To graph a sequence, let a term's position number [tex]n[/tex] in the sequence be [tex]x[/tex]value.
What is an arithmetic sequence?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.
Starting with a number and repeatedly adding a fixed constant (d) to it is an easy technique to create a series. An arithmetic sequence is this kind of sequence.
Definition: A sequence of the form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence.
The term [tex]a_{n}[/tex] is the corresponding y value
Plot the ordered pairs
Make a table then plot the ordered pairs ([tex]n, a_{n}[/tex])
Position, [tex]n[/tex] Term, [tex]a_{n}[/tex] ([tex]n, a_{n}[/tex])
1 -15 (1, -15)
2 0 (2, 0)
3 15 (3, 15)
4 30 (4, 30)
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Mr. Bean puts $5000 in a mutual
fund that increases in value by 11% each
year. How many years will it take him to
reach $23,000 in his mutual fund?
Answer:
It's going to take 32.7 years
Is this graph a function or nonfunction
Answer:
Not a function
Step-by-step explanation:
If we use the vertical line test, we can get an answer quite easily. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function.
If we were to move a vertical line across the above graph, it would touch two places, so therefore it is not a function.
Find the value of e4.243 to the nearest ten thousandth.
Answer:
Step-by-step explanation:
4.2430
if m/1 +m/5=234°, find m26=
Answer:
if m/1 +m/5=234°, find m26=
m26 = 234° - (1 + 5)m = 234° - 6m
m26 = 234° - 6(26)
m26 = 234° - 156°
m26 = 78°
Complete the sentences to compare the x- and y-intercepts for each function.
f(x) = -1/2 x + 10
g(x) = -4x - 12
The y-intercept of function fis
The x-intercept of function fis
but the y-intercept of function g is
but the x-intercept of function g is
The y-intercept of function f is 10 The x-intercept of function f is 20 but the y-intercept of function g is -12 but the x-intercept of function g is -3.
What are the x and y-intercepts?The places where a function or equation's graph crosses or "touches" the x-axis of the Cartesian Plane are known as the x-intercepts. This may be compared to a point with a y-value of zero. The locations where a function or equation's graph crosses or "touches" the y-axis of the Cartesian Plane are known as the y-intercepts. This may be compared to a point with a zero x-value.
Given two functions f(x) = -1/2 x + 10 and g(x) = -4x - 12
For function f(x)
Y-intercept of f(x) = -1/2 * 0 + 10 = 10
X-intercept of f(x) => -1/2x + 10 = 0
X-intercept of f(x) => x = 20
For function g(x)
Y-intercept of g(x) = -4*0 - 12 = -12
X-intercept of g(x) => -4x -12 = 0
X-intercept of g(x) => x = -3
Therefore, Function f's y-intercept is 10 Function f's x-intercept is 20, but the function g's y-intercept is -12 and its x-intercept is -3.
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please I need help on some math bro this my test
(x^2+12x-28) / (6x^2 ) ÷ (x-2) / x^2
Show all steps
/ <-- means divided by
Factorization is the reverse process of expansion of mathematical expression to simple terms. The factorized term is: [tex]\frac{x + 14}{6}[/tex]
Factorization is a procedure in which a given number of terms of a mathematical expression is reduced by collecting common terms. It involves reducing a given mathematical expression to a simple form of terms.
Given that:
[tex]\frac{x^{2}+ 12x - 28}{6x^{2} }[/tex] ÷ [tex]\frac{x - 2 }{x^{2} }[/tex]
[tex]\frac{x^{2}+ 12x - 28}{6x^{2} }[/tex] x [tex]\frac{x^{2} }{x -2}[/tex]
[tex]\frac{x^{2} + 12x - 28}{6(x - 2)}[/tex]
Factorizing the numerator, we have;
[tex]x^{2} + 12x - 28[/tex] = (x - 2) (x + 14)
So that,
[tex]\frac{(x- 2) (x + 14)}{6(x - 2)}[/tex]
[tex]\frac{(x + 14)}{6}[/tex]
Thus the factorized form of the given question is [tex]\frac{1}{6}[/tex](x - 14).
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1/3(6z + 7.2) = 0.5 (8z + 2) - 0.4
Answer:
z = 0.9
Step-by-step explanation:
1/3(6z + 7.2) = 0.5 (8z + 2) - 0.4
Step 1) (2z +2.4)=(4z+1) - 0.4
Step 2) (2z +2.4)=(4z+0.6)
Step 3) 1.8 = 2z
Step 4) 1.8/2 = z
Step 5) 0.9 = z
Answer:
.9
Step-by-step explanation:
it is 0.9 i did this assignment with my teacher
The second side of a triangular deck is 5 feet longer than the shortest side, and the third side is 5 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 56 feet, what are the lengths of the three sides?
The lengths of the three sides are 14 feet, 19 feet and 23 feet respectively.
How to determine the length of the sidesThe formula for determining the perimeter of a triangle is expressed as;
Perimeter = a + b + c
Where; a, b and c are the length of the sides
From the information given, we have that;
y = 5 + zx = 2z - 5Perimeter = 5656 = 2z- 5 + 5 + z + z
collect like terms
56 = 4z
Make 'z' the subject of formula
z = 56/4
z = 14
Shortest side, z = 14 feet
Second side, y = 5 + z = 19 feet
Third side, x = 2z - 5 = 2(14) - 5 = 23 feet
Hence, the values are 14 feet, 19 feet and 23 feet respectively.
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the researcher does not need to report the dates when the survey was done because it is not relevant to the results. group of answer choices true false
The dates the survey was conducted are not crucial to the findings, so the researcher is not required to report them. It is "false" to say that.
Explain the importance of data in survey?This information is thorough data that was acquired from the a target audience regarding a particular subject to perform research.
The methods for gathering survey data and doing statistical analysis are numerous. The required sample of people's input and opinions are gathered through a variety of media.With key stakeholders, particularly customers and staff, surveys are a useful data collecting and analysis technique that are frequently used to identify requirements or gauge satisfaction.Data are essential for characterizing, calibrating, confirming, validating, and evaluating models that forecast the long-term structural performance and effectiveness of materials in harsh settings. Many models would be useless without sufficient data to validate and evaluate them.Thus, it is "false" to say that the dates the survey was conducted are not crucial to the findings, so the researcher is not required to report them.
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HELPPPPPPPZZZZ!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
x = 36
Step-by-step explanation:
First find the difference of size for the two givens sides on figure A and figure B. On figure A we have the given side 45, and Figure B the given size 27. Subtract the two to get 18. So the difference of scale is 18 for the two figures. So in order to find x just add the 18 to the 18 in figure B, and you get 36.
Please Help!!!! I will Brainlist!!! The question is in the picture!
Answer:
H=5
Step-by-step explanation:
25=1/2h(2+8)
25=1/2h(10)
25=10*h/2
what is dividend by 2 equals 25?
50
what times 10 equals 50?
5
HELP MEE!!! 25 points!!
Solve. What is x in the inequality? x– (–11) ≤ 1
Answer:
x≤−10
Step-by-step explanation:
x−(−11)≤1
Step 1: Simplify both sides of the inequality.
x+11≤1
Step 2: Subtract 11 from both sides.
x+11−11≤1−11
x≤−10
pleaseee need brainliest
I need help please I dont get this .
Answer:
Below
Step-by-step explanation:
The line has negative slope and y-axis intercept = 2 from inspection
two points on the line are needed to calculate the slope
find two easy to work-with points
like (-3,4) and (4,-1)
slope = (y1-y2) / ( x1-x2) = (4 - -1) / ( -3-4) = -5/7
Slope intercept form y = mx +b m is slope b is intercept of y-axis
soooo ... y = -5/7 x + 2
The graph is rather fuzzy:
I looked a little longer and decided points (-4,5) and (4,-1) may be more accurate:
slope = 5--1 / -4-4 =- 6/8 so then the answer would be y = -3/4x + 2
Please, help me solve.
Answer:
The answer is 81.85%
Step-by-step explanation:
Given;μ = 116σ = 14The z score is used to determine by how many standard deviations the raw score is above or below the mean.
The z score is given by:
z = x - μ/σ
where,
x = raw scoreμ = meanσ = standard deviationFor x = 88
z = 88 - 116/14
z = (-2)
For x = 130
z = 130 - 116/14
z = (1)
Thus,
P(88 < x < 130) = P(-2 < z < 1)
= P(z < 1) - P(z < -2)
= 0.8413 - 0.0228 = 81.85%
Thus, 81.85% of the population would be between 88 and 130.
Write a quadratic equation for the graph below:
The equation of the parabola would be [tex]y = \frac{1}{4}(x + 1)^2 - 4[/tex].
What is a parabola?
A parabola is a curve that is shaped like a U or a mirror image of a U. It is a type of conic section, which is a curve that is formed by the intersection of a plane and a cone.
The equation of a parabola can be written in the form y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola and a is a coefficient that determines the shape of the curve.
To find the equation of the parabola described in the problem, we can first find the values of h and k and then substitute them into the equation.
We know that the vertex of the parabola is (-1, -4). Therefore, h = -1 and k = -4.
Substituting these values into the equation y = a(x - h)^2 + k, we get:
y = a(x - (-1))^2 + (-4)
= a(x + 1)^2 - 4
Now we can use the fact that the parabola passes through the points (-5, 0) and (3, 0) to find the value of a.
Substituting x = -5 into the equation, we get:
y = a((-5) + 1)^2 - 4
= a(4)^2 - 4
= 16a - 4
Since the point (-5, 0) lies on the parabola, y must equal 0 when x = -5. Therefore, we have the equation 16a - 4 = 0. Solving for a, we find that a = 1/4.
Substituting this value back into the equation for y, we get:
[tex]y = \frac{1}{4}(x + 1)^2 - 4[/tex]
Hence, the equation of the parabola would be [tex]y = \frac{1}{4}(x + 1)^2 - 4[/tex].
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The equation of the parabola would be [tex]y=\frac{1}{4}(x+1)^2-4[/tex].
What is a parabola?
A parabola is a curve that is shaped like a U or a mirror image of a U. It is a type of conic section, which is a curve that is formed by the intersection of a plane and a cone.
The equation of a parabola can be written in the form y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola and a is a coefficient that determines the shape of the curve.
To find the equation of the parabola described in the problem, we can first find the values of h and k and then substitute them into the equation.
We know that the vertex of the parabola is (-1, -4). Therefore, h = -1 and k = -4.
Substituting these values into the equation y = a(x - h)^2 + k, we get:
y = a(x - (-1))^2 + (-4)
= a(x + 1)^2 - 4
Now we can use the fact that the parabola passes through the points (-5, 0) and (3, 0) to find the value of a.
Substituting x = -5 into the equation, we get:
y = a((-5) + 1)^2 - 4
= a(4)^2 - 4
= 16a - 4
Since the point (-5, 0) lies on the parabola, y must equal 0 when x = -5. Therefore, we have the equation 16a - 4 = 0. Solving for a, we find that a = 1/4.
Substituting this value back into the equation for y, we get:
[tex]y=\frac{1}{4}(x+1)^2-4[/tex].
Hence, the equation of the parabola would be [tex]y=\frac{1}{4}(x+1)^2-4[/tex].
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!What is the range of temperatures in the data STEM AND LEAF!
To win the game, the team must score at least 8 goals. What inequality represents the number of goals, g, the team must score? Drag and drop the appropriate symbol to complete the inequality. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. g 8
The inequality represent the number of goals the team must score g ≥ 8.
What is inequality?An inequality show the relationship between two values in an algebraic equations that are probably not equal.
The statement about a game in which various teams are the playing:
It is given that To win that game, the team must scores at least 8 goals.
The meaning of word at least is that , the team can score either 8 goals or more than the 8 goals.
So, we will write this situation in terms of the inequality as follows:
The value of g will be greater than or equal to 8.
= g ≥ 8.
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State the theorem that proves the triangles are congruent. Then write a congruence statement.
These two triangles are congruent by angle angle side(AAS) congruency theorem.
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
From the given figure line segment AB is similar to line segment CD.
Angle E is congruent to angle D hence line segment AB is congruent to line segment BC.
So, These two triangles are congruent by angle angle side congruency theorem.
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Manuel is riding his bike. The graph represents the distance Manuel travels from his house over time.
Describe what is happening as depicted in the graph.
Observing the nature of the graph and the pattern it develops relating time and distance covered by Manuel, The graph explains the nature of distance covered in bike with respect to time.
What is a graph?A representation of the relationship between two variables, often measured along one of two right-angled axes each.
What are different types of graphs?Different types of graphs are:
Statistical Graphs.Exponential Graphs.Logarithmic Graphs.Trigonometric Graphs.Frequency Distribution Graph.Manuel drives away from house for 2 units of time and stayed at a place for another 2 units of time. He start to bike towards the house for 2 units of time and again started to travel away for a single unit of time. He stayed at a place for 2 unit of time and bike back to the house in 5 units of time.
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Help solve number 16 of a proof please
1. Given
2. Alternate interior angles theorem
3. Given
4. Vertical angles
5. ASA
75 divided by 18 what do it equal
Could you guys also show how you got it? Thanks!
After solving the linear equation in two variables we get the value of x=13 and y =-24/5
What is linear equation in two variable?
If an equation is written in the form axe + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables.
Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.
Such an equation has a pair of numbers as its solution, one for x and one for y, which further equalizes the two sides of the equation.
A system of linear equations in two variables can be solved using one of five techniques. These techniques are described below:
Method of GraphicalMethod of Cross Multiplication, Cross Multiplication MethodElimination MethodDeterminant Method2x+5y=2 multiply this equation by 2
we get,
4x+10y=4
And the other equation is :-
5x+10y=17
Subtracting both the equation we get :-
4x+10y=4
5x+10y=17
- - -
________
-x =-13
x=13
y=2-26/5
y=-4.8 or -24/5
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Find the Surface area of the composite figure.
The surface area of the composite figure is 1856.53cm²(nearest hundredth)
What is a composite shape?A composite shape can be defines as a shape created with two or more basic shapes. We often refer to composite shapes as compound and complex shapes.
The figure has two shapes; a cylinder and an hemisphere.
Therefore the total surface area of the composite figure = surface area of cylinder + surface area of hemisphere.
The surface area of cylinder= 2πr(r+h)
= 2× 3.14 × 5.5( 5.5+40)= 1571.57cm²
The surface area of hemisphere= 3πr²
= 3×3.14×5.5²
= 284.96cm²
Therefore the surface area of the composite figure is 1571.57cm² + 284.96cm²= 1856.53cm²(nearest hundredth)
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D
Question 6
Is this a function? Explain, why or why not!
Edit View Insert Format Tools Table
12pt
Paragraph | BI U Av v ²0.
B
>
>
100 pts
By using the concept of function, it can be seen that the given graph represents a function.
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here the values on the x axis represents the domain and the values on the y axis represents the Range.
From the graph it can be seen that
Every point of the domain maps to unique point on the range.
So this is a function
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xochitl has $2 worth of nickels and dimes. she has a total of 24 nickels and dimes altogether. graphically solve a system of equation in order to determine the number of nickels, x. and the number of dimes, y, that xochitl has
By using simultaneous linear equation, it can be calculated that
Xochitl has 8 nickels and 16 dimes
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Let the number of nickel Xochitl has be x and the number of dimes Xochitl has be y
She has a total of 24 nickels and dimes altogether
x + y = 24 .... (1)
Xochitl has $2 worth of nickels and dimes
0.05x + 0.1y = 2
5x + 10y = 200
x + 2y = 40 ..... (2)
From the graph, it is clear that the two simultaneous linear equation intersects at (8, 16)
So x = 8, y = 16
Xochitl has 8 nickels and 16 dimes
The graph has been attached
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thankss. STEP BY STEP??
Answer:
4
Step-by-step explanation:
Constant of proportionality is the same as slope in the context of a linear function, which is defined as Δy / Δx. We can find this by taking two points and finding the difference in their x- and y-coordinates.
I'll use (1, 4) and (2, 8).
[tex]\textrm{slope}=\dfrac{8-4}{2-1} = \dfrac{4}{1} = 4[/tex]
Express the given statement in the form of expression.
5 less than three times a number x .
The expression to represent the above statement is
The statement 5 less than three times a number x is expressed as an expression to 3x - 5
What is an algebraic expression?An algebraic expression can be described as an expression made up of coefficients, terms, factors, variables and constants.These expressions are also composed of some mathematical and arithmetic operations.
They include;
Addition
Division
Multiplication
Subtraction
Parentheses
Bracket, etc
From the information given, we have that; The number is x. The number is 5 times lesser than three times the value of xThis can be represented as; 3x - 5
Hence, the expression represented is 3x - 5
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The tail of a 1-mile long train exits a tunnel exactly 3 minutes after the front of the train entered the tunnel. If the train is moving 60 miles per hour, how long is the tunnel? Hint : How far does the front of the train move in 3 minutes?
Answer:
The tail of a 1-mile long train exits a tunnel exactly 3 minutes after the front of the train entered the tunnel. If the train is moving 60 miles per hour, how long is the tunnel? Hint : How far does the front of the train move in 3 minutes?
Explanation
The front of the train moves 3 miles in 3 minutes. Therefore, the tunnel must be 1 mile long.
Answer:
2 miles long
Step-by-step :
The tail of the train starts one mile from the mouth of the tunnel and it must travel that distance plus the length of the tunnel in 3 minutes.
Let t = tunnel length
t + 1 = distance the tail must travel in 3 minutes.
3 minutes = 1/20 hr
(t+1) miles / 60 m/hr = 1/20 hr
t + 1 = 60/20
t+1 = 3
Subtract 1 from each side:
t = 2
The tunnel is 2 miles long.
help me please points
The value of x in the linear inequality 5/8x - 1 ≥ 9 is x ≥ 16
Linear InequalityLinear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. These values could be numerical or algebraic or a combination of both.
An inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠).
In the problem given;
5/8x - 1 ≥ 9
Solving for x in the inequality;
x ≥ 16 which can be represented using an interval notation as [16, ∞)
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