It looks like there may be a typo in the function you provided. It appears that you meant to write "f(x) = 80(0.5)^x", which would represent the distance after a pendulum begins swinging, where x is the number of swings.
This function indicates that the distance traveled by the pendulum decreases by half with each swing. For example, after the first swing, the distance traveled would be 80(0.5)^1 = 40 units. After the second swing, the distance traveled would be 80(0.5)^2 = 20 units. And so on.
The exponent x in the function represents the number of swings, so the distance traveled by the pendulum can be calculated by plugging in the desired value of x into the function. For example, to calculate the distance traveled after 10 swings, we can plug in x = 10:
f(10) = 80(0.5)^10 = 0.390625 units
This indicates that the pendulum has traveled a distance of approximately 0.39 units after 10 swings.
does the point (2, 8) satisfy the equation y = 4x?
The point satisfies the equation ! 8 = 4 × (2)
Answer:
Yes
Step-by-step explanation:
If you plug in the numbers to the equation, you should get:
8 = 4(2)
Then,
8 = 8
therefore, (2,8) does satisfy the equation y = 4x.
Sarah competes in a long jump competition.
Her first jump is 4.25m
Her best jump is 12% more than this
However her best jump is 15% lower than the winning jump
Work out the length of the winning jump
Answer: 5.474 m
Step-by-step explanation:
first jump = 4.25
best jump = first jump * 1.12
winning jump = best jump *1.15
Compare the two linear functions listen below
The slopes of function 1 and function 2 are respectively; -4 and 2. Thus, function 1 has a negative slope
How to find the slope of a linear function?The slope is simply defined as the change in the y-values divided by corresponding change in x-values.
1) Now, the formula for the slope between two coordinates is;
Slope = (y₂ - y₁)/(x₂ - x₁)
Let us take two coordinates from the table as;
(0, 50) and (1, 46). Thus;
Slope = (46 - 50)/(1 - 0)
Slope = -4
2) The general equation for equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, we are given the equation as;
c = 2d + 10
Comparing to the standard form, we have;
Slope = 2
Thus, function 1 has a negative slope
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Please help
Initial amount:
Factor:
Equation:
The factoring of the equation is 6x(x + 8). The process of factoring involves determining what to multiply to produce an expression.
How to factor the equation?The process of factoring involves determining what to multiply to produce an expression.
It resembles "dividing" an expression into several smaller expressions.
There are three steps involved in factoring completely:
A GCF should ideally be factored out of the expression.
As much as you can, factor a trinomial.
Put as many factors as you can into a Difference Between Two Squares.
The Grouping method, the difference in two squares, and the sum or difference in cubes are the four primary methods of factoring. The Greatest Common Factor (GCF) is another.
It should be noted that the given expression must be factored based on the provided information.
The expression given is:
6x² + 48x
The common factor is 6x
6x(x + 8)
Therefore, the factoring of the equation is 6x(x + 8).
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How do you translate coordinate points on a graph?
The translation of the coordinate points on the graph by linear displacement in comparison of original points ( x , y ) get translated to ( x + h, y + k ) where h ∈R , k ∈R.
As given in the question,
Let us consider original coordinate point on a given graph be ( x ,y ).
Translation represents the change in the linear displacement or the location without changing the shape and size.
Shift of the point may be horizontally or vertically.
Let 'h' and 'k' be the horizontal and vertical shift.
If the horizontal shift is right then it is represented by x + h
If the horizontal shift is left then it is represented by x - h
If the vertical shift is up then it is represented by y +k
If the vertical shift is down then it is represented by y - k.
Therefore, the translation of the coordinate points on a given graph represented by original points ( x , y ) get translated to ( x + h, y + k ) where h ∈R , k ∈R.
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Which exponential function has an initial value of 2?
Of(x) = 2(3)
Of(x) = 3(2)
X
-2
-1
f(x)
18
1
4
On solving the provided question, we can say that - here in the equation, [tex]x^2- x = 4[/tex]
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
so, x = 2
therefore
[tex]x^2- x \\6-2\\4[/tex]
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Find the domain and range of the function graphed below. PLEASE SHOW YOUR WORK!!
The domain and range of the function on the graph are:
D: [-2, 1)R: [0, 4]How to find the domain and range of the function below?Remember that for any function y = f(x), we define the domain as the set of possible inputs (possible values of x) and the range is the set of the possible outputs of the function (possible values of y).
To find the domain we need to look at the horizontal axis. The minimum is at x = -2 with a colored circle, so x = -2 belongs to the domain.
The largest value is at x = 1, now with an open circle, then this value does not belong to the domain. Thus the domain is:
D: [-2, 1)
For the range we need to look at the vertical axis, the minimum is at zero and the maximum at 4, then the range is:
R: [0, 4]
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Can you make a triangle with 3 different length sides?
Yes, you can make a triangle with three different length sides.
1. Draw three lines of different lengths on a piece of paper.
2. Connect the ends of the lines to form a triangle.
3. The triangle will have three different length sides. The lengths of the sides depend on the lengths of the three lines you drew.
4. To make sure the triangle is valid, use the triangle inequality theorem. This theorem states that the sum of any two sides of a triangle must be greater than the third side.
5. Measure each side of the triangle with a ruler and add them together.
6. Compare the sum of the two sides to the third side. If they are not equal or greater, adjust the lines to create a valid triangle.
7. Once the triangle is valid, it will be a triangle with three different length sides.
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Is the interval 0 to infinity open?
So the only boundary point of [0,∞) and (0,∞) is 0 itself. It is in [0,∞), so that set is closed. It is not in (0,∞), so that set is open.
In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between. Other examples of intervals are the set of numbers such that 0 < x < 1, the set of all real numbers
the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element).
Real intervals play an important role in the theory of integration, because they are the simplest sets whose "length" (or "measure" or "size") is easy to define. The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure.
Intervals are central to interval arithmetic, a general numerical computing technique that automatically provides guaranteed enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff.
So the only boundary point of [0,∞) and (0,∞) is 0 itself. It is in [0,∞), so that set is closed. It is not in (0,∞), so that set is open.
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Please help I have a learning disability
Determine whether the two expressions are equivalent. If so, tell what property is applied. If not, explain why.
72 - (63 - 8) and (72 - 63) - 8
yes, it uses the Identity Property
yes, it uses the Associative Property
yes, it uses the Commutative Property
No they are not equivalent. The first expression equals 17 and the second equals 1.
Answer: yes, it uses the Associative Property
Step-by-step explanation:
Given the picture below, where would point A’ be located after a dilation of 2 centered at point D (red point)
After dilation, the co-ordinate of point A will be (-4,4) while B will be (2,4) and of C will be (-2,0).
After dilation, how do you locate points?The distance between the point of dilation and the point you are dilating must be multiplied by three if the point you are dilating is directly above the point of dilation and you are dilating by 3. You inserted your new point there.
How can a point be widened by two?The x-value of each point will be multiplied by 2 to enlarge the image by a factor of two. The x and y values of each point will be multiplied by 2 to enlarge the figure by a factor of 2.
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Is 5x 3y a linear equation in two variables?
Yes, 5x - 3y = 7 is a linear equation in two variables (x and y)
A linear equation in two variables is an equation in the form ax + by = c, where a, b, and c are real numbers and a and b are not both 0. In this equation, 5x 3y, the coefficients of the variables are 5 and 3, respectively, so a = 5 and b = 3. Therefore, 5x 3y is a linear equation in two variables.
A linear equation in two variables (x and y) is an equation that can be written in the form ax + by = c, where a and b are real numbers and a and b are not both 0. This means that any equation that has two variables with real coefficients will be a linear equation. For example, 5x 3y is a linear equation in two variables because the coefficients of the variables x and y are 5 and 3, respectively. Therefore, 5x 3y is a linear equation in two variables.
the complete question is : Is 5x-3y=7 a linear equation in one variable?
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Jason considered two similar televisions at a local electronics store. The generic version was based on the brand name and was the size of the brand name. If the generic television set is 12 inches by 24 inches, what are the dimensions of the brand name television
The brand-name television's measurements are 32 inches by 64 inches, so answer (C) is accurate.
How to find the television's measurements Calculation?Given: The generic version was created based on the brand name and was three eighths the size of the brand name.
12 inches by 24 inches is the size of the standard television set.
Allowing for x by y as the brand name's measurements
12 inches divided by three eighths
8/3 x = 12
x = 12 * 8 / 3 = 32 inch
and y=3/8 inches equals 24 inches
8/3 y = 24
y = 24 * 8 / 3 = 64 inch
As a result, the brand-name television has the following measurements: 32 by 64 inches.
Therefore, choice (C) is the appropriate response.
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The complete question is: Jason considered two similar televisions at a local electronics store. The generic version was based on the brand name and was the size of the brand name. If the generic television set is 12 inches by 24 inches, what are the dimensions of the brand name television?
a) 7.5 inches by 15 inches
b) 28 inches by 56 inches
c) 32 inches by 64 inches
d) 4.5 inches by 9 inches
(Simplify: 7a + 6 - 3 - 2
Please hurry its timed
The best option regarding the solutions of the trigonometric equation 2sin(θ) + 1 = 0 in this problem is given as follows:
d. θ = 330º + 360ºn, θ = 210 + 360ºn.
How to solve the trigonometric equation?The trigonometric equation for this problem is defined as follows:
2sin(θ) + 1 = 0
Then, isolating the sine, we have that:
2sin(θ) = -1
sin(θ) = -1/2.
The values of theta for which the sine is of negative 1/2 are given as follows:
θ = 210º, θ = 330º.
(as the sine is negative for the third and fourth quadrant, hence we have to find the equivalent angle to 30º in each of these quadrants).
One entire lap over the unit circle is equivalent to 360º, hence adding 360º n times to any of these solutions is also a solution to the trigonometric equation, meaning that option d is correct.
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A cookery course is divided into two groups. In group X, the average score in the test was 76. In group Y, the average score in the test was 70. If the average score of all 30 trainees in the course was 74, how many trainees are in group X
On solving the provided question, we can say that by equation 8 trainees are in group X
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
Let a be the number of trainees in group X
76*a + 70 (30 - a) = 30*74
76a + 2,100 - 70a = 2,220
6a = 120
a = 20
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Which function best represents the sequence 10, 13, 16, 19, 22..., where n is a positive whole number?
a(n) = 7+3n
Ob(n) = 10 + 3n
Oc(n) = 7+3
Od(n) = 10 +3"
Answer:
first function
Step-by-step explanation:
there is a common difference between consecutive terms , that is
13 - 10 = 16 - 13 = 19 - 16 = 22 - 19 = 3
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 10 and d = 3 , then
[tex]a_{n}[/tex] = 10 + 3(n - 1) = 10 + 3n - 3 = 7 + 3n
(b) Felipe is deciding how many people to take to the movies. The table below
shows the cost for different sized groups of people.
Check
Number in group
Cost (in dollars)
2
10
3 9
15 45
The cost for each person is not always the same.
OThe cost for each person appears to be the same.
Predicted number in group for a cost of $50:
Answer:
Step-by-step explanation:
from the form we know, 10/2=15/3=45/9=5.so we need select the second choice, the number of group 50 dollar is 50/5=10
the anwser is second choice, fill 10 in blank.
if u like this, pls 5 stars. tku!
i need help ive been stuck on it for ages
Answer:
Don't join the points with lines
Make the numbers on the vertical axis larger
Label the axes
Step-by-step explanation:
Make all the points different colours → I don't think that would be useful. Unless the teacher asked you to in class, it's probably not a good answer.
Put the title on the bottom → Same. Unless the teacher asked you to in class, it's not really useful and probably not a good answer.
Don't join the points with lines → Teachers ask indeed not to do this, so I think it's a good answer. Most of the time they prefer students to use curves (hope it's the good translation).
Make the numbers on the vertical axis larger → Since both axes represent notes, it would be easier to compare with the same scale. If that's what the teacher meant, then I think it's correct.
Label the axes → This one is interesting, because right now we don't what they represent at all.
Hope it helps, good luck for your exercices :)
pls help with this its due today
Using PEMDAS to solve the algebraic expression, the value is 2
What is Mathematical OperationMathematical operations are operations that involve the manipulation of numbers, variables, and/or equations. Examples of mathematical operations include addition, subtraction, multiplication, division, exponentiation, and root extraction.
In this problem, we can use PEMDAS to solve this algebraic expression.
[(3/5 + 0.425 - 0.005) ÷ 0.1] / [30.5 + 1/6 + 3 (1/3)] + [6(3/4) + 5(1/2)] / 26 ÷ 3(5/7)] - 0.05
This will become;
[10.2 / 34] + [12.25 / 7] - 0.05
Dividing and adding the numbers will give us;
(0.3 + 1.75) - 0.05 = 2
The value is 2
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Find the measurements of the exterior angles of the polygon
Explain (not optional)
On solving the question, sum of exterior angle is 360 degree. Hence, the value of x is 120°.
How do you calculate a triangle's total exterior angles?The exterior angle of a triangle is equal to the sum of its two opposite interior angles, according to the external angle theorem. Remember that the total external angle, measured from each vertex, is always 360°. Alternatively stated, d + e + f = 360°.The angle that is created between a triangle's extended side and one of its sides is known as the external angle. A triangle has a total of 360 degrees in its outside angles.
x + ( x+6) +114 = 360
2x = 240
x = 120
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What is the distance between -6 1/3 and 4 5/12
[tex]10\frac{1}{12}[/tex] is the distance between [tex]-6\frac{1}{3}[/tex] and [tex]4\frac{5}{12}[/tex]
What is Distance?The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
We need to find the distance between [tex]-6\frac{1}{3}[/tex] and [tex]4\frac{5}{12}[/tex]
The given fractions are mixed fractions we have to convert them to improper fractions
[tex]-6\frac{1}{3}[/tex] =-17/3
[tex]4\frac{5}{12}[/tex] =53/12
Now we have to find the difference
53/12-(-17/3)
53/12+17/3
53+68/12
121/12
[tex]10\frac{1}{12}[/tex]
Hence, [tex]10\frac{1}{12}[/tex] is the distance between [tex]-6\frac{1}{3}[/tex] and [tex]4\frac{5}{12}[/tex]
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A developer wants to develop a 18-acre subdivision. He figures that the streets and common area will take up about 20% of this overall area. If the minimum lot size is to be 10,000 SF, how many lots can the developer have on this property
Developer has 627264 square feet land available.
What means lot size?The minimum permissible quantity of an asset that is accepted for purchasing.
How many lots the developer has as per question?
A developer wants to develop 18-acre property = 784080 square feet area
he notices that street and common area will take up about 20% of total area.
hence, the remaining area for developing works = 80%
the amount of land rest for the developer = 784080 ×80 /100
= 627264 square feet.
there is a rule that minimum lot size is to be 10000 square feet for developing works,
the above amount 627264 square feet lot can the developer have on this property that is higher than the minimum lot value.
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MATH HELP CALC
LOOK AT IMAGE
The right Riemann sum for the given function is 2.5.
Firstly, we must find the width of each of the subintervals Δx,
We know n = 4, a = 0, b = 2
∴ Δx = b - a / n
Δx = 2 - 0 / 4
Δx = 1/2
The width of each rectangle is 0.5
Next, we must find the locations of the right endpoints of the rectangles -
x1 = a + Δx(1) = 0.5
x2 = a + Δx(2) = 1
x3 = a + Δx(3) = 1.5
x4 = a + Δx(4) = 2
Now that we have the width of each rectangle, Δx = 0.5, and the right endpoints for the rectangles, x1 = 0.5, x2 = 1, x3 = 1.5, x4 = 2.
we can compute the right Riemann sum.
Computing the sum of the areas of the rectangles:
∑Δx f(x) = ∑ 0.5f(xi)
= 0.5 f(x1) + 0.5 f(x2) + 0.5 f(x3) + 0.5 f(x4)
= 0.5 (0.5) + 0.5 (1) + 0.5 (1.5) + 0.5 (2)
= 2.5
[tex]\int\limits^2_0 {x^{3} } \, dx[/tex] ≈ 2.5
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What are 2 types of domain names?
TLDs are the most common type of domain name and are typically three or more characters after the final dot in a domain name. ccTLDs are two-letter domains that represent a specific country or region.
Domain names are used to identify websites on the internet. There are two main types of domain names: top-level domains (TLDs) and country code top-level domains (ccTLDs).
TLDs are the most common type of domain name and are typically three or more characters after the final dot in a domain name. Examples of TLDs include .com, .org, .net, .edu, and .gov.ccTLDs are two-letter domains that represent a specific country or region. Examples of ccTLDs include .us for the United States, .au for Australia, .ca for Canada, .uk for the United Kingdom, and .fr for France.
When registering a domain name, users should choose a TLD or ccTLD that best suits their needs. For example, if they are targeting a global audience, they should consider a .com TLD. If they wish to target a specific country, they should consider a ccTLD.
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18=0. 125. Which calculation is NOT a way to find 58?
CLEAR CHECK
A. 5÷8
B. 5⋅0. 125
C. 0. 5+0. 125
D. 1−0. 125
The correct option is D. 1 − 0. 125 is NOT the correct way to find the value of fraction 5/8.
Explain the term fraction?a numerical expression in which the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator as well as denominator of a complex fraction. The numerator of a proper fraction is less than every denominator.Consider the given options;
A. 5÷8
5÷8 = 5/8 (correct)
B. 5⋅0. 125
5*0.125 = 0.625
5*0.125 = 5/8 (correct)
C. 0. 5+0. 125
5+0. 125 = 0.625
5+0. 125 = 5/8 (correct)
D. 1−0. 125
1−0. 125 = 0.785
1−0. 125 = 7/8 (not correct)
Thus, option D is not the correct way to solve the equation.
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The correct question is attached.
In 2010, the population of a city was 59,000. From 2010 to 2015, the population grew by 7.3%. From 2015 to 2020, it fell by 5.3%. To the nearest whole number, by what percent did the city grow from 2010 to 2020?
To the nearest percent, the percent by which the population grew from 2010 to 2020 is; 2%
How to find the percentage growth?Percentage increase is defined as the difference between the final value and the initial value, expressed in the form of a percentage.
Now, we are told that;
Initial Population in 2010 = 59000
From 2010 to 2015, the population grew by 7.3%. Thus;
Population in 2015 = 1.073 * 59000 = 63307
Now, we are told that from 2015 to 2020, it fell by 5.3%. Thus;
Population in 2020 = 63307 * (100% - 5.3%)
= 59952
Thus, percentage increase from 2010 to 2020 = (59952 - 59000)/59000) * 100% = 1.61% ≈ 2%
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The quadrilaterals ABCD and JKLM are similar.
Find the length x of JK.
B
K
A
U
S
3. 5
2. 1
3
M
2. 1 L
D
3
c
X
0
X 5 ?
The length x of JK is 3.6 units
Here, quadrilaterals ABCD and JKLM are similar.
We know that the corresponding sides of similar triangles are in proportion.
So, by definition of similar triangles,
AB/JK = BC/KL = CD/LM = AD/JM
To find: the length x of JK
So, consider an equation
AB/JK = AD/JM
Substitute the length of each side in above equation.
4/x = 2/1.8
(4 × 1.8)/x = 2
(4 × 1.8)/2 = x
x = 2 × 1.8
x = 3.6
Therefore, the length of JK = 3.6 units
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How to answer this question
The value of x to the nearest degree will be 112°.
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
There are three angles are shown in figure.
That is,
⇒ 59°, 108°, and 81°.
Now, We know that;
Sum of all four angles is 360°.
So, We can formulate;
⇒ 59° + 108° + 81° + x = 360°
⇒ 248° + x = 360°
⇒ x = 360° - 248°
⇒ x = 112°
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Solve (x – 3)2 = 49. Select the values of x. –46 -4 10 52
Answer: 27.5
Step-by-step explanation:
[tex](x-3)2 = 49\\x-3 = \frac{49}{2} \\x-3 = 24.5\\x = 24.5 + 3\\x = 27.5[/tex]