Answer:
b
Step-by-step explanation:
Use the Avogadro constant of 6.02 x 10^23
Complete the equation of the line through
(
−
8
,
−
2
)
(−8,−2)left parenthesis, minus, 8, comma, minus, 2, right parenthesis and
(
−
4
,
6
)
(−4,6)left parenthesis, minus, 4, comma, 6, right parenthesis
The linear function through the points (-8,-2) and (-4,6) is given as follows:
y = 2x + 14.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the linear function.The intercept b represents the value of y when x = 0.Given two points, the slope is calculated as the change in y divided by the change in x, hence:
m = (6 - (-2))/(-4 - (-8))
m = 8/4
m = 2.
Hence:
y = 2x + b.
When x = -8, y = -2, hence the intercept b is obtained as follows:
-2 = 2(-8) + b
b = 14.
Hence the equation is:
y = 2x + 14.
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Sydney and two of her friends want to
go to a concert by one of their favorite
bands. Sydney found a deal that was
$102.51 for three tickets. How much
does each ticket cost?
The cost of each ticket is $34.17
How to determine the cost of each ticketTo find the cost of each ticket, we need to divide the total cost of the tickets by the number of tickets.
In this case, the total cost of the tickets is $102.51 for three tickets.
So, to find the cost of one ticket,
We can divide $102.51 by 3:
Using the above as a guide, we have the following:
$102.51 ÷ 3 = $34.17
Hence, each ticket costs $34.17.
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La semana pasada Pedro y Pablo fueron al doctor a una consulta de rutina si Pedro pesa 43 kg y Pablo pesaba 94 libras quien pesa más ?
Pedro weighs slightly more than Pablo.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Examples:
1 hour = 60 minutes
1 minute = 60 seconds
1 km = 1000 m
We have,
Pedro weighs = 43 kg
Pablo weighs = 94 pounds.
Now,
1 kg = 2.205 pounds
Multiply 43 on both sides.
43 kg = 43 x 2.205 pounds
43 kg = 94.815 pounds
94.815 pounds > 94 pounds
We can see that Pedro weighs slightly more than Pablo.
Thus,
Pedro weighs slightly more than Pablo.
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The complete question in English.
Last week, Pedro and Pablo went to the doctor for a routine checkup. If Pedro weighs 43 kg and Pablo weighs 94 pounds, compare their weights to the same unit of measurement.
Who weights more?
factor each polynomial by grouping
^(3)+4x^(2)+2x+8
4b^(3)-6b^(2)+10b-15
2m^(3)+4m^(2)+6m+12
7r^(3)-35r^(2)+6r-30
10a^(3)+4a^(2)+5a+2
The required factor each polynomial by grouping are factored.
What are polynomials?A polynomial is an algebraic expression in which the operators "+" and "-" are used to separate terms, and the exponents of the variables are consistently non-negative integers. Polynomials include, for instance, x² + x + 5, y² + 1, and 3x³ - 7x + 2.
According to question:1)1) [tex]x^3+4x^2+2x+8[/tex]
can be factored by grouping as:
[tex]x^3 + 2x + 4x^2 + 8[/tex]
= [tex]x(x^2+2) + 4(x^2+2)[/tex]
= [tex](x+4)(x^2+2)[/tex]
2) [tex]4b^3-6b^2+10b-15[/tex]
can be factored by grouping as:
[tex]2b^2(2b-3)+5(2b-3)[/tex]
=[tex](2b-3)(2b^2+5)[/tex]
3)[tex]2m^3+4m^2+6m+12[/tex]
can be factored by grouping as:
[tex]2m^2(m+2) + 6(m+2)[/tex]
= [tex](2m^2+6)(m+2)[/tex]
= [tex]2(m^2+3)(m+2)[/tex]
4) [tex]7r^3-35r^2+6r-30[/tex]
can be factored by grouping as:
[tex]7r^2(r-5)+6(r-5)[/tex]
=[tex](7r^2+6)(r-5)[/tex]
[tex]10a^3+4a^2+5a+2[/tex]
can be factored by grouping as:
[tex]2a^2(5a+2)+1(5a+2) = (2a^2+1)(5a+2)[/tex]
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f(3/4) If f(x) =2x-1/4
If the given function is f(3/4), then evaluation of function (3/4) = 5/4.
What is expression ?
An expression is a mathematical phrase that can contain numbers, variables, and operators such as addition, subtraction, multiplication, and division. It can also contain functions, exponents, and other mathematical symbols.
Expressions can be used to represent a wide range of mathematical concepts, such as equations, inequalities, and formulas. They can be as simple as a single number or variable, or they can be more complex, involving multiple operations and variables.
What is function ?
In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output. In other words, a function is a rule or mapping that assigns a unique output to each input.
Functions can be expressed using a variety of mathematical expressions, such as algebraic formulas, graphs, and tables. They are used to model relationships between variables in many areas of mathematics, science, engineering, and other fields.
According t o given condition :
To find f(3/4), we simply substitute 3/4 in place of x in the given function f(x):
f(3/4) = 2(3/4) - 1/4
Simplifying the expression, we get:
f(3/4) = 6/4 - 1/4
f(3/4) = 5/4
Therefore, if the given function is f(3/4), then evaluation of function (3/4) = 5/4.
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How do you make a transfer function in Matlab?
With MATLAB 's "t f" function, you may build a transfer function. A transfer function object is created by the "t f" function and can be used to manipulate transfer functions
So, you can create a transfer function with the aid of MATLAB's "t f" function. The "t f" function generates a transfer function object that can be used to manipulate transfer functions in a variety of ways, such as multiplying, adding, and inverting them. The MATLAB "t f" function can produce transfer functions using the following syntax. The numerator and denominator coefficients of the transfer function are "num" and "den", respectively and they are used to compute the system equation: sys = t f(num, den). The coefficients of "num" and "den" can be visualised as vectors, with "s" serving as the Laplace variable and the coefficients as descending powers of "s." Consider using the transfer function equation below as an example to create
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solve this problem pls a question of inequality
Answer:
x > - 6
Step-by-step explanation:
[tex]\frac{x}{2}[/tex] > - 3 ( multiply both sides by 2 to clear the fraction )
x > - 6
To raise money for charity, Carmen and her friends start the Pampered Pooch Pet Wash. The first day they are open, they forget to put up posters and only raise a little money. The next day, they hang posters all over the neighborhood and raise $55.50. In all, Carmen and her friends raise $65.50 on the first two days they are open.
Julie will reach her goal 21 days before Mary.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
Mary and Julie both have a goal of raising $1000 for charity.
Mary raises money in every 4 days = $12.
In one day Mary raises money = 12/4
= $3
Mary needs time to reach her goal = 1000/3
= 333.33 ≈ 334 days
Julie raises money in every 6 days = $19
In one day Julie raises money = 19/6
= $3.1666 ≈ $3.2
Julie needs time to reach her goal = 1000/ 3.2
= 312.5 ≈ 313 days
Difference of the days between both of them to reach their goal
= 334 - 313 = 21 days
Julie will reach her goal first, 21 days before Mary.
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What is the value of root 216?
Answer: The square root of 216 is equal to approximately 6.485281.
Step-by-step explanation:
The square root of 216 is equal to the number that, when multiplied by itself, gives 216. The value of the square root of 216 can be found using several methods, including estimation, the long division method, and a calculator. Here, I'll provide a step-by-step explanation using estimation.
Step 1: Estimate the value of the square root.
One way to estimate the value of the square root of 216 is to find two perfect squares that are close to 216, and whose square roots are therefore close to the square root of 216. In this case, the perfect squares closest to 216 are 144 (12^2) and 225 (15^2). Since 216 is closer to 144, the square root of 216 is likely to be closer to 12 than to 15.
Step 2: Refine the estimate.
To refine the estimate of the square root of 216, we can average the two closest perfect squares and their square roots. In this case, the average of 12 and 15 is 13.5, and this is a better estimate of the square root of 216 than either 12 or 15 alone.
Step 3: Improve the estimate using a more precise method.
One method for finding an even more precise estimate of the square root of 216 is to use the Newton-Raphson formula for finding square roots. This formula involves repeatedly applying the following equation:
x_n+1 = (x_n + n/x_n) / 2,
where x_n is the nth estimate of the square root, and n is the number whose square root we are trying to find (in this case, n = 216). We can start with an initial estimate, such as x_0 = 13.5, and iterate the formula until the estimate converges to a desired level of precision.
Step 4: Use a calculator or other tools to find the exact value.
Finally, we can use a calculator or computer program to find the exact value of the square root of 216 to as many decimal places as desired. The exact value of the square root of 216 is equal to approximately 6.485281.
Which function will approach positive infinity the fastest?
O f(x)= 100(1.5)*
O f(x) = 100x5 + 200x³ + 100
Of(x) = 200(1.45)*
O f(x) = 200x3 + 100x² + 100
Answer:
Step-by-step explanation:
fx
An antique dresser was $115, but is on sale for
30% off. If there is a 10% tax added to the sale
price, how much will the dresser cost?
Answer:
$88.55
Step-by-step explanation:
First find how much the 30% off discount will be.
115 x 0.30 = 34.5
Subtract it from original price
$115 - 34.5 = $80.5
Now find the 10% tax
80.5 x 0.10 = 8.05
Add that to the price
$80.5 + 8.05 = 88.55
The dresser's final sale price is $88.55
The table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10. The second column, Height in inches, has the entries, 8, 12, 16, 20, 24. The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool? The height of the water increases 2 inches per minute. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when the pool is filled.
The correct statement that describes how the slope relates to the height of the water in the pool is: The height of the water increases 2 inches per minute, the correct option is A.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
where (x₁, y₁) and (x₂, y₂) are the two points that you are trying to find the slope between.
We are given that;
The time in minutes: 2, 4, 6, 8, 10
Height in inches: 8, 12, 16, 20, 24
Now,
The slope of the line through the points is 2, which means that for every 1 unit of time (in minutes) that passes, the height of the water in the pool increases by 2 units (in inches).
Therefore, by the given slope answer will be height of the water increases 2 inches per minute.
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i don’t understand how to get answer
Answer:
You probably know that it is a good idea to brush your teeth every day. What does this do that helps prevent tooth decay?
Step-by-step explanation
What value for x makes the equation −13(x + 11) + 12x = -26 true
Answer:
x= -177
Step-by-step explanation:
−13(x + 11) + 12x =-26
x=-177
Janice is at her favorite store checking out. She wants to buy a few shirts (s) that cost $14 each and a pair of jeans that cost $32. She wants to spend less than $88. How many shirts can she buy without going over her limit? Write an inequality to represent the scenario. Then, solve.
The number of shirts that Janice can buy without going over her limit is; 3 shirts
How to solve Inequality word problems?The number of shirts she can buy is denoted as s.
Cost of each shirt = $14
Cost of a pair of jeans = $32
She wants to spend less than $88.
Thus, the inequality that depicts this problem is;
14s + 32 < 88
Subtract 32 from both sides to get;
14s < 56
Divide both sides by 14 to get;
s < 4
Thus, maximum number of shirts will be 3 shirts
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What type of graph is shown, and what is the growth factor?
linear function; growth factor of 2
linear function; growth factor of 4
exponential function; growth factor of 2
exponential function; growth factor of 4
The graph is a linear function with a growth factor of 4
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The graph has the shape of a straight line, so it is linear.
The graph starts at point (0, 0). It passes through point (1, 4).
slope = 4/1 = 4
The slope is 4. Growth factor is the same as slope for a linear function.
Hence, the graph is a linear function with a growth factor of 4
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Find the volume.
(Pls help…. I’ve tried many times but ain’t near the answer)
The volume of the composite figure is equal to 1395 square inches.
How to determine the volume of the composite figure
In this problem we need to determine the volume of a composite figure, which is the result of combining the volumes of a right prism and a pyramid, whose volume formulas are listed below:
Pyramid
V = (1 / 3) · w · l · h
Prism
V = w · l · h
Where:
w - Width, in inchesl - Length, in inchesh - Height, in inchesNow we proceed to determine the volume of composite solid:
V = (9 in) · (15 in) · (7 in) + (1 / 3) · (15 in) · (9 in) · (10 in)
V = 1395 in³
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In many classes, a passing test grade is 60 (A = 60). Using the formula A = 10 R,
what raw score (R) would a student need to get a passing grade after her score is
adjusted?
A student need a raw score of 36.
How to determine the raw score (R) of the student?
We can find the raw score (R) of the student by substituting A = 60 into the the formula and then solve for R. That is:
A = 10√R
√R = 60/10
√R = 6
R = 6²
R = 36
Thus, a student need a raw score of 36 to get a passing grade after her score is adjusted.
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8x - 7y = 56
plot on the graph
Answer: put tow points, 1 on the x-axis (horizontal) and the other 1 on y-axis (vertical).
x = 7
y = -8
and you make a straight line , connecting them
What is the value of 50g in tbsp?
The conversion rate for grams to tablespoons is 1 gram is equal to 0.2 tablespoons. This conversion is useful for both converting small amounts of ingredients in recipes and converting larger amounts of ingredients in recipes.50 grams is equal to 10 tablespoons."
This means that 50 grams is equal to 10 tablespoons. To calculate the value of 50 grams in tablespoons, we can use the following formula:50 grams x 0.2 tablespoons = 10 tablespoons.The value of 50 grams in tablespoons is 10 tablespoons.To convert from grams to tablespoons, the basic formula is to multiply the weight in grams by 0.2. This conversion is useful for converting small amounts of ingredients in recipes, as many recipes call for weights in grams rather than tablespoons. For example, if a recipe calls for 20 grams of butter, this would be equal to 4 tablespoons. To convert from tablespoons to grams, the basic formula is to multiply the weight in tablespoons by 5. This conversion is useful for converting larger amounts of ingredients in recipes, as many recipes call for weights in tablespoons rather than grams. For example, if a recipe calls for 8 tablespoons of sugar, this would be equal to 40 grams. To summarize, the value of 50 grams in tablespoons is 10 tablespoons. This conversion is useful for both converting small amounts of ingredients in recipes and converting larger amounts of ingredients in recipes.
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Suppose ABC is a right triangle, and cos (B) =a/c, which of the following much also be true ?
Answer:
option 1 --> sec A = c/a
option 3 --> sin(b) = b/c
option 4 --> Sin(A) = a/c
Step-by-step explanation:
Since cos is adjacent, we know the legs are a and b and the hypotenuse is c
For angle B
sin (opposite over hypotenuse) = b/ctan (opposite over adjacent) = b/acsc (hypotenuse over opposite) = c/bsec (hypotenuse over adjacent) = c/bcot (adjacent over opposite) = a/bFor Angle A
sin = a/ccos = b/ctan = a/bcsc = c/asec = c/bcot = b/aThe average temperatures for two of the world's hottest places are given. Determine which location has the warmer average temperature and by how many degrees Fahrenheit
Location A: 85.3°F and Location B: 29.3°C
The location with the warmer average temperature is
(Round to the nearest tenth of a degree as needed.)
which is warmer by about F
Location A has the warmer average temperature, by about 0.6°F (rounded to one decimal place).
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To compare the temperatures of Location A and Location B, we need to convert the temperature of Location B from Celsius to Fahrenheit. We can use the formula:
°F = (°C × 9/5) + 32
Substituting the given temperature of Location B, we get:
°F = (29.3 × 9/5) + 32 = 84.74°F (rounded to two decimal places)
So, the average temperature of Location A is 85.3°F and the average temperature of Location B is 84.74°F (rounded to two decimal places).
Therefore, Location A has the warmer average temperature, by about 0.6°F (rounded to one decimal place).
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what is the meaning of permutations and combinations?
Answer:
Step-by-step explanation:
Permutations and combinations are mathematical concepts that deal with counting the number of different arrangements or selections of objects from a set.
Permutations:
A permutation is an arrangement of objects in a specific order. For example, consider a set of three letters: A, B, and C. There are 3! = 6 possible permutations of these letters, which are ABC, ACB, BAC, BCA, CAB, and CBA. The notation "3!" is the factorial notation, which means 3 × 2 × 1.
Combinations:
A combination is a selection of objects, where the order does not matter. For example, consider a set of three letters: A, B, and C. There are 3 C 2 = 3 possible combinations of two letters from this set, which are AB, AC, and BC. The notation "3 C 2" is the combination notation, which means the number of ways to choose k objects from a set of n objects.
In summary, permutations deal with the arrangement of objects in a specific order, while combinations deal with the selection of objects without regard to the order.
using diagonals from a common vertex, how many triangles could be formed from a 21-gon?
Total 816 triangles that can be formed using diagonals from a common vertex of a 21-gon.
What are Diagonals?In mathematics, a diagonal is a line joining two vertices of a polygon or solid whose vertices do not lie on the same edge. Diagonals are generally defined as oblique lines or slanted lines connecting the vertices of a shape. A diagonal is defined as a horizontal shape with sides/edges and corners.
Solution of the given problem:
Firstly, choose 3 vertices of 21-gon which are not adjacent to each other.
Secondly, connect all three vertices to a common vertex.
Now, there are 18 vertices that are not adjacent to common vertex and there are now 18 diagonals that can be drawn to the common vertex up to these vertices.
To form a triangle using these diagonals, we need to choose 3 of these 18 vertices, this can be calculated using the binomial coefficient formula:
18 choose 3 = 18! / (3! * (18 - 3)!) = (18 * 17 * 16) / (3 * 2 * 1) = 816
Thus, total 816 triangles can be formed.
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Can somebody help with number 8 find the value of each variable using the properties of a Parallelogram p
Answer: (9,8) A
Step-by-step explanation: how the mandle 10 30 6 150 144
Find the measure of the missing angle
Answer:
a = 149 degrees
Step-by-step explanation:
Angles must add up to 180 degrees so,
180 - 31 = 149.
What is the value of the following function when x = 0?
y=-5
y=-2
Y=-1
Y= 0
The numeric value of the function when x = 0 is found replacing each instance of x by zero in the definition of the function.
If a graph is given, then the numeric value is given as the value of y when the function crosses the y-axis.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
Supposing we have a function definition, then the numeric value at x = 0 is found replacing each instance of x by zero.
On graph, x = 0 is when the graph of the function touches or crosses the y-axis.
Missing InformationThe problem is incomplete, hence the general procedure to obtain the numeric value at x = 0 was presented.
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factor the following:
(a-b)*z+3(b-a)^2
The factored expression of (a-b) * 2 + 3(b-a)^2 is (-2 + 3(b - a))(b - a)
How to factor the expressionFrom the question, we have the following parameters that can be used in our computation:
(a-b)*z+3(b-a)^2
Express properly
So, we have
(a-b) * 2 + 3(b-a)^2
Rewrite as
-2(b - a) + 3(b - a)^2
Factor out b - a from the expression
So, we have
(-2 + 3(b - a))(b - a)
Hence, the factored expression is (-2 + 3(b - a))(b - a)
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What is the value of 300m in miles
Answer:
Step-by-step explanation:0.18
Help with geometry. Given ABC is congruent to MNO. m < A = 51 , m < N = 67 , and m < B = (2x + 7) What is the value of x?
The value of x is given as follows:
x = 30.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.For the two similar triangles, we have that B and N are equivalent angles, hence they are congruent and the value of x is given as follows:
2x + 7 = 67
2x = 60
x = 60/2
x = 30.
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