The one-to-one function is obtained as f(x) = 4x + 1 which is a linear function.
What is a function?A function y = f(x) is defined as a one to one relation between sets X and Y. The set X is called the domain while Y is called the range of f(x).
A function can either have one-to-one or many-to-one mapping.
One-to-one mapping implies unique element in the domain for each element in the range while for many-to-one mapping there are many elements in the domain for one element in the range.
The given functions are y = [2x] , y = x² and f(x) = 4x + 1 respectively.
They can be examined one by one as follows,
(a) y = [2x]
It is a greatest integer function.
At x = 1.1, y = [2 × 1.1] = [2.2] = 2
And, for x = 1.2, y = [2 × 1.2] = [2.4] = 2
It implies for different values of x, the function has same value.
Thus, it is not one-to-one function.
(b) y = x²
Find values of the function at two different x as,
x = -2, f(x) = (-2)² = 4
And, for x = 2, f(x) = 2² = 4.
It implies for different values of x, the function has same value.
Thus, it is not one-to-one function.
(c) f(x) = 4x + 1
It is a equation of a straight line.
Which implies it has different values for different values of x.
Thus, it is a one-to-one function.
Hence, out of the given functions only f(x) = 4x + 1 is one-to-one.
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What happens when you log an e?
When you log an e, you are essentially taking the natural logarithm of the number. This means that you are taking the logarithm of a number to the base e, which is about 2.718. The result of this calculation is the number of times the number must be multiplied by itself to get the original number.
For example, if you were to log an e, it would be equal to 1, since e x e = e. If you log a number bigger than e, such as 8, the result would be equal to 2.079, which means that 8 must be multiplied by itself twice (2.079 times) to get the original 8.
In general, when you log a number, you can think of it as a way of seeing how many times that number needs to be multiplied by itself to get the original number. This can be useful in many fields, from mathematics to engineering to physics, to find the mathematical relationship between two numbers.
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Pls help this is math work
Answer:
∠ R = 35° , ∠ T = 45°
Step-by-step explanation:
since the triangles are similar then corresponding angles are congruent, so
∠ R = ∠ U = 35°
∠ T = ∠ Q = 45°
Can you help me with this
What is the degree of 2 polynomial?
A polynomial with a degree of two is referred to as a quadratic polynomial.
What is a quadratic polynomial?When the highest power of a variable term in a polynomial expression equals 2, the term is considered a quadratic polynomial. The exponent of a polynomial is all that is considered when determining its degree. It does not account for the power of a coefficient or constant term.
When a quadratic polynomial is equated to 0, it generates a quadratic equation or a quadratic function. The solutions to a quadratic equation are known as its roots or zeros.
A quadratic polynomial is a second-degree polynomial with the highest degree term having the value 2 as its coefficient. A quadratic equation is written in its general form as ax² + bx + c = 0.
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What are the 3 parts to a chemical word equation?
The three main parts to a chemical word equations are the reactants , the products and the arrow .
What is a Chemical Equation ?
A chemical equation is defined as a representation of a chemical reaction expressing it in in terms of symbols of the substances.
The three main parts of the Chemical Equation are :
(i) The Reactants : During a chemical reaction, these elements combine and undergo some chemical changes. They are present on left side of reaction equation.
For Example : [tex]CH_{4} + 2O_{2}[/tex] ;
(ii) The Arrow : It indicates formation of products from reactant . It is represented as " → " ;
(iii) The Products : Products are the result of chemical reactions between their reactants. It is present on right side of the chemical equation.
For example, : [tex]CO_{2} +2H_{2} O[/tex]
So , overall Chemical Equation can be written as : [tex]CH_{4} + 2O_{2}[/tex] → [tex]CO_{2} +2H_{2} O[/tex] .
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For which values of x does each expression make sense? square root of x-2 over square root of x-3
the answer is x>3
this is the answer becuase x-3 cannot be 0 because tou cant divide by zero and it cant be negative because it is in the square root notation which cant be negative without the use of inaginary numbers
Write an inequality with the solution x > or equal to 4. The inequality should have the variable on both sides, a fractional coefficient of the variable on the left side, and a fraction anywhere on the right side.
The inequality equation ( x ≥ 4 ) is given as ( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
x ≥ 4 be equation (1)
On simplifying the equation , we get
Divide by 4 on both sides of the equation , we get
( x / 4 ) ≥ 1
Adding x on both sides of the equation , we get
x + ( x/4 ) ≥ 1 + x
Now , adding ( 1/4 ) on both sides of the equation , we get
x + ( 1/4 ) + ( x/4 ) ≥ 1 + x + ( 1/4 )
On simplifying the equation , we get
( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x
Therefore , the value of A is ( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x
Hence , the inequality equation is ( 1/4 ) + ( 5x/4 ) ≥ ( 5/4 ) + x
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f(x)=3^√x-1
Find f(27) and f(-343)
need to find cube root
On solving the provided question, we can say that - the value of the cube root is 19683 = 27
what is cube root?In mathematics, y3 = x since the cube root of a number x equals a number y. Each non-zero real integer has precisely one real cube root, one set of complex conjugate cube roots, and three different complex cube roots. When a number is multiplied three times, the result is the cube root of that number. Three cube roots, the final cube root, is the symbol for the cube root. The opposite of cubing an integer is finding the cube root of that number. Prime factorization is a fairly straightforward technique that may be used to get a number's cube root. The sign stands for a cube root.
here,
we have f(27)
cube will be [tex]( 27 )^3[/tex] = 19683
and f(-343) = -7
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Solve equations - two sides
(135a)
Solve
2x - 7=7x +5
Answer:
x=-12/5
Step-by-step explanation:
2x-7=7x+5
2x-7x=5-(-7)
-5x=5+7
x=12/-5
x=-12/5
What is slope and intercept of the line 2x 3y 6?
The slope of linear eqution of two variables x and y, i.e., 2x+3y = 6 is -2/3 and intercept is 2 .
The slope-intercept form expression of a linear equation is y = mx + c --------->(1)
Where m --> slope of the straight line and
c --> the x - intercept .
The expression for slope is represented as :
m = (y₂ - y₁) / (x₂ - x₁) ------>(2)
where (x₁, y₁) and (x₂, y₂) are any two points lying on the straight line. Once the slope m is determined then the general equation of the straight line can be determined easily.
Now we have , the equation in the problem statement is 2x + 3y = 6. firstly , we can rewrite it in the slope-intercept form as :
3y = 6 - 2x
=> y = 6/3 - 2x/3
=> y = -2x/3 + 6/3
=> y = (-2/3)x + 2
comparing the above eqution with eqution(1) we get , m = -2/3 and c = 2. So, slope and intercept of eqution 2x + 3y = 6 are -2/3 and 2 respectively.
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What is the height of the triangle 12 units?
The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.
what is triangle ?
A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the sum of the angles in a triangle.
given
Given, side length, a = 12 units.
the height of equilateral triangle, h = (a√3)/2.
Substituting the value of 'a',
h = (12√3)/2 = 6√3 =
10.39 units.
The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.
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Shade the points in the plane whose x-coordinates are greater than their y-coordinates. Write the inequality that describes these points.
The inequality that describes these points is y ≤ -1/2(x) -3. The graph is given the attachment.
How to graph an inequality?To graph a linear inequality in two variables (say, x and y), start with y on one side. Consider the related equation obtained by changing the inequality sign to an equality sign. This equation's graph is a straight line.
If the inequality is strict (< or >), draw a dashed line. If the inequality is not strict (≤ or ≥), draw a solid line.
Finally, choose one point that is not on either line ((0,0) is usually the easiest) and determine whether these coordinates satisfy the inequality or not. If they do, shade the half-plane containing that point. If they don't, shade the other half-plane.
Graph each of the system's inequalities in a similar way.
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\frac { 32 x ^ { 2 } } { y } + \frac { 108 y ^ { 2 } } { x } y 32x 2 + x 108y 2
Therefore , the solution of the given problem of fraction comes out to be 4((2x)³ + (3y)³) /xy.
What exactly is a fraction?To represent a whole, divide it into any number of comparable parts, or fractions. How many units of a particular size there are is expression using fractions in standard English. 8, 3/4. Parts of a whole are included. Numbers in mathematics are stated as a ratio of the fraction to the denominator. These are each simple fractions that represent an integer. A fraction is contained in the exponent or population of a complicated fraction. When a fraction is true, its numerators are less than its denominators. An amount that makes up a fraction of a whole is called a fraction. You can assess the whole by dissecting it into smaller pieces. For instance, 12 is used to denote half of a total number or item.
Here,
Given : 32x²/y + 108y²/x
=> (32x³+ 108y³ ) /xy
=> 4(8x³ + 27y³) /xy
=> 4((2x)³ + (3y)³) /xy
Therefore , the solution of the given problem of fraction comes out to be
4((2x)³ + (3y)³) /xy.
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How do you solve systems by substitution step by step?
Answer:
1.Solve one of the equations for either variable.
2.Substitute the expression from Step 1 into the other equation.
3.Solve the resulting equation.
4.Substitute the solution in Step 3 into one of the original equations to find the other variable.
5.Write the solution as an ordered pair.
6.Check that the ordered pair is a solution to both original equations.
Step-by-step explanation:
Does 4 8 10 make a right triangle?
No, 4, 8 and 10 cannot be the sides of a right triangle. So 4, 8 and 10 does not make a right triangle.
In a right triangle, the side opposite the right angle (the hypotenuse) is the longest side. The side opposite the 90-degree angle is the hypotenuse and it follows the Pythagorean theorem which states that the square of the hypotenuse is equal to the sum of the squares of the legs, so:
c² = a² + b²
In this case, c = 10, a = 8 and b = 4,
so 8² + 4² = 64 + 16 = 80 ≠ 10²
That is it does not follows the theorem. Therefore, 4, 8 and 10 cannot be the sides of a right triangle.
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6. Jenna wants to hang outdoor stringed lights on her house along the roof line
and horizontally across, connecting the ends of the roof line to create a triangle.
What is the approximate length, in feet, of lights that she needs to create one
triangle?
A. 48
B. 64
C. 80
D. 98
The approximate length, in feet, of lights that she needs to create one triangle is 64
This is an approximate estimate as the exact length would depend on the specific measurements of the roof line. However, if the roof line is a typical house roof and the string lights are hung horizontally across to connect the ends of the roof line, creating a triangle, the approximate length of lights needed would be the hypotenuse of the triangle (the longest side) which is equal to the square root of (leg 1^2 + leg 2^2).
A typical house roof is approximately 40 feet wide and 20 feet tall, which creates a right triangle with legs of 40 and 20. The hypotenuse of this triangle (the length of lights needed) would be approximately 64 feet (the square root of (40^2 + 20^2) = 64).
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Can someone help me please? Picture attached
Answer:
Step-by-step explanation:
A^2 + B^2 = C^2
12^2 + B^2 = 18^2
144 + B^2 = 324
Subtract 144 from both sides
B^2 = 324 - 144
B^2 = 180
[tex]\sqrt{180}[/tex] = 13.416
B^2 = 13.4
How do you determine area?
Answer:
You multiply one side and then the other. Basically doing hxw
What happens to the signs when you reflect a point across both axes?
when we reflect a point (p, q) over the y-axis the y-coordinate stays the same but the x-coordinate changes signs so the image is (-p, q).
Reflect a point
A reflection point occurs when a figure is constructed around a single point known as the point of reflection or center of the figure.
coordinates
it is usually a pair of numbers: the first number shows the distance along, and the second number shows the distance up or down.
image of point
The image of the point about the line y=x can be obtained by interchanging the x-coordinate and y-coordinate of the point.
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Mike has $21 to spend at the mall. He spends all of his money on bracelets for his sisters. Bracelets cost $3 each. How many bracelets dose he buy?
Answer:
7
Step-by-step explanation:
How much money should be put into a savings account now that earns 6.0% a year compounded weekly if you want to have 70000 in 15 years?
If you want to have $70,000 in 15 years, you need start saving money now in a savings account that earns 6.0% annually compounded weekly.
How does compound interest work?When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest.Compounding is effective for both promised and unguaranteed products. All or part of your money could be lost.
Use the compound interest formula and enter the figures you are familiar with. Then find a solution for the unknown number.
A = P(1 +r/n)^(nt)
where A represents the balance of the account, P represents the amount invested, r represents the yearly rate, n represents the number of times per year interest is compounded, and t is the number of years.
Filling in the given values, we have ...
70000 = P( 1 + 0.06/52)^(52*15) = P(2.4583)
P = 70000/2.4583 = 28474.96
You would need to deposit 28474.96 in order to have 70000 in 15 years.
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In ΔSTU, = 670 inche, u = 630 inche and ∠U=67°. Find all poible value of ∠S, to the nearet degree
The measure of ∠S is 59.4° for trignometric identities
What are trigonometric identities?
There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
ΔSTU:
s = 50 inches
t = 58 inches
u = 630 inches
Applying the cosines rule on ΔSTU.
s² = t² + u² - 2 x t x u x cos S
cos S = (t² + u² - s²) / 2tu
cos S = (58² + 27² - 50²) / (2 x 58 x 27)
cos S = (3364 + 729 - 2500) / 3132
cos S = 0.5086.
∠S = (0.5086)
∠S = 59.4°
Thus,
∠s angle value is 59.4°.
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Show youR WORK please send. A photo it could help
Answer:
Step-by-step explanation:
1 ft= 12 inches
So 5ft = 60 Inches
4= 0.3
Thus, Its 60.3
What are the 4 steps to solve by elimination?
Elimination is a very easy method when it comes to solving simultaneous equations.
First, the best thing to do is bring the equations down to their lowest form. Try to remove the fractions in the co-efficient and have the equation in the standard form where every variable is expressed as individually as possible.
The next thing to do is to select a variable and manipulate the equations in such a way that the coefficients of that variable across all of the equations are the same. Here select any 2 equations to work on first if more than 2 are given
Now take one of the equations and multiply it by -1.
Add the equations up to eliminate the variable and derive the other variable(s)
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What’s the equation to find angles in a parallelogram
HELP!!! I WILL GIVE YOU 24 POINTS!!!THINK SMaRTER| Sense or Nonsense? . Emilio and Julia used different ways to find ‡ + 4. Emilio used a rodel to find the quotient. Julia used a related multiplication equation to find the quotient. Whose answer makes sense? Whose answer is nonsense? Explain your reasoning.
Answer:
24
Step-by-step explanation:
24 it's could be ok. I think 24 is good.
Answer: I think it's nonsense??? Not quite sure...
Step-by-step explanation:
Please hurry, it's due in two days
Answer:
C (3, -2) is in the Fourth Quadrant.
The equation of the line is Y=2
The Line x=-1 would be a straight vertical line on the point x=-1.
Step-by-step explanation:
I have attached three pictures, one of all the quadrants labeled for you to help in the future, one of a visual of y=2 with the points labeled, and one of a visual of the line x = -1.
Audrey has x pounds of red grapes and y pounds of green grapes. she has less than 5 pounds of grapes in all. which are reasonable solutions for this situation? check all that apply. (–1, 2) (1, 3.5) (2, 2) (4.5, 0.5) (5, 0)
The reasonable solutions for this situation is (1, 3.5) and (2, 2)
What is Graph?A graph is a visual representation of data or information, typically used to display the relationship between two or more variables. Graphs are used to make it easier to understand and analyze data, and can be used to convey information in a clear and concise manner.
Audrey has x pounds of red grapes and y pounds of green grapes.
She has less than 5 pounds of grapes in all, hence:
x + y < 5
Also, x ≥ 0, y ≥ 0
a) The option (–1, 2) is wrong because x = -1 < 0
b) The option (1, 3.5) is correct because 1 + 3.5 = 4.5 < 5
c) The option (2, 2) is correct because 2 + 2 = 4 < 5
d) The option (4.5, 0.5) is wrong because 4.5 + 0.5 = 5 which is not less than 6.
e) The option (5, 0) is wrong because 5 + 0 is not less than 5
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The Top-Notch Middle School had athletes from all the grades playing on a sports team.
6th grade 7th grade 8th grade
Basketball 2 4 7
Baseball 1 6 5
Soccer 7 4 4
Football 8 15 10
The Top-Notch Middle School had athletes from all the grades playing on a sports team.
Explain what the ratio 5:73 represents.
The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.
The ratio 5:73 represents the ratio of 7th grade football players to total athletes.
The ratio 5:73 represents the ratio of total athletes to 7th grade football players.
The ratio 5:73 represents the ratio of 6th grade athletes to total athletes.
Based on the information presented, the ratio represents 8th-grade baseball players to total athletes.
What is a ratio?A ratio is a mathematical expression that shows the proportion or the number of a specific element in a category compared to the number of another element in the same category. For example, if you count the animals on a farm the ratio of cows to chickens can be 5:7, which means that for every 5 cows there are 7 chickens.
What does the ratio 5:73 mean?5 : This is the number of baseball players who are in 8th-grade
73: This is the total of players. You get this number if you add all the numbers given.
Based on this, this ratio is comparing the number of baseball players and total players, which means the meaning of this ratio is " the ratio of 8th grade baseball players to total athletes".
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What is the average rate of the function from x =2 to x =4 write as whole number
Answer:The average rate of the function from x = 2 to x = 4 is 6.
Step-by-step explanation: