a) f is strictly increasing function then f is one to one
b) f: R-> R such that f(x) = x^n where n is even is not one to one
suppose that f is strictly increasing function
we have to prove that f is one to one
let us assume f(x1) = f(x2)
we have to prove x1=x2
since f is strictly increasing function
then x2>x1 and x1> x2
this implies that x1=x2
and Hence f is one to one function
b) f:R->R such that f(x) = x^ n where n is even is not one to one
because f(1)= f( -1)
but -1 is not equal to 1 therefore f is not one to one function
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Ramona wrote 14 letters to friends each month for n months in a row. Write an expression to show how many total letters Ramona wrote.
Answer:
let y represent number of months in a row and
let S represents sum of letters that have been sent in y number of months
This simply means that we can write equation:
14*y = S
For any number of months we express it in equation above and we get total number of letters she wrote.
Answer:
[tex]{ \sf{total = 14n \: \: letters}}[/tex]
f(x) = 4x²-3x, what is the value of f (2) ?
Answer:
Step-by-step explanation: : f(x) = 4x² + 3x – 7f(-2) = 4(-2)²+3(2)-7f(-2) =16+6-7 =32-7 = 25.
Hello is this correct
Answer:
Correct
Step-by-step explanation:
Surface area of a sphere = 4 pi r^2
diameter = 28 then r = 14 ft
4 (pi)(14^2) = 2463 ft^2
looks correct for your value of pi =3.14
The difference of two and a number is 7.
2 + n = 7
2 - n = 7
n - 2 = 7
n + 2 = 7
Answer:
the answer for n is 5
Step-by-step explanation:
2 + n = 7
n = 7-2
n = 5
0.21 / 1.008. Pls helppp
What is the value of |-3.25| And |-4.25|
The values are |-3.25| = 3.25 and |-4.25| = 4.25
How to determine the values of the expressions?The expressions are given as
|-3.25| and |-4.25|
The above expressions are absolute value expressions
And as a general rule, an absolute value expression, when evaluated must follow the following rule
|±a| = a
Using the above as a guide, we have
|-3.25| = 3.25
Also, we have
|-4.25| = 4.25
Hence, the values of the expressions are |-3.25| = 3.25 and |-4.25| = 4.25
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r(x) = 4x² + 2x - c(x) = 10x + 25
(r-c) (x)
The most appropriate choice for function and subtraction of function will be given by-
(r-c)(x) = [tex]4x^2-8x-25[/tex]
What is function and subtraction of function?
A function from A to B is a rule that assigns to each element of A a unique element of B
A is the domain set and B is the co-domain set.
Subtraction of function
Suppose f(x) and g(x) are two functions. Then
(f - g)(x) = f(x) - g(x)
Here,
r(x) = [tex]4x^2 + 2x[/tex]
c(x) = [tex]10x+25[/tex]
(r-c)(x) = r(x) - c(x) = [tex](4x^2+2x)-(10x +25)[/tex]
= [tex]4x^2+2x -10x-25[/tex]
= [tex]4x^2-8x-25[/tex]
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9x+y=11, -6x-y=-8
solve for x and y using system of elimination
Answer:
3
Step-by-step explanation:
9x+y=11 .....(1)
-6x-y=-8 ....(2)
Add equation 1 to equation 2
-6x+9x -y+y =-8+11
3x=3
Divide both sides by 3
3x/3=3/3
Jacob had $180 in his savings account at the beginning of summer vacation. over the next 12 weeks, he mowed lawns in his neighborhood earning $145 and spending $55 each week. he deposited all of his weekly profits to his savings account each week. when summer vacation is over, he plans to spend $180 per month. for how many months can he make withdrawals from his saving account until his balance is $0?
Jacob will need 7 months to spend all the money.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Jacob had $180 in his savings account at the beginning of summer vacation. over the next 12 weeks, he mowed lawns in his neighborhood earning $145 and spending $55 each week. he deposited all of his weekly profits into his savings account each week. when summer vacation is over, he plans to spend $180 per month.
The number of months will be calculated as:-
Total money in the account = 180 + 12(145-55)
Total money in the account = $1260
Total months = 1260 / 180
Total months = 7 months
Therefore, Jacob will need 7 months to spend all the money.
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Graph the function f(x)=-3x+1.
Use the line tool and select two points to graph.
+Move Line
Undo
Redo
x Reset
The y-intercept is (0, 1).
Substituting [tex]x=-3[/tex] yields [tex]f(x)=-\frac{1}{3}(-3)+1=2[/tex].
So, draw the line through (0, 1) and (-3, 2).
Question: 4 + 2x - 7(2)³
1. What is the variable?
2. What is the coefficient of the variable?
3. What is the term with the variable?
Answer:
1: x
A variable is a letter in an equation that represents an unknown value or a value that can change.
2: 2
A coefficient for a variable is the leading number in front of the variable. It tells you how many times the variable happens
3: 2x
A term is a multiplication or division statement separated by a +/- sign.
Hope that helps
What is the slope of the line that passes through the points (6, -5)(6,−5) and (6, -4)(6,−4)?
Answer:
Undefined
Step-by-step explanation:
The x-coordinates are ths same, so this is a vertical line. Vertical lines have undefined slope.
The. median, range, and mode for the following numbers:8,7,12,7,11,10,7,12
Answer:
median = 9
range = 5
mode = 7
Step-by-step explanation:
median = 9 is in the middle of 10 and 8
range = 12 - 7
mode = there are 3 7s
Mode : the quantity that appears the most in a sequence
Because 7 is the number that appears the most ( 3 times ), it is the mode.
Range : the difference between the largest number and the smallest number
In this case, 12 is the biggest and 7 is the smallest -> Range = 5.
Median : the "middle number" (for example, if the sequence has 7 numbers, the 4th number will be the median. if the sequence has 8 numbers, the median will be the average of the 4th and 5th number, and of course from increasing order.)
There are 8 numbers in the sequence, from lowest to highest : 7,7,7,8,10,11,12,12.
So, the median = (8+10)/2 = 9.
Aldo spent $17.49 at the store. How much change will he receive if he pays with a $20 bill?
Answer:
he will receive $2.51
Step-by-step explanation:
Simplify a raised to the negative third power over quantity 2 times b raised to the fourth power end quantity all cubed
Here is the answer
I hope it helped you
The equation 270 = f + 6.50(30) represents the cost of printing the shirts at a second printing company. Find the solution to the equation and state what it represents in this situation
The solution to the equation is f = 75.
The initial charge or setup cost is represented by the intercept or f.
What is the slope-intercept function?The linear function is expressed using the slope of the line and the y-intercept in the slope-intercept form. Its form is y = mx+ b where the slope is m and the y-intercept is b.Given equation: 270 = f + 6.50(30)
We must identify the equation's solution and explain what it represents in this situation.
The equation above is written in the form of a slope-intercept function where 6.50 is the gradient or slope of the function and 30 equals the number of shirts. The total cost of printing is 270.
The equation 270 = f + 6.50(30) can be solved as follows:
270 = f + 6.50(30)
⇒ f = 270 - 195 = 75
Therefore, the initial charge or setup cost is represented by the intercept or f. As a result, the setup fee is 65.
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In the diagram below, the numbers in each box is the sum of two numbers below it. Work out the missing numbers for boxes A and B.
The value of the missing number in box A is [tex]1\frac{1}{2}[/tex]
The value of the missing number in box B is [tex]7\frac{1}{4}[/tex]
What are the missing numbers?In order to determine the value of A, subtract [tex]1\frac{1}{4}[/tex] from [tex]2\frac{3}{4}[/tex]. Subtraction is the mathematical operation that is sued to determine the difference between two or more numbers
A = [tex]2\frac{3}{4}[/tex] - [tex]1\frac{1}{4}[/tex]
[tex]1\frac{3 - 1}{4}[/tex] = 1 [tex]\frac{2}{4}[/tex] = [tex]1\frac{1}{2}[/tex]
In order to determine the value of B, add [tex]4\frac{1}{2}[/tex] and [tex]2\frac{3}{4}[/tex] together. Addition is the process used to determine the sum of two or more numbers.
B = [tex]4\frac{1}{2}[/tex] + [tex]2\frac{3}{4}[/tex]
[tex]6\frac{2 + 3}{4}[/tex] = [tex]6\frac{5}{4}[/tex] = [tex]7\frac{1}{4}[/tex]
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what is 130x1000 well I've been on this app and it has answered this question for me and and can for u to and can I know how this app has helped you with mathematics??
the answer to 130x1000 is
130,000
((50+50+50)*85)*0.9=
Answer:
(150*85)*0.9
=12750*0.9
=11475
Answer:
11475
Step-by-step explanation:
((50+50+50)*85)*0.9=
(150*85)*0.9=
12750*0.9=
11475
CARD #7:
Rectangle BCDE will be dilated by
3
a scale factor of
2°
Gabe says the
rectangle will
be reduced.
Gabi says the
rectangle will
be enlarged.
Gabi is correct to say that the rectangle will be enlarged when it will be dilated by a scale factor of 3/2.
What does the scale factor determine?The image's size will depend on the scale factor, which is used to dilate a mathematical entity (compared to the original object).An expansion happens when the scaling factor's absolute value exceeds one.Compression happens when the scale factor's absolute value falls below one.When the scale factor's absolute value is 1, neither expansion nor compression takes place.As it is given that the rectangle BCDE is dilated by the scale factor of 3/2 which is more than 1, so the rectangle will expand or enlarge.
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The complete question is: "Rectangle BCDE will be dilated by a scale factor of 3/2.
Gabe says the rectangle will be reduced.
Gabi says the rectangle will be enlarged."
What is 44 millimeters converted to m
Show that (a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)=0
Answer:
this equation is always trueStep-by-step explanation:
Show that (a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)=0
(a−b)⋅(a+b)+(b−c)⋅(b+c)+(−a+c)⋅(a+c)=0
(a^2−b^2)+(b^2−c^2)+(−a^2+c^2)=0
(a^2−c^2)+(−a^2+c^2)=0
0=0
this equation is always true
[tex]\left(a-b\right)\left(a+b\right)+\left(b-c\right)\left(b+c\right)+\left(c-a\right)\left(c+a\right)=0[/tex]
[tex]\left(a-b\right)\left(a+b\right)+\left(b-c\right)\left(b+c\right)+\left(c-a\right)\left(c+a\right)-\left(b-c\right)\left(b+c\right)=0-\left(b-c\right)\left(b+c\right)[/tex]
[tex]\left(a-b\right)\left(a+b\right)+\left(c-a\right)\left(c+a\right)=-\left(b-c\right)\left(b+c\right)[/tex]
[tex]\left(a-b\right)\left(a+b\right)+\left(c-a\right)\left(c+a\right) = a^2-b^2+\left(c-a\right)\left(c+a\right) =a^2-b^2+c^2-a^2 =-b^2+c^2[/tex]
[tex]-\left(b-c\right)\left(b+c\right) =-\left(b^2-c^2\right) =-b^2-\left(-c^2\right) =-b^2+c^2[/tex]
[tex]-b^2+c^2=-b^2+c^2[/tex]
[tex]0=0[/tex]
It is always true because 0=0.
PLSSS HELP 20 POINTS I NEED IT BEFORE 12 PM SATURDAY
Graph each parabola and identify the axis of symmetry, focus, and directrix.
2x^2 − 8y=0
For given parabola 2x² - 8y = 0,
the axis of symmetry : y-axis
focus : (0, 1)
directrix : y = -1
In this question, we have been given an equation of parabola 2x² − 8y = 0
We need to graph the parabola and identify the axis of symmetry, focus, and directrix.
2x² - 8y = 0
2x² = 8y
x² = 8y/2
x² = 4y
The graph of the parabola x² = 4y is as shown below.
From this graph, the vertex is (0, 0)
We know that, for a parabola of the form x² = 4ay, the focus is (0, a) and directrix is y = -a
For the parabola x² = 4y, a = 1
So, the focus is (0, 1) and the directrix is y = -1
And the axis of symmetry for the parabola x² = 4y is the y-axis.
Therefore, for given parabola 2x² - 8y = 0,
the axis of symmetry : y-axis
focus : (0, 1)
directrix : y = -1
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What is the value of x (3x-10)° 152°
Select all ratios equivalent to 4:16
5:8 3:12. 15:32
Answer:
3:12 is equivalent 4:16
Step-by-step explanation:
5:8 = 0.625
3:12 = 0.25
15:32 = 0.48...
and 4:16 is 0.25, equal to 3:12
:]
(Brainliest would help a lot) Tell me if this is incorrect!
Sarah has three sisters. lea is 4 less than 3 times the age of sarah. rachel is 3 years less than one-half sarah’s age. amanda is 1 year older than twice the age of sarah. if the sum of the ages of the four sisters is 46 years, how old is each sister?
Answer:
Sarah=x
Lea=3x-4
Rachel=1/2x-3
Amanda=2x+1
Sum=46
x+3x-4+1/2x-3+2x+1=46
6.5x-6=46
6.5x=52
x=52/6.5x
x=8
input x in each sister's age:
Sarah= 8 years
Lea = 3(8)-4=20 years
Rachel = 1/2(8)-3=1 year
Amanda = 2(8)+1=17years
Step-by-step explanation:
Step by step please
Pls help
Answer:
n= -3
Step-by-step explanation:
The solution is attached
Each box holds 48 pencils. The chart below shows the number of pencils in 1 box and 5 boxes.
Using a proportional relationship, we have that:
The table is completed as follows: x = 4, y = 192; x = 6, y = 288; x = 9; y = 432;6 boxes are not enough for 300 pencils, 7 are needed.What is a direct proportional relationship?A direct proportional relationship is a function in which the output variable is found with the multiplication of the input variable and the constant of proportionality k, as follows:
y = kx.
From the table in this problem, the constant is given as follows:
k = 240/5 = 48/1 = 48.
Hence the relationship is:
y = 48x.
Then:
When x = 4, y = 48(4) = 192.When x = 6, y = 48(6) = 288.When x = 9, y = 48(9) = 432.For 300 pencils, the number of boxes is given by:
48x = 300
x = 300/48
x = 6.25.
There are not decimal parts of a box, a complete box is needed, hence 7 boxes are needed, meaning that 6 boxes are not enough for 300 pencils.
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Is the following relation a function? x y −1 −2 2 3 3 1 6 −2 a Yes b No
Yes, the provided relation is, indeed, a function. Each x value has just one y value.
In the given table,
x y
-1 -2
2 3
3 1
6 -2
A relationship is a function if each x-value has its y-value.
In the relationship, each x-value has a unique and unique y-value. For example, a value of -1 is -2, a value of 2 is 3, a value of 3 is 1, and a value of 6 is -2.
Although the inclusion of (-1,-2) and (-3) suggests that this is not a one-to-one or infusion function of (6,-2).
As a result, the given relationship is a function. Each x-value has only one y-value.
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How many miles is 100% of 44 miles?
Answer: 44 miles
Step-by-step explanation: any percentage can be written as a decimal. for example, 50% is 0.50 or 25% is 0.25. in this case, 100 percent is 1.00. now that we know what 100 percent is, we multiply 44 by 1.00(100%). my old math teacher told me that whenever you have something OF something, you multiply them togethor. in other words, of means times. this problem can be written 1.00 times 44.