The explicit form that would be used to find the nth term in the sequence is aₙ = 2 + 3n
What is arithmetic sequence?
The difference between each consecutive term in an arithmetic sequence is constant.
An explicit formula for an arithmetic sequence is a = d(n - 1) + c, where d is the common difference between consecutive terms.
According to the given question:
The first term in an arithmetic sequence is 5 that is a = 5
Now, the third term in the sequences is -1
a₃ = a + 2d
By substituting the value of a and a₃ we can find d for the arithmetic sequence.
-1 = 5 + 2d
2d = -6
d = -3
So, the explicit form that would be used to find the nth term in the sequence is
aₙ = 5 - (n - 1)(-3)
Simplifying further to get
aₙ = 2 + 3n
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if a cone has a volume of 28.63 and a diameter of 4.5 what is the height
Answer:
height = 5.4 units
Step-by-step explanation:
r = 4.5/2 = 2.25
B = πr² = 3.14(2.25²) = 15.90
V = 1/3Bh
28.63 =1/3(15.90)h
85.89 = 15.90h
h = 5.40 units
Help???? I don’t know which one it is
Answer:
A
Step-by-step explanation: Rreminder be happy and stay confident <3
The price of an item has been reduced by 5%. The original price was $20. what is the price of the item now?
Answer:
I think its 19
I know the answers to this problem. I will give brainiest to the first one who ANSWER IS CORRECT.
255 X 35 X 97 X 56 ÷ 2
Answer:
24240300
Step-by-step explanation:
multiply the numbers thand divide by 2.
A bag of flour weighs 15 kg. A baker has one bag of flour. She uses 1.065 kg every day. How much flour does she use in 8 days? How much flour is left over after 8 days?
Answer:
She uses 8.52 kgs of flour in 8 days
There are 6.48 kgs of flour left over after 8 days.
Step-by-step explanation:
First, you need to multiply 1.065 by 8 to get how much flour she uses in 8 days.
1.065 times 8 is 8.52. She uses 8.52 kgs of flour in 8 days.
Now, to get how much flour is left over after 8 days, you need to subtract 8.52 from 15 kgs.
15 - 8.52 = 6.48 kgs.
76.57143 nearest tenth
Answer:
76.6
Step-by-step explanation:
so the nearest tenth is 76.57143
Answer:76.6
Explanation:
PLEASE HELP
The filament of a car headlight is a thin wire that glows when electricity passes through it. Parabolic reflectors with a filament at the focus send light out in a straight beam. The cross section of a 2 inch deep headlight reflector has the equation y2=6x.
A. Draw a sketch of this situation. Include the location of the focus in your drawing.
B. How wide is the beam of light projected from the headlight's reflector? Show all work and give your answer as a decimal rounded to hundredths place.
Answer:
A. Please find attached the drawing of the reflector showing the location of the focus created with Microsoft Excel
B. The width of the beam of light projected from the headlight's reflector is approximately 6.93 inches
Step-by-step explanation:
The given equation representing the cross section of the headlight reflector is y² = 6·x
The shape of the reflector = Parabolic
The general equation of a parabola is (y - k)² = 4·p·(x - h)
The focus of the parabola, Focus = (h + p, k)
By comparison to the general equation of a parabola, from the equation of the reflector, we have;
k = 0, h = 0, 4·p = 6
∴ p = 6/4 = 3/2 = 1.5
∴ The focus of the parabola = (1.5, 0)
A. Please find attached the graph of the equation of the cross-section of the reflector, showing the filament at the focus, created with Microsoft Excel
B. The depth of the reflector is x = 2 inches
A vertical or horizontal parabola has two x-values for a given y-value or two y-values for a given x-value respectively
For the given horizontal parabola, the width of a parabola at a point is the difference between the two y-values at the point
At x = 2, we have;
y² = 6 × x = 6 × 2 = 12
∴ y = ±√(12)
The two y-values at x = 2 are y₁ = √(12) and y₂ = -√(12)
The width of the parabola, w = y₁ - y₂
The width of the parabola at x = 2, w = √(12) - (-√(12))
∴ w = √(12) +√(12) = 4·√3
The width of the parabola at x = 2, w = 4·√3 inches
The width of the parabola at x = 2 = The width of the beam of light projected from the headlight's reflector = 4·√3 inches
By giving the answer as a decimal and rounded to the hundredths place, we have;
The width of the beam of light projected from the headlight's reflector ≈ 6.93 inches.
48. A wire is securely attached from the top of
a 26-foot pole to a stake on the ground
14 feet from the base of the pole. Find the
length of the wire to the nearest tenth of a
foot.
A. 21.9 feet
B. 24.3 feet
C. 28.7 feet
D. 29.5 feet
Answer:
D. 29.5 feet
Step-by-step explanation:
1) First you use the pythagorean theorem a^2+b^2=c^2
2) 26^2+14^2=c^2 The wire is the hypotenuse.
3) Simplify the equation. 676+196=c
4) 872=c
5) Find the square root of 872 and round to the nearest tenth.
6) Your answer is 29.5 feet.
Hope this helps!
Solve this problem please.
Answer:
Step-by-step explanation:
i dont know
Answer:
y = -1/2x+5
Step-by-step explanation:
South Street: y = 2x-4
Perpendicular slope to 2 is -1/2
Find any point on new street: (2,4)
4 = -1/2(2) + b
4= -1 + b
5 = b
use exterior angle measures to solve for h
Answer:
h = 125
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles, that is
h = 63 + 62 = 125
PLS HELP ASAP Find the volume of the hemisphere. Round to the nearest tenth.
the hemisphere ft(or radius i guess) is 4
Answer:
If the radius is 4, then:
Volume = 1/2(4/3)(π)(r³) = 1/2(4/3)(3.14)(4³) = 134.0 ft³
Rena used the steps below to evaluate the expression (StartFraction (x Superscript negative 3 Baseline) (y Superscript negative 2 Baseline) Over 2 (x Superscript 4 Baseline) (y superscript negative 4 Baseline) EndFraction) Superscript negative 3, when x = negative 1 and y = 2.
Step 1:
Substitute x = negative 1 and y = 2 into the expression.
(StartFraction (negative 1) Superscript negative 3 Baseline (2) Superscript negative 2 Baseline Over 2 (negative 1) Superscript 4 Baseline (2) superscript negative 4 Baseline) EndFraction) Superscript negative 3
Step 2:
Simplify the parentheses.
(StartFraction (2) Superscript 4 Baseline Over 2 (negative 1) Superscript 4 Baseline (negative 1) cubed (2) squared EndFraction) Superscript negative 3 Baseline = (StartFraction (2) squared Over 2 (negative 1) Superscript 7 Baseline EndFraction) Superscript negative 3
Step 3:
Evaluate the power to a power.
StartFraction (2) Superscript negative 6 Baseline Over 2 Superscript negative 3 Baseline (negative 1) Superscript negative 21 baseline EndFraction
Step 4:
Use reciprocals and find the value.
StartFraction 1 Over 2 cubed (2) Superscript 6 Baseline (negative 1) Superscript 21 Baseline EndFraction = StartFraction 1 Over 8 times 64 times (negative 1) EndFraction = Negative StartFraction 1 Over 512 EndFraction
In which step did Rena make the first error?
Answer:
c) Step 3
Step-by-step explanation:
Answer:
Its D
Step-by-step explanation:
the person above me is wrong :)
The length of a rectangle is 3 m less than double the width, and the area of the rectangle is 44 m. Find the dimensions of the rectangle
Answer:
Length of Rectangle is 3 cm less than twice the width
Area is 44 m2 ; let W = width; 2W - 3 = Length
Arect = L times W
44 = W ( 2W - 3 )
44 = 2W2 - 3W
0 = 2W2 - 3W - 44
Factoring
0 = ( 2W - 11 )( W +4)
2W - 11 =0 ; W + 4 = 0
W = 11/2 W = -4 (width can not be a negative number)
Therefor: width is 11/2 and length is 8
is .849 greater than .90
Answer:
NO it isnt.
Step-by-step explanation:
Go right of the decimal and throught the different place values. Since the number just right of the decimal is the highest place value, whichever number is greater, holds the greater value.
Help me please I will give Brainiest answer
Answer:
A= 1,0 B=0, -3 C=-6, 5 D= -3, -5
Each piece of cardboard is 0.3 centimeters thick. If Tyler stacks 5 pieces of cardboard on top of one another, how thick will the stack be?
Answer:
1.5 inches thick
Step-by-step explanation:
What is the perimeter of this tile
3in 3in
Is it in or in^2
Answer:
12
Step-by-step explanation: each side is 3, and there are 4 sides so 3*4=12
A number s divided by 2
Answer:
s/2 is the equation
Step-by-step explanation:
I’m about to spam questions if you can answer them please do .
Answer:
x is 70
Step-by-step explanation:
hope this helps you
Movie tickets are $4 for regular admission and $3 for seniors. On a night where there were 190 people and total sales of $720 how many regular admission tickets were sold?
A. 50
B. 150
C. 40
D. 140
Answer:
150
Step-by-step explanation:
So if we rearrange the second equation we can get:
s = 190 - a
Now we substitute this into the first equation:
4a + 3(190 - a) = 720
4a + (570 - 3a) = 720
4a + 570 - 3a = 720
4a - 3a = 720 - 570
a = 150
Here is the histogram of a data distribution.
5 4 3 2
1'2'34'5'6'7'8'9 '10
Which best describes the shape of this distribution?
O A. Bimodal symmetric
B. Bimodal skewed
O c. Uniform
O D. Unimodal skewed
O E. Unimodal symmetric
The given histogram is unimodal skewed.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
This histogram is unimodal skewed.
There are two parts to this answer. The first part has to do with the number of modes.
This would be the item that is occurring the most frequently. In this case the mode is only 4.
It is occurring more than any other.
The second part of this has to do with the distribution of the data as it is displayed on the histogram.
There are 4 pieces of data that are only occurimg one time on the right of the histogram. We call this skewing the data.
When both sides looks almost the same we say it is symmetric.
Hence, the given histogram is unimodal skewed.
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guyssss ANYONEEE PLSSS!!!!!I NEED HELP LIKE ACTUALLY
Answer:
infinite number of solutions
6x - 12 = 84
x = ?
find x
Answer:
x=16
Step-by-step explanation:
Answer:
6x-12=84 x=16 hope that helps
Step-by-step explanation:
6x-12=84x
+12 +12
6x=96
then you divide 6 by 96 and thats how you get 16
I need help please! I don’t understand.
does anyone know the answer for this problem :P
Answer:
A: 6x^2 + 19x + 3
Step-by-step explanation:
6x + 1 (x +3)
use the foil method so first do 6x(x) and you get 6x^2 then 6x(3) + x(1) and you get the 19x then you just do 3(1) and you get your answer which as stated above is 6z^2 + 19x + 3
What’s the slope (rate of change) for the red?
Solve for x and show your work! For each equation choose if there are:
• zero solutions for x • exactly one solution for x • or an infinite number of solutions for x.
3x + 5 = 7 + 3x
2(3x + 9) = 18 + 6x
Since multiplication is implied algebra we often don't need to actually write the times symbol ‘×'. Re-write this algebraic equation without the times symbol. a × b = 4 × c
Answer:
ab=4c
Step-by-step explanation:
Since a and b are being multiplied, we can just right ab. Since 4 and c are being multiplied, we ca just right 4c.
Answer:
ab=4c
Step-by-step explanation:
Basically, if you see any variables that are together like that or numbers side by side with letters, it means it's just being multiplied! This doesn't however, work with numbers next to numbers. So for example:
Say you have a x b = 5 x 5c
It would be ab = 5 x 5c Because only letters get put next to each other. That's really the only way I know how to explain it. Have a great day and good luck!
Find the areas of the trapezoids
Answer:
12 units²
Step-by-step explanation:
The area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height and b₁, b₂ the parallel bases
Here h = 4 ( perpendicular distance between the bases ) and
b₁ = SR = 2, b₂ = TA = 4 , then
A = [tex]\frac{1}{2}[/tex] × 4 × (2 + 4) = 2 × 6 = 12 units²
Ming took a cab across town. His fare was $22, and he leaves an 18, percent tip.
What is the total amount Ming pays the cab driver?
Answer:Ming pays $25.96 to the cab driver.
Step-by-step explanation:
Ming took a cab across town, his fare of cab = $22.00
He leaves a tip of 18% of total fare = 18% of $22.00
Total amount = (18% of $22) + $22.00
( 18/100× 22) + 22.00
= (0.18 × 22) + 22.00
= 3.96 + 22.00
= $25.96
Ming pays $25.96 to the cab driver.