Answer:
The formula is [tex]a_n = 3n-2[/tex]
The 14th term is 40, in other words, [tex]a_{14} = 40[/tex]
========================================================
Explanation:
The given sequence is 1, 4, 7, 10, ...
Subtract each adjacent term:
4-1 = 37-4 = 310-7 = 3This shows that each term is increasing by 3. This is the common difference, so d = 3.
The first term is [tex]a_1 = 1[/tex]
The nth term of the arithmetic sequence is...
[tex]a_n = a_1 + d(n-1)\\\\a_n = 1 + 3(n-1)\\\\a_n = 1 + 3n-3\\\\a_n = 3n-2\\\\[/tex]
As a check, let's plug in say n = 3 to find that:
[tex]a_n = 3n-2\\\\a_3 = 3(3)-2\\\\a_3 = 9-2\\\\a_3 = 7\\\\[/tex]
The third term is 7, which matches with the sequence given to us. I'll let you confirm the other values.
-----------
We'll repeat this idea but now for n = 14 to find the 14th term of the sequence.
[tex]a_n = 3n-2\\\\a_{14} = 3(14)-2\\\\a_{14} = 42-2\\\\a_{14} = 40\\\\[/tex]
The 14th term is 40.
You can make a table of values to help confirm the answer. In the first column you'll have the values of n (1,2,3,...) all the way up to 14. The second column will consist of the sequence 1, 4, 7, 10, ... each time going up by 3 until you reach the 14th term of 40.
Can someone solve this rational equation and plz don’t link files
r=13/2
After I solved it it was kinda easy
Answer:
r=13/2
Step-by-step explanation:
f(x) and g(x) below, find the value of (fog)(-8).
f(x) = 3x²-3x - 8
g(x) = -x - 7
Therefore , the solution of the given problem of function comes out to be fog(-8)= 622.
Function: A DefinitionA function is a relationship between a collection of sources or one product for each input. Simply described, a function is a group of equations linked to a single, distinct output. A declaration, rule, or law that specifies the relationship between two variables is known as a function in mathematics (the dependent variable). When a rules of this kind is employed, there is just one output. by photographer Alex Federspiel. This sentence provides a y=x2 example. Any input for x has only one output for y. Since x is indeed the input value, y is, by definition, a function of x.
Here,
Given :
f(x) = 3x²-3x - 8
g(x) = -x - 7
To find : fog)(-8)= ?
Thus,
We find
=> F(g(x)) => 3g(x)² -3g(x) - 8
=> f(-x-7) =3⋅(-x-7)²-3⋅(-x-7)-8
At x =-8
=> 3(-8-7)² - 3(-8-7)-8
=> 3(225)-3(15) -8
=> 675 - 45 -8
=> 622
Therefore , the solution of the given problem of function comes out to be fog(-8)= 622.
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Write and solve an equation to find what fraction of the student f voted for fruit juice or water
If [tex]\frac{1}{4}[/tex] of fruit punch is pineapple juice. About [tex]\frac{1}{6}[/tex] of the fruit punch is orange juice, then fraction of punch that is pineapple juice or orange juice is [tex]\frac{5}{12}[/tex] .
The fraction of pineapple juice in fruit punch is = [tex]\frac{1}{4}[/tex] ;
the fraction of orange juice in fruit punch is = [tex]\frac{1}{6}[/tex] ;
the equation that can be used to find the fraction of fruit punch that is pineapple juice or orange juice is
⇒ [tex]Frcation Of (Pinapple Juice +Orange Juice)[/tex]
substituting the values ,
we get the equation as ;
⇒ [tex]\frac{1}{4} +\frac{1}{6}[/tex]
taking LCM as 4 and 6 as 12 and solving further ,
we get ;
⇒ [tex]\frac{3}{12} +\frac{2}{12}[/tex] ; = [tex]\frac{5}{12}[/tex] .
Therefore , the fraction of fruit punch that is pineapple juice or orange juice is [tex]\frac{5}{12}[/tex] .
The given question is incomplete , the complete question is
About 1/4 of fruit punch is pineapple juice. About 1/6 of the fruit punch is orange juice. Write and solve an equation to find the fraction of the punch that is pineapple juice or orange juice .
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Students in a statistics class took their first test. The following are the scores they earned. Create a frequency distribution and histogram for the data using a lower class limit of 49.5 and a class width of 10. Describe the shape of the distribution Search Search Select an answer variable(s), the correct graph to make is a a) Since data were collected for? Select answer b) For this one the class width is given to be the following: class width Complete the frequency relative frequency table using the given class width. Round relative frequencies to 3 decimal places. Frequency Relative Frequency Classes 495 c) Which of the following is the correct histogram for the given data? Frey 495 595 695 795 Histogram for Test I Score 895 995 Q Search Search 5 Spring ZOO) Final El Pl E U M QUI PUUVITU 495 595 69.5 79.5 Histogram for Test / Score 89.5 99.5 Q a Frequency 49.5 595 695 795895995 Histogram for Test / Score Frequency 595 603 795 Histogram for Tere d) What shape is the histogram above? Select an ant Q Search Search LE
a) Since data were collected for "score quantitative" variable(s), the correct graph to make is a histogram
b) For this one the class width is given to be the following: class with = 10 . See the attachment for table
c) See the attachment for the graph
What is histogram ?
A histogram is a collection of rectangles with bases and the gaps between class boundaries. All of the rectangles are contiguous, and each rectangle bar represents some kind of data. Rectangles have heights that are proportionate to the corresponding frequencies for both related and dissimilar classes.
a) Since data were collected for "score quantitative" variable(s), the correct graph to make is a histogram
b) For this one the class width is given to be the following: class with = 10 . See the attachment for table
c) See the attachment for the graph
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HELP ME HELP ME PLEASEEEE I NEED QUICK
Answer:
<ABC and <CB both add up to 90 degrees and fit in the angle <ABD so they could be 45 degrees, or one could be 20 degrees while the other is 70, they just have to add up to 90 degrees
Step-by-step explanation:
GIVE THIS ANSWER FAST I WILL GIVE BRAINLIEST
Q IF 2X^3+AX^2-BX-15 HAS 2X+3 AS A FACTOR AND LEAVES A REMAINDER -5 WHEN DIVIDED BY(X-1),FIND THE VALUES OF A AND B
Answer:
could you just give the
Step-by-step explanation:
equation so I could try to solve it
A line passes through 3,1 and 0,-3 whats the equation
Answer:
y=(this is a fraction) 4/3 times x-3
Step-by-step explanation:
please help with math question!!
Answer:
b. cubic
Step-by-step explanation:
hope this helps :)
The table shows the linear relationship between x, the altitude in feet, and y, the boiling point of water in degrees Fahrenheit.
What are the slope and y-intercept of the line that models this situation? I
The slope and the y-intercept of the given data table will be option A) Slope= -0.0018, y-intercept = 212
The y-intercept of any linear equation is the point at which the line or the curve intersects the vertical i.e the Y- axis.
To find this intercept, the value of x is taken to be 0 in the model, since on the Y-axis, the value of x is 0.
Here from the given table, we need to check the boiling point or the value of Y for which the value of the altitude or the x value is 0
Hence we get the y-intercept as 212° F.
Now, the formula for slope
= change in y/ change in x
here we will take any two data rows and divide the difference in boiling points by the difference in altitudes.
Taking the first 2 rows gives us
Slope = -0.9/500
= -0.0018
Hence we choose option A) Slope = -0.0018, y-intercept = 212
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Complete Question
The table shows the linear relationship between x, the altitude in feet, and y, the boiling point of water in degrees Fahrenheit. What are the slope and y-intercept of the line that models this situation?
A. Slope= -0.0018, y-intercept = 212
B. Slope= 0.0018, y-intercept =-212
C. Slope =212, y- intercept= 0.0018
D. Slope=-212, y-intercept = 0.0018
how many 1/4 are in 6
Answer:
24
Step-by-step explanation:
To answer this you simply need to divide 6 by 1/4
or
6÷1/4
which is also equivalent to 6*4
this will get you 24
What is another name for angle 1?
∠JNL
∠N
∠MNK
∠NLJ
Answer: JNL
Step-by-step explanation: We can give angle 1 another name by using 3 letters which include the letter of the vertex point in the middle, and two other letters of the two rays that meet at the vertex point.
The size of each exterior angle in a regular polygon is 15°. Work out how many sides the polygon has.
8. Which of the following expressions is a factored form
expression 3x
2 − 10x − 8 ?
a. (3x-4)(x+2)
b. (3x-2)(x-4)
c. (3x-2)(x+4)
d. (3x+2)(x-4)
e. (3x+4)(x+2)
Answer:
D
Step-by-step explanation:
(3x+2)(x-4)
3x^2-12x+2x-8
3x^2-10x-8=0
simplify (2√2+3√5) square 2
Answer:
The answer is 22.4
Find the volume of a cone
Answer:
96π or 301.59 in³
Step-by-step explanation:
V(cone) = 1/3πr²h
= 1/3·π·6²·8
= 96π or 301.59
Answer:
301.58
Step-by-step explanation:
In a television survey, 4 out of 5 people liked comedy shows more than reality shows. If 6,000 people were surveyed, how many people preferred comedy shows?
Answer:
4,800
Step-by-step explanation:
6,000/5
1,200x4
4,800
1. Circle which of the following ways to prove that a quadrilateral is a parallelogram. (5 pts.)
I. quadrilateral with both pairs of opposite sides congruent
II. quadrilateral with both pairs of opposite angles congruent
ILI. quadrilateral with one pair of opposite sides both congruent and parallel
A. I only
B. II only
C. I, II and III
D. III only
E. I and II
quadrilateral with both pairs of opposite sides congruent
What is a parallelogram?
A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.
Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.
If both pairs of opposite sides of a quadrilateral are congruent , then the quadrilateral is a parallelogram.
So, the option I only is correct
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For each graph, determine whether x and y are proportional.
If r and y are proportional, fill in the blank with a number in simplest form.
Graph 1
Graph 2
Graph 3
HELP PLEASE
What is the slope of the line?
Answer:
4
Step-by-step explanation:
slope, m = (y₂ - y₁)/(x₂ - x₁)
plug in the values, and we get m = (3 - (-1))/((3 - 2) = 4
As x increases by 1, y increases by 4.
-1
Step-by-step explanation:
The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.
pls help ASAP what do I put in the box (question is in screenchot)
Answer:
where is the question????
Answer:
where
Step-by-step explanation:
please help! i've tried to solve it but not getting the right answer
Answer:
Sorry I don't know this one, I got 5.32
Step-by-step explanation:
I need help to get the answer
The length BC of the right triangle is 18 units.
How to find the side of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The length BC of the right triangle can be found as follows:
Therefore, using proportion because triangle ABC is similar to triangle BDC.
x / 36 = 9 / x
cross multiply
x × x = 36 × 9
x² = 324
square root both sides of the equation
x = √324
x = 18 units
Therefore,
BC = 18 units
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how to get the Y intercept when you don't have a 0 X coordinate?
Answer: You plug in y as 0 into your equation.
Step-by-step explanation:
Do the above thing OK.
What’s the equation to find angles in a parallelogram
103M) solve on the interval 0 ≤ x < 2pi
sin ( 4x ) = √3 / 2
solving sin ( 4x ) = √3 / 2 , the value of x is 15°
What is trigonometry?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
For angle of 30° and 60°
sin 30° = 1/2
cos 60° = √3/2
tan60° = √3
for angle 60 °
sin60° = √3/2
cos 60° = 1/2
tan60° = 1/√3
since sin(4x) = √3/2
and sin 60° = √3/2
sin60° = sin(4x)
this means 60° = 4x
divide both sides 4
x = 60/4
x = 15°
therefore the value of x is 15°
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The ratio of the sides of a triangle is 3:5:6. If the perimeter of the triangle is 154 feet, what are the side lengths?
The side length of the triangle are
33 feet55 feet66 feetHow to find the side length of the triangleA triangle with given ratio of sides as 3 : 5 : 6 and a perimeter of 154 feet is calculated from the formula of perimeter which is
= a + b + c
where
a, b, and c are the dimensions of the side length of the triangle:
Using the values given in the problem we have
let the ratio be a multiple of x such that
154 = 3x + 5x + 6x
154 = 14x
x = 11
a = 3 * 11 = 33 feet
b = 5 * 11 = 55 feet
c = 6 * 11= 66 feet
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which function is equal to -1/2?
Using the regression line, or line of best fit, predict the resale value of an 8-year-old car with an original cost of $15,000.a.The 8-year-old car could be worth approximately $2000.b.The 8-year-old car could be worth approximately $5000.c.The 8-year-old car could be worth approximately $3000.d.The 8-year-old car could be worth approximately $4500.
The 8-year-old car could be worth approximately $3000.
The graphs that show the association between two variables in a data collection are called scatter plots. It displays data points either on a Cartesian system or a two-dimensional plane.
The X-axis is used to represent the independent variable or characteristic, while the Y-axis is used to plot the dependent variable. These diagrams or graphs are frequently used to describe these plots.
In the graph attached below, we can see that when the age of the car is 8 years, the resale value of the car is between points 40 and 20.
Thus, The 8-year-old car could be worth approximately $3000.
(Refer to the image attached for the complete question and graph)
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Jack split 25 jellybeans between his brother and himself so that his brother has one more than twice the number Jack has. How many jellybeans does each have?
Answer:
Jack has 8 and his brother has 17
Step-by-step explanation:
j = # jack has
b = # brother has
j + b = 25
b = 1 + 2j (brother has one more than twice the amount jack has)
j + 1 + 2j = 25
3j = 24
j = 8
b = 25-8 or 17
How do you graph the polar curve r=5cosθ? Drag an equation, variable, or phrase into each box to correctly complete the statements.
Answer:
See graph below
Step-by-step explanation:
The equation r=5cosθ basically means the graph is going to be a circle with a radius of 5/2=2.5 to the right on the horizontal axis since it's cosine.
To graph the function r=5cosθ, we graph the function f(x) = 4cos(x), such that functional values are used as the corresponding values of θ and a radius of 2.5
How to graph the function?The function is given as:
r=5cosθ
The above means that, we want to graph the function f(x) = 4cos(x), such that functional values are used as the corresponding values of θ.
The radius r is calculated using;
r = 5/2
r = 2.5
Hence, the graph of r=5cosθ has a radius of 2.5
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