The coefficient of 8.2N1602 is 8.2N.
The given number is 8.2N1602, and you're required to find the coefficient of the number. The coefficient is the numerical factor that a term is multiplied by in an algebraic expression.
It is usually a number, but it may also be a letter that represents a number. The coefficient is the number that appears before the variable or term. For instance, in 3xy, 3 is the coefficient.In the given number, the coefficient is 8.2N, which is a decimal number.
A decimal is a number that uses place value and a decimal point to show the value of digits to the right of the decimal point.In general, decimals are a method of writing fractions that have a denominator of 10 or a power of 10.
The decimal 8.2 is 8 and 2 tenths, or 8.2/10. To convert a decimal number to a fraction, multiply the decimal by the appropriate power of 10 to make the decimal whole. In this case, we have 8.2N, which is already in decimal form.
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Simplify 9√2 – 3√7 + 8 – 28 (1 point)
The graphs of f(x) and g(x) are shown below.
On a coordinate plane, a straight line with negative a slope represents f (x) = negative x. The line goes through points (0, 0), (negative 6, 6) and (6, negative 6). On a coordinate plane, a straight line with a positive slope represents g (x) = 2 x. The line goes through points (negative 3, negative 6), (0, 0) and (3, 6).
Which of the following is the graph of (g – f)(x)?
On a coordinate plane, a straight line with a negative slope goes through points (negative 2, 6), (0, 0), and (2, negative 6)
On a coordinate plane, a straight line with a negative slope goes through points (negative 6, 6), (0, 0), and (6, negative 6).
On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).
On a coordinate plane, a straight line with a positive slope goes through points (negative 6, negative 6), (0, 0), and (6, 6).
Mark this and return
The correct statement regarding the graph of the linear function (g - f)(x) is given as follows:
On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).
How to define the functions?The function f(x) in this problem is defined as follows:
f(x) = -x.
The function g(x) in this problem is defined as follows:
g(x) = 2x.
Hence the subtraction of the two functions is given as follows:
(g - f)(x) = g(x) - f(x)
(g - f)(x) = 2x - (-x)
(g - f)(x) = 3x
Which has a positive slope, hence the correct option is given as follows:
On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).
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What’s the answer please help
The composite function for this problem is given as follows:
16.
How to define the composite function of f(x) and g(x)?The composite function of g(x) and f(x) is defined by the function presented as follows:
(g ∘ f)(x) = g(f(x)).
For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).
The functions for this problem are given as follows:
f(x) = 4.g(x) = 5x - 4.Hence the composite function is given as follows:
(g ∘ f)(x) = g(f(x)) = g(4) = 5(4) - 4 = 20 - 4 = 16.
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Which inequality represents the values of that ensure triangle ABC exists?
A
2x + 4
B
T
18
OA. < x < 1/1
Α.
OB.
6x
O c. 1 < x < 5
O D. 2 < < 6
C
To ensure that triangle ABC exists, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's assume that the lengths of the sides of triangle ABC are represented by the variables a, b, and c.
According to the options provided, the inequality that represents the values of x that ensure triangle ABC exists is:
C. 1 < x < 5
This is because if we substitute x with values within this range, the resulting lengths of the sides will satisfy the triangle inequality theorem.
To prove that the inequality 1 < x < 5 ensures the existence of triangle ABC, we need to show that for any value of x within this range, the lengths of the sides of triangle ABC satisfy the triangle inequality theorem.
The triangle inequality theorem states that for any triangle with side lengths a, b, and c, the sum of the lengths of any two sides must be greater than the length of the third side. In other words, for triangle ABC, we have:
a + b > c
b + c > a
c + a > b
Let's consider the inequality 1 < x < 5. This means that x is greater than 1 and less than 5.
To prove that triangle ABC exists for this range of x, we need to show that the lengths of the sides a, b, and c satisfy the triangle inequality theorem.
Let's consider the lengths of the sides in terms of x:
Side a = 2x + 4
Side b = x + 18
Side c = 6x
We will check if the inequalities hold for these side lengths:
a + b > c:
(2x + 4) + (x + 18) > 6x
3x + 22 > 6x
22 > 3x
b + c > a:
(x + 18) + 6x > 2x + 4
7x + 18 > 2x + 4
5x > -14
c + a > b:
6x + (2x + 4) > x + 18
8x + 4 > x + 18
7x > 14
From these inequalities, we can see that for any value of x within the range 1 < x < 5, the side lengths satisfy the triangle inequality theorem. Therefore, triangle ABC exists when 1 < x < 5.
This completes the proof that the inequality 1 < x < 5 ensures the existence of triangle ABC.
When plotting points on the coordinate plane below, which point would lie on both the x-axis and the y-axis?
A coordinate plane.
The point that would lie on both the x-axis and the y-axis is (0, 0)
How to determine the point on the x-axis and the y-axisFrom the question, we have the following parameters that can be used in our computation:
Plotting points on a coordinate plane
The general rule is that
The point on the x-axis and the y-axis is the origin
This means that the point that would lie on both the x-axis and the y-axis is (0, 0)
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he equation of the graphed line is 2x - 3y = 12.
7
6
5
432
2
4
-5-4-3-2-11
±
-2
-3
5
1 2 3 48 67 x
What is the x-intercept of the graph?
O-4
0-13/1/2
N/m
O
O 6
Answer:
when y=0
2x=12
we divide by 2 on both sides
x= 6
Prove that "If α is an ordinal and β ∈ α, then β is an ordinal" ?
If α is an ordinal and β ∈ α, then β satisfies all three properties of an ordinal. Therefore, β is also an ordinal.
To prove the statement "If α is an ordinal and β ∈ α, then β is an ordinal," we need to demonstrate that if α is an ordinal and β is an element of α, then β satisfies the three properties of an ordinal:
Well-Ordering: Every element of β is strictly well-ordered by the membership relation ∈. This property holds because α is an ordinal and satisfies the well-ordering property, and β being an element of α inherits this property.
Transitivity: For any two elements γ and δ in β, if γ ∈ δ and δ ∈ β, then γ ∈ β. Since β is an element of α and α is transitive, the transitivity property carries over to β.
Trichotomy: For any two elements γ and δ in β, either γ ∈ δ, δ ∈ γ, or γ = δ. Again, this property is inherited from α, as β is an element of α.
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An image of a rhombus is shown.
a rhombus with a base of 18 centimeters and a height of 15.5 centimeters
What is the area of the rhombus?
16.75 cm2
33.5 cm2
139.5 cm2
279 cm2
The area of the rhombus with a base of 18 centimeters and a height of 15.5 centimeters is 139.5 cm² (option c).
To find the area of a rhombus, we can use the formula:
Area = (base * height) / 2.
Given that the base of the rhombus is 18 centimeters and the height is 15.5 centimeters, we can substitute these values into the formula:
Area = (18 cm * 15.5 cm) / 2.
Multiplying the base and height gives us:
Area = (279 cm²) / 2.
Dividing 279 cm² by 2 gives us the final area:
Area = 139.5 cm².
Therefore, the area of the rhombus is 139.5 cm².
Thus, the correct option is c.
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Explain how to find the area and perimeter of the following triangles: A (-6, -1) B(-3, 3) C(5, -3)
Area: 11.18 sq units
Perimeter: 26.18 units
To find the area and perimeter of the triangle with vertices A(-6, -1), B(-3, 3), and C(5, -3), follow these steps:
1. Find the lengths of the sides:
- Side AB: Calculate the distance between points A and B using the distance formula: AB = √[(x₂ - x₁)² + (y₂ - y₁)²]
Substitute the coordinates: AB = √[(-3 - (-6))² + (3 - (-1))²] = √[3² + 4²] = √(9 + 16) = √25 = 5 units
- Side BC: Calculate the distance between points B and C using the distance formula: BC = √[(x₂ - x₁)² + (y₂ - y₁)²]
Substitute the coordinates: BC = √[(5 - (-3))² + (-3 - 3)²] = √[8² + (-6)²] = √(64 + 36) = √100 = 10 units
- Side CA: Calculate the distance between points C and A using the distance formula: CA = √[(x₂ - x₁)² + (y₂ - y₁)²]
Substitute the coordinates: CA = √[(-6 - 5)² + (-1 - (-3))²] = √[(-11)² + 2²] = √(121 + 4) = √125 = 11.18 units
2. Calculate the perimeter:
Perimeter = AB + BC + CA = 5 + 10 + 11.18 = 26.18 units
3. Find the area using the Shoelace Formula:
Area = 0.5 * |(x₁y₂ + x₂y₃ + x₃y₁) - (x₂y₁ + x₃y₂ + x₁y₃)|
Substitute the coordinates: Area = 0.5 * |(-6 * 3 + (-3) * (-3) + 5 * (-1)) - (-3 * (-1) + 5 * 3 + (-6) * (-3))|
Simplify: Area = 0.5 * |(-18 + 9 - 5) - (3 + 15 + 18)|
= 0.5 * |-14 - 36|
= 0.5 * |-50|
= 0.5 * 50
= 25 sq units
Therefore, the area of the triangle is 25 square units and the perimeter is 26.18 units.
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Which of the systems of linear equations will have no solution?
Question 15 options:
y = 12 – 3x
y = 2x – 3
y = x – 1
-5x + y = -5
2x + y = 9
2x + y = 5
y = 2x
3x + 2y = 21
The system of equations given in option 4, y = 2x and 3x + 2y = 21, will have no solution.
2x + y = 9
2x + y = 5
The graph is attached
How to find the equation without solutionA system of linear equations will have no solution if the lines represented by the equations are parallel, meaning they have the same slope but different y-intercepts.
Looking at the given options:
y = 12 – 3x
y = 2x – 3
y = x – 1
-5x + y = -5
2x + y = 9
2x + y = 5
y = 2x
3x + 2y = 21
Option 3, 2x + y = 9 and 2x + y = 5, represents parallel lines.
The slopes of the lines are the same (both equations have a coefficient of -2 for x and 1 for y), but the y-intercepts are different
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Is the relation in the table a function?
X
5
8
11
14
17
y
11
14
5
10
14
A. No. One input value has more than one output value.
B. Yes. Each input value corresponds to only one output value.
C. No. One output value has more than one input value.
D. Yes. Each output value corresponds to only one input value.
Answer:
The correct answer is C. No. One output value has more than one input value. A relation is a function if and only if each input value corresponds to exactly one output value. In this case, the output value 14 corresponds to two different input values, 8 and 17, so the relation is not a function.
Use the diagram in the box to convert the given measurements to the unit indicated. 18.8 hm to m
How to convert 18.8 hm (hectometers) to meters using the diagram. So, 18.8 hm is equal to 1,880 m after converting using the diagram.
Here is how to convert 18.8 hm to m using the diagram:
1. Start with the given measurement, which is 18.8 hm.
2. Locate "hecto" on the diagram and see that it is 2 units away from "m" (meter).
3. Since you want to convert from hm to m, you need to move 2 units to the left on the diagram.
4. Moving 2 units to the left on the diagram brings you to the meter (m) unit.
5. Each time you move one unit to the left on the diagram, you divide the original measurement by 10. Since you moved 2 units to the left, you need to divide 18.8 by 100 (10 raised to the second power).6. Therefore, 18.8 hm is equal to 1,880 m after converting using the diagram.
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What is the distance from point N to M in the figure below?
L
8.3
N
7.5
0
OA. 7.7
7.7
B. 1.74
C. 8,3
OD. 7.5
OE. 0.8
OF. 3.55
M
Answer:
Step-by-step explanation:
Distance from point N to M can be calculated using the Pythagoras theorem. According to Pythagoras theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Here, side LN is the hypotenuse, and NM and ML are the other two sides. Therefore, LM can be calculated using the Pythagorean theorem as follows:
NM² + ML² = LN²
7.5² + 8.3² = LM²
56.25 + 69.29 = LM²
125.54 = LM²
LM = √125.54
LM ≈ 11.2
Therefore, the distance from point N to M is equal to the length of the side LM which is approximately 11.2. Hence, the correct option is not available in the given alternatives.
Which graph represents the system
enter the number that belongs in the green box 37 5 120
The number that fit in into missing value is 7.707
What is Law of Sines?Rule of Sines The sine law, sine formula, sine rule, or law of sines is an equation in trigonometry that connects the lengths of any triangle's sides to the sines of its angles. Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle.
[tex]\frac{sin A}{a} = \frac{sinB}{b} = \frac{sin C}{c}[/tex]
The value of the third angle = 180-(37+120)
=23 degree
let x be the missing side
[tex]\frac{sin 23}{5} =\frac{sin37}{x}[/tex]
x=[tex]\frac{ sin37 *5}{ sin23 }[/tex]
x =[tex]\frac{0.6018 * 5}{ 0.39073}[/tex]
=7.707
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Julian is mixing drops of food coloring to create green frosting for a cake. He uses 18 drops of yellow dye and 12 drops of blue dye. Find the ratio of drops of blue dye to total drops of dye. Express as a simplified ratio
The simplified ratio of blue dye drops to the total drops of dye is 2:5. This means that for every 2 drops of blue dye, there are 5 drops of dye in total.
To find the ratio of drops of blue dye to the total drops of dye, we need to determine the total number of drops of dye used. Julian used 18 drops of yellow dye and 12 drops of blue dye, which gives us a total of 18 + 12 = 30 drops of dye.
Now, let's find the ratio of blue dye drops to the total drops of dye. The ratio can be expressed as "blue dye drops: total drops of dye." In this case, the number of blue dye drops is 12, and the total number of drops of dye is 30.
To simplify the ratio, we can divide both numbers by their greatest common divisor (GCD). The GCD of 12 and 30 is 6. Dividing both numbers by 6, we get 12 ÷ 6 = 2 and 30 ÷ 6 = 5.
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Which expression is equivalent to the given expression?
[tex] 2x^2 - 11x - 6 [/tex]
Hello!
2x² - 11x - 6
= (2x² + x) + (-12x - 6)
= x(2x + 1) - 6(2x + 1)
= (x - 6)(2x + 1)
Jay rode his motorcycle 100 mi into the mountains. On the return trip he was able to average 5 mi/hr faster. If the round trip
took 5 hr, how fast (to the nearest tenth of a mile per hour) did he travel going each way?
7.5 mi/hr going; 12.5 mi/hr returning
75.3 mi/hr goirfg; 80.3 mi/hr returning
none of the answer choices
O 2.7 mi/hr going; 7.7 mi/hr returning
O 37.7 mi/hr going; 42.7 mi/hr returning
With speed of 7.5 mi/hr and 12.5 mi/hr fast he would be going and returning respectively.
To solve this problem, let's denote the speed of Jay's motorcycle on the outbound trip as "x" miles per hour. Since he was able to average 5 mi/hr faster on the return trip, his speed on the return trip would be "x + 5" miles per hour.
We know that the total time for the round trip is 5 hours. The time taken for the outbound trip is the distance divided by the speed, which is 100 / x. The time taken for the return trip is the distance divided by the speed, which is 100 / (x + 5).
According to the problem, the total time for the round trip is 5 hours. Therefore, we can set up the equation:
100 / x + 100 / (x + 5) = 5
To solve this equation, we can multiply through by x(x + 5) to eliminate the denominators:
100(x + 5) + 100x = 5x(x + 5)
Expanding and simplifying the equation, we get:
200x + 500 = 5x^2 + 25x
Bringing all terms to one side and simplifying further, we obtain a quadratic equation:
5x^2 + 25x - 200x - 500 = 0
5x^2 - 175x - 500 = 0
Factoring the equation, we find:
(x - 7.5)(x + 12.5) = 0
So, x = 7.5 or x = -12.5. Since speed cannot be negative, the only valid solution is x = 7.5.
Therefore, Jay traveled at a speed of 7.5 mi/hr on the outbound trip and 7.5 + 5 = 12.5 mi/hr on the return trip.
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A water taxi carries passengers from harbor to another. Assume that weights of passengers are normally distributed with a mean of 180 lb and a standard deviation of 43lb. The water taxi has a stated capacity of 25 passengers, and the water taxi was rated for a load limit of 3500 lb.
Once upon a time in a land not so far away, there was a bright and sprightly water taxi. Let's call it 'HappiNess'. She was known far and wide for her distinct yellow hue, and her chirpy charm was the talk of the harbor. She carried people from one harbor to another with pride and style, and had quite a reputation for always being on time.
Now, passengers, as varied and vibrant as the rainbow itself, came from all walks of life. It just so happened that on average, they tipped the scales at around 180 lb. You'd think that's a bit too precise for an estimate, wouldn't you? But you see, in this magical realm, statisticians have fairy dust. And, just like how fairy godmothers knew the exact size of Cinderella's shoe, our statisticians sprinkled their dust and found that passenger weights in our story followed a 'normal distribution'. Quite like the shape of a bell, but let's imagine it as an enchanted hill with the most common weights at the peak and the rare, lighter and heavier weights as the slopes on either side. The enchantment was such that the weights of passengers varied by around 43 lb on either side of 180 lb.
Now, HappiNess was as robust as she was sprightly, but every ship, no matter how bright and yellow, has its limits. She could carry a merry crowd of 25 passengers at a time. Any more than that and she'd risk becoming the 'GrumpiNess', and no one wanted that! Besides, she was rated for a load limit of 3500 lb - that's the magic number beyond which HappiNess would start losing her cheer.
Imagine one fine day, a crowd of 25 average-sized passengers (each 180 lb) decided to board HappiNess. That would be quite an adventure, right? Because 25 passengers, each weighing 180 lb, totals to 4500 lb - a number that exceeds the HappiNess' load limit of 3500 lb. And we'd never want to risk her becoming GrumpiNess, would we?
So, we better make sure that we don't overburden HappiNess, even if that means fewer tales of seafaring adventures. The key is to ensure a balance, quite literally, so she can continue to be the HappiNess we all love and enjoy. After all, it's all about staying afloat and riding the waves with a smile, isn't it?
What is the square root of 0.327 up to 2 Decimal Places
Answer:
To find the square root of 0.327 up to 2 decimal places, you can use a calculator or mathematical software. The square root of 0.327 is approximately 0.57.
What is the y-intercept of the function f(x)=4-5x?
Answer: the y-intercept is at four
Step-by-step explanation: 4 is the point which the function cross the y axis on a graph
A discrete random variable z has a probability mass function given byP(Z=z) =k(3/4)^z, for Z=0,1,2,...Find the value of constant K and P(Z<3)
The value of the constant k in the probability mass function is 1/4, and P(Z < 3) is equal to 37/64.
To find the value of the constant k in the probability mass function (PMF) and calculate P(Z < 3), we can use the properties of a discrete random variable and the given PMF.
First, we know that the sum of probabilities for all possible values of a discrete random variable must equal 1. Therefore, we can write:
∑ P(Z = z) = 1
Now let's substitute the given PMF into the summation:
∑ k[tex](3/4)^z[/tex] = 1
We can simplify this expression by factoring out the constant k:
k ∑ [tex](3/4)^z[/tex] = 1
Next, we need to evaluate the summation term. The summation represents a geometric series with a common ratio of 3/4. The sum of a geometric series is given by:
∑[tex]r^n[/tex] = 1 / (1 - r), where |r| < 1
In this case, the summation term becomes:
∑ [tex](3/4)^z[/tex] = 1 / (1 - 3/4)
Simplifying further:
∑ [tex](3/4)^z[/tex] = 1 / (1/4) = 4
Now, we can substitute this value back into the previous equation:
k * 4 = 1
Solving for k:
k = 1/4
Therefore, the value of the constant k is 1/4.
Now let's calculate P(Z < 3) using the PMF:
P(Z < 3) = P(Z = 0) + P(Z = 1) + P(Z = 2)
Substituting the given PMF with k = 1/4:
P(Z < 3) = (1/4)(3/4)^0 + (1/4)(3/4)^1 + (1/4)(3/4)^2
= (1/4)(1) + (1/4)(3/4) + (1/4)(9/16)
= 1/4 + 3/16 + 9/64
= 16/64 + 12/64 + 9/64
= 37/64
Therefore, P(Z < 3) is equal to 37/64.
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The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 31
hours and the median is 27.2
hours. Twenty-four of the families in the sample turned on the television for 16
hours or less for the week. The 7th percentile of the data is 16
hours.
Step 2 of 5: Approximately how many families are in the sample? Round your answer to the nearest integer.
Answer:
We can use the information that 24 families watched 16 hours or less to estimate the sample size. Since the 7th percentile is 16 hours, we know that 7% of the sample watched 16 hours or less. Therefore, we can set up a proportion:
(24 / x) = 0.07
where x is the total number of families in the sample. Solving for x, we get:
x = 24 / 0.07 ≈ 343
Rounding to the nearest integer, we can estimate that there are approximately 343 families in the sample.
Earth has more than 60,000 tree species. Each look different and grows at a different rate. Pick a tree species below. If you planted a seed in year 0, calculate the dimensions of the trees trunk in years 1,2,3, and 10. Would you say that the tree grows by the same amount each additional year?
One of the species of trees is the Oak. If a seed of an Oak tree is planted, and it is assumed that the diameter of the seed is 0, the tree would grow by approximately 3.3 inches in year 1, 6.6 inches in year 2, 9.9 inches in year 3, and 33 inches in year 10. It cannot be said that the Oak tree would grow by the same amount each additional year.
Some years, the tree might grow more, while other years, it might grow less.Trees are perennial plants that have a single main stem, a supporting structure of branches and leaves, and the ability to produce wood.
A tree that is mature and has a single stem is known as a "single-trunked" or "single-stemmed" tree; trees with several stems originating at or near the ground are known as "multi-stemmed" or "clonal" trees.The height and trunk diameter of a tree increase as it matures.
The growth rate of each tree species is determined by various variables such as weather, altitude, and soil fertility.
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Which expression is equivalent to 2m(3/2 m + 1) +3 (5/3 m-2)
The expression 2m(3/2m + 1) + 3(5/3m - 2) is equivalent to 11m/3 - 3.
To simplify the given expression, let's distribute and combine like terms:
2m(3/2m + 1) + 3(5/3m - 2)
First, distribute 2m to the terms inside the parentheses:
= (2m * 3/2m) + (2m * 1) + (3 * 5/3m) - (3 * 2)
Simplifying each term:
= (3) + (2m) + (5m/3) - 6
Next, combine like terms:
= 2m + (5m/3) - 3
To add the terms 2m and (5m/3), we need a common denominator.
The common denominator is 3:
= (6m/3) + (5m/3) - 3
Combining the terms with the common denominator:
= (6m + 5m)/3 - 3
= 11m/3 - 3
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Question Translate to a proportion: What percent of 43 is 21? Let p = the percent. Provide your answer below:
Answer: p=48.8372093%
Step-by-step explanation:
Step-by-step explanation:
100% = 43
1% = 100%/100 = 43/100 = 0.43
21 is that many % as times 1% fits into 21 :
p = 21 / 0.43 = 48.8372093... %
Write the expression in factored form.
81m4 - nª
The factored form of the expression 81m^4 - n^2 is (9m^2 + n)(9m^2 - n).
To factor the expression 81m^4 - n^2, we need to look for common factors and apply algebraic factoring techniques.
We start by recognizing that 81m^4 can be written as (9m^2)^2, which is a perfect square. Similarly, n^2 is also a perfect square.
Applying the difference of squares formula, we can factor the expression as follows:
81m^4 - n^2 = (9m^2)^2 - n^2
= (9m^2 + n)(9m^2 - n)
Now, the expression is factored in terms of (9m^2 + n) and (9m^2 - n). These factors represent the difference of two squares, where (9m^2 + n) is the sum of two squares (9m^2 and n^2) and (9m^2 - n) is the difference of two squares.
The factored form of the expression 81m^4 - n^2 is (9m^2 + n)(9m^2 - n).
Factoring expressions can be a useful technique to simplify and analyze mathematical expressions. In this case, we were able to factor the expression by recognizing perfect square terms and applying the difference of squares formula.
Factoring can help in solving equations, simplifying expressions, and identifying important patterns and relationships in mathematics.
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Identify the steps followed to solve the equation 5 - 3 (x+3) = 11 - 8x
Answer:
Everything looks right except the first one which is Distributive Property.
Step-by-step explanation:
multiplying out - 3(x - 3) is considered distributive property as you are distributing the -3 to the x and the 3.
-3 * x = -3x and -3 * 3 = -9
In the picture below, which lines are lines of symmetry for the figure? A only 2 b 2 and 4 c 1 and 3 d 1 2 and 3
Answer:
B. 2 and 4 es la respuesta correcta
Determine any data values that are missing from the table, assuming that the data represent a linear function. x y 1 2 2 6 4 a. 2 c. 14 b. 10 d. 16
The equation of the linear function is y = 4x - 2. The missing value in the table is 14.
The missing value in the given table is 10. Assuming that the data represent a linear function, we can use the slope formula (m = (y2 - y1) / (x2 - x1)) to find the missing value.
We can choose any two sets of coordinates from the table to find the slope, then use that slope to find the missing value. For example, using the coordinates (1, 2) and (2, 6), we get:m = (6 - 2) / (2 - 1) = 4
Therefore, the equation of the linear function is y = 4x + b, where b is the y-intercept. To find b, we can plug in any set of coordinates into the equation and solve for b.
For example, using the coordinates (1, 2), we get:2 = 4(1) + bSimplifying the equation, we get:b = -2Therefore, the equation of the linear function is y = 4x - 2. We can now use this equation to find the missing value when x = 4:y = 4(4) - 2 = 14Therefore, the missing value in the table is 14.
We are given a table of x and y values. We need to find the missing value assuming that the data represent a linear function. To find the missing value, we can use the slope formula (m = (y2 - y1) / (x2 - x1)).
This formula gives us the slope of the line passing through two points, which is the rate at which y changes with respect to x. We can then use this slope to find the missing value in the table.
Using the coordinates (1, 2) and (2, 6), we get a slope of 4. This means that for every 1 unit increase in x, y increases by 4 units. Therefore, the equation of the linear function is y = 4x + b, where b is the y-intercept.
To find b, we can plug in any set of coordinates into the equation and solve for b. Using the coordinates (1, 2), we get b = -2. Therefore, the equation of the linear function is y = 4x - 2.
Finally, we can use this equation to find the missing value when x = 4. Plugging in x = 4, we get y = 4(4) - 2 = 14. Therefore, the missing value in the table is 14.
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