The properties of the graph of a function include domain, range, symmetry, asymptotes, intercepts, increasing or decreasing, continuity, smoothness, behaviour at infinity and shape.
1) Domain: The set of all input values (x-values) that produce a valid output (y-value) for the function.
2) Range: The set of all output values (y-values) that can be produced by the function for any valid input value in the domain.
3) Symmetry: A graph may be symmetric with respect to the x-axis, y-axis, or origin.
4) Asymptotes: A line that the graph of a function gets arbitrarily close to, but never touches.
5) Intercepts: The points where the graph of a function crosses the x- and y-axes.
6) Increasing or Decreasing: A function can be increasing over a certain interval, decreasing over a certain interval, or both.
7) Continuity: A function is continuous if its graph has no breaks or gaps.
8) Smoothness: A function is smooth if its graph has no sharp corners or links.
9) Behavior at Infinity: The behavior of a function at positive or negative infinity can be determined by analyzing the degree and leading coefficient of its equation.
10) Shape: The shape of a graph can be used to classify functions as linear, quadratic, exponential, logarithmic, etc.
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If a is 200% of b, what percent of 5a is 4b?
250% (percent) of 5a is 4b.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
here, given that,
a is 200% of b
i.e. a=2b
Now, 5a=10b
So, we have,
5a/4b
=10b/4b
=5/2
=250%
Hence, 250% (percent) of 5a is 4b.
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If you place a 39-foot ladder against the top of a 23-foot building, how many feet will
the bottom of the ladder be from the bottom of the building? Round to the nearest
tenth of a foot.
Answer:
31.5 ft
Step-by-step explanation:
Use the Pythagorean Theorem
a² + b² = c²
Plug in the knowns
a² + 23² = 39²
Subtract 23² from both sides
a² = 39² - 23²
a² = 1521 - 529
a² = 992
Take the square root of both sides
a = 31.496031496
Rounded
a = 31.5 ft
The bottom of the ladder from the bottom of the building will be equal to 31.5 ft.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the given instructions in the question,
Use the equation of Pythagoras's theorem
a² + b² = c²
Put in the known values in the above equation,
a² + 23² = 39²
a² = 39² - 23²
a² = 1521 - 529
a² = 992
a = √992
a = 31.496 or,
a = 31.5 ft
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a forest covers 59,000 acres. A survey finds that 0.6% of the forest is old oak trees How many are acres of old oak trees are there?
Answer:
354acres
Step-by-step explanation:
Total acre = 59000
Percentage of old oak acre trees is 0.6%
Therefore, the acres of old trees are calculated:
59000 * (0.6÷100) = 354acres
A guy wire is attached to an upright pole 6 meters above the ground. If the wire is anchored to the ground 5 meters from the
base of the pole how long is the wire? Give your answer to two decimals.
A guy wire is attached to an upright pole 6 meters above the ground. If the wire is anchored to the ground 5 meters from the base of the pole 7.81 m long is the wire. This can be solved by using the concept of Pythagoras theorem.
What is Pythagoras theorem?The widely accepted geometric principle known as the Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs (the side opposite the right angle).
The hypotenuse side of a right-angled triangle's square is equal to the sum of its other two sides, according to Pythagoras' Theorem. The perpendicular, base, and hypotenuse of this triangle are its three designated sides.
Let, assume ΔABC is a right-angled triangle
where, AC = 6m be the pole.
AB = 5m is the length of a guy wire and is attached to stake B
By Pythagoras theorem,
BC² = AB² + AC²
or, BC² = (5)² + (6)²
or, BC² = 36 + 25
or, BC = √61 m
or, BC = 7.81 m
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Factor by gcf 6x2+3x+21 The 2 is supposed to be small.
Given:
The expression is:
[tex]6x^2+3x+21[/tex]
To find:
The factor of the given expression by GCF.
Solution:
We have,
[tex]6x^2+3x+21[/tex]
Here, 3 is the greatest common factor (GCF) of [tex]6x^2,3x,21[/tex].
Taking out GCF, we get
[tex]6x^2+3x+21=3(2x^2+x+7)[/tex]
Therefore, the required factor form of the given expression is [tex]3(2x^2+x+7)[/tex].
Mai is making personal pizzas. For 4 pizzas, she uses 10 ounces of cheese. how much cheese does mai use per pizza? At this rate, how much cheese will she need to make 15 pizzas? Please help its due tomorrow
Mai uses 10 ounces of cheese to make 4 pizzas, so she uses 10/4 = <<10/4=2.5>>2.5 ounces of cheese per pizza.
To make 15 pizzas, she will need 152.5 = <<152.5=37.5>>37.5 ounces of cheese.
What coins would I need to make 77 cents fewest possible
Answer:
Step-by-step explanation: Two quarters, 50 pennies: N = 52 (N+1 = 53) One quarter, 75 pennies: N = 76 (N+1 = 77) 100 pennies, N = 100 (N+1 = 101) 6 nickels, 70 pennies: N = 76 (N+1 = 77)
Answer:
2 quarters, 2 dime's, 1 Nickel, 2 penny's
Step-by-step explanation:
Well u well need to quarters because 2 quarters are $25 cent then u well need 2 dimes because when your counting dime's that 10 20 30 40 50 so to dime's and 1 Nickel that makes $75 cents so u need 2 penny's and that makes 77
Can someone please help me
Explanation is[tex]^{}[/tex] in a file
bit.[tex]^{}[/tex]ly/3gVQKw3
Freda bought a sandwich for $4. 00 and a drink for94$. Her grandson ordered a meal for$6. 35. What was the total price of all three items when 8% sales tax was added?Explain how touse estimation to check whether your answer is reasonable
The answer is $112.70 The Question is a simple Sales tax rate calculating problem.
How do you solve sales tax problems?Multiplying the purchase price by the sales tax rate will provide the sales tax. Don't forget to round the sales tax rate from percent to decimal. The price of the purchase is increased after the sales tax has been calculated. The entire cost is what the client pays as a result.
Sales tax rate = Sales tax percent / 100.
Sales tax = List price x Sales tax rate.
Given,
Rate of sandwich is = $4. 00
Rate of drink is = 94$
The rate of a meal that Her grandson ordered is =$6. 35.
What was the total price of all three items when 8% sales tax was added?
Total price of all three items without tax = 4 + 94 + 6.35
= $104.35
Total price of all three items with tax = (100% + tax) * Price
= (100% + 8%) * 104.35 = 108% * 104.35
= 1.08 * 104.35 = 112.698
≅ $112.70
The estimation to check if the result is reasonable by putting the answer in the original equation.
E.g. x + 4 = 10; x = 10 - 4
We get that x = 6
Plug in x = 6 in x + 4 = 10.
6 + 4 = 10.
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A circle has centre C and radius 4 cm.
The diagram shows the circle with a point
D which lies on the circle. The tangent at D
passes through the point E. EC = √65 cm.
Find
a) the size in radians of angle DCE
b) the area of the shaded region
Step-by-step explanation:
EC = 165 cm (Given) Tangent of circle also makes 90°.
a) sind = Perpendicular Hypotenuse = CD = EC 165 => 0 = Sin = 0.519 ~ 0.52 =29.7448 ~ 29.75° =<E
By angle sum property of triangle. <D+<E+ <C = 180°
90° + 29.75 + LC = 180°
<C = 180-90-29.75 = 60.25° <C= 60.25°
<DCE = <C = 60.25 x π/180 = 1.052 radians.
(b) Area of triangle DCE = 1/2 x b x h = 1/2 x ED X 4
ED² + CD² = EC² ED² + 4² = (√65)² => EC² = 65-16 = 49 ED=7
Area = 1/2 x 7 x 4 = 14 cm²
Area of sector a π x 4²x 60.25/360 = 8.4125 cm2
Area of shaded region= Area ADCE Area of sector -
= 14-8.4125 = 5.5875 cm²
(a) <DCE = 1.052 radians b) Area shaded of region = 5.5875cm²
If the amount of space between support towers is between 200 and 300 feet, determine the number of towers you will use.
SHOW ALL WORK TO EARN CREDIT.
What is an example of a similarity transformation geometry?
We refer to the enlargement or reduction of one of two figures as a similarity transformation. For example: When one of two figures can be produced from the other and the ratio of their corresponding sides is equal, we say that the two figures are comparable. Similar figures come in a variety of sizes and shapes.
Either a geometric similarity or a matrix transformation that produces a likeness are referred to as "similarity transformations" in this context. Space items are changed into comparable things by similarity transformations. Fractals and iterated function systems are based on essential principles such as similarity transformations and the idea of self-similarity.
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in an isosceles triangle, if the measure of a base angle is 74∘, what is the measure of the vertex angle?
Answer:
the measure of vertex angle is 32°
Answer:
32°
Step-by-step explanation:
An isosceles triangle has 2 congruent base angles, both 74° , then
vertex angle = 180° - (74 + 74)° = 180° - 148° = 32°
solve the system using elimination method: -6x-8y=10. 2x-4y=10. i need the whole problem solved, i need to show the problem, and i dont want any links. please help, thank you so much, no links and I need the problem shown
Answer:
(5,0)
Step-by-step explanation:
-6x-8y=10
(2) 2x-4y=10 (2)
4x-8y=20
add the systems
2x=10
divide 10 by 2
x=5
substitute 5 into x
2(5)-4y=10
10-4y=10
-4y=
y=0
(Pls help!!) Find the volume of each cylinder in terms of π. Which cylinder has the greatest volume? Cylinder A: diameter7 in., height12 in. Cylinder B: diameter12 in., height7 in.
Answer: Cylinder B has the greater volume
Step-by-step explanation:
Cylinder A= 147πinch cubed
Cylinder B=252π inch cubed
(if youre using savvas or something like that, use the pie symbol and it might work if youre having difficulties.)
NEED HELP ASAP
NO LINKS AND NO JUST SAYING HI, PLEASE ANSWER LEGITIMATELY! THANK YOU!!!! <3
Answer:
74
Step-by-step explanation:
For two weeks the highest temp each day was recorded in four different cities. Line L, M, N, & P are graphs of the temp over time in Lubbock, Memphis, New Orleans, & Phoenix. Which statement is true?
A. the high temp in Lubbock increased as time passed
B. the high temp in Memphis decreased steadily
C. Initially, the high temp was warmer in Phoethen in Memphis
D. The high temp in Phoenix rose faster than the temp in New Orleans
A) 2
B) 4
C) 10
D) 6
Answer:
this is B 4
Step-by-step explanation:
For a project in her Geometry class, Violet uses a mirror on the ground to measure the height of her school’s football goalpost. She walks a distance of 6.65 meters from the goalpost, then places a mirror flat on the ground, marked with an X at the center. She then walks 4.25 more meters past the mirror, so that when she turns around and looks down at the mirror, she can see the top of the goalpost clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.75 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.
Answer: To find the height of the goalpost, we can use the information provided in the problem and the concept of similar triangles. Since Violet is looking down at the mirror, the line of sight from her eyes to the top of the goalpost forms a right angle with the ground. This right angle creates two similar triangles, one between her eyes, the ground, and the top of the goalpost, and the other one between the mirror on the ground, the goalpost, and a point on the ground that is the same distance from the mirror as the top of the goalpost is from Violet's eyes.
Since similar triangles have the same angle measures, we can set up the following proportion:
(distance from mirror to point on the ground) / (distance from mirror to top of goalpost) = (distance from Violet's eyes to ground) / (height of goalpost)
We can now use the information provided in the problem to solve for the height of the goalpost.
(6.65+4.25)/x = 1.75 / H
x = (6.65+4.25) * (1.75/H)
Where x is the distance from mirror to top of the goalpost.
Substitute the known values and solve for H
H = 1.75*(6.65+4.25) / x = 1.75*10.9 / x
We know that x = 4.25, so
H = 1.75*10.9 / 4.25 = 4.093 m
The height of the football goalp
Step-by-step explanation:
Which of the following are possible solutions for this inequality?
I need to factor completely to get an answer for
n²-10n+24
I need to get factors in parenthesis like (n +/- #) (n +/- #)
I need it before tomorrow
Answer:
(n - 6)(n -4)
Step-by-step explanation:
Find two numbers that add to - 10 and multiply to +24.
In this case, -6 * -4 satisfies these requirements.
A construction worker is tasked with tiling two square rooms, room A and room B. Room B has side lengths that are double the side lengths of room A. The construction worker uses one box of tiles to complete the flooring of room A.
How many boxes of tiles will they need to complete the flooring of room B? Assume the boxes of tiles are identical.
Therefore, since the area of room B is four times the area of room A, four boxes of tiles will be needed to complete the flooring of room B.
Define Volume and Area.The area is the volume a flat, two-dimensional item occupies in a plane. The space occupied by a three-dimensional object is referred to as its volume. Area is measured in square units. Volume is measured in cubic units.
What is Surface Area?The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.
Since the side lengths of room B are double the side lengths of room A, the area of room B is four times the area of room A.
The number of tiles needed to cover a floor is equal to the area of the floor divided by the area of each tile.
Since the boxes of tiles are identical, the number of tiles in each box must also be identical.
Therefore, since the area of room B is four times the area of room A, four boxes of tiles will be needed to complete the flooring of room B.
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Un comerciante tiene dos clases de aceite, la primera de 6 euros el litro y la segunda de 7.2 euros el litro.¿Cuantos litros de cada clase hay que poner para obtener 60 litros de mezcla a 7 euros el litro?
AnswerNo nin
Step-by-step explanation:
dsfsfsdffsfsfsfs is bad
what is m<FDG?
Parts of a circle and central angles
Answer:
m<FDG = 120 degrees
Step-by-step explanation:
90 + 150 + x = 360
subtract 90 and 150 from both sides
x = 120
round 3.967 to the hundredth place
Find the value of x.
Answer:
x = 68 degrees
Step-by-step explanation:
The right angle symbol tells us its 90 degrees.
90 degrees - 22 degrees = 68 degres
Answer:
x = 68 degrees
Step-by-step explanation:
It is given that this angle is a right angle. A right angle means that it is 90 degrees.
One part of the angle is 22 degrees so the other is labled x.
90 - 22 = 68 degrees
Therefore, x=68 degrees
Tate is trying to decide if he should spend $100 to purchase virus protection software for his new computer
Answer: Hello your question is vague hence I will give a more general answer
answer : Tate spending $100 to purchase virus protection will help protect his computer from Viruses that can cause Damages worth more than $100. therefore he should purchase the virus protection.
Step-by-step explanation:
Virus protection software ( i.e. Anti-virus software) is a set of computer programs written into the computer or any other electronic Gadget like a Phone with the purpose of protecting, detecting and removing malicious software ( computer viruses ) from the computer
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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1/2 X (6 X 4)divided by + 3 + 2
Answer:
1/108
Step-by-step explanation:
A function multiplies its input by 3/4 then adds 7 to get its output. Use function notation to represent this function.
f(x)=_____
In function notation, the function is represented as f(x) = (3/4)x + 7.
In function notation, the function is represented by the letter "f" followed by the input value inside parentheses. The input value is typically represented by the letter "x". In this case, the function takes "x" as its input and performs the operation of multiplying it by 3/4 and then adding 7 to get the output. We can represent this function using the equation f(x) = (3/4)x + 7.
It's worth noting that the function notation is a way to express a mathematical relationship between two variables, the input variable (x) and the output variable (f(x)), in which every input value of x corresponds to exactly one output value. This equation represents the same function regardless of the input value, and it can be used to find the output for any input value by simply substituting it in the equation.
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