What is the letter in mathematics?

What is the letter ƒ in mathematics?

Answers

Answer 1

The letter f usually indicates that the equation is a function in the notation f(x).

Example: f(x) = x + 1

It is a fancier/more proper replacement for the variable 'y'. The same is used for the letter g as in g(x) and h as in h(x).

OR

It could just be a regular ole variable

Example: f + 1 = 7, solve for f

Answer 2

The letter f usually indicates that the equation is a function in the notation f(x).

Example: f(x) = x + 1

It is a fancier/more proper replacement for the variable 'y'. The same is used for the letter g as in g(x) and h as in h(x).

It could just be a regular ole variable

Example: f + 1 = 7, solve for f

Related Questions

What is the domain of this function?

{x| x > }

Answers

Notice that it starts at x = 0 with closed dot then it goes to the right.

So the domain would be {x | x ≥ 0}

Hope this helps.

The graph defines the function for all values of x greater than or equal to zero.
{x | x ≥ 0}

_____
The solid dot at (0, 9) indicates x=0 is part of the domain. The arrow at the right end of the line indicates the domain extends to +∞.

When the sum of 5 and three times a positive number is subtracted from the square of the number, 0 results. Find the number.

Answers

[tex]x-the\ number\\\\x^2-(5+3x)=0\\\\x^2-5-3x=0\\\\x^2-3x-5=0[/tex]

[tex]Use\ the\ quadratic\ formula:\\a^2x+bx+c=0\\\\\Delta=b^2-4ac\\\\if\ \Delta > 0\ then\ x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\if\ \Delta=0\ then\ x_0=\dfrac{-b}{2a}\\\\if\ \Delta < 0\ then\ no\ solution[/tex]

[tex]x^2-3x-5=0\\\\a=1;\ b=-3;\ c=-5\\\\\Delta=(-3)^2-4\cdot1\cdot(-5)+3+20=29 \ \textgreater \ 0\\\\\sqrt\Delta=\sqrt{29}\\\\x_1=\dfrac{3-\sqrt{29}}{2\cdot1}=\dfrac{3-\sqrt{29}}{2} \ \textless \ 0\\\\x_2=\dfrac{3+\sqrt{29}}{2\cdot1}=\dfrac{3+\sqrt{29}}{2} \ \textgreater \ 0[/tex]

[tex]Answer:\ \boxed{x=\dfrac{3+\sqrt{29}}{2}}[/tex]

Final answer:

To solve for the positive number when the sum of 5 and three times the number is subtracted from the square of the number to yield zero, set up and solve the quadratic equation x^2 - 3x - 5 = 0 using the quadratic formula.

Explanation:

The student has asked for help in finding a positive number when the sum of 5 and three times the number is subtracted from the square of the number, and the result is 0. This involves setting up a quadratic equation and solving for the number.

Let's denote this positive number as 'x'. According to the problem statement, the equation can be written as:

x2 - (5 + 3x) = 0.

We can then expand and simplify this equation:

x2 - 5 - 3x = 0

And, rearrange it into standard quadratic form:

x2 - 3x - 5 = 0

Next, we can either factorize this equation, if possible, or use the quadratic formula to find the value of 'x' that satisfies the equation. Since this equation does not factor neatly, we use the quadratic formula:

x = ∛2 - 4ac) / 2a

In this case, a = 1, b = -3, and c = -5. Plugging these into the quadratic formula, we find the two possible solutions for x. Only the positive solution is relevant since the problem states that the number is positive.

find any points of discontinuity for each rational function. Sketch a graph. Describe any verticals or horizontal asympyoyes and any holes

(X^2-4)/(X+2)(X^2-49)

Answers

For
y = (x^2 -4)/((x +2)(x^2 -49))
the numerator factors to (x -2)(x +2), so the factor of (x +2) will cancel with that in the denominator, leaving
y = (x -2)/(x^2 -49)

There are points of discontinuity at the hole, x=-2, and at each of the vertical asymptotes, at x=-7, +7.
The horizontal asymptote is y=0.

Final answer:

To find the points of discontinuity and sketch the graph of the rational function (x^2-4)/(x+2)(x^2-49), we need to determine the values of x that make the denominator equal to zero. We find that x = -2, x = 7, and x = -7 are the points of discontinuity. We can then sketch the graph by plotting the vertical asymptotes at x = -2, x = 7, and x = -7, and determining the behavior of the function on each side of those points.

Explanation:

To find the points of discontinuity for the rational function (x^2-4)/(x+2)(x^2-49), we need to determine where the denominator is equal to zero. The denominator has two factors, (x+2) and (x^2-49). Setting each factor equal to zero, we find that x = -2, x = 7, and x = -7. These are the points where the function has vertical asymptotes or holes.

To sketch the graph, we can start by plotting the vertical asymptotes at x = -2, x = 7, and x = -7. Next, we can examine the sign of the function on each side of the vertical asymptotes to determine the behavior of the graph. Finally, we can plot any holes in the graph at the corresponding x-values.

Additionally, we should determine if there are any horizontal asymptotes. For rational functions, horizontal asymptotes occur when the degree of the numerator is less than or equal to the degree of the denominator. In this case, the degree of the numerator is 2 and the degree of the denominator is 3, so there is no horizontal asymptote.

Q7 Q26.) Find the quotient of the complex numbers and leave your answer in polar form.

Answers

For any complex numbers in polar form [tex]c_1 = r_1\text{cis}(\theta_1),\ c_2 = r_2\text{cis}(\theta_2)[/tex]

(Where [tex]\text{cis}(\theta) = \cos(\theta) + i\sin(\theta)[/tex])

Then [tex]\dfrac{c_1}{c_2} = \dfrac{r_1}{r_2}\text{cis}(\theta_1-\theta_2)[/tex]

So then for your problem, that would be

[tex]\dfrac{z_1}{z_2} = \dfrac37\text{cis}\left(\dfrac\pi8-\dfrac\pi9\right)=\boxed{\dfrac37\text{cis}\left(\dfrac\pi{72}\right)}[/tex]

So that would be [tex]\boxed{\dfrac37\left(\cos\left(\dfrac\pi{72}\right)+i\sin\left(\dfrac\pi{72}\right)\right)}[/tex]

Hope this helps.

which values of x are solutions of the equation x^3+ x^2-2x=0

Answers

Factor out the x first leaving you with a quadratic. Factor that expression completely to get that x = 0, 1, -2. You have to have 3 solutions since your original expression is raised to the 3rd power.

Help!!!!!!!!!!!!!!!!

Answers

The answer is 35 degrees. x= 35 degrees

In the above line:
∠y + 56 + 51 = 180

To find y, simplify, isolate and simplify again to get y. Remember, what you do to one side, you do to the other.

∠y + 107 = 180
∠y + 107 (-107) = 180 (-107)
∠y = 180 - 107
∠y = 73°

A triangle is = 180°. With this knowledge, you can find ∠x (the last angle).

Plug in 73° for y

y = 73

73 + 72 + x = 180

Simplify.

x + 145 = 180

isolate the x, subtract 145 from both sides

x + 145 (-145) = 180 (-145)

x = 180 - 145

x = 35°

A) 35° is your answer

hope this helps

Jamie mowed 7 lawns. He earned $10, $15, $12, $15, $8, And $15 for six lawns. How much did he earn the seventh time if the mean of the data is 12

Answers

the missing number to find the mean of 12 is 9.

Translate the given statement into an algebraic inequality or compound inequality: The IRS says you are in a certain tax bracket if your taxable income, i, is over $24,500, but not over $59,725.

Answers

A person is in Tax bracket if the taxable income is more than $24,500 but not over $ 59,725.

This means, the taxable income can be more than $ 24,500 but less than or equal to $ 59,725.

If i represents this taxable income, we can write the inequality as:

$ 24,500 < i ≤ $ 59,725

Answer:

C. your welcome

Isabel created the tree diagram to represent the different ways she could order a salad at her favorite restaurant.

According to the diagram, how many combinations of lettuce type, dressing, and topping are possible?

Answers

your answer for this is 12

Answer: Option B

(B) 12

Step-by-step explanation:

2-2*3+3. What is the correct answer

Answers

6 I think because 2-2=0 and 3+3=6

The correct answer is: " -1 " .
________________________________________________________
Note:
_________________________________________________________

2 - 2 * 3 + 3 =

2 - (2 * 3) + 3 =

(2 - 6) + 3 =

-4 + 3 = -1 .
_____________________________________________________
The correct answer is: " -1 " .
_____________________________________________________

How many different ways are there to choose 10 donuts from 20 varieties if at most 4 chocolate donuts are chosen?

Answers

Let [tex]c[/tex] be the number of chocolate donuts chosen. Then for any choice of non-chocolate donut, you have 19 varieties from which to choose. So, for example, if exactly 4 donuts are chocolate, that leaves 16 donuts to be chosen from the 19 remaining varieties. There are [tex]19^{16}[/tex] ways of doing this.

If instead exactly 3 donuts are chocolate, then you have [tex]19^{17}[/tex] ways of choosing the others.

Continuing the pattern, we see that the total number of ways to choose up to 4 chocolate donuts is given by

[tex]\displaystyle\sum_{c=0}^419^{20-c}=19^{20}\sum_{c=0}^419^{-c}[/tex]

which comes out to be

39 678 289 291 775 535 447 366 041

Lupe can ride her bike at a rate of 20 mph when there is no wind. On one particular day, she rode 2 miles against the wind and noticed that it took her the same amount of time as it did to ride 3 miles with the wind. How fast was the wind blowing

Answers

2/20-w=3/20+w
40+2w=60-3w
5w=20
w=4mph

The speed of the wind is 4 mph.

Let, the speed of the wind is W mph.

When Lupe rides with the wind, her effective speed is 20 + W mph, and when she rides against the wind, her effective speed is 20 - W mph.

We are given two pieces of information:

Lupe rode 2 miles against the wind, and it took her the same amount of time as riding 3 miles with the wind.

The time taken to cover a distance is equal to the distance divided by the speed.

Using this information, we can set up two equations:

Time taken against the wind = Time taken with the wind

2 / (20 - W) = 3 / (20 + W)

Now, let's solve for W:

2(20 + W) = 3(20 - W)

40 + 2W = 60 - 3W

5W = 20

W = 20 / 5

W = 4 mph

The speed of the wind is 4 mph.

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There is 3\8 of a pizza in one box and 1/8 of a pizza in another box. How much altogether

Answers

Hello!

3/8 + 1/8 = 4/8

4/8 = 1/2

There is 1/2 of a pizza left

Hope this helps!

4/8 or 1/2 as the simplified version

Hope this helps!

Need help on 1-6 please I need to solve for x and I need to get this done.

Answers

1-3 are about trigonometric ratios (SOH CAH TOA). 4, 5 are about the Law of Cosines, and 6 uses the Law of Sines.

1. Sin = Opposite/Hypotenuse
x = 10*sin(40°) ≈ 6.428

2. Sin = Opposite/Hypotenuse
x = arcsin(7/12) ≈ 35.69°

3. Tan = Opposite/Adjacent
x = 18/tan(52°) ≈ 14.063

4. b^2 = a^2 +c^2 -2ac*cos(B)
B = arccos((a^2 +c^2 -b^2)/(2ac)) = arccos((7^2 +13^2 -8^2)/(2*7*13))
B = arccos(11/13) ≈32.20°

5. Same formula.
x = √(a^2 +c^2 -2ab*cos(B)) = √(157-132cos(42°)) ≈ 7.675

6. The ratio of side lengths is the same as the ratio of the sines of the opposite angles.
6/10 = sin(x)/sin(100°)
x = arcsin((6/10)*sin(100°)) ≈ 36.22°

a(3x-8)=b-18x
what is a value?
what is b value?

Answers

we have that
a*(3x-8)=b-18x
3ax-8a=18x+b
The only way for this to happen (non-trivially) is if the coefficients of x are equal, and the constant terms are equal
so
3ax=18x-----> 3a=18--------> a=6
-8a=b---------> b=-8*6-------> b=-48

the answer is
a=6
b=-48

determine the domain of the function h(x)= 9x/x(x^2-36)

Answers

Final answer:

The domain of the function h(x)=9x/x(x²-36) is all real numbers except 0, 6, and -6, because the function is undefined at these points.

In conclusion, the domain of h(x) is x ∈ ℝ, x ≠ 0, x ≠ 6, x ≠ -6.

Explanation:

The question asks to determine the domain of the function h(x) = 9x / x(x² - 36).

The domain of a function consists of all the real numbers x for which the function is defined. In this case, the function will be undefined when the denominator is zero because division by zero is not defined in mathematics.

To find these values, we set the denominator equal to zero and solve the resulting equation:

x(x² - 36) = 0.

This can be factored further as x(x - 6)(x + 6) = 0, which gives us the zero points of x = 0, x = 6, and x = -6.

Therefore, the domain of h(x) is all real numbers except 0, 6, and -6.

In conclusion, the domain of h(x) is x ∈ ℝ, x ≠ 0, x ≠ 6, x ≠ -6.

Kim spun the spinner 75 times and got a three 30 times. What is the experimental probability?

Answers

The experimental property of what?

Experimental probability of getting three would be 30 / 75 because according to what happened, you got three 30 times out of 75.

So 30 / 75 = 0.4 = 40%

Hope this helps.

ABC has coordinates of A(–5, –7), B(6, –3), and C(2, 7). Find the coordinates of its image after a dilation centered at the origin with a scale factor of 2.

Answers

When a figure is dilated about the origin, every coordinate is multiplied by the scale factor.

A' = 2A = (-10, -14)
B' = 2B = (12, -6)
C' = 2C = (4, 14)

Final answer:

The coordinates of the image after dilation with a scale factor of 2 are A'(-10, -14), B'(12, -6), C'(4, 14).

Explanation:

Your question involves geometry and specifically, dilation transformations. A dilation is a transformation that moves each point along the ray from the center of dilation to the point. The number given as the scale factor tells you how much to move. In this case, we are asked to dilate the given points with a scale factor of 2 centered at the origin (0,0).

So, each coordinate of the original triangle should be multiplied by 2. Let's find each coordinate after dilation:

A: -5*2, -7*2 = A'(-10, -14)B: 6*2, -3*2 = B'(12, -6)C: 2*2, 7*2 = C'(4, 14)

So, the coordinates of the image after a dilation with a scale factor of 2 are A'(-10, -14), B'(12, -6), and C'(4, 14).

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A particular hybrid car travels approximately 204 mi on 4 gal of gas. Find the amount of gas required for a 714-mi trip.

Answers

i think its 13.1 gallons for a 714 mile trip

The car needs 14 gallons of gas for the 714 mile trip.

To determine the amount of gas required for a 714-mile trip, we can set up a proportion based on the given information:

We know that the car travels 204 miles on 4 gallons of gas. We need to find the amount of gas needed for 714 miles. Let the gas required for 714 miles be X gallons

First, let us set up the proportion:

204 mi / 4 gal = 714 mi / X gal

Next, we solve for x (the amount of gas required for 714 miles):

204 mi × X gal = 714 mi × 4 gal204X = 2856X = 2856 / 204X = 14

Therefore, the car requires 14 gallons of gas for a 714-mile trip.

Express this equation in word form:
5 + ( 2 x 6 )

Answers

Answer: Five plus Two times Six

The parenthesis equation is two times six. Then out of that is 5. So it's 5 plus 2 times six.

-DustinBR

(Not sure this is college stuff) So basically, whatever is in parentheses has higher priority over the other numbers, so whatever is in those will be multiplied/subtracted/added/divided first. So you multiply those, then add 5 to it.

if I have 300 apples and eat 123 how many do I have left?

Answers

300 - 123 = 177

You have 177 apples left.

300-123=177
You will have 177 apples left.

sandra has 5 toy cars .Each toy car has a mass of 8 grams .what is the total mass of all 5 cars?

Answers

Final answer:

The total mass of Sandra's 5 toy cars is calculated by multiplying the mass of one toy car (8 grams) by the total number of cars, resulting in a total mass of 40 grams.

Explanation:

The question requires us to calculate the total mass of Sandra's toy cars. Since each toy car has a mass of 8 grams, we can find the total mass by multiplying the mass of one car by the number of cars, which is 5 in this case. Therefore, the calculation we need to perform is 8 grams times 5, which will give us the total mass of all the toy cars combined.

To solve: 8 grams/car × 5 cars = 40 grams.

Thus, the total mass of all 5 toy cars that Sandra has would be 40 grams.

Charles owed $390 to his friend. On the first day Charles paid his friend $12. Each following week the amount Charles paid his friend increased by the same amount. After 10 payments, Charles had paid back the full amount. By how much did each payment increase?

Answers

The rate at which Charles amount increased will be given by:
Amount owe=$390
Payment=$10
Number of payments=10
thus using the formula:
A=P(1+r)^n
plugging the values we get:
390=10(1+r)^10
solving for r we get
39=(1+r)^10
r=0.4425
thus the amount increased by 44.25%

A triangular traffic island has a base half as long as its height. The island has an area of 25 m2 . Find the base and the height.

Answers

The height is 13 and the base is 26. I hope this helped and if possible i just posted a question starting with the word PLEEZ. So if you can help me answer that it would be great!

I hate to contradict the first answer, but I calculated the question and got base = 5 and height = 10.

Dan uses a compass to draw an arc from Q, as shown. He wants to construct a line segment through R that makes the same angle with line segment QR as line segment PQ.

first chart

Which figure shows the next step to construct a congruent angle at R?

Charts 2 3 4 & 5

Answers

Answer:

Chart 2.

Step-by-step explanation:

In the figure Dan has constructed an angle at point Q.He wants to cinstruct an angle ar point R which is congruent to angle made at point Q.To construct the angle at point R Dan needs to draw an arc at point R .He will put the compass on point R and draw an arc .This is shown in the figure 2.

The figure is added below.

Please answer this question I need it fast:

Together, Mary Sue and Betty have 603 necklaces. Mary Sue has 115 more necklaces than Betty. How many necklaces does Betty have?

Answers

Let's call:
M = necklaces owned by Mary Sue
B = necklaces owned by Betty

You know that:
M + B = 603
M - B = 115

Therefore, when you have the sum and the difference of two numbers, in order to find the biggest number you have to sum the sum and the difference and divide it by 2, and in order to find the smallest number you have to subtract the difference from the sum and divide it by 2:

M = [(M + B) + (M - B)] ÷ 2
   = [603 + 115] ÷ 2
   = 359

B = [(M + B) - (M - B)] ÷ 2
   = [603 - 115] ÷ 2
   = 244

Hence, Mary Sue has 359 necklaces and Betty has 244 necklaces.

Answer:

mary sue: 359, betty; 244

Step-by-step explanation:

⇔↓⊕㏒㏑∞

Please help confused

Answers

the mean is the average,
add the numbers in the set and divide by the quantity of numbers:
9 + 15 + 22 + 45 + 50 +60 + 65 = 266
266 / 7 = 38
the mean = 38

the absolute deviation is subtracting the number from the mean: ( all numbers are positive)

38 - 9 = 29

38 - 15 = 23

38-22 = 16

45-38 = 7

50 -38 = 12

60-38 = 22

65-38 = 27

How many positive integers $N$ from 1 to 5000 satisfy both congruences, $N\equiv 5\pmod{12}$ and $N\equiv 11\pmod{13}$?

Answers

Use the Chinese remainder theorem. Suppose we set [tex]N=5\cdot13+11\cdot12[/tex]. Then clearly taken modulo 12, the second term vanishes, and incidentally [tex]5\cdot13\equiv65\equiv5\pmod{12}[/tex]; taken modulo 13, the first term vanishes, but the second term leaves a remainder of 2. To counter this, we can multiply the second term by the inverse of 12 modulo 13, which is 12 since [tex]12^2\equiv144\equiv11\cdot13+1\equiv1\pmod{13}[/tex].

So, we found that [tex]N=5\cdot13+11\cdot12^2=1649[/tex], but the least positive solution is [tex]1649\equiv89\pmod{\underbrace{156}_{12\cdot 13}}[/tex], and in general we can have [tex]N=89+156k[/tex] for any integer [tex]k[/tex].

Now, since [tex]5000=32\cdot156+8[/tex], or [tex]4992=32\cdot156[/tex], we know that there are 32 possible integers [tex]N[/tex] that satisfy the congruences.

Kayla bought 9/4 pounds of apples. What is that weight as a mixed number?

Answers

The weight as a mixed number is 2 1/4.

A church has 10 bells in its bell tower. before each church service 3 bells are rung in sequence. no bell is rung more than once. how many sequences are there?

Answers

Answer:

720

Step-by-step explanation:

Given : A church has 10 bells in its bell tower.

Before each church service 3 bells are rung in sequence.

To Find: How many sequences are there?

Solution:

Since we are given that 3 bells are rung in sequence. no bell is rung more than once.

So, we will use permutation.

Formula :[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]

Since A church has 10 bells in its bell tower.

So, n =10

We are also given that Before each church service 3 bells are rung in sequence . So, r =3

So, the number of possible sequence = [tex]^{10}P_3[/tex]

= [tex]\frac{10!}{(10-3)!}[/tex]

= [tex]\frac{10!}{(7)!}[/tex]

= [tex]\frac{10 \times 9 \times 8 \times 7!}{(7)!}[/tex]

= [tex]10 \times 9 \times 8[/tex]

= [tex]720[/tex]

Hence there are 720 sequences.

There are 120 different sequences in which the 3 bells can be rung in sequence before each church service without any bell being rung more than once.

To find the number of sequences in which the 3 bells can be rung in sequence out of 10 bells without any bell being rung more than once, you can use the concept of combinations.

The number of ways to choose 3 distinct bells out of 10 is given by the binomial coefficient "10 choose 3," which is denoted as C(10, 3) and calculated as follows:

C(10, 3) = 10! / (3!(10 - 3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120

So, there are 120 different sequences in which the 3 bells can be rung in sequence before each church service without any bell being rung more than once.

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