The exponent form that represents the side length of the square is √x
How to determine the side length of the square.From the question, we have the following parameters that can be used in our computation:
Area = x in.²
The area of a square is calculated as
Area = Side length²
substitute the known values in the above equation, so, we have the following representation
Side length² = x
Take the square root of both sides
Side length = √x
Hence, the expression is √x
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Figure out the polynomial being multiplied on top and then fill in the missing boxes
Based on given polynomial, The complete equation is = x² - 6x - 3.
What is Exponent Law in Polynomial Multiplication?A polynomial can be multiplied in just three steps.
The first step is to multiply each term in one polynomial by each term in the other polynomial using the distributive law.
Use the exponent rule to sum powers of related variables.
Then, to simplify the resulting polynomial, add or eliminate like elements.
The fact that multiplying two polynomials always yields a degree higher than the degree of the original polynomials should not be overlooked.
If a variable has the same exponent but various exponents for the provided polynomials, we must use the exponent law.
Given,
a______________
x² (b) __ -6x³ (c)__
9x 9x³ (d)___ -27x
We know that (a) is some polynomial in the form Ax² + Bx + c
Based on the above table,
It is clear that
on multiplying x² × 1 term = (b)
x² × 2 term = -6x³
⇒ 2 term = -6x³ / x² = -6x (1)
x² × 3 term = (c)
Now,
9x × 1 term = 9x³
⇒ 1 term = x² (2)
9x × -6x = (d)
⇒ d = -54x² (3)
9x × 3 term = -27x
3 term = -3 (4)
From (1), (2) and (4),
The complete equation is = x² - 6x - 3
Value of (b) = x² × 1 term = (b)= x² × x² = x⁴
Value of (c) = x² × 3 term = (c) = x² ₓ -3 = -3x²
Value of (d) = -54x² [From (3)]
So the complete table is -
(a) x² - 6x - 3
x² (b) -6x -6x³ (c) -3
9x 9x³ (d) -54x² -27x
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Which of the following variables are quantitative?Number zip codeFavorite colorShoe sizeArea code
Quantitative variables can be used to measure and contrast data because they have numerical values. Measurements like shoe size, height, weight, and temperature are examples of quantitative variables.
Quantitative variables can be used to measure and contrast data because they have numerical values. They come in discrete or continuous forms. While continuous variables have an infinite number of possible values, such as decimal numbers, discrete variables have specific values, such as integers or whole numbers. Measurements like shoe size, height, weight, and temperature are examples of quantitative variables. Quantitative variables can be used to describe a population's varied characteristics, such as the median age or annual income of a given group. The average height of men and women, for example, might be used to compare two populations. The use of quantitative variables is crucial for comprehending and analyzing data. They enable academics to spot patterns and trends in data They enable researchers to find patterns and trends in data, anticipate the future, and form conclusions.
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the complete question is
Which of the following variables are quantitative? Number zip codeFavorite colorShoe sizeArea code and Shoe size.
Chang received a $50.00 gift card for a photo center. He used it to buy prints that cost 6 cents each. The remaining balance, B (in dollars) on the card after buying x prints is giving by the following functions?
Answer: B = 50 - 0.06x
Step-by-step explanation:
This equation shows that the remaining balance on the gift card (B) is equal to the initial amount of the gift card (50) minus the cost of the prints (0.06x) where x is the number of prints purchased.
A recipe requires a cooking temperature of 280°C. Determine the equivalent of this temperature in °F.
Answer: To convert a temperature from degrees Celsius (°C) to degrees Fahrenheit (°F), you can use the following formula:
°F = (9/5) x °C + 32
So, to convert 280°C to °F:
°F = (9/5) x 280 + 32 = 536 + 32 = 568°F
So the equivalent of 280°C in °F is 568°F
Step-by-step explanation:
the solid whose base is the region bounded by x-y^2 and the line y-1 and whose cross sections perpendicular to the base and parallel to the x-axis are squares
The solid whose base is the region bounded by the parabola y = x^2 and the line y = 1 and whose cross sections perpendicular to the base and parallel to the x-axis are squares is a parabolic pyramid.
A parabolic pyramid is a pyramid whose base is a parabola and whose lateral faces are formed by rectangles that are perpendicular to the base. The height of the pyramid is determined by the y-coordinate of the point where the parabola and the line y = 1 intersect. The length of the side of the square cross section is determined by the x-coordinate of the point where the parabola and the line y = 1 intersect.
The base of the solid is a parabolic region, defined by the parabola y = x^2 and the line y = 1, and the cross sections are squares, perpendicular to the base, and parallel to the x-axis. This solid is called a parabolic pyramid.
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Select the correct answer from each drop-down menu. Prism M and pyramid N have the same base area and the same height. Cylinder P and prism Q have the same height and the same base perimeter. Cone Z has the same base area as cylinder Y, but its height is three times the height of cylinder Y. The figures and have the same volume. Reset Next
The figures cone Z and cylinder Y have the same volume.
What is volume?Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic metre (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.
Given, Prism M and pyramid N have the same base area and the same height. Cylinder P and prism Q have the same height and the same base perimeter. Cone Z has the same base area as cylinder Y, but its height is three times the height of cylinder Y.
The formula for volume of the cone Z is given by
Volume = 1/3* pi * radius *radius *height
The formula for volume of the cylinder Y is given by
Volume = pi * radius *radius *height
Since, it is given that Cone Z has the same base area as cylinder Y, but its height is three times the height of cylinder Y.
Thus, substituting in the formula of volume of the cone Z, we get,
Volume = 1/3* pi * radius *radius *3*height
Simplifying, we have,
Volume = pi * radius *radius *height
Hence, the volume of the cone Z = volume of the cylinder Y
Thus, the figures cone Z and cylinder Y have the same volume.
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determine whether each of the following formulas is a tautology, contingency, or contradiction (this means always true, sometimes true, never true). show how you arrived at each answer. use equivalence-style proofs.
From the given formulas, formula A is a tautology or always true. Formula B is a contradiction or never true. And, formula C is contingency or sometimes true.
Using the truth table, a given expression is said to be in tautology when all the values are true. The given expression is said to be a contradiction when all the values are false or never true. And the given expression is said to be contingency when the values are either true or false.
In the given formulas, formula A (p→q)∨(q→r) is a tautology. This is because the values in all rows are true (T).
In the given formulas, formula B (¬(¬(p∧q)→(p→¬q))) is a contradiction. This is because the values in all rows are false (F).
In the given formulas, formula C ((¬p∨q)→q) is a contingency. This is because some values are true and some are false.
The complete question is -
Determine whether each of the following formulas is a tautology, contingency, or contradiction (this means always true, sometimes true, never true). Show how you arrived at each answer. Use equivalence-style proofs.
A. (p→q)∨(q→r)
B. ¬(¬(p∧q)→(p→¬q))
C. ((¬p∨q)→q)
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radius = 8.8 cm and height = 4.7 cm what's the volume?
According to the given information in the question the volume of the cylinder is approximately 1232.5 cm³.
What are volume and mass?A three-dimensional object's volume is the area it takes up, and it is expressed in cubic units. Cm3 and in3 are examples of cubic units.On the other hand, an item's mass can be used to calculate how much matter it contains. The weight of an object is a common way to determine mass (in units like pounds or kilograms).
Which is a volume unit?The most popular units of volume in the decimal system of measurement are ml. and liters.
V = * r² * h is the formula for a cylinder's volume.
V = π * (8.8 cm)² * 4.7 cm
V = π * 77.44 cm² * 4.7 cm
V ≈ 1232.5 cm³
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a marketing agency selected a random sample of television viewers to test the claim that the proportion of viewers who watch a particular show is less than 0.20 at a level of significance of 0.05. the test yielded a p -value of 0.47. assuming all conditions for inference were met, which of the following is the correct conclusion?
Correct conclusion , Proportion of viewers is not less than 0.20.
What is proportion ?
A proportion is a way to express the relationship between two or more quantities or values. It is a statement that asserts that two ratios or fractions are equal, such as "2/5 is equal to 4/10". Proportions can be written in different ways, such as "2 to 5 is equal to 4 to 10", or "2:5 = 4:10".
the proportion of viewers who watch the particular show is less than 0.20. The p-value of 0.47 is greater than the level of significance of 0.05, meaning that the results of the test are not statistically significant and do not provide enough evidence to reject the null hypothesis that the proportion of viewers who watch the particular show is greater than or equal to 0.20. Therefore, the marketing agency cannot conclude that the proportion of viewers who watch the particular show is less than 0.20.
Correct conclusion , Proportion of viewers is not less than 0.20.
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Average movie prices in the United States are in general lower than in other countries.It would cost $81.22 to buy three tickets in Japan plus two tickets in Switzerland.Three tickets in Switzerland plus two tickets in Japan would cost $77.03.How much does an average movie ticket cost in each of these countries?
Answer:
It is not possible to determine the average movie ticket price in each of these countries with the given information. The statement "Average movie prices in the United States are in general lower than in other countries" is not relevant to determine the average movie ticket price in Japan and Switzerland. The information provided is the cost of 3 tickets in Japan and 2 tickets in Switzerland, and also the cost of 3 tickets in Switzerland and 2 tickets in Japan. This information cannot be used to determine the average movie ticket price in each country as it is not clear how many people are going to the movies and the different prices of the movies. More information is needed.
Describe where the particle changes direction and the intervals where the particle speeds up or slows down. (20 points)
At the locations where the acceleration graph veers off, the particle changes course. It accelerates at positive slope acceleration graph intervals and decelerates during negative slope acceleration graph intervals.
At the locations where the acceleration graph veers off, the particle changes course. At these locations, the particle's acceleration is zero and the slope of the graph flip-flops from positive to negative. The particle changes direction at this point. The particle either speeds up or slows down in the intervals before and after the point of inflection. The particle is speeding up during the intervals where the acceleration graph has a positive slope, and slowing down during the intervals where the acceleration graph has a negative slope. We can determine how the particle is changing direction and whether it is speeding up or slowing down by examining the slope of the acceleration graph.
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ayuden gente pipi ,a rectangular garden has a walkway around it .the area of the garden is 6(4.5x+2.5).the combined area of the garden and the walkway is 6.5(6x+4)find the area of the walkway around the garden as the sum of two terms
The circumference of the walkway is 26 x + 16 when two words are added together.
Discover the product of two terms for the walkway's circumference around the garden?A walkway around a rectangular garden.
The garden's size is 4(4.5 x + 1.5) square meters.
The garden's and the walkway's combined area is 5.5(8 x + 4)
We must locate the location of the walkway.
By deducting the size of the pathway from the area of the
from the combined area, a rectangle
Simplify it to provide the combined area as 5.5(8 x + 4)
The total area is equal to 5.5(8 x) Plus 5.5. (4)
∴Area added together: 44 x + 22
Simplify: The garden's area is 4(4.5 x + 1.5).
The garden's size is equal to 4(4.5 x) Plus 4. (1.5)
The garden's size is equal to 18 x + 6.
Subtract the garden's area from the total area now.
The walkway's area is equal to (44 x + 22) minus (18 x + 6)
Area of the walkway is equal to 44x + 22 - 18 x - 6
- Add similar phrases.
The walkway's size is equal to (44 x - 18 x) +. (22 - 6)
Walkway area equals 26 x plus 16
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please help me with math
Answer: 3rd Picture
Step-by-step explanation: Equation: y=1/3x+4
Intercepts y axis at 4, and with the slope equation (rise/run), then it rises 1 and runs 3, thus being the 3rd picture.
find all values of in the interval [) that have the given function value. group of answer choices 154, 268 degrees 146, 238 degrees 115, 195 degrees 135, 225 degrees
By applying Trigonometry functions it can be concluded that cos θ = -√2/2 will be met if θ = 135° or 225° (option D)
Trigonometry is a branch of mathematics that studies the relationship between side lengths and angles of triangles.
Trigonometry functions can be defined by means of a right triangle, where ABC is a right triangle, a and b are the sides of the triangle and c is the hypotenuse of the triangle.
sin A = opposite side (a) / hypotenuse (c)
cos B = adjacent side (b) / hypotenuse (c)
tan C = opposite side (a) / adjacent side (b)
There are some special angles whose sin, cos, and tan values are frequently used:
0° 30° 45° 60° 90°
sin 0 1/2 √2/2 √3/2 1
cos 1 √3/2 √2/2 1/2 0
tan 0 √3/3 1 √3 ~
These values change over the interval:
sin: positive in the interval [0°,180°] and negative in the interval [180°,360°]cos: positive in the interval [0°, 90°] and [270°,360°], and negative in the interval [90°,270°]tan: positive in the interval [0°, 90°) and [180°,270°), and negative in the interval (90°,180°] and (270°,360°]We have to find all values in the interval [0,360°) that have the given function value cos θ = -√2/2.
cos θ = √2/2
θ = 45°
Since cos will have a negative value in the interval [90°,270°], then we get the value of θ is 135° and 225°.
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For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h in simplest form. f(x)=4x²-7 on (1,b)
On the interval (1,b), f(x)=4x2-7 changes at an average rate of 8b-11. To determine this, divide the difference between the function at b and 1 (4b2-7-3) by the difference between the intervals (b-1).
The average rate of change of a function on an interval is a measure of the change in the output of the function over the given interval. It can be calculated by taking the difference of the output between the endpoints of the interval, and dividing by the difference between the endpoints of the interval. For the given function f(x)=4x²-7 on the interval (1,b), the average rate of change is 8b-11This is obtained by dividing the output difference between 1 and b (4b2-7-3) by the output difference between the intervals (b-1). Our average rate of change is given by this formula: (4b2-7-3) / (b-1) = 8b-11. This average rate of change provides us with a general understanding of the function's rate of change across the specified interval. The output of the function increases at a constant rate as the input increases in this situation because the rate of change grows linearly as b increases.
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Two mechanics worked on a car. The first mechanic charged $115 per hour, and the second mechanic charged $60 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $2600. How long did each mechanic work? First Mechanic hours Seconds Mechanic hours
Answer:
Step-by-step explanation:
Each mechanic worked a total of 12.5 hours each.
The solution to x2 – 10x = 24 is
✔ 12 or –2
.
The solution to 2x2 – 11 = 87 is
✔ 7 or –7
.
The solution to 3x2 – 12x + 24 = 0 is
✔ 2 + 2i or 2 – 2i
.
The solution to x^2 – 10x = 24 is 12 or -2. The solution is obtained by solving the algebraic equation.
What is algebraic equation?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). For the algebraic equation, the expression must contain an equals to sign.
We are given equation as x^2 - 10x = 24
This can be re-written as x^2 - 10x - 24 = 0
In order to find the solution, we need to solve the equation for x.
So,
⇒x^2 - 10x - 24 = 0
⇒x^2 - 12x + 2x - 24 = 0
⇒x (x - 12) + 2 (x - 12) = 0
⇒(x - 12) (x + 2) = 0
⇒x = 12 , -2
Hence, the solution to x^2 – 10x = 24 is 12 or -2.
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Since there are multiple question, so the question answered above is
The solution to x2 – 10x = 24 is
✔ 12 or –2
a circular disk is to be manufactured with a radius of 26 cm. use differentials to estimate the maximum error in the calculated area of the disk if the possible error in measuring the radius is 0.25 cm.
The maximum error in calculating the area of the disk is approximately 0.25 cm * 2π * 26 cm = 16.3 cm².
The maximum error in the calculated area of the disk can be estimated using differentials. A = r2, where r is the circle's radius, is the formula for calculating a circle's area.. Differentiating this equation with respect to r gives us A' = 2πr. Plugging in the given values, we get A' = 2π * 26 cm = 161.6 cm². If the possible error in measuring the radius is 0.25 cm, then the maximum error in calculating the area of the disk is 0.25 cm * A' = 0.25 cm * 161.6 cm² = 16.3 cm². Therefore, the maximum error in the calculated area of the disk is approximately 16.3 cm².
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In the expression n +23 23 is a?
Hey there!
We are given the expression [tex]n + 23[/tex].
In this expression, [tex]n[/tex] represents the dependent variable; this changes with the input value once determined.Now [tex]23[/tex] on the other hand represents the constant; this variable never changes.Hence, 23 is the constant.
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Josiah takes a multiple-choice quiz that has three questions. Each question has five answer options. if he randomly chooses his answers, what is the probability that he will get all three correct
Answer: 1/15
Step-by-step explanation: 3*5=15
2-2 the following sample data represent the per pound cost of raw materials used in processing batches of a chemical feedstock: $12.01 $14.90 $11.24 $14.40 $12.87 11.30 16.98 15.23 12.38 12.90 12.29 11.51 12.06 15.06 11.16 10.12 14.82 17.02 12.56 13.95 11.13 12.14 13.41 15.67 12.17 12.15 12.57 14.21 13.21 16.50 13.81 15.58 11.10 12.03 11.20 12.27 17.05 12.57 13.11 13.31 13.84 11.62 12.33 16.31 12.74 14.25 18.63 13.34 13.43 14.78 Construct a table for the sample frequency distribution having $2 widths for the class intervals, with $10.00 as the first tower limit Interval 1 frequency Interval 2 frequency - Interval 3 frequency - Interval 4 frequency Interval 5 frequency -
Interval 1: 10 a.m. to 12 p.m., Frequency: 6, Interval 2: 12 p.m. to 14 p.m., Frequency: 8, Interval 3: 14 p.m. to 16 p.m., Frequency 5, Interval 4: 16 p.m. to 18 p.m., Frequency 2, and Interval 5: 18 p.m. to 20 p.m., Frequency 1.
The first lower limit of the sample frequency distribution for the provided data is fixed at $10.00, with an interval width of $2.00. The frequency of Interval 1 is 6, and it runs from 10:00 to 12:00. The frequency of Interval 2 is 8, and it lasts from 12:00 to 14:00. With a frequency of 5, interval 3 runs from 14:00 to 16:00. The frequency of interval 4 is 2, and it lasts from 16:00 to 18:00. With a frequency of 1, interval 5 runs from 18.00 to 20.00. The data range and frequency of each value are shown in this table, giving a comprehensive picture of the data. You can use this table to determine suitable pricing strategies for the product.
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place value 75,232 = ___ in expanded form
7 × 10000 + 5 × 1000 + 2 × 100 + 3 × 10 + 2 × 1
Please help me, I will give best answer a brainlist
Here we are interested in finding the slope of the line. From the given graph we can see that that the line passes through points (-5,0) and (0,-3) . We know that slope can be calculated by ,
[tex]\longrightarrow slope \ (m)=\dfrac{y_2-y_1}{x_2-x_1} =\tan\theta [/tex]
hence here ,
[tex]\longrightarrow m =\dfrac{y_2-y_1}{x_2-x_1}\\[/tex]
[tex]\longrightarrow m =\dfrac{0-(-3)}{-5-0}\\[/tex]
[tex]\longrightarrow m =\dfrac{3}{-5}\\ [/tex]
[tex]\longrightarrow m =\dfrac{-3}{5}\\ [/tex]
[tex]\longrightarrow \underline{\underline{ m = -0.6}}[/tex]
And we are done!
1. Find the sum of the measures of the interior angles of a convex 22-gon.
The sum of interior angles of the given 22 sided convex polygon is; 3600°
What is the sum of interior angles of a polygon?When it comes to finding the sum of the interior angles of a a convex polygon that has n sides, we can say that its interior angle sum is given by the following equation:
S = ( n − 2) × 180°.
where;
n is the number of sides of the convex polygon
Thus, for a 22 sided convex polygon;
S = (22 - 2) × 180°
S = 20 × 180°
S = 3600°
That represents the sum of interior angles of the given polygon.
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A manager bought lunch for her coworkers. Each person picked either a salad or a burger. The salads cost $8 each and the burgers cost $4 each. If the manager spent $152 and bought lunch for 28 people, how many of each item did she buy?
Answer:
10, 8
Step-by-step explanation:
Let x be the number of salads and y be the number of burgers.
We know that:
x + y = 28 (the total number of people)
8x + 4y = 152 (the total cost in dollars)
We can use the first equation to solve for one variable in terms of the other.
x = 28 - y
Now we can substitute this expression into the second equation:
8(28 - y) + 4y = 152
224 - 8y + 4y = 152
224 = 12y
y = 18 (burgers)
We can then use this value to find the number of salads
x = 28 - y = 28 - 18 = 10 (salads)
So the manager bought 10 salads and 18 burgers
several students wonder which is a better buy a 40 pack of pencil top erasers for $2.82 or a 2 pack of pencil top erasers for $0.12. they use different methods to arrive at an answer
If several students wonder which is a better buy a 40 pack of pencil top The option that is the best is option 2 because it is cheaper.
How to find the option that is the best?Option 1
40 pack of pencil top erasers = 2.82/ 40
40 pack of pencil top erasers = 0.07
40 pack of pencil top erasers = 7 cent cost of each pack
Option 2 :
2 pack of pencil top erasers =0.12/ 2
2 pack of pencil top erasers = 0.06
2 pack of pencil top erasers = 6ent a pack
Based on the above calculation the second option is better than the first option based on the fact that you tend to get pencils cheaper per pack.
Therefore option 2 is better.
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- A person has a beginning balance of $660. She pays $90 on the ninth day, and she
charges $320 on the 28th day. What amount of interest is due on her account if it has an
APR of 26 percent?
The total amount of interest due on the account is $8.36.
What is the simple interest?
Simple interest is a method of calculating the interest on a loan or deposit. It is calculated as the principal amount multiplied by the interest rate, multiplied by the number of time periods (usually in years).
To calculate the interest due on the account, we first need to determine the number of days for which the interest will accrue. Since the payment was made on the 9th day and the charge was made on the 28th day, the interest will accrue for 28 - 9 = 19 days.
We then use the formula for simple interest: Interest = Principal x Rate x Time
In this case, the Principal is the beginning balance of $660, the Rate is the APR of 26% (which must be converted to a decimal by dividing by 100), and the Time is the number of days for which the interest will accrue (19 days).
So the Interest = $660 x 0.26 x (19/365) = $8.36
Therefore, the total amount of interest due on the account is $8.36.
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Rewrite as equivalent rational expressions with denominator (5a+2)(a−4)(a+2). 2/5a^2-18a-8, 8a/5a^2+12a+4
Answer: To rewrite the given expressions as equivalent rational expressions with the denominator (5a+2)(a−4)(a+2), we need to factor the denominators of the given expressions and cancel out any common factors between the numerator and denominator.
2/5a^2-18a-8
We can factor the denominator: 5a^2-18a-8 = (5a+8)(a-1)
Now we can cancel out the common factor of (a-1) from the numerator and denominator
2/(5a+8)
8a/5a^2+12a+4
We can factor the denominator: 5a^2+12a+4 = (5a+4)(a+1)
Now we can cancel out the common factor of (a+1) from the numerator and denominator
8a/(5a+4)
Now we can multiply the numerators and denominators of both expressions with (5a+2)(a−4)(a+2)
(2*(5a+2)(a−4)(a+2)) / (5a+8)(a-1)(5a+2)(a−4)(a+2) = 2(a−4)(a+2) / (5a+8)(a-1)
(8a*(5a+2)(a−4)(a+2)) / (5a^2+12a+4)(5a+2)(a−4)(a+2) = 8a(5a+2) / (5
Step-by-step explanation:
You owe $278.94
on your credit card. Because you have not paid your bill on time, you have to add a past due charge of $23 , an over-limit fee of $ 30 , and a service charge of 8% of the amount owed on the credit card (without the past due charge and over limit fees). If you wish to send a check for the total amount immediately, how much should you write the check for?
Answer:
chnbntyehjejejdbhdhehgeuru382863yrh
Use the zoom controls to magnify the Moon until it fills the entire Sky Chart. Read the field of view display on the bottom left corner of the Status Bar. Roughly, what is the angular diameter of the Moon?
59 arc minutes (59')
30 arc minutes (30')
30 arc seconds (30")
15 arc minutes (15')
We frequently have no idea of their distance from us when we observe things in the night sky. For instance, although having the appearance of being inside a sphere with a very big radius that surrounds the Earth, the stars are actually all located at vastly different distances from our Solar System.
The angle that an object makes (subtends) as observed by an observer is its angular diameter. This is illustrated in the image below, where an observer at A (who is closer to the object) perceives the object's angular diameter as being larger than an observer at B. The terms "angular diameter" and "distance between two objects, measured on the celestial sphere" are interchangeable.
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