fluid ounces of orange juice and 18 fluid ounces of pineapple juice. Which
graph has a slope that best represents the ratio of orange juice to pineapple juice in this
bottle?
Juice
Juice
у
20
Amount of
Orange Juice (fl oz)
Amount of
Orange Juice (fl oz)
X
x х
0 2 4 6
8 10
Amount of
Pineapple Juice (fl oz)
0 2. 4 6 8 10
Amount of
Pineapple Juice (fl oz)
Juice
Juice
Amount of
Orange Juice (fl oz)
Amount of
Orange Juice (fl oz)
X
0 2 4 6 8 10
Amount of
Pineapple Juice (fl oz)
0 2 4 6 8 10
Amount of
Pineapple Juice (fl oz)
Answer:
option B. G
Step-by-step explanation:
Let
y ---->ounces of orange juice
x ---> ounces of pineapple juice
we know that
The ratio of orange juice to pineapple juice is equal to
substitute the given values
simplify
Verify each graph
Remember that the formula of slope is "rise over run", where the "rise" (means change in y, up or down) and the "run" (means change in x, left or right)
we have
that means
5 ounces of orange juice per 3 ounces of pineapple juice
Graph F
The slope is
Graph G
The slope is
Graph H
The slope is
Graph J
The slope is
The value of 2 is the value closest to 1.67
therefore
The graph that has a slope that best represents the ratio of orange juice to pineapple juice is Graph GStep-by-step explanation:
The ratio of orange juice to pineapple juice in this bottle is 5: 3, so the correct option is G.
Given that a bottle contains 30 fluid ounces of orange juice and 18 fluid ounces of pineapple juice, to determine which graph has a slope that best represents the ratio of orange juice to pineapple juice in this bottle, the following calculation must be performed:
30/18 = Major Common Divisor is 6 (30/6) / (18/6) = X 5/3 = X
Therefore, the ratio of orange juice to pineapple juice in this bottle is 5: 3, so the correct option is G.
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serious answers only<3 i really need to get this done before i get grounded and i used to be good at math but during quarantine all of my skill just went away
Answer:
-3 1/2
Step-by-step explanation:
-4.5 + 1 = -3.5
what is the height of a rectangular prism that has a volume of 2880 cubic inches and a base of 240 inches
Answer:
h = 12 in
Step-by-step explanation:
To find the height, divide the volume by the base:
2880 in^3
height: ------------------ = 12 in
240 in
The ratio of the areas of two smaller similar quadrilaterals is 81/16. The perimeter of the smaller is 32 centimeters. What is the perimeter of larger quadilaterals
The circumference of a circle is 18π in. What is the area, in square inches? Express your answer in terms of \piπ.
Answer:
A = 81π
Step-by-step explanation:
if circumference is 18π then diameter is 18 and radius is 9
A = πr²
A = 9²π or 81π
please answer no links
Answer:
56.54in^2
Step-by-step explanation:
Answer:
18π in^2 (roughly 56.5 in^2)
Step-by-step explanation:
The area of a semicircle is half the area of a circle. So the area would be 1/2πr² instead of πr².
Since the diameter is 12 inches, the radius would be half of that, making the radius r=12/2=6 inches.
Plugging in r=6 into our formula, we see that the area of the semicircle is 1/2π(6)²=1/2π(36)=18π inches^2
So your final area is 18π in^2 (roughly 56.5 in^2)
Pls help me on this what is the correct answer
Answer:
C 61,705
Step-by-step explanation:
10.9% of 35,000 = 3,815
3,815 x 7 = 26,705 (interest is added per year and 3,815 is the interest amount)
35,000 + 26,705 = 61,705 ( the original loan plus the interest for 7 years)
choose the correct vertical asymptote(s).
Glven the function, f(x) =
x+1
X-4
O x= -4, x= 4
O x= 4
O x= -2, x = 2
O x= 2
which set of side lengths will form a right triangle 8,15,17
7,24,26
6,8,11
10,24,25
Type the correct answer in each box. Use numerals instead of words.
Consider the quadratic equation x² + 10x + 27 = 0.
Completing the square leads to the equivalent equation (x + ___)² = ___.
.
Answer:
(x + 5)² = 2 ==> x² + 10x + 27 = 0
Completing the square of the given quadratic equation leads to the equivalent equation (x + 5)² = -2.
What are Quadratic Equations?Quadratic equations are polynomial equations of second degree.
The general form of a quadratic equation is ax² + b x + c = 0.
Given quadratic equation is,
x² + 10x + 27 = 0
We have the algebraic identity that,
(a + b)² = a² + 2ab + b²
The given quadratic equation is in the form of a² + 2ab + b², where a = x.
So, 2xb = 10x
⇒ b = 5
Now, b² = 25.
So, the given can be written as,
(x² + 10x + 25) + 2 = 0
(x + 5)² = -2
Hence the equivalent form is (x + 5)² = -2.
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A small tree was planted at a height of 5 feet. The tree has been planted for 16 months, and is now 61 feet tall. Which equation could
be used to find x, the average number of feet the tree grew each month?
A. 5x + 16 = 61
B.16x + 5 = 61
C. 61x + 5 = 16
D. 16x + 61 = 5
Answer:
B
Step-by-step explanation:
The height of a triangle is 6 m more than its base. The area of the triangle is 56 m². What is the length of the base?
Answer:
8
Step-by-step explanation:
x(x+6)/2=56
x^2(6x)=112
x^2(6x)-112=0
By trial and error, we can try base =1, height = 7, etc
base =8
height = 14