Solution :
Properties of Functions:
Definition of a Function: A function is a rule or formula that associates each element in the set X (an input) to exactly one and only one element in the set Y (the output). Different elements in X can have the same output, and not every element in Y has to be an output.
Definition of the Domain of a Function: The set of all possible inputs of a function is defined as the domain. The domain of a real-valued function defined by a formula for y in terms of x will be the set of all x input-values that result in a real y output-value unless the domain of the function is further restricted.
Definition of the Range of a Function: The set of all possible outputs of a function is defined as the range. The range of a real-valued function defined by a formula for y in terms of x will be the set of all y output-values that result from the x input-values in the domain.
Function Notation: Given that f(x) is given by some formula containing x, f(B) will be the same formula with each x replaced by B.
Linear Function Definition: If a function may be written in the form f(x) = mx + b where x is the independent variables and m and b are constants, then f(x) represents a linear function. The variable m is defined as the slope and the point (0, b) represents the y-intercept. An equation in this form is known to be in Slope-Intercept Form.
Linear Function Slope Definition: Given that f(x) = mx + b, then m is defined as the slope where:
for any two points (x1, y1) and (x2, y2) on the line. Graphically, the slope represents the change in y with respect to x on the graph of the line.
Linear Functions of Parallel Lines If two linear functions are given by f(x) = m1x + b and g(x) = m2x + b, and m1 = m2, then the graphs of f(x) and g(x) will consist of two lines that are parallel to each other.
Linear Functions of Perpendicular Lines If two linear functions are given by f(x) = m1x + b and g(x) = m2x + b, and m1 = -1/m2, then the graphs of f(x) and g(x) will consist of two lines that are parallel to each other.
Graphs of Even Functions Given a function f(x), if f(c) = f(-c) for all c in the domain, then f(x) is an even function and its graph will have symmetry with respect to the y-axis.
Graphs of Odd Functions Given a function f(x), if f(c) = -f(-c) for all c in the domain, then f(x) is called an odd function and its graph will have symmetry with respect to the origin. Symmetry with respect to the origin implies that a 180-degree rotation of the graph about (0,0) results in an identical graph.
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solve for y
-4=-2+y/2
Answer:
y = -4
Step-by-step explanation:
-4 = -2 + y/2
-2 = y/2
2(-2) = y
y = -4
Slope intercept form (-6,19) and (3,-2)
Answer:
[tex]y = -\dfrac{7}{3}x +5[/tex]
Step-by-step explanation:
The general equation of a line in slope-intercept form is
y = mx + b
where m = slope and b = y-intercept is rise over run
[tex]m = \dfrac {(y_{2} - y_{1})} {(x_{2} - x_{1})}[/tex]
where (x₁, y₁) and (x₂, y₂) are any two points on the line
[tex]m = \dfrac{-2 - 19}{3 - (-6)}\\\\[/tex]
[tex]\\\\m= \dfrac{-21}{9}[/tex]
[tex]m = -\dfrac{7}{3}[/tex]
So slope-intercept form is
[tex]y = -\dfrac{7}{3}x +b\\\\[/tex]
[tex]-2 = -\dfrac{7}{3}\cdot 3 +b\\\\\\\\-2 = -7 + b\\\\[/tex]
or 7 -2 = b
==> b = 5
[tex]y = -\dfrac{7}{3}x +5[/tex]
Evaluate each expression for the given value of x
2x for x=3
Value of the expression 2x at x=3 is 6.
By considering the given expression
2x=2(3)=6
A mathematical expression is created when we successfully combine numbers and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.
An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules.
Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing.
Expression. Equation. A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.
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1. Give two other names for CD.
2. Give another name for plane M.
3. Name three points that are collinear. Then name a fourth point that is not collinear with these three points.
4. Name a point that is not coplanar with points A, C, E.
1. The other two names for CD is DC and line m
2. The another name for plane M is plane AEB , ABE ,BEA ,ACE.
3. The points which are collinear are A ,C , B and the point which is not collinear is D or E .
4. The point that is not coplanar with points A, C, E is D.
A line can be defined as a series of straight lines extending in opposite directions. A collinear point is a point that lies on the same straight line or a single line. Two or more points on a line are said to be collinear if they are close or far apart. The word "coplanar" means "on the same plane".1. CD lies on m so , other name for CD can be DC and line m.
2. As point A , B , E lies on plane M so , other name for plane M can be AEB , ABE , BEA and ACE .
3. As A , C and B are in straight line hence , they are collinear and point D and E are not in collinear with these three points .
4. Only D point is not on the plane hence , it is not coplanar with points A, C, E.
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luis is making a wooden model of a flag for his school project. He found a bargain on square pieces of plywood. If his flag is to be 18 inches by 12 inches,what is a reasonable area for the square piece of plywood he must purchase if he only wants to make one cut in the wood?
NEED SOON
The reasonable area for the square piece of plywood he must purchase if he only wants to make one cut in the wood would be 216 sq inches.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
We have been given that the flag is to be 18 inches by 12 inches, then;
The area of the rectangle = length × Width
The area of the rectangle = 18 x 12
= 216
Since the area of flag will be equal to area for the square piece of plywood.
The area of a square of side length l is given by l squared;
A(l) = l²
216 = 14.6²
Hence, the reasonable area for the square piece of plywood he must purchase if he only wants to make one cut in the wood would be 216 sq inches.
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A group of friends wants to go to the amusement park. They have $183 to spend on
parking and admission. Parking is $8, and tickets cost $25 per person, including tax.
Write and solve an equation which can be used to determine x, the number of people
who can go to the amusement park.
The equation is 25x + 8 = 183
The value of x is 7
How to determine the value of x ?The group of friends have $183 to spend
The cost of parking is $8
The tickets cost $25 per person
The equation can be written as follows
25x + 8 = 183
Collect the like terms
25x= 175
Divide by the coefficient of x which is 25
x= 175/25
x= 7
Hence the value of x is 7 and the equation is written as 25x + 8 = 183
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ace company provided the following data on december 31, 2021: cash 1,500,000 inventories 280,000 prepaid supplies 120,000 land 360,000 furniture & fixtures 60,000 accounts payable 385,000 salaries & wages payable 12,000 net sales and other revenue 770,000 cost and expenses 340,000 retained earnings, jan. 01, 2021 1,100,000 on december 31, 2021, what amount should be reported as current assets
Amount reported as Current Assets = 1,912,000
Current assets are items that a corporation utilizes, replaces, or turns into cash during a typical operating cycle. They are also known as short-term assets (typically less than 12 months). It sets them apart from long-term assets or those that a company utilizes for more than a year. Current assets are referred to as liquid assets since they may be converted into cash more readily than long-term assets.
The balance sheet shows both current and long-term assets, which combined comprise all of the company's assets.
Amounts reported as Current Assets are :
Cash = 1,500,000
Inventories = 280,000
Prepaid Supplies = 120,000
Salaries and Wages Payable = 12,000
Total Amount = 1,500,000 + 280,000 + 120,000 + 12,000 = 1,912,000
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Given g(x) = − 4x + 8, identify the domain, range, and x-intercept of the function.
Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0)
Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (−2, 0)
Domain: −4 < x < 8; Range: − 4 < y < ∞; x-intercept (2, 0)
Domain: −4 < x < 8; Range: −∞ < y < 4; x-intercept (−2, 0)
Domain of a function means all possible inputs or all the numbers that can be put in place of x to get some output
Range of a function means all possible outputs or all the numbers that are the result of all the inputs or value of y
Intercept is the point on graph whose one coordinate is zero. There are two types of intercepts - X intercept where the y coordinate is zero and Y intercept where the value of x coordinate is zero
the function given is g (x) = -4x +8
The domain of the given function is all real numbers or - infinite < x< infinite
The range of the given function is all real numbers or - infinite < x< infinite
The x intercept of of the given function is where y = 0
so, 0 = -4x + 8
-8 = -4x
x = 2
The x intercept is (2,0)
Hence, the domain, range, and x-intercept of the function g(x) = − 4x + 8 are Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0) which is first option
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Step-by-step explanation:
Took test
In a class of 30 children, 60% of the children are girls. How many boys are there in the class?
Answer:12 boys
Step-by-step explanation:100-60=40 40% of 30 is 12
A glider begins its flight 3/4
mile above the ground. After 45 minutes, it is 3/10
mile above the ground. Find the change in height of the glider. If it continues to descend at this rate, how long does the entire descent last?
The change in height is
mile(s).
The entire descent lasts
hour(s).
Skip to navigation
Answer:Answer One: 3 miles. Answer Two: 105.
Step-by-step explanation:
A typical paper bag at a grocery store cannot hold more than 49 pounds. Let p represent the number of pounds a typical paper bag can hold.
Create an inequality to represent the situation. Move a symbol to the lines to create the inequality.
P___49
Answer: = is it maybe
if not sry
p≤49 is the inequality to represent the situation.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that a typical paper bag at a grocery store cannot hold more than 49 pounds.
Let p represent the number of pounds a typical paper bag can hold.
We have to find the inequality to represent the situation
As grocery store cannot hold more than 49 pounds which means it holds less than or equal to 49.
p≤49
Hence, p≤49 is the inequality to represent the situation.
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two rectangles have the exact same area. the measurements of the first rectangle is 3k by 3.calculate the value of k
The value of k is 6.
Given we have length as 3k and the width as 3 of the first rectangle.
length = k₊3 and width = 6 of the second recatngle
Two rectangles has the same exact area.
area = length × breadth
3k × 3 = (k₊3)6
9k = 6k ₊ 18
3k = 18
k = 18/3
k = 6
hence we get the value of k as 6.
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Use synthetic division to find the quotient. 2x⁴ - 4 - 7x - 38x²/x - 4
Answer: A binomial (of the form ax+b).
Step-by-step explanation:
2x⁴ - 4 - 7x - 38x²/x-4=ax+b , hope this is correct
Jamar writes 4 x 6 = 24 to find the total number of
marbles he has. How might Jamar describe what each
factor represents in the multiplication equation?
There 6 number of bags and each bag will have 4 marbles in it.
What is Unitary Method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
4 x 6 = 24
If 24 represents total bof marbles.
So, we can assume that there 6 number of bags and each bag will have 4 marbles in it.
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Simplify each expression.
log (a²-10a+25) + 1/2 log 1/(a-5)³ - log (√a-5)
After simplifying logarithm equation is : [tex]log_{10} \frac{(a-5)^\frac{1}{2} }{a^\frac{1}{2}-5 } \\[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log a × b = log a + log blog a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression can be written as,
[tex]log_{10}(a^2-10a+25) + \frac{1}{2} log_{10}\frac{1}{(a-5)^3} - log_{10}(\sqrt{a} -5)\\\\[/tex]
apply formulas for log a + log b and log a - log b
[tex]log_{10}(a^2-10a+25) + log_{10}(\frac{1}{(a-5)^3})^\frac{1}{2} - log_{10}(\sqrt{a} -5)\\\\= > log_{10}(a^2-10a+25).(\frac{1}{(a-5)^3})^\frac{1}{2} - log_{10}(\sqrt{a} -5)\\\\= > log_{10}\frac{(a^2-10a+25). (\frac{1}{(a-5)^3})}{(\sqrt{a} -5) } \\\\= > log_{10} \frac{(a-5)^\frac{1}{2} }{a^\frac{1}{2}-5 } \\[/tex]
Thus, after solving the logarithm equation is : [tex]log_{10} \frac{(a-5)^\frac{1}{2} }{a^\frac{1}{2}-5 } \\[/tex]
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if 251x=100 two, find x
Answer:
X = 102/251
Step-by-step explanation:
251x = 102
/ /
251 251
X= 102/251
5/12 simplified as a fraction
Answer:
Step-by-step explanation:
You can't simplify 5/12 any more. That is the simplest form
Answer:
5/12 is the simplest form already
Simplify each number.
6¹/₂ . 12¹/₂
[tex]6^{\frac{1}{2} } .12^{\frac{1}{2} }[/tex] can be simplified into 8.48.
Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.
Prime factorization of 6= 2 x 3
Prime factorization of 12= 3 x 2 x 2
According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.
i.e., [tex](x^{m} )^{n} = x^{mn}[/tex]
Another law of indices says that if two terms having same base are multiplied together, then their indices are added.
i.e., [tex]a^{m} X a^{n} = a^{m+n}[/tex]
According to the given condition,
Applying the laws of indices mentioned above,
∴[tex]6^{\frac{1}{2} } .12^{\frac{1}{2} }[/tex] = [tex](2 X 3)^{\frac{1}{2} } . (3 X 2^{2}) ^{\frac{1}{2} }[/tex]
= [tex](3^{2} X 2^{3})^{\frac{1}{2} }[/tex]
= [tex]\sqrt{72}[/tex] = 8.48.
Thus, [tex]6^{\frac{1}{2} } .12^{\frac{1}{2} }[/tex] can be simplified into 8.48.
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The supertanker and the iceberg are headed straight toward each other. The supertanker traveling at a speed of 12 miles per hour, while the iceberg is traveling at 0.5 miles per hour. If the two are exactly 50 miles apart, in how many hour will the hit
If the two are exactly 50 miles apart, it will hit in
T=0.25hours
This is further explained below.
If the two are exactly 50 miles apart, in how many hour will they hit?Generally, the equation for Time is mathematically given as
T=v/d
Therefore
T=(12+0.5)/50
T=0.25hours
In conclusion, If the two are exactly 50 miles apart, it will hit in
T=0.25hours
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Write in index form using a unit fraction 10 √ 34
Answer:
2.6
i thank
Step-by-step explanation:
A grain of rice weighs about 0.03 g.
a) Write the mass of a grain of rice in standard form.
In the USA, about 4.3 million tonnes of rice are eaten each year.
b) 1 tonne = 1 million grams
What is the mass, in grams, of rice eaten in the USA each year?
Give your answer in standard form.
a) The mass of a grain of rice in standard form; 0.3×10⁻¹ gram.
b) The mass, in grams, of rice eaten in the USA each year: 4.6×10¹² grams.
What is described as scientific notation?Scientific notation is a handy way to shorten extremely large numbers with positive exponential values and also very small numbers with negative exponential values. To shorten long numbers in scientific notation, employ positive exponents and decimals.For the given question;
a) Weight of the rice grain is 0.03 g.
Shift the point to one decimal of the right and replace it with 10⁻¹ for this.
= 0.3×10⁻¹
Thus, the number in standard form becomes 0.3×10⁻¹ grams.
b) In USA, the rice eaten per year = 4.3 million tonnes.
1 tonne = 1 million grams
And, we know, one million can be written as.
1 million = 10⁶
4.3 million tonnes = 4.6×10⁶ tonnes.
Now, if 1 tonne = 1 million grams.
Then, multiply both side by 4.6×10⁶.
4.6×10⁶ × 1 tonne = 4.6×10⁶×1 million grams.
4.6×10⁶ tonnes = 4.6×10⁶ million grams.
Again convert million as 10⁶.
= 4.6×10⁶×10⁶
= 4.6×10⁶⁺⁶
= 4.6×10¹²
Thus, in USA 4.6×10¹² grams of rice is eaten each year.
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PLEASE ANSWER RIGHT AWAY
4⁰ + 9 x 2 – 5³
show work please im doing a test
The simplified form of the expression is -106
Simplifying an expressionFrom the question, we are to simplify the given expression
The given expression is
4⁰ + 9 x 2 – 5³
Simplifying
4⁰ + 9 x 2 – 5³
First, evaluate the exponents
5³ = 125
4⁰ = 1
Thus, the expression becomes
1 + 9 x 2 – 125
Simplifying further
1 + 18 - 125
= 19 - 125
= -106
Hence, the simplified form of the expression is -106
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A police car drives 46 miles in 1 hour and 55 minutes what is the average speed in miles per hour
The average speed of the police is 23.96 miles per hour
How to calculate the average speed ?
The distance is 46 miles
The time is is 1 hour 55 minutes, convert the minutes
= 55/60
= 0.92 + 1
= 1.92
The average speed can be calculated as follows
= distance/time
= 46/1.92
= 23.96
Hence the average speed of the police car is 23.96 miles per hour
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3. Suppose you graph the information in the table. Find the slope of a line drawn through the points.
Answer:
I can't see the information in the table but I can tell you how to do it
Step-by-step explanation:
pick two points on the graph, then do this: (y2-y1)/(x2-x1)
this will help you to find the slope of the line
The Sierpinski triangle (pictured below) is a fractal image. The original figure is an equilateral triangle. In each step, the computer splits every triangle in the design into 4 congruent equilateral triangles, and removes the center one from the design. The area remaining in a particular design after n steps can be shown using the following expression:
25√3 / 2 * (3/4)^n
What does 25√3 / 2 signify in the expression? (Image Shown Below)
O Each step multiplies the area 25√3 / 2.
O The original figure had an area of 25√3 / 2 square units.
O Each step increases the area of the figure by 25√3 / 2 square units.
O After many steps, the figure will have an area of 25√3 / 2 square units.
The original figure had an area of 25√3 / 2 square units option (B) is correct.
What is the triangle?In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
It is given that:
The Sierpinski triangle is a fractal image:
The original figure is an equilateral triangle.
The area remaining in a particular design after n steps can be shown using the following expression:
= 25√3/2 (3/4)ⁿ
Plug n = 0
= 25√3/2 (3/4)⁰
= 25√3/2 square units
The expression 25√3/2 represents the area of the image of the triangle(shown in the first number image)
Thus, the original figure had an area of 25√3 / 2 square units option (B) is correct.
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In the figure below, /BC/= 2cm, /AB/= 3cm and ZACD= 1500, what is the value of sin A? A D 150° с A√3 B √√3 2 2cm 2/3 3cm B DE 2 3
Answer:
E 1/3
Step-by-step explanation:
m<ACB = 30° because of supplementary angles.
Use the Law of Sines
sin C/AB = sin A/BC
sin 30°/3 = sin A/2
sin A = (2 × sin 30°)/3
sin A = (2 × 0.5)/3
sin A = 1/3
Answer: E 1/3
The dimensions of a rectangular prism are shown below with one 1/2 feet with 1 foot high 2 1/2 feet the weight of the size of a small Cubes 1/2 of each how many small cubes can be packing rectangle prism show your work
Final Answer:
Rectangular Prism: A rectangular prism is a three-dimensional shape, having six faces, where all the faces (top, bottom, and lateral faces) of the prism are rectangles such that all the pairs of the opposite faces are congruent. Like all three-dimensional shapes, a rectangular prism also has volume and surface area.
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Solve each trigonometric equation for θ in terms of y .
y=2 cosθ+1
Answer:
Θ = [tex]cos^{-1}[/tex] ( [tex]\frac{y-1}{2}[/tex] )
Step-by-step explanation:
y = 2cosΘ + 1 ( subtract 1 from both sides )
y - 1 = 2cosΘ ( divide both sides by 2 )
[tex]\frac{y-1}{2}[/tex] = cosΘ , then
Θ = [tex]cos^{-1}[/tex] ( [tex]\frac{y-1}{2}[/tex] )
Find 29- 3f + 2g, when f=4 and g=3
29-3f+2g
=29-3(4)+2(3)
=29-12+6
=23