Therefore, amu (atomic mass unit) and Avogadro's number are not the same things.
Define amu (atomic mass unit).
A unit of measurement for atomic and molecular weight is the atomic mass unit (amu).
What is molecular weight?Molecular weight, commonly known as molecular mass, is the mass of a substance's molecules, calculated using the atomic weight of carbon-12, which is 12.
No, amu and Avogadro's numbers are not the same things because An atomic mass unit (amu) is a unit of measurement for atomic and molecular weight. It is defined as one twelfth of the mass of a neutral atom of carbon-12. It is commonly used in chemistry to express the masses of atoms and molecules While Avogadro's number (N) is a fundamental constant of nature that relates the number of atoms or molecules in a sample to the mass of that sample. It is defined as the number of atoms or molecules in one mole of a substance. It is approximately 6.022 x 10^23 atoms or molecules per mole.
So, amu is a unit of measurement for atomic and molecular weight, while Avogadro's number is a constant that relates the number of atoms or molecules in a sample to the mass of that sample.
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Find the length of the third side. If necessary round to the nearest tenth
The side lengths of a right-angle triangle can be calculated using the Pythagorean Theorem. Which states that the square of the hypotenuse is equal to the sum of squares of the other sides in the triangle.
[tex]a^2+b^2=c^2[/tex]
the hypotenuse is always the longest side of a triangle and is always the opposite side length to the right anglerearranging the equation can help calculate the third side:
[tex]c^2-a^2=b^2[/tex]
[tex](5)^2-(4)^2=b^2[/tex]
[tex]25-16=b^2[/tex]
[tex]9=b^2[/tex]
[tex]\sqrt{9}=\sqrt{b^2}[/tex]
[tex]{ {{b_1=+3} \atop {b_2=-3}} \right.[/tex]
note: a length can never be negative so never take into account a negative answer
b = 3
Part A: Maci made $170 grooming dogs one day with her mobile dog grooming business. She charges $60 per appointment and earned $50 in tips. Write an equation to represent this situation. (4 points)
Part B: Logan made a profit of $210. 00 as a mobile groomer. He charged $75. 00 per appointment and received $35. 00 in tips, but also had to pay a rental fee for the truck at $10. 00 per appointment. Write an equation to represent this situation. (4 points)
Part C: Explain how the equations from Part A and Part B differ. (2 points)
The equations for parts A and B are 170 = 60x + 50 and 210 = 75x + 35 - 10x, respectively.
What is an equation ?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
The statement is not an equation if there is no "equal to" sign in it.
According to our question-
A) It is stated that Maci once earned $170 by grooming dogs.
For each appointment, she charges $60, and she received $50 in tips. Consequently, the equation to illustrate this is;
170 = 60x + 50
the number of appointments is x.
B) Logan earned $210.00 in profit. He charged $75.00 for each session and got $35.00 in gratuities. In addition, he had a $10.00 truck rental fee per appointment. In order to represent this, the equation is;
210 = 75x + 35 - 10x
the number of appointments is x.
C) The quantity of tips they will receive even without an appointment varies between the formulae.
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How do you find the terminal point of a line segment?
To find the terminal point of a line segment, identify the starting point, measure the length and direction, and use these parameters to calculate the coordinates of the terminal point.
To find the terminal point of a line segment, first identify the starting point of the line. Then, measure the length of the line segment and the direction in which it is going. Finally, use a combination of the starting point coordinates, the length, and the direction to calculate the coordinates for the terminal point of the line.
1. Identify the starting point of the line.
2. Measure the length of the line segment and the direction in which it is going.
3. Use the starting point coordinates, the length, and the direction to calculate the coordinates of the terminal point.
4. The coordinates of the terminal point are the location of the line segment’s endpoint.
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A pole that is 3.2 m tall casts a shadow that is 1.32 m long. At the same , a nearby tower casts a shadow that is 46.75 m long. How tall is the tower? Round your answer to the nearest meter.
Answer:
The tower is 113 meters.
Step-by-step explanation:
We are given a pole and a tower that both create a shadow.
Hence, the figures made are triangles.
If you draw the figure (attached to this response), you can see the two triangles are similar triangles.
⭐What are similar triangles?
two triangles whose corresponding side lengths are proportional and have the same shapeStrategycreate a proportion of the ratios of the corresponding side lengthssolve for the length of the towerCreate a ratio for the corresponding side lengthsThe length of the height of the pole (3.2) corresponds to the length of the height of the tower (x).
The length of the shadow of the pole (1.32) corresponds to the length of the shadow of the tower (46.75).
Therefore, our two ratios are:
[tex]\frac{3.2}{x}[/tex] and [tex]\frac{1.32}{46.75}[/tex]
Create a proportion for the corresponding side lengthsA proportion is when you set two ratios equal to each other:
[tex]\frac{3.2}{x} = \frac{1.32}{46.75}[/tex]
Solve for the length of the tower (x)To solve for x, cross multiply by multiplying the opposite parts of the fraction together.
[tex]\frac{3.2}{x} = \frac{1.32}{46.75}\\46.75(3.2) = 1.32x\\149.6 = 1.32x\\\\113 = x[/tex]
∴ The tower is 113 meters tall!
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what is 2.38 correct to 2 significant figures
Answer: 2.4
Step-by-step explanation:
we start from the right most digit, that is 8. Since 8 is greater than 5, we add 1 in the number before 8, that is 3. When we add 3 and 1 we get 4. This way, we get our answer 2.4 , which is correct to 2 significant figures.
hope that helps...
we the following mixed operations word problems
During a normal day, there are 782 passengers in average that
are late for their plane each day. However, during the
Christmas holidays, there are 1,835 passengers that are late for
their planes each day which caused delays of 14 planes. How
many more passengers are late for their planes in each day
during the Christmas holidays?
An average of 782 travelers miss their flight each day during a typical day. In contrast, 1,835 passengers are late for their flights every day over the Christmas holiday, which results in 14 planes being delayed.
1,053 travelers (2,835-782 = 1,053)
During the Christmas holidays, there are 1,053 extra passengers who are late for their flights.
How do you figure out the average number of days late?In order to compute WADO, we multiply the total amount of each overdue invoice by the number of days past due, then divide that total by the number of days past due. You may figure out your average daily sales by dividing your total sales over a certain period of time by the number of days in that same period.
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What is the general formula for Logarithms?
The general formula for logarithms is [tex]log_b(x) = y[/tex].
What is a logarithmic function?
A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x) = log_b(x),[/tex] where b is the base of the logarithm.
The general formula for logarithms is:
[tex]log_b(x) = y[/tex]
This means that b raised to the power of y is equal to x.
Where b is the base of the logarithm, x is the number that we are taking the logarithm of, and y is the result or the logarithm of x to the base b.
Hence, the general formula for logarithms is [tex]log_b(x) = y[/tex].
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The general formula for logarithms is [tex]log_b(x)=y[/tex].
What is a logarithmic function?
A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x)=log_b(x)[/tex] where b is the base of the logarithm.
The general formula for logarithms is:
[tex]log_b(x)=y[/tex]
This means that b raised to the power of y is equal to x.
Where b is the base of the logarithm, x is the number that we are taking the logarithm of, and y is the result or the logarithm of x to the base b.
Hence, the general formula for logarithms is [tex]log_b(x)=y[/tex].
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Can you make a triangle with 3 different length sides?
Yes, you can make a triangle with three different length sides.
1. Draw three lines of different lengths on a piece of paper.
2. Connect the ends of the lines to form a triangle.
3. The triangle will have three different length sides. The lengths of the sides depend on the lengths of the three lines you drew.
4. To make sure the triangle is valid, use the triangle inequality theorem. This theorem states that the sum of any two sides of a triangle must be greater than the third side.
5. Measure each side of the triangle with a ruler and add them together.
6. Compare the sum of the two sides to the third side. If they are not equal or greater, adjust the lines to create a valid triangle.
7. Once the triangle is valid, it will be a triangle with three different length sides.
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Simplify the expression below:
20-10y-7y + 9
A) Зу — 29
B) 3y + 11
C) 3y + 29
D) -17y + 11
E) -17y + 29
To simplify the expression 20-10y-7y + 9, we can combine like terms.
Like terms are terms that have the same variables raised to the same exponents. For example, 10y and -7y are like terms because they both have the variable y raised to the exponent 1.
We can start by combining the like terms:
20 - 10y - 7y + 9
= 20 + (-10y - 7y) + 9
= 20 + (-17y) + 9
Next, we can combine the constants:
20 + (-17y) + 9
= (20 + 9) + (-17y)
= 29 + (-17y)
The simplified expression is: 29 + (-17y)
[tex]20-10y-7y + 9[/tex]
Combine Like Terms:
[tex](-10y+-7y)+(20+9)[/tex]
[tex]-17y+29[/tex]
[tex]\fbox{Option E}[/tex]
Use synthetic division to find all the real zeros of the polynomial.
f(x) = x³ + x² - 8x - 6
so hmmm we look at hmm x³ + x² - 8x - 6 so how do squeak out a factor out of it, well, using the rational root test and using our p/q checking for factors, we find that likely factors can be ± 6/1 and ±(3, 2, 1) / 1, anyhow so we check some of those and hopefully without boring you to death we find that -3 works, we can always use the remainder theorem to check if that's true, by simply plugin in f(-3) and if it's indeed a factor, that'd give us 0, well, f(-3) = -27 + 9 +24 +6 = 0, holly smokes!! is a factor.
well, all that jazz means that -3 is a factor, namely the factor is really x = -3 or x + 3 = 0 so the factor is (x+3) and for our synthetic division we'll use the -3 version, Check the picture below.
so we end up with the factors of (x+3)(x²-2x-2), now for the 2nd factor what we can do to break it up is use the quadratic formula
[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-2}x\stackrel{\stackrel{c}{\downarrow }}{-2} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}[/tex]
[tex]x= \cfrac{ - (-2) \pm \sqrt { (-2)^2 -4(1)(-2)}}{2(1)} \implies x = \cfrac{ 2 \pm \sqrt { 4 +8}}{ 2 } \\\\\\ x= \cfrac{ 2 \pm \sqrt { 12 }}{ 2 }\implies x=\cfrac{2\pm\sqrt{2^2\cdot 3}}{2}\implies x=\cfrac{2\pm 2\sqrt{3}}{2}\implies x=1\pm\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} (x+3)(x-1+\sqrt{3})(x-1-\sqrt{3}) \end{array}}~\hfill[/tex]
now, just to clarify, all those are real roots, and the last two come from simply setting x = 1 ± √3 to 0 to get the factors.
A quadrilateral
is a polygon with four sides. Consider
the quadrilateral and the dashed segment. What is the sum
of the measures of the four interior angles of this quadrilateral?
Draw a different quadrilateral. Can you guess the sum
of the measures of its angles? Is it possible to generalize about
the angles of a quadrilateral?
The sum of the measures of the four interior angles of a quadrilateral is always 360°
What is a quadrilateral?A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles.
Given is, A quadrilateral is a polygon with four sides. Consider the quadrilateral and the dashed segment
If we draw one diagonal to quadrilateral we will get two triangles i.e. △ABC and △ACD and we know that sum of the angles of a triangle is 180°
Sum of angles of quadrilateral ABCD = sum of angles of △ABC + sum of the angles △ACD
= 180° + 180°
= 360°
If we take examples of a square or a rectangle, we know that they are also a quadrilateral and also their each angle is right angle, i.e. 90°
Therefore, the sum of their interior angles will = 90×4 = 360°
Hence, we can say that the sum of the measures of the four interior angles of a quadrilateral is always 360°
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Can u please help?.........................
The coordinates of the point P on the directed line segment that partitions the segment into a ratio of 2 to 3 is the ordered pair (3, 0).
How to determine the coordinates of point P?In this scenario, we would use line ratio to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 3 to 2.
In Mathematics, line ratio can be used to determine the coordinates of the point P and this is modeled by this mathematical expression:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Substituting the given parameters into the line ratio formula, we have;
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
P(x, y) = [(2(9) + 3(-1))/(2 + 3)], [(2(6) + 3(-4))/(2 + 3)]
P(x, y) = [(18 - 3)/(5)], [(12 - 12)/5]
P(x, y) = [15/5], [0/5]
P(x, y) = [3, 0]
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Complete Question:
Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-1, -4), B(9, 6); to 3. The coordinates of P are?
What is 6 divided by 9.51
Answer:
The result of 6 divided by 9.51 is approximately 0.63.
Answer:
0.63091482649
Step-by-step explanation:
Write an equation of the line that passes through (3,-4) and is perpendicular to y=1/2x+7.
A(3,-1); y= 1/3x +10
write an equation of the line passing through the given point that is parallel to the given line
the equation of the desired line is x = 3y + 6.
To find the equation of a line that is parallel to the given line
y = 1\3x + 10
and passes through the point (3,-1), since parallel lines have the same slope.
Therefore, the slope of the desired line is also 1\3.
Since the desired line passes through the point (3,-1), we can use the point-slope formula to write its equation:
y - (-1) = 1\{3}(x - 3)
Simplifying, we get
y + 1 = 1\ 3x - 1
Multiplying both sides by 3, we get
3y + 3 = x - 3
Adding 3 to both sides, we get
3y + 6 = x
Therefore, the equation of the desired line is x = 3y + 6.
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Please help me !!
this the last question !!
Answer:
2 ≥ p
Step-by-step explanation:
-14 ≤ -7p
Divided both sides by -7. Because divided by a negative number, the < will turn to >
So, the equation is
2 ≥ p
Because there is an equal, the circle will be close and to the left of 2.
Answer:
2 ≥ p
Step-by-step explanation:
Have a great day :) <3
pls help with his i dont get it at all
Answer:
D.
Step-by-step explanation:
They are parallel would be the best explanation. AB and PQ are in a sense the same segment but PQ is AB translated.
The side of a square is 2.5 find its perimeter and area
Answer:
perimeter = 10
area = 6.25
Step-by-step explanation:
Every square has four equal sides. If we know one side is 2.5, then all sides are 2.5.
2.5*4 = 10
To find the area of a square you multiply the height and length. Since all sides of a square are the same, you just multiply 2.5 with itself.
2.5*2.5=6.25
1/3x-2 × 9x²-4/3x²-13x-10 - 7/x-1
Answer:
Step-by-step explanation:
Combine multiplied terms into a single fraction
one-third x minus 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1
1 x over 3 end fraction minus 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1
Multiply by 1
1 x over 3 end fraction minus 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1
x over 3 end fraction minus 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1
Multiply the numbers
x over 3 end fraction negative 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1
x over 3 end fraction negative 18 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1
A lacrosse team is raising money by selling cheesecakes. The players plan to sell an entire cheesecake for 24. 00 each and slices of cheesecake for 3. 50 each. If they want to raise at least 700 how many of each could they sell
the total of 29 cheesecake and 2 slices of cheesecake will be making $703.
What is the arithmetic operation?
The four basic arithmetic operations are addition, subtraction, multiplication, and division of two or more quantities. They all fall under the umbrella of mathematics, and among them is the study of numbers, particularly the order of operations, which is crucial for all other branches of the subject, such as algebra, data organisation, and geometry. To solve the problem, you must be familiar with the fundamentals of mathematical operations.
A lacrosse team is raising money by selling cheesecakes.
The players plan to sell an entire cheesecake for 24. 00 each and slices of cheesecake for 3. 50 each.
A multiplier of 24 close to 700 is 29
So 29 cheesecake will cost 696.
Now they need more 4 dollars to raise so they have to sell 2 slices, which will be 7$.
So the total of 29 cheesecakes and 2 slices of cheesecake will be making $703.
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What is the answer to inequality?
The direction of inequality is reversed when you multiply or divide both sides by a negative value.
When expressions are compared using the operators "less than" (), "less than or equal to" (=), "greater than" (>), or "greater than or equal to" (>=), an inequality is created.
Example- x + 3 <= 10
A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement. So, 4 is a solution for example 1, while 8 is not.
The solution set of an inequality is the set of all solutions.
The solution set of example 1 is the set of all x <= 7. In interval notation, this set is (-inf, 7], where we use inf to stand for infinity.
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What number multiple by 7/9 has the product of 1?
Answer: In mathematics, the reciprocal of a number is 1 divided by that number. So the reciprocal of 7/9 is 1/(7/9) which can be simplified to 9/7.
Therefore, 9/7 is the number that when multiplied by 7/9 will result in the product of 1.
Another way of arriving at the same solution is to remember that the product of a number and its reciprocal is always 1. In this case, the number is 7/9, and its reciprocal is 9/7.
Step-by-step explanation:
Find the product using any method. (Need some help!!)
Answer:
2n^2-8n-24
Step-by-step explanation:
Uhm i just did this one with one of my classmates like 2-3 months ago so it just came to mind.
Hope this helped tho! :)
2. Write a factored form function, f(x) for a cubic function that has zeros (- 7, 0) and (3, 0)
The cubic equation in factor form f(x) = (x + 7) · (x - 3) · (x - r) contains zeros (- 7 , 0) and (3, 0), for r = 0: f(x) = (x + 7) · (x - 3) · (x - r).
How to derive a cubic equation in factor form
Cubic functions are polynomials with grade 3 and whose standard form is described by the following form:
y = a · x³ + b · x² + c · x + d
Where a, b, c, d are real coefficients. The factor form of a cubic function is described by the following definition:
y = a · (x - r₁) · (x - r₂) · (x - r₃)
Where:
a - Lead coefficient.r₁, r₂, r₃ - Real zeros.Replace all known variables in factor form of cubic equation: (a = 1, r₁ = - 7, r₂ = 3, r₃ = r)
f(x) = (x + 7) · (x - 3) · (x - r)
Variable r means that there is more than one answer concerning the expression, if we assume that r = 0, then the particular solution is f(x) = (x + 7) · (x - 3) · x.
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Hello- some help please!! I will give you brainlist :]
Answer:
standard form
= x⁶ + 53x⁵ + 2x⁴ -2
Step-by-step explanation:
the degree is 6.
leading coefficient is 1
this is called a polynomial.
it has 4 terms
Blair has a box of candy to sell. She has 4 chocolate bars, 4 fruit chews, 1 pack of bubble gum and 3 sour candies. If she chooses a piece of candy at random, how many possible outcome are there?
Answer:
12 possible outcomes
Step-by-step explanation:
The equation to find the possible outcomes is:
possible outcomes x total
We know she picks 1, so we have
1 x 12 = 12 possible outcomes
So, there are 12 possible outcomes
Write a possible explicit rule, then find a 10-
(0, 7, 26, 63, 124, ...)
n³ - 1
Explicit rule: an = n³
a10 =
Here the 10th term of this arithmetic sequence is 999.
What is an arithmetic sequence in math?An arithmetic sequence is one in which each phrase grows by adding or removing a certain constant, k. In a geometric sequence, each term rises by dividing by or multiplying by a certain constant k.A series of integers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.Using the method for locating the nth term, we may locate a particular term in an arithmetic series. Step 1: An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d. Therefore, enter the numbers a = 2 and d = 3 into the formula to determine the nth term.Given data :
an = n³ - 1
a1 = 1³ - 1 = 1 - 1 = 0
a2 = 2³ - 1 = 8 - 1 = 7
a3 = 3³ - 1 = 27 - 1 = 26
a4 = 4³ - 1 = 64 - 1 = 63
a5 = 5³ - 1 = 125 - 1 = 124
a10 = 10³ - 1 = 1000 - 1 = 999
I saw that these numbers were one less than the cubes. So the answer is
a_n = n^3 - 1
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I really need help on this question
Step-by-step explanation:
2×4=8
8×2/3
8×2=16
16×3=48
ans = 48
Find value of c
[tex]48c+ 6 = 408 \div 4[/tex]
Answer:
2
Step-by-step explanation:
408 / 4 = 102
48c + 6 = 102
48c = 102 - 6
48c = 96
c = 96/48
c = 2
Hence, the value of c is 2.
Answer:
[tex] \sf \: c = 2[/tex]
Step-by-step explanation:
Given equation,
→ 48c + 6 = 408 ÷ 4
Now the value of c will be,
→ 48c + 6 = 408 ÷ 4
→ 48c + 6 = 102
→ 48c = 102 - 6
→ c = 96 ÷ 48
→ [ c = 2 ]
Hence, the value of c is 2.
Solve the system of equation using the elimination multiplication method 3c+6d=18
6c-2d=22
show your work
So the solution to the system of equations is:
c = 4, d = 1
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, separated by the 'equal' sign.
Define quadratic equation.x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given equation I is [tex]3c+6d=18[/tex] and equation II is [tex]6c-2d=22[/tex]
We can start by multiplying the first equation by -2 and adding it to the second equation. This will eliminate the d variable:
[tex]-6c - 12d = -36[/tex]
[tex]6c - 2d = 22[/tex]
[tex]0c - 14d = -14[/tex]
solving this we know value of [tex]d=1[/tex]
So we know that d = 1, and we can substitute that into the first equation to find the value of c:
[tex]3c + 6d = 18[/tex]
[tex]3c + 6(1) = 18[/tex]
[tex]3c = 12[/tex]
[tex]c = 4[/tex]
So the solution to the system of equations is:
[tex]c = 4, d = 1[/tex]
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