In respοnse tο the query, we can state that Therefοre, the simplified equatiοn expressiοn fοr f(x+h) - f(x)/h is: 10x + 5h + 3
What is equatiοn?In a math equatiοn, twο assertiοns are cοnnected by the equals sign (=), which denοtes equivalence. A mathematical assertiοn used in algebraic equatiοns establishes the equivalence οf twο mathematical statements. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14. Tο cοmprehend the relatiοnship between the twο sentences written οn οppοsing sides οf a letter, utilise a mathematical fοrmula. The lοgο and the specific prοgramme typically cοrrespοnd. An illustratiοn wοuld be 2x - 4 = 2.
functiοn f(x) intο the fοrmula fοr f(x+h) - f(x)/h, and then simplify the resulting expressiοn algebraically.
f (x + h) — f (x)
= [5(x + h)² + 3(x + 10] — [5x² + 3x]
= [5(x² + 2xh + h²) + 3x + 314 — [5x² + ax]
= [5x² + 10xh + 5k² + 3x + 3h] — [5x² + 3x]
= 10xh + 5h² + 3h f(x+h) - 1(x) h
= 10x + 5k + 3
Therefοre, the simplified expressiοn fοr f(x+h) - f(x)/h is:
10x + 5h + 3
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Solve the system of equations below, using the technique of your choice.
x+y=8
-x+4y= 2
The solution to the system of equations is x = 6 and y = 2.
The system of equations can also be solved using the elimination method.
what is the elimination method?We are aware that a system of linear equations is a collection of two or more equations with at least two unknown variables. Finding the answers to the unknown variables in a system of equations is the process of solving a linear equation. There are numerous ways to identify the answers to the unknown variables. These include the cross-multiplication method, elimination method, substitution method, and graphic method.
from the question:
A system of equations can be solved in a variety of methods, including substitution, elimination, and matrices. I'll apply the substitution technique here:
x = 8 - y is the result of the first equation.
We can solve for y by substituting this expression for x in the second equation:
-x + 4y = 2
-(8 - y) + 4y = 2 (substituting x = 8 - y)
-8 + 5y = 2 (simplifying)
5y = 10 (adding 8 to both sides)
y = 2 (dividing by 5)
Knowing y, we can now use this quantity to solve one of the initial equations to determine x:
x + y = 8
x + 2 = 8 (substituting y = 2)
x = 6 (subtracting 2 from both sides)
Hence, x = 6 and y = 2 are the answers to the system of equations.
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I need the steps to solve this question any help
The solution is:
Net income = $31,130
Total Assets = Owner's Equity and Liabilities = $104,230
What is income?Income can be stated as the consumption and saving opportunity gained by an entity within a specified timeframe, which is normally expressed in monetary terms. Income is that which means difficult to define conceptually and the definition may be different across fields.
here, we have,
The Income Statement of Profit or Loss and the Statement of Financial Position can be prepared as follows:
Sugar Almonds Ltd
Income Statement of Profit or Loss
For the Year Ended 31st December 2020
Particulars $ $
Sales Revenue 93,700
Cost of sales:
Opening inventory 12,000
Purchases 49,000
Closing inventory - income statement (24,350)
Cost of sales (36,650)
Gross profit 57,050
Operating expenses:
Administrative Expenses (850)
Rent paid (2,000)
Telephone (900)
Wages (21,650)
Travel expenses (330)
Total operating expenses (25,730)
Interest income (expense):
Interest paid (190)
Net income 31,130
Sugar Almonds Ltd
The Statement of Financial Position
As at 31st December 2020
Particulars $ $
Fixed Assets
Premises at cost 70,000
Vehicles at cost 5,800
Total Fixed Assets 75,800
Current Assets
Cash 630
Bank 2,100
Closing inventory - Statmt of fin positn 24,350
Trade Receivables 1,350
Total Current Assets 28,430
Total Assets 104,230
Owner's Equity
Capital 72,000
Drawings (6,450)
Net income 31,130
Total Owner's Equity 96,680
Current Liabilities
Trade Payables 6,400
VAT 1,150
Total Current Liabilities 7,550
Owner's Equity and Liabilities 104,230
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PLS HELPPP THYANK UUU PLS The data below shows the colors preferred by a group of people. We want to plot this on a pie chart. What will be the central angles of each of these categories?
Red=
blue=
green=
purple=
The Central Angle of each color is:
Red= 100°
Blue= 150°
Green= 50°
Purple = 60°
what is Central Angle?According to the definition of a central angle in geometry, it is the angle that the arc of a circle occupies in its centre. The angle's arms are formed by the two radii. Knowing the ratio of the curve to the circle using the central angle is helpful.
To draw a pie chart we have to find the central angle.
For Red
= 20/72 x 360
= 100 degree
For Blue
= 30/72 x 360
= 150
For Green
= 10/72 x 360
= 50
For Purple
= 12/ 72 x 360
= 60
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Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Answer:
x = 2 (True)
Step-by-step explanation:
Can someone help I lost my brain cells xd 7 only
Answer: 81.75
Make 7 an improper fraction:
[tex]\frac{109}{12}[/tex] = [tex]\frac{k}{9}[/tex]
(9)(109) = 12k
981 = 12k
k = 81.75
Mrs. Foley new rug is 7 feet long and 6 feet wide. What is the area of the rug draw a model to show
The rug covers 42 feet of space. We calculate the area of a rectangle to determine it. A rug is woven fabric or animal skin used as a floor covering.
Why do you use the word rectangle?It is a shape with four straight sides and four right angles that is not square, especially if the sides next to it are uneven.
When a 2-D enclosed shape has four sides, four corners, and four right angles (90°), it is referred to as a rectangle. When opposing sides of a diagram are equal and parallel, the shape is referred to as a rectangle.
Area of rectangle = L × B
So, Area of rug = 7 × 6
= 42 feet
Therefore the required answer is 42 Feet.
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construct a right angle triangle with one side 4cm and hypotenuse 5cm.
Answer:
See the explanation below.
Step-by-step explanation:
You need to calculate the remaining side.
Pythagorean theorem: c^2 = a^2 + b^2
=> 5^2 = 4^2 + b^2
b^2 = 25 - 16 = 9
b = √9 = 3
Draw a right triangle with the sides of 3cm and 4cm are perpendicular to form 90 degrees angle. Then connect the ends of 2 lines to form the hypotenuse which will be 5 cm long.
If we invest $9,000 at 10% simple interest, how much will we have saved in 15 years?
Answer:
$13,500
Step-by-step explanation:
I = (P·r·t) / 100
I = (9,000·10·15) / 100
I = 1,350,000 / 100
I = $13,500
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Thanks.
whats 5.6 divied by 8 i need steps ITS DUE TOMMROW AND IM GOING TO GET MInus 100 IF I DONT ANSWER THIS QUESTION
Answer:
Step-by-step explanation: 5.6 / 8 = 0.7
Test Prep While working at the school store, John sold a jacket for $40.00 and notebooks for $1.50 each. If he collected $92.50, how many notebooks did he sell?
By answering the above question, we may state that John consequently variable sold 35 notepads.
What is a Variable?A variable is anything that may be altered in the context of an experiment or mathematical idea. A single symbol is frequently used to denote a variable. Generic symbols for variables are the letters x, y, and z. Variables are qualities with a wide range of values that may be investigated. These include characteristics like height, age, wealth, place of birth, academic standing, and kind of residence, to mention a few. The two primary groups of variables can be separated using numerical and categorical approaches.
Let's define the variables first:
Let's call John's sales of notebooks "n" the quantity.
Each notebook costs $1.50, hence the whole profit from notebook sales is $1.50.
John earned a total of $92.50, according to the issue, thus we can create the following equation:
$40.00 + 1.5n = $92.50
Now that "n" is solved, we can:
$1.5n = $92.50 - $40.00
$1.5n = $52.50 \sn = 35
John consequently sold 35 notepads.
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Find the probability that one client drives less than 10,000 miles a year and has an accident
The probability that one client drives less than 10,000 miles a year and has an accident is 0.06.
What is probability?The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%Given is a table as shown in the image attached.
It is aske to find the probability that one client drives less than 10,000 miles a year and has an accident. Form the table, we can write the cell corresponding to driving less than 10,000 miles and having the accident as 0.06.
Therefore, the probability that one client drives less than 10,000 miles a year and has an accident is 0.06.
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Find the area of triangle ABC to nearest tenth.
12. A = 20, c = 4 cm, b = 7 cm
13. C = 55, a = 10 m, b = 15 m
14. B = 42, a = 3 ft, c = 9 ft.
The areas of triangles ABC are
12. The area is 4.8 cm²
13. The area is 61.4 m²
14. The area is 9.0 ft²
What is the area of a triangle?The area of a triangle is the region occupied by the triangle.
12. Area of triangle ABC
Given that
A = 20, c = 4 cm, b = 7 cmArea of triangle ABC is A = 1/2bcsinA
= 1/2 × 7 cm × 4 cm × sin20°
= 7 cm × 2 cm × sin20°
= 14 cm² × sin20°
= 14 cm² × 0.3420
= 4.788 cm²
≅ 4.8 cm²
The area is 4.8 cm²
13. Area of triangle ABC
Given that
C = 55, a = 10 m, b = 15 mArea of triangle ABC is A = 1/2absinC
= 1/2 × 10 m × 15 m × sin55°
= 5 m × 15 m × sin55°
= 75 cm² × sin55°
= 75 cm² × 0.8192
= 61.436 cm²
≅ 61.4 cm²
The area is 61.4 cm²
14. Area of triangle ABC
Given that
B = 42, a = 3 ft, c = 9 ft mArea of triangle ABC is A = 1/2acsinB
= 1/2 × 3 ft × 9 ft × sin42°
= 1/2 × 27 ft² × sin42°
= 13.5 ft² × sin42°
= 13.5 ft² × 0.6691
= 9.033 ft²
≅ 9.0 ft²
The area is 9.0 ft²
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write cubed root 21 in the form 21k
The general format of the exponential expression is given as follows:
[tex]a^{\frac{n}{m}}[/tex]
In which:
The base is given by a.The exponent is given by n.The radicand is given by m.The radical form is given as follows:
[tex]\sqrt[m]{a^n}[/tex]
Meaning that the equivalence relation is given as follows:
[tex]\sqrt[m]{a^n} = a^{\frac{n}{m}}[/tex]
That is:
The radicand is the numerator of the fraction in the exponent.The radical is the denominator of the fraction in the exponent.Hence the relation for the cube root of 21 is given as follows:
[tex]\sqrt[3]{21} = 21^{\frac{1}{3}}[/tex]
(applying the conversion of the fractional exponent to a radical expression).
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Which of these statements is true? A.The radius of a circle is about three times its diameter.B. The diameter of a circle is equal to the radius.C. The diameter of a circle is two times the radius. D. The radius and the diameter are not related.
C. The diameter of a circle is two times the radius.
Jen has driven 15 miles on her way to the mall. this distance is 3/5 of the total distance. if d represents the total distance in miles, which equation can be used to find d
This can be resolved with d = 25 miles by multiplying equation both sides by
Which equation can be used to find d?If Jen has driven 15 miles, and this is 3/5 of the total distance, we can use the following equation to find the total distance d:
15 = (3/5) * d
To solve for d, we need to isolate it on one side of the equation. We can start by dividing both sides of the equation by 3/5, which is the same as multiplying by its reciprocal, 5/3:
15 * (5/3) = d
Simplifying the expression on the left side, we get:
25 = d
Therefore, the total distance Jen needs to travel to get to the mall is 25 miles.
In summary, the equation that can be used to find the total distance d, given that Jen has driven 15 miles and this is 3/5 of the total distance, is:
15 = (3/5) * d
Which can be solved for d by multiplying both sides by 5/3, giving:
d = 25 miles
In conclusion, assuming that Jen has driven 15 miles, which is 3/5 of the entire trip, the equation that can be used to determine the whole distance d is:
15 = (3/5) * d
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The box plot displays the number of push-ups completed by 9 students in a PE class.
A box plot uses a number line from 9 to 45 with tick marks every 2 units. The box extends from 17.5 to 40.5 on the number line. A line in the box is at 30. The lines outside the box end at 10 and 42. The graph is titled Push-Ups In PE and the line is labeled Number of Push-Ups.
Which of the following represents the value of the lower quartile of the data?
42
40.5
17.5
10
Given that 17.5 is the bottom end of the box, the lower quartile's value equation (Q1) must fall between 17.5 and 30. Hence, the appropriate response is 17.5
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
25% of the data fall inside the lower quartile (Q1), which is represented by that number. Q1 is situated near the bottom of the box in the box plot.
According to the description, the box's boundary is at 30, and its size ranges from 17.5 to 40.5 on the number line. As a result, the median value of the middle 50% of the data is 30, with a range of 17.5 to 40.5.
There are some data points outside the middle 50% since the lines outside the box finish at 10 and 42.
Given that 17.5 is the bottom end of the box, the lower quartile's value (Q1) must fall between 17.5 and 30. Hence, the appropriate response is
17.5
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Find two values of θ, 0≤θ<2π, that satisfy the following equation.
Answer:
π/4, 7π/4
Step-by-step explanation:
You want the values of θ in the range 0 ≤ θ ≤ 2π such that cos(θ) = √2/2.
CosineThe cosine function has the value √2/2 for angles ±45° = ±π/4 radians and those angles added to an integer multiple of 2π. In the domain of interest, the angles are ...
θ = π/4 and 7π/4
A certain disease has an incidence rate of 0.4%. If the false negative rate is 8% and the false positive rate is 2%, compute the probability that a person who tests positive actually has the disease
Answer:
To compute the probability that a person who tests positive actually has the disease, we need to use Bayes' theorem:
P(D|P) = P(P|D) * P(D) / P(P)
where:
P(D|P) is the probability of having the disease given a positive test result
P(P|D) is the probability of testing positive given that the person has the disease (also known as sensitivity), which is 1 - false negative rate = 0.92 in this case
P(D) is the incidence rate of the disease, which is 0.4% = 0.004
P(P) is the probability of testing positive, which can be computed using the false positive rate as 1 - specificity = 1 - 0.98 = 0.02
Plugging in the values, we get:
P(D|P) = 0.92 * 0.004 / 0.02 = 0.184
Therefore, the probability that a person who tests positive actually has the disease is 0.184, or about 18.4%.
HELPPP PLS thank you pls
The piecewise function graphed is given as follows:
y = x² + 4, x < 2.y = -x + 4, x ≥ 2.How to define the piecewise function?A piece-wise function is a function that has different definitions, based on the input x of the function.
For this problem, the intervals are given as follows:
x < 2.x ≥ 2.For the first interval, the interval is open due to the open circle, and the quadratic function is a translation up 4 units of y = x², hence^:
y = x² + 4, x < 2.
For the second interval, which is the closed interval, we have a decaying line with slope of -1 and x-intercept of 4, hence:
y = -x + b
0 = -4 + b
b = 4.
Hence:
y = -x + 4, x ≥ 2.
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Jenny tiene 50 fichas cuadradas. Ordena las fichas en una matriz rectangular de 4 hileras. ¿Cuántas fichas sobrarán?
If Jenny has 50 square tiles and arranges them in a rectangular array with 4 rows, then she would have a total of 48 tiles, with 2 tiles left over.
How to find the number of tilesIf Jenny arranges the tiles in a rectangular array with 4 rows, this means each row will have 50/4 = 12.5 tiles. However, since we cannot have half a tile, we need to round down to the nearest whole number, which is 12.
Therefore, each row will have 12 tiles, and the total number of tiles used will be 4 x 12 = 48. To find out how many tiles are left over, we need to subtract the total number of tiles used from the original number of tiles: 50 - 48 = 2. So, there will be 2 tiles left over.
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[tex]\frac{2}{5+\sqrt{3} }[/tex]
[tex]\frac{2}{5+\sqrt{3}}[/tex] fraction can be simplified to [tex](10 - \sqrt{23}) / (22)[/tex] .
What are fractions?
A fraction is a number that represents a part of a whole. It consists of two numbers, a numerator and a denominator, separated by a horizontal or diagonal line. The numerator represents the number of parts being considered, while the denominator represents the total number of equal parts in the whole.
For example, 1/2 represents one part out of two equal parts, or one-half of the whole. Fractions can also represent values less than one, greater than one, or even negative values.
To rationalize the denominator, we can multiply both the numerator and denominator by the conjugate of the denominator, which is 5 - 3^(1/2):
[tex]\frac{2}{5+\sqrt{3}}[/tex] * [tex]\frac{(5-\sqrt{3})}{(5-\sqrt{3})}[/tex]
= [tex]\frac{2*(5-\sqrt{3})} {(5+\sqrt{3}) (5-\sqrt{3})}[/tex]
= [tex](10 - \sqrt{23}) / (25 - 3)[/tex]
= [tex](10 - \sqrt{23}) / (22)[/tex]
Therefore, [tex]\frac{2}{5+\sqrt{3}}[/tex] can be simplified to [tex](10 - \sqrt{23}) / (22)[/tex]
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Complete question:
simplify the given fraction [tex]\frac{2}{5+\sqrt{3}}[/tex]
bill is in the process of installing an above ground swimming pool in his yard. if the diameter of the pool is 35 feet what is the approximate circumference of the pool
Answer:
Step-by-step explanation:
[tex]C=\pi d[/tex]
[tex]=\pi \times 35[/tex]
[tex]\approx 109.96 feet[/tex]
Answer:
110. feet approximately
Step-by-step explanation:
circumference means a closed boundary of a curved shape. Mainly known as a circle. To find circumference, use the formula c= π (pie) times diameter.
35 × π ≈ 110
Hope this helps :)
Doreen lives 3/5 mile from the library. Sheila lives 1/3 as far away from the library as Doreen
Select yes or no for each statement
Does Doreen live father from the Library than Sheila
Yes or No
Does Sheila live 1/5 mile from the library
Yes or No
Does Sheila live twice as far from the library as Doreen
In a group of 15 children, 5 said they are an only child, 3 said they have 1 sibling only, 4 said they have exactly 2 siblings, and 3 said they have exactly 3 siblings.
What is the average number of siblings for this group?
Enter your answer as a decimal, rounded to the nearest tenth, in the blank.
Answer:
1.3
Step-by-step explanation:
To find the average number of siblings for the group, we need to calculate the total number of siblings and divide by the total number of children.
Out of the 15 children:
5 are only children, so they have 0 siblings each.
3 have 1 sibling each, so there are 3 * 1 = 3 siblings in total.
4 have 2 siblings each, so there are 4 * 2 = 8 siblings in total.
3 have 3 siblings each, so there are 3 * 3 = 9 siblings in total.
The total number of siblings is 0 + 3 + 8 + 9 = 20.
The average number of siblings for the group is 20/15 = 1.3 (rounded to the nearest tenth).
Therefore, the average number of siblings for this group is 1.3.
Answer:
1.3
Step-by-step explanation:
PLEASE simplify 2x +24 =64
Answer:
x = 20
Step-by-step explanation:
2x + 24 = 64
2x = 40
x = 20
Let's check
2(20) + 24 = 64
40 + 24 = 64
64 = 64
So, x = 20 is the correct answer.
Answer:
[tex] \sf \: x = 20[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 2x + 24 = 64
Then the value of x will be,
→ 2x + 24 = 64
→ 2x = 64 - 24
→ 2x = 40
→ x = 40 ÷ 2
→ [ x = 20 ]
Hence, the value of x is 20.
{x|x is an even, negative integer and x > - 25}
The number of elements in set A is n = 12 elements of the set A is given by A = { -24 , -22 , -20 , -18 , -16 , -14 , -12 , -10 , -8 , -6 , -4 , -2 }
What is Set Theory Formula?The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.
Given data ,
Let the set notation be represented as S
Now , the value of S is
S = {x|x is an even, negative integer and x > - 25}
Now , the value of the set A is given by all the numbers greater than -25 which are negative and even
So , A = { -24 , -22 , -20 , -18 , -16 , -14 , -12 , -10 , -8 , -6 , -4 , -2 }
The number of elements in set A = 12 elements
Therefore , the value of n = 12 elements
Hence , the set A = { -24 , -22 , -20 , -18 , -16 , -14 , -12 , -10 , -8 , -6 , -4 , -2 }
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the box and whisker plots below show the average monthly temperature for Mexico City, Mexico, and Shanghai, china, in degrees Fahrenheit
The percentage of temperatures for Shanghai that falls between 46 degrees Fahrenheit and 78 degrees Fahrenheit is A. 50 %.
Where does 50 % of the temperature fall ?The interquartile range (IQR) of a box and whisker plot is defined as the difference between the third quartile (Q3) and the first quartile (Q1). It represents the spread of the middle 50% of the data.
On a box plot, the interquartile range (IQR) is represented by the box itself. The box extends from the first quartile (Q1) to the third quartile (Q3) and contains the middle 50% of the data.
This means that for Shanghai, the temperatures of 46 degrees Fahrenheit and 78 degrees Fahrenheit represent the IQR which means that this is 50 % of the temperature.
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The full question is:
The box-and-whisker plots below show the mean monthly temperatures (°F) for Mexico City, Mexico, and Shanghai, China. What percent of the temperatures for Shanghai fall between 46°F and 78°F? *
Select one,
{-3, -2,-1,0}
{-3,-2,2,3}
(-3,-2,-1,-0]
{-3, -2,-2,-3)
The domain of the function shown on the graph is {-3, -2, 2, 3 }.
What is the domain of the function on the graph?The domain of a function is the set of all possible input values (also known as the independent variable or x-values ) for which the function produces a valid output (also known as the dependent variable or y-values).
In other words, it is the set of values that can be plugged into the function to produce a meaningful result.
In this case, there are four (4) points on the graph.
The coordinates of the points are;
Point 1: x = -3 and y = 5Point 2: x = -2 and y = 5Point 3: x = 2 and y = 5Point 4: x = 3 and y = 5Since the domain are the set of the x-values, the domain of the function of the graph will be;
Domain : {-3, -2, 2, 3 }
Therefore, option B) {-3, -2, 2, 3 } is the correct answer.
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Please help me. it’s timed!!!! Use the drawing tools to form the correct answer on the graph.
Plot function h on the graph.
J-4,
lz + 5,
h (x)
=
x < -3
X -3
Answer:
The function h(x) is defined as:
h(x) = { x + 4, if x < -3
{ 2x + 5, if x >= -3
To plot this function on the graph, you would plot the points (-4, 0) and (-3, -1) for the first part of the function, and then plot the line with slope 2 passing through the point (-3, 2) for the second part of the function.
Step-by-step explanation:
Select the correct answer from each drop-down menu.
Complete each statement about the key features of function g(x).
What are functions ?
Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
What are asymptotes ?
An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. In other words, Asymptote is a line that a curve approaches as it moves towards infinity.
An asymptote of the curve y = f(x) or in the implicit form: f(x,y) = 0 is a straight line such that the distance between the curve and the straight line lends to zero when the points on the curve approach infinity.
There are three types of asymptotes namely:
1) Vertical Asymptotes
2) Horizontal Asymptotes
3) Oblique Asymptotes
The point to note is that the distance between the curve and the asymptote tends to be zero as it moves to infinity or -infinity.
What are domain of a function ?
The domain of a function is the set of values that we are allowed to plug into our function.
This set is the x values in a function such as f(x).
What is range of a function ?
The range of a function is the set of values that the function assumes. This set is the values
that the function shoots out after we plug an x value in. They are the y values.
To know more about functions click:
https://www.britannica.com/science/function-mathematics
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