Answers
The explicit formula for the sequence -28, -31, -34, -37, ..., is aₙ= -28 -3d.
What is an arithmetic sequence?A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given:
-28, -31, -34, -37, ...
The general formula of an arithmetic sequence:
aₙ= a₁ + (n)d,
where a₁ is the first term and d is the common difference.
First, we will find the common difference between consecutive terms.
Here,
a₁ = -28
To find the common difference:
a₂ - a₁ = -31 + 28 = -3
a₃ - a₂ = -34 + 31 = 3
a₄ - a₃ = -37 + 34 = 3
Hence, d = -3.
Substitute the values to the formula,
aₙ= a₁ + (n)d,
aₙ= -28 + (-3)d,
aₙ= -28 -3d
Therefore, aₙ= -28 -3d is the required sequence.
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Related Questions
The capacity of a teaspoon is 0.015 L. How many teaspoons of oil are there in 1.2 L? Please help .
Answers
Answer:
80 teaspoons
Step-by-step explanation:
According to the scenario, computation of the given data are as follows,
Teaspoon capacity = 0.015 L
Total quantity = 1.2L
So, we can calculate the number of teaspoons in 1.2L oil by using following formula,
Number of teaspoons = Total quantity ÷ Teaspoon capacity
By putting the value of following, we get
Number of teaspoons = 1.2 ÷ 0.015
= 80 teaspoons
Hence, there are 80 teaspoons of oil in 1.2L.
Find the area of the following trapezoids b1=8 cm, b2=15 cm, h=11 cm
Answers
Answer:
126.5 cm2
Step-by-step explanation:
First, the equation to find the area of a trapezoid is A= 1/2(b1 + b2)h , where b1 is the first length and b2 is the second length and h is the height. For these measurements, you would simply factor them into the equation- A= 1/2(8 + 15)11. Then using pemdas, 8+15= 23... multiplied by 1/2 equalling 11.5. Then multiply 11.5 by 11 to get your answer of 126.5 then add the units.
[ 2 ( 7 . 25 ) + 2 ( 24 )] - 10
Answers
Answer: 57 over 2
57
2
=28 and 1 over 228
1
2
=28.5
Result57 over 2 equals 28 and 1 over 2 equals 28.5
Step by step
Step 1 of 4: Multiply.
Multiply
( Highlighted:2 Highlighted:× Highlighted:7.25 + 24 ) − 10 = ( Highlighted:1450 over 100
1450
100
+ 24 ) − 10
Step 1 of 4: Multiply, sub-step a: Multiply.
Multiply
725 over 100
725
100
× 2 = ( 725 × 2 ) over 100
725 × 2
100
= 1450 over 100
1450
100
Step 1 of 4: Multiply.Hide
Step 2 of 4: Add.
Add
( Highlighted:1450 over 100
1450
100
Highlighted:+ Highlighted:24 ) − 10 = ( Highlighted:3850 over 100
3850
100
) − 10
Step 2 of 4: Add, sub-step a: Convert integer to fraction.
Convert integer to fraction
24 = 24 over 1
24
1
Step 2 of 4: Add, sub-step b: Find common denominator.
Find common denominator
1450 over 100
1450
100
+ 24 over 1
24
1
= ( 1450 × 1 ) over ( 100 × 1 )
1450 × 1
100 × 1
+ ( 24 × 100 ) over ( 1 × 100 )
24 × 100
1 × 100
= 1450 over 100
1450
100
+ 2400 over 100
2400
100
100 is the least common multiple of denominators 100 and 1. Use it to convert to equivalent fractions with this common denominator.
Step 2 of 4: Add, sub-step c: Add.
Add
1450 over 100
1450
100
+ 2400 over 100
2400
100
= ( 1450 + 2400 ) over 100
1450 + 2400
100
= 3850 over 100
3850
100
Step 2 of 4: Add.Hide
Step 3 of 4: Subtract.
Subtract
3850 over 100
3850
100
− 10 = 2850 over 100
2850
100
Step 3 of 4: Subtract, sub-step a: Convert integer to fraction.
Convert integer to fraction
10 = 10 over 1
10
1
Step 3 of 4: Subtract, sub-step b: Find common denominator.
Find common denominator
3850 over 100
3850
100
− 10 over 1
10
1
= ( 3850 × 1 ) over ( 100 × 1 )
3850 × 1
100 × 1
− ( 10 × 100 ) over ( 1 × 100 )
10 × 100
1 × 100
= 3850 over 100
3850
100
− 1000 over 100
1000
100
100 is the least common multiple of denominators 100 and 1. Use it to convert to equivalent fractions with this common denominator.
Step 3 of 4: Subtract, sub-step c: Subtract.
Subtract
3850 over 100
3850
100
− 1000 over 100
1000
100
= ( 3850 − 1000 ) over 100
3850 − 1000
100
= 2850 over 100
2850
100
Step 3 of 4: Subtract.Hide
Step 4 of 4: Simplify.
Simplify
2850 over 100
2850
100
= 57 over 2
57
2
= 28 and 1 over 228
1
2
Step-by-step explanation:
hello please help i’ll give brainliest
Answers
Answer:
A
Explanation:
help need answered today PLEASE
first answer thats correct will get brainly crown
Answers
Answer:
2/3
Step-by-step explanation:
Slope = rise / run = 2 / 3
Because points A, B, C, and D are collinear (meaning on the same line), the slope for line segment AB is the same as the slope for segment DC.
Answer:
2/3.
Step-by-step explanation:
The 2 triangles are similar so their corresponding sides are in same ratio.
The sides BA and CD are collinear so theire slopes are the same.
Slope of BA = rise/run = 2/3 so slope of DC is also 2/3.
50x4-(3 divided by 2)
Answers
198.5 is the answer
50X4-(3÷2)=198.5
Answer: 198.5
Step-by-step explanation:
= 50x4-(3 divided by 2)
= 50x4-(3/2)
= (50 x 4) - ( 3/2 )
= (200) - (3/2)
= 200 - 1.5
= 198.5
Gloria has $4500 saved to take a trip to Disney World Florida. The entire trip will cost her $6,375. She plans to go in 3 years. How much does she have to save each month to take the trip to Florida?
Answers
Answer:
$52.08
Step-by-step explanation:
There are 12 months in a year, so 3 years will have 36 months.
Find how much money she has to save in total:
6375 - 4500
= 1875
Divide this by 36 to find how much she has to save each month:
1875/36
= $52.08
So, she will have to save approximately $52.08 each month
Jessica works 7 days a week at an internship in Paris, France. She makes 70 Euros per day. When she comes back to America she needs to know how many dollars per week she was making. What is the correct amount? ( 1 Euro = 1.17 dollars)
A. $573.30/week
B. $335.65/week
C. $479.50/week
D. $357.66/week
Answers
Answer: D
Step-by-step explanation:
i got this question before
Using the least common denominator rename 3/5 and 1/20
Answers
3/5 -> 12/20
1/20 -> 1/20
Answer:
12/20 and 1/20.
Step-by-step explanation:
The least common denomiator between 3/5 and 1/20 is 20.
For the first equation, we multiply the numerator and denominator by 4 to get 12/20.
The second equation's denominator is already 1/20, so we can leave it as is.
The final answer is 12/20 and 1/20.
Help! No links please
Answers
Answer: Indont know but I think it is the last one
Step-by-step explanation:
Sorry if I am wrkng
A plane flew 390 nautical miles in 45 min. Find its average speed in knots ( nautical miles per hour)
Answers
Answer:
Step-by-step explanation:
1.change minutes to hours,45 minutes is [tex]\frac{3}{4}[/tex] hours
2.then use 390÷ [tex]\frac{3}{4}[/tex]=390·[tex]\frac{4}{3}[/tex]=130·4=520 nautical per hour
Find the volume of the cone. Round your answer to the nearest tenth.
Answers
Answer:
261.79
Step-by-step explanation:
V= 1/3 N r2 h
To solve the equation: 14 = t +72 This is a(n)
equation (type an math operation) In order to solve it, you need to use
(type a math operation). You would
_(type a math operation and a number) on both sides of the
equation. The final answer is t =
(type a number)
Answers
Answer:
t=-58
Step-by-step explanation:
[tex]14=t+72\\14-72=t+72-72\\-58=t[/tex]
A forest covers 78,000 acres. A survey finds that 0. 4% of the forest is old-growth trees. How many
acres of old-growth trees are there?
There are
acres of old-growth trees.
Answers
Answer:
There would be 312 acres of old tree growth for 0.4% of the forest. There would be 31.2 acres of old tree growth for 0.04%. I wasn't sure if you meant 0.4 or 0.04.
What two angles measure 90 degrees?
Answers
The two angles measure 90 degrees are called as complementary angles.
What are complementary angles?
In geometry, complementary angles are defined as two angles whose sum is 90 degrees.
The two angles' complement and supplement are determined by the sum of their measurements. The two angles are said to be complimentary if their combined measurement equals that of a straight angle.
In other words, a right angle results from the combination of two complimentary angles (90 degrees). Angles 1 and 2 are said to be complementary if their sum of angles equals 90 degrees (i.e., 1 + 2 = 90°), and as a result, they are referred to as each other's partners.
two angles that add up to 90 degrees are known as complementary angles. For example, 60° and 30°.
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What is the radius of a hemisphere with a volume of 38153 in”, to the nearest tenth
of an inch?
Answers
Answer:
26.3
Step-by-step explanation:
Delta Math
The radius of a hemisphere with a volume of [tex]38153[/tex] in", to the nearest tenth of an inch is [tex]26.3[/tex].
What is radius?A circle's or sphere's radius is any line segment that connects the object's centre to its perimeter in classical geometry; in more contemporary usage, it is also the length of those line segments.
The word "radius" is derived from the Latin word "radius," which also refers to the spoke of a chariot wheel. Use the equation [tex]r =\frac{D}{2}[/tex] to determine the radius, which is equal to half the diameter. This is the same process used to determine a circle's radius from its diameter.
A hemisphere's volume is equal to [tex]\frac{2}{3} \pi r^3[/tex] cubic units. Where is an estimated constant with a value of [tex]3.14[/tex]. The hemisphere's radius is denoted by "r."
Required calculations are:
V = r
r = radius.
Given, V = 38153 in³
[tex]38153 = \frac{2}{3} \pi r^3[/tex]
[tex]r^3 = \frac{3 \times 38153}{2 \times \pi }[/tex]
[tex]r = 3\sqrt{\frac{3 \times 38153}{2 \times \pi }}[/tex]
r =26.3 in
Therefore, the radius of a hemisphere with a volume of [tex]38153[/tex] in", to the nearest tenth of an inch is [tex]26.3[/tex].
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Eva is going to invest in an account paying an interest rate of 6.1% compounded continuously. How much would Eva need to invest, to the nearest ten dollars, for the value of the account to reach $71,000 in 7 years?
The answer is 46320
Answers
Answer:
$46,320
Step-by-step explanation:
Given that
The rate of interest is 6.1%
The amount is $71,000
And, the time period is 7 years
We need to find out the invested amount
As we know that
In the compounded continously, the following formula should be used
Amount = Invested amount × e^(rate × time period)
$71,000 = Invested amount × e^(6.1% × 7)
$71,000 = Invested amount × e^0.427
$71,000 = Invested amount × 1.5326
So, the investment amount is
= $71,000 ÷ 1.5326
= $46324,912
= $46,320
Write a situation to describe the equation below:
C=50+16x
Answers
y = 2x + 3
y = 2x + 1
Answers
Answer:
This is how you graph it
Step-by-step explanation:
As seen in the equations above, this equation can fit into the equation y=mx+b. M = slope, where is how we will be able to plot the points. Since the slope for both is two, we would go up 2 then right 1, from the y intercept. Which is the point we will be starting at. Plot two points directly on the y-axis at (0,3) and (0,1). Then go back to the slope and go up 2 and right 1. I hope I helped!
What happens if you log a log?
Answers
The guidelines apply to logarithms of any base anyway a comparable base ought to be used all through a calculation. This guideline tells us how to add two logarithms together. Adding log An and log B achieves the logarithm of the consequence of An and B, that is log Stomach muscle.
As demonstrated by the norm of logs, a log of a base with similar bases will drop and will leave simply the power. Logarithms are models, and when you increment, you will add the logarithms. The log of a thing is the number of logs.
In case you have comparable systems on the different sides of a circumstance, they offset each other! Recollect that this conceivably works when the logarithms on the different sides of the circumstance have a comparable base.
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Find the area of the sector.
Answers
The formula for sector area is simple - multiply the central angle by the radius squared, and divide by 2: Sector Area = r² * α / 2.
20PTS 20PTS-Find the perpendicular line
Answers
Answer:
y = 3x - 2
Step-by-step explanation:
See the attached worksheet. Look for an equation of the form y=mx+b, where m is the slope and b is the y-intercept. The slope of the line can be determined by taking two points on the line to calculate the Rise/Run. The points selected for this example are (0,-2) and (2,4). This makes the Rise/Run (6/2), or 3. The y-intercept, b, is -2 as per point (0,-2).
The equation for this (non)-prependicular line is thus y = 3x - 2.
1) The graph of g(x) is shown below. Which statement given below is FALSE?
Please help!
Answers
=======================================================
Explanation:
Let's go through the answer choices one by one to see which are true, and which are false.
Choice A) This is true because as we approach x = 2 from the left hand side, the y values get closer to y = 1 from the top Choice B) This is true. As we get closer to x = 4 on the left side, the blue curve is heading downward forever toward negative infinity. So this is what y is approaching when x approaches 4 from the left side.Choice C) This is true also. The function is continuous at x = -3 due to no gaps or holes at this location, so that means its limit here is equal to the function value. Choice D) This is false. The limit does exist and we find it by approaching x = -4 from either side, and we'll find that the y values are approaching y = -2. In contrast, the limit at x = 2 does not exist because we approach two different y values when we approach x = 2 from the left and right sides (approach x = 2 from the left and you get closer to y = 1; approach x = 2 from the right and you get closer to y = -2). So again, the limit does exist at x = -4; however, the function is not continuous here because its limiting value differs from its function value.Choice E) This is true because the function curve approaches the same y value from either side of x = 6. Therefore, the limit at x = 6 exists.The diagram shows two proportional right triangles.
What is the perimeter of the larger triangle?
Answers
The perimeter of the possible larger triangle with possible side lengths of 24, 32 and 40 is 96 units
What is the perimeter of a plane figure?The perimeter of a figure is the length of the boundary surrounding the figure.
Two triangles that have proportional dimensions are similar triangles
The dimensions (arranged in the order of corresponding sides) of the possible similar right triangles in the question, obtained from a related question, having two similar right triangles, posted online are;
First (larger) triangle side lengths; 24, 32, and xSecond (smaller) triangle side lengths; 9, 12, and 15The similarity of the triangles (proportional corresponding sides, indicates that we get;
[tex]\dfrac{24}{9} = \dfrac{32}{12} = \dfrac{x}{15}[/tex]
Therefore, by cross multiplication, we get;
32 × 15 = 12 × x
x = 32 × 15 ÷ 12 = 40
The perimeter of the larger triangle is; 24 + 32 + 40 = 96
The perimeter of the larger triangle is 96 units.Please find attached the possible diagram of proportional right triangles, created with MS Word, obtained from a question with regards to proportional right triangles online.
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PLEASE HELP I NEED U > I BEGG
Answers
Answer: I think 48 degrees
Step-by-step explanation: they are both diagonal
hope this helps, have a great day!! :D
Answer:
It is also 48
Step-by-step explanation:
1 and 3 are vertical to each other therefore their degree is both the same.
Which one of the following solids can produce this two dimensional shape when sliced vertically
Answers
The solid that can produce the given two-dimensional shape when sliced vertically is option 2.
What is vertical alignment?When we examine anything vertically, we see it from top to bottom. When something is standing, it is referred to as the alignment.
What is horizontal alignment?When we examine objects horizontally, we do it from left to right. When anything is in the sleeping posture, it is known as the alignment.
The given shape is a rectangle. When the rectangular prism is sliced in a vertical manner the solid will represent the given shape that is a rectangle.
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Which ordered pair is a solution to the equation?
y=x54−3
(−5, −7)
(5, −1)
(10, −11)
(−10, 5)
Answers
Answer:
y=4/5x-3 - (-5, -7)
Step-by-step explanation:
So to solve this, lets just plug in each value for x, and see if the y value we get is equal to one of our answers.
So we have (-10, 5)
Well plug in -10 for 4/5x we get:
-40/5=-8
Next we take that value and solve:
y=-8-3
y=-11
The answer for this was 5, not -11.
Ill skip a few steps:
(10, -11):
Plug in 10 we get:
y=8-3 which is y=5. This is not right, for it needed to be -11.
Next we have (5, -1)
This gets us y=4-3 this is y=1 which is not -1. So thats not right.
Finally we have (-5, -7):
This gets us y=-4-3 this is y=-7. What was our y value? -7!
So the answer is (-5, -7)
I hope this helps! :)
simplify when x=4 x^2-4
Answers
Answer:
12
Step-by-step explanation:
X=4[tex] \sf \rightarrowtail \: {x}^{2} - 4 \\ \sf \rightarrowtail \: {(4)}^{2} - 4 \\ \sf \rightarrowtail \: 16 - 4 \\ \sf \rightarrowtail \: 12[/tex]PLEASE HELP!! The first answer WITH STEPS gets BRAINLY!
Mr. Lehman is a piano tuner. He charges his clients a fixed amount for a house call plus his labor which is based on an hourly rate. The graph below shows how much Mr. Lehman charges as a function of the time required to tune a piano
Which of the following best represents Mr. Lehmans hourly rate for labor?
A. 10$
B. 15$
C. 20$
D. 25$
Answers
=Mr.Lehmans hourly rate for labor is 20$
=30+40=70-50=20
Answer:
The Answer is 15$
You'd need to get the slope
it tells us how he charges with respect to Time
So picking any Point on the graph. Let's say (0,10) and (2,40)
m(slope) = y2-y1/x2-x1
= 40-10/2-0
=30/2
= 15$
Picking other points would still give this value
what is the perimiter of this 1/4 circle
A. 7.85in
B. 12.9in
C. 17.9in
D. 31.4in
Answers
===========================================================
Explanation:
A full circle of radius 5 inches would have a perimeter or circumference of...
C = 2*pi*r
C = 2*3.14*5
C = 31.4
This value is approximate because pi = 3.14 is approximate.
The distance around a full circle with radius 5 inches is roughly 31.4 inches, but we only want a quarter of this. Therefore, the distance around the curved portion of the quarter circle is roughly C/4 = (31.4)/4 = 7.85 inches.
Choice A would be the answer if your teacher only cared about the curved portion. However, don't forget about the straight line portions that also make up the quarter circle. Choice A might have been put there as a trick answer.
We'll add on the two copies of the radius 5 inches to get a total perimeter of 5+5+7.85 = 10+7.85 = 17.85 = 17.9 inches, which points to choice C as the answer.
---------------
Side note:
If we used a more accurate version of pi, say the version stored in your calculator, then the perimeter is roughly
5+5+(2*pi*5)/4 = 17.8539816339744
Rounding to the nearest tenth leads to the same answer of 17.9 inches