The equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5².
Based on the calculations, the equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5²
The equation of a circle.
Mathematically, the standard form of the equation of a circle is given by;
(x - h)² + (y - k)² = r²
Where:
h and k represent the coordinates at the center.
r is the radius of a circle.
The midpoint of the given points represents the center of this circle:
h = (4 + 4)/2 = 4
k = (5.5 + 10.5)/2 = 8
Next, we would determine the radius by using the distance formula for coordinates:
r = √[(x₂ - x₁)² + (y₂ - y₁)²]
r = √[(4 - 4)² + (10.5 - 5.5)²]
r = √[0² + 5²]
r = √25
r = 5 units.
Therefore, the equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5².
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Identify the domain of the function shown in the graph
Answer:
C. All real numbers.
Step-by-step explanation:
The domain is the set of all x values that are used by points on the graph. This is a sine wave, and we assume it extends infinitely far to the left and right. Even without that assumption, you can eliminate the other answers.
A. This describes the numbers on the x-axis between 0 and 5, inclusive. But the graph includes many more points with x-coordinates beyond that interval.
B. The same sort of thing: the graph extends well beyond the interval of x values between -5 and 5, inclusive.
D. This would mean the graph has only points with positive x-coordinates, but there are many with negative (or 0) x-coordinates.
help me please omg im in a rush
Answer:48
Step-by-step explanation:
PQ has endpoints P(0, 0) and Q(8, 4). Find the coordinates of the midpoint of PQ
O
O
O
(4,4)
(2,4)
(4,2)
if you were to solve the following system by substitution, what would be the best variable to solve for and what from what equation 3x 6y
so here you the answer is 9
If x = false and y = false, is the statement: not x or not y
a) true
b) false
Answer:
false
Step-by-step explanation:
X is equal to Y
therefore,
X = Y
X= false
Y = false
so,
false = false
Someone do this please
Answer: 102 degrees
Step-by-step explanation:
The remote angle theorem is that two remote angles are equivalent to the exterior angle. Both 51 degrees are remote angles, and angle 4 is the exterior.
51 + 51 = Angle 4
Angle 4 = 102 degrees
Answer fast in steps
Use the drawing tool(s) to form the correct answer on the provided number line. Consider the given functions. Function 1 Function 2 Graph shows a polynomial function plotted on a coordinate plane with vertical axis g of x. A curve enters quadrant 3 at (minus 5, minus 40), goes through (minus 4, 0), (minus 2, 32), (0, 15), (2, 0), and exits quadrant 1 at (4, 30). Represent the interval where both functions are decreasing on the number line provided.
Both functions decrease at (-1, 2)
How to determine the decreasing intervals of the function?The complete question is added as an attachment
The polynomial function f(x) is represented by the graph.
From the graph, the polynomial function decreases at (-2, 2)
The absolute function is given as;
f(x) = =5|x + 1| + 10
The vertex of the above function is
Vertex = (-1, 10)
Because a is negative (a= -5), the vertex is a maximum.
This means that the function decreases at (-1, ∞)
So, we have
(-2, 2) and (-1, ∞)
Combine both intervals
(-1, 2)
This means that both functions decrease at (-1, 2)
See attachment 2 for the number line that represents the interval where both functions are decreasing
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Suppose the number of residents within five miles of each of your stores is asymmetrically distributed with a mean of 19 thousand and a standard deviation of 7.6 thousand. What is the 95th percentile for the average number of residents within five miles of each store in a sample of 75 stores
The 95th percentile for the average number of residents within five miles of each store is 20219.86.
Given mean of 19000 , sample size of 75 stores and standard deviation of 7600.
We have to find the 95th percentile for the average number of residents within five miles of each store in a sample of 75 stores.
We have to first find the margin of error to calculate the upper level of confidence interval.
Margin of error is the difference between the real values and calculated values.
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where z is the critical value of z at given confidence level.
σ is standard deviation
n is the sample size.
z value at 95% confidence level is 1.39. (one tailed)
Put the values in the formula to get margin of error.
Margin of error=1.39*7600/[tex]\sqrt{75}[/tex]
=10564/8.66
=1219.86
Upper level=19000+1219.86
=20219.86
Hence the 95th percentile is 20219.86 for the average number of residents within five miles of each store in a sample of 75 stores.
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(08.01)Angela wants to know how many families in her neighborhood plan to attend the parade. She puts all 120 of the neighborhood addresses in a hat and draws a random sample of 30 addresses. She then asks those families if they plan to attend the parade. She finds that 40% of the families plan to attend the parade. She claims that 40% of the neighborhood families would be expected to attend the parade. Is this a valid inference?
A) Yes, this is a valid inference because the 30 families speak for the whole neighborhood
B)Yes, this is a valid inference because she took a random sample of the neighborhood
C)No, this is not a valid inference because she did not take a random sample of the neighborhood
D) No, this is not a valid inference because she asked only 30 families
Using sampling concepts, the correct option regarding the validity of the inference is given as follows:
B) Yes, this is a valid inference because she took a random sample of the neighborhood.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
For example:
I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So I ask, lets say, 1000 randomly selected New York state residents whether they are Buffalo Bills fans, and expand this to the entire population of New York State residents. If I had taken 1000 residents just from Buffalo, it would not be a representative sample.
In this problem, all addresses in the neighborhood are considered, hence a random sample was taken and the correct option is given as follows:
B) Yes, this is a valid inference because she took a random sample of the neighborhood.
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Please help! I'm giving 25 points!!
The volume of the oceans on Earth is approximately 1,386 million km^3. As the Earth's temperature rises, the ice in the polar icecaps melts into the oceans, increasing the volume of the oceans. If 1 cm^3 of ice melts, it turns into approximately 0.92 cm^3 water.
1) There are approximately 3,800 cm^3 in a gallon. If 1.9 m^3 of ice melts, how many gallons of water does this produce? (Round your answer to the nearest gallon.)
2) Scientists estimated that the addition of 1,000 km^3 of water would increase sea levels by 364 cm. Greenland's ice sheet is especially vulnerable to melting. Recent reports indicate a melting average of 195 km^3 of ice per year from Greenland, resulting in additional yearly 179.4 km^3 of water. If melting continues at this rate, how many centimeters would the sea increase after 6 years? (Round your answer to the nearest centimeter.)
1. The number of gallons of water produced is 460 gallons
2. The amount in cm the sea would increase after 6 years is 392 cm
1. How to determine the number of gallons producedWe'll begin by by converting 1.9 m³ to cm³. This is illustrated below:
1 m³ = 1×10⁶ cm³
Therefore,
1.9 m³ = 1.9×10⁶ cm³
Next, we shall determine the volume of water produced from 1.9 m³ (i.e 1.9×10⁶ cm³) of ice. This is illustrated below:
From the question given,
1 cm³ of ice = 0.92 cm³ of water
Therefore,
1.9×10⁶ cm³ of ice = 1.9×10⁶ × 0.92
1.9×10⁶ cm³ of ice = 1.748×10⁶ cm³ of water
Finally, we shall determine the number of gallons produced. This is illustrated below:
From the question given,
3800 cm³ of water = 1 gallon
Therefore,
1.748×10⁶ cm³ of water = 1.748×10⁶ / 3800
1.748×10⁶ cm³ of water = 460 gallon
Thus, 460 gallons were produced
2. How to determine the amount in cm the sea would increase to after 6 yearsFrom the question given above,
1000 Km³ = 364 cm
Therefore,
179.4 Km³ = (179.4 × 364) / 1000
179.4 Km³ = 65.3016 cm per year
To obtain the increase after 6 years, multiply 65.3016 by 6 as shown below:
65.3016 × 6 = 392 cm
Thus, the sea will increase 392 cm after 6 years
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When the mean and standard deviation of the process are operating such that the upper and lower control limits are acceptable relative to the upper and lower specification limits, we say the process is
The process is Capable.
According to statement
When the mean and standard deviation of the process are operating such that the upper and lower control limits are acceptable relative to the upper and lower specification limits
and when these conditions are fulfilled then the process is to be called CAPABLE.
So, The process is Capable.
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In your own words, explain the concept of a variable. Discuss how you can teach a class about the use of variables and how they can be used to create an algebraic expression.
VARIABLE is a symbol which is used for representation in a math.
According to the statement
we have to explain about the what is a variable.
So, VARIABLE is a symbol which is used for representation in a math.
It represent the so many things like Algebra, Matrix,Vector etc. and also so many things.
A variable may also be called a data item.
It is used to represent a data like country name, name, age, date of birth etc.
we know that the every thing is changeable. So, like ther things variables are also changeable.
The changing of variable parameters is called as variation. In problems relating to two or more variables, it is seen that the value of a variable changes with the change in the value.
So, VARIABLE is a symbol which is used for representation in a math.
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How many terms are in the sequence shown?
38, 36, 34, ..., -20
Answer:
30 terms
Step-by-step explanation:
In the sequence, the value of each term decreases by 2.
38, 36, 34, 32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10, -12, -14, -16, -18, -20.
1+ (38 - (-20))/2 = 1+ 29 = 30
Denise wants to enlarge her prom photo. She wants to increase the
size 4 times the original photo. If the original photo is 6 inches by 8 inches,
how many times larger is the new photo?
4
40
16
8
After enlargement, the new photo would be 16 times larger. The answer is C: 16.
What is an Enlargement?An enlargement can be described as a type of dilation in transformation which involves increasing the dimensions of an original image by a given scale factor, so that the new image is similar to the original image. Their sizes would be different while their shapes remain the same. Also, the ratio of their corresponding dimensions would be the same.
Given the following:
Dimension of original photo = 6 inches by 8 inches
Scale factor = 4
To find the new dimensions of the new photo, multiply the corresponding dimensions of the original photo by 4, thus:
6 × 4 = 24 inches
8 × 4 = 32 inches
New dimensions = 24 by 32
Area of original photo = 6 × 8 = 48 in.²
Area of new photo = 24 × 32 = 768 in.²
768/48 = 16
This means that the new photo is 16 times larger than the original photo.
The answer is: C. 16.
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Which answer represents the following conditional statement in shorthand?
if megan is swimming, then it is warm outside.
The expression which represents the given conditional statement in shorthand is: S → W.
What is a conditional statement?A conditional statement can be defined as a statement that can be written to contain both a hypothesis and conclusion. Thus, it typically has the form "if P then Q."
Where:
P and Q represent sentences.
If Megan is swimming = S
It is warm outside = W
Therefore, if Megan is swimming, then it is warm outside is represented by S → W.
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PLEASE ANSWER WILL GIVE YOU ALOT OF POINTS
The theorems that prove that lines are parallel includes:
Alternate interior angle theorem.Converse of corresponding angles postulate.How to prove lines are parallel?Parallel lines are the lines that do not intersect or meet each other at any point in a plane.
Theorems that prove that lines are parallel includes:
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a 90% confidence interval for a proportion is found to be (0.22,0.28). What is the sample proportion
The value of sample proportion is found to be 0.253.
What is the sample proportion?The sample proportion [tex]\hat{p}[/tex] indicates the percentage of people in a sample who exhibit a particular quality or attribute.
Divide the number of individuals (or items) who possess the desired attribute by the overall sample size to obtain the sample proportion.
Now, according to the question;
The 90% confidence interval for a proportion is found to be (0.22,0.28).
The confidence interval for the sample is given as-
Confidence interval = Sample proportion ± Margin of Error
Let [tex]\hat{p}[/tex] be the sample proportion.
The level of significance = 1 - 0.90
= 0.10 (10%)
From z-value table, at a significance level of 5% (two-sided), z has a critical value of 1.645.
90% confidence interval = [tex]\hat{p} \pm 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]
Thus, 0.22 = [tex]\hat{p} - 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex], and
0.28 = [tex]\hat{p} + 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]
Covert both equation in the form of [tex]\hat{p}[/tex] and equating to each other.
[tex]\begin{aligned}&0.22+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\&1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-0.22\\&2 \times 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.06\\&\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=\frac{0.06}{2 \times 1.645}\\&\sqrt{\frac{\hat{\nu}(1-\hat{p})}{n}}=0.02\end{aligned}[/tex]
Take square root,
[tex]\begin{gathered}\frac{\hat{p}(1-\bar{p})}{n}=0.0004 \\n=\frac{\hat{p}(1-\bar{p})}{0.0004}\end{gathered}[/tex]
Substituting the value of 'n' in the receptive equation to get the value of [tex]\begin{aligned}0.22 &=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\0.22 &=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{p(1-\hat{p})}} \times 0.0004 \\0.22 &=\hat{p}-1.645 \times \sqrt{0.0004} \\0.22 &=\hat{p}-(1.645 \times 0.02) \\0.22 &=\hat{p}-0.033 \\\hat{p}=& 0.22+0.033=0.253\\\end{aligned}[/tex]
Therefore, the value of sample proportion is 0.253.
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What addition/subtraction equation should I put?
Answer:
7 - 10
Step-by-step explanation:
Because it is -3 and 7 - 10 = -3
What is the range of the function graphed below?
y
-8 -6
B.
C.
+
O D.
-2
8
6+
4+
2+
-2-
-4-
-6+
OA -∞0 < y < 2
-∞ < y < ∞
-2 < y < ∞
-∞0 < y < -2
-8-
N
10
--00
Y
+x
Answer:
D
Step-by-step explanation:
Range is the 'y' values a graph can have
you can see that the 'y' values can be anythig from - inf to + 2
The range of the function is [2, -∞].
What is a function?A function has an input and an output.
A function can be one-to-one or onto-one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
From the graph,
We see that the function line y values are from 2 to negative infinity.
This means,
The range is [2, -∞].
Thus,
The range of the function is [2, -∞].
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Simplify :-
(3x-2y) (3x+2y) (9x²+4y²)
Answer:
[tex]\huge\boxed{\sf 81x^4 - 16y^4}[/tex]
Step-by-step explanation:
Given expression:= (3x - 2y)(3x + 2y)(9x² + 4y²)
Using formula:[tex](a+b)(a-b)=a^2-b^2[/tex]= [(3x)² - (2y)²] (9x² + 4y²)
= (9x² - 4y²)(9x² + 4y²)
Using the above formula again
= (9x²)² - (4y²)²
= 81x⁴ - 16y⁴[tex]\rule[225]{225}{2}[/tex]
Javid travels to work by bus or by train.
The daily bus fare is £2.50
The daily train fare is £3.50
In 5 days he spends a total of £14.50
On how many days did he travel by bus?
Javid travelled by bus for 3 days using a simultaneous equation
What is simultaneous equation?
This refers to equations that are solved together in order to determine the values of unknown variables.
In this case, the total amount spent on daily bus or train can be determined as the fare price multiplied by the number of days
Let X be the number of days that Javid took bus
total spent on bus=2.50X
Let Y be the number of days that Javid took train
total spent on train=3.50Y
Total spent=2.50X+3.50Y
14.50=2.50X+3.50Y
Secondly, X plus Y gives 5 days
5=X+Y
multiply the second equation by 2.50 and the first by 1
14.50=2.50X+3.50Y
12.50=2.50X+2.50Y
subtract the second equation from first
2=Y
substitute for Y
5=X+Y
5=X+2
X=5-2
X=3
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The number of days that he travelled by bus is; 3 days
How to Solve Simultaneous Equations?Let x be the number of days that Javid travelled by bus.
Let y be the number of days that Javid travelled by train.
Thus;
Total spent on bus = 2.50x
Total spent on train = 3.50y
Overall total spent is;
2.5x + 3.5y = 14.50 -----(1)
Total number of days is 5 days and so;
x + y = 5 -----(2)
Making x the subject in eq 2 gives us;
x = 5 - y -----(3)
Put eq 3 in eq 1 to get;
2.5(5 - y) + 3.5y = 14.50
12.5 - 2.5y + 3.5y = 14.5
y = 14.5 - 12.5
y = 2 days
Thus;
x = 5 - 2
x = 3 days
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Centipedes differ from millipedes in that centipedes are cylindrical, have poison claws and 2 pairs of appendages per body segment
Centipedes differ from millipedes in that centipedes are cylindrical, have poison claws, and 2 pairs of appendages per body segment: FALSE
What are Centipedes?Their bodies have an elongated, cylindrical form that can appear flat at times. Adults can range in size from half an inch to 6.5 inches. Despite its "thousand-legger" moniker, most have less than 100 legs. Despite having so many legs, these arthropods move slowly.Most centipedes can only bite with their poison claws just under the head, causing a bee-like sting; however, Scolopendra can harm a person with the sharp claws of its many walking legs.Centipedes have only one pair of legs on each body segment, which can be seen protruding from their flattened bodies. The number of body segments varies by species, and the number of pairs of legs ranges from 15 to 177, plus or minus one.As it is given in the description, centipedes have only one pair of legs on each body segment. So, the whole statement becomes False.
Therefore, the statement "centipedes differ from millipedes in that centipedes are cylindrical, have poison claws, and 2 pairs of appendages per body segment" is FALSE.
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Complete question:
Centipedes differ from millipedes in that centipedes are cylindrical, have poison claws, and 2 pairs of appendages per body segment. TRUE or FALSE
can someone please help mee
Answer:
[tex]\frac{\sqrt{731}}{30}[/tex]
Step-by-step explanation:
We first observe that the angle is located in quadrant III
This allows us to draw a triangle as attached in the attachments.
Using this triangle, we can find sin([tex]\theta_1[/tex]).
Remembering that sin(theta) = [tex]\frac{opp}{hypo}[/tex], we can see from the attached image that it is [tex]\frac{\sqrt{30^2 - 13^2}}{30}[/tex], then simplifying [tex]\sqrt{30^2 - 13^2}[/tex] using a calculator, we get [tex]\sqrt{731}[/tex].
So our final answer is the answer shown above.
You may be wondering how did the side lengths appear on the triangle.
From cos(theta_1), we remember that cos(theta) = adj/hypo, so, we can draw our triangle using that the adjacent of the theta = -13 (another reason why is because the angle is in quadrant three), and hypo is 30.
A group of restaurant owners surveyed a list of people to determine how preferences of meats compared to preferences of grains, and if they are related. The results are in the table above. Based on the table, is there evidence of association between chicken preferences and rice preferences
There is no association between the chicken preferences and rice preferences. Option C
What is association?There is an association between two variables when they both decrease or increase simultaneously. In many cases, the association between the variables can be shown using the correlation coefficient when the relationship is plotted on Cartesian coordinates.
If we look at the table, we can see that there is no association between the chicken preferences and rice preferences because because the proportion of chicken and rice eaters to all chicken eaters is lower than all rice eaters to all eaters; and because the proportion of chicken and rice eaters to all rice eaters is lower than all chicken eaters to all eaters.
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The vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4). The vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4). Which conclusion is true about the quadrilaterals? (5 points)
The measure of their corresponding angles is equal.
The ratio of their corresponding angles is 1:2.
The ratio of their corresponding sides is 1:2
The size of the quadrilaterals is different but shape is same.
The measure of their corresponding angles is equal the vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4) and the vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4). This can be obtained by plotting the quadrilaterals on a graph paper and comparing the figures.
Which conclusion is true about the quadrilaterals?Given that,
vertices of quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4)
vertices of quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4)
(x,y) ; (x, y-8)
ABCD is reflected across the line y=4 to get the quadrilateral EFCD.
Reflection means the size and shape of the quadrilaterals is same ⇒quadrilateral ABCD and quadrilateral EFCD are congruent.
Thus corresponding parts of congruent triangles are equal, corresponding angles will be equal.
Hence the measure of their corresponding angles is equal the vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4) and the vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4).
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Question 1
Which equation represents the relationship shown in the table
at the right?
Answer:
Option (4)
Step-by-step explanation:
When x = 0, y = -3.
Eliminate Option 1.Also, the slope is
[tex]\frac{-1-(-3)}{1-0}=2[/tex]
So, the equation is y = 2x - 3.
v²=u²+2as. If u = 12, a = -3 and s=18, Find v
Answer:
v=6
Step-by-step explanation:
v²=u²+2as
v²=12²+2(-3)(18)
v²=144-108
v²=30
v=6
A function is a relation where each input value is assigned to (1) ___ one output value.the (2) ___ of a function is the set of all input values, or x-values, for which the function is defined. the (3) ___ of a function is the set of all output values, or y-values, for which the function is defined. to write the equation y = ax + b in function notation, substitute (4) ___ for y. options for 1: a. exactly b. at least c. less than options for 2: a. range b. interval c. domain d. rate of change options for 3: a. range b. rate of change c. interval d. domain options for 4: a. f(x) b. a c. b d. x
The blanks can be filed by exactly, domain, range, and, f(x) respectively.
While we've got a feature in formulation form, it also includes a simple count to assess the function. For example, the feature f(x)=5−3x2 f ( x ) = 5 − 3 x 2 can be evaluated with the aid of squaring the enter cost, multiplying by means of three, and then subtracting the product from 5.
You write capabilities with the function name observed by way of the established variable, together with f(x), g(x), or maybe h(t) if the function depends upon time. You read the function f(x) as "f of x" and h(t) as "h of t". functions no longer need to be linear. The feature g(x) = -x^2 -3x + 5 is a nonlinear characteristic.
A user is an actual-valued feature on a vector area, usually of functions. as an example, the electricity practical at the unit disk assigns various to any differentiable feature, For the practical to be non-stop, it's miles necessary for the vector space. of capabilities to have the perfect topology.
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Geometry question need explanation on finding the answer