The required expression is 30 - 10√5 which is in the form a + b√5, where a = 30 and b = -10.
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
The expression is given in the question, as follows:
(5-√5)²
Expanding the above expression,
(5)² + (√5)² - 2 × 5 × √5
25 + 5 - 10√5
30 - 10√5
Compare the above expression to the form a + b√5, and we get
a = 30 and b = -10
Thus, the required expression is 30 - 10√5.
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Sierra is trying to decide whether her to rent an apartment for $1,200 per month or take out a mortgage for $1, 395 per month. After how many months will the difference in total cost be $48, 750 if the rent does not go up in price?
-150 months
-200 months
-300 months
-250 months
Step-by-step explanation:
the difference is
1395 - 1200 = $195
how many months until that sums up to $48 750 ?
by checking how often $195 fit into $48,750 :
48750 / 195 = 250
so, it will take 250 months to reach that level.
What are the Applications of Differentiation of Trigonometric Functions?
Differentiation of trigonometric functions has wide-ranging applications in many fields, including physics, engineering, finance, and signal processing. It is used to calculate rates of change, solve optimization problems, model signals, analyze experimental errors, and more.
The applications of differentiation of trigonometric functions are wide-ranging and can be found in many fields, including science, engineering, and finance. Some specific applications of differentiation of trigonometric functions include:
1. Calculating rates of change: In physics, the rates of change of trigonometric functions (such as the velocity and acceleration of a moving object) can be calculated using differentiation.
2. Optimization problems: In engineering and other fields, optimization problems involving trigonometric functions (such as finding the maximum or minimum value of a function) can be solved using differentiation.
3. Signal processing: In electrical engineering and telecommunications, trigonometric functions are used to model signals and their derivatives are used to calculate signal properties such as frequency and amplitude.
4. Financial mathematics: In finance, trigonometric functions can be used to model interest rates and other financial phenomena, and differentiation can be used to calculate financial derivatives such as options.
5. Error analysis: In scientific research, differentiation can be used to analyze experimental errors and estimate uncertainties in measurements.
These are just a few examples of the many applications of differentiation of trigonometric functions. The use of trigonometric functions and their derivatives is widespread and plays a critical role in many fields of study.
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Shelby needs the total
weight of her suitcase to be
under 50 lbs. Currently,
Shelby's suitcase weighs
42.5 lbs. How many more
pounds can Shelby pack in
her suitcase and still stay
within her limit?
Help please I’m stuck on a question and I’d greatly appreciate it
Answer: I think that the unknown measure is 22.
Step-by-step explanation: The bottom and height combined is the value of the longer line.
If you flip a coin 2 times, what is the best prediction possible for the number of times it will land on tails?
The probability that it would have to land on tails is 1
How to solve for the probabilityThe coin is known to have two sides.
The two sides of a coin are the head and the tail
the probability of head is given as 50 percent
The probability of tail is also given as 50 percent
Given that the coin is going to be flipped two times, the probability that it would have to land on tail is given as
2 * 50 percent
= 2 * 0.5
= 1
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What is the value of 20 milliliters in tablespoons?
The volume unit milliliter (mL) can be converted to tablespoon (tbsp). One tablespoon is equal to 15 milliliters, so 20 milliliters is equal to 1.333 tablespoons
. This conversion can be done by dividing 20 milliliters by 15 milliliters to get the exact number of tablespoons. The formula for this conversion is:Tablespoons = Milliliters ÷ 15 .The calculation for 20 milliliters is as follows: Tablespoons = 20 mL ÷ 15 .Tablespoons = 1.333 tbsp.Therefore, 20 milliliters is equal to 1.333 tablespoons. To convert other volumes of milliliters to tablespoons, you can use the same formula and calculation. For example, if you want to convert 30 milliliters to tablespoons, you would use the formula: Tablespoons = Milliliters ÷ 15 Then calculate: Tablespoons = 30 mL ÷ 15 Tablespoons = 2 tbsp,In conclusion, the conversion of milliliters to tablespoons can be done using the formula: Tablespoons = Milliliters ÷ 15. When using this formula, the number of tablespoons is calculated by dividing the volume of milliliters by 15. For example, 20 milliliters is equal to 1.333 tablespoons and 30 milliliters is equal to 2 tablespoons.
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if a recipe calls for 4 cups of milk, how many fluid ounces are used?
The required number of fluid ounces used are calculated to be 32 fluid ounces.
A fluid ounce has a liquid capacity of 1/16 of a US liquid pint or 1/128 of a US gallon in the US system and 1/20 of a pint or 1/160 of an Imperial gallon in the imperial system.
In each cup, there are known to be 8 fluid ounces.
A recipe is said to be made up of 4 cups of milk.
The total number of fluid ounces used are to be calculated.
1 cup → 8 fluid ounces
4 cups → 4 × 8 = 32 fluid ounces
Thus, the required number of fluid ounces used are calculated to be 32 fluid ounces.
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if a data set is skewed to the left, how will the mean and median compare?
If a data set is skewed to the left, meaning that it has a long tail to the left (lower values), then the mean will be lower than the median. The median is less sensitive to outliers than mean.
In a data set that is skewed to the left, the mean will be less than the median. The term "skewed to the left" or "negative skewed" refers to the fact that the distribution of the data has a longer tail on the left side (towards smaller values) than on the right side.
When a data set is skewed to the left, it means that there are more lower values than higher values. As a result, the median (which is the middle value) will be larger than the mean (which is the average of all the values). The mean will be pulled down towards the lower values, making it smaller than the median.
For example, consider the following data set: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The mean of this data set is 5.5, while the median is 5.5. However, if we add several low values to the data set, it will become skewed to the left: 1, 1, 2, 3, 3, 4, 5, 6, 7, 8, 9, 10.
The mean of this data set is now 4.5, while the median is still 5.5. The mean has moved towards the lower values, making it smaller than the median.
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A skilled mason is tiling the floor of 10 m long and 5 m wide room by square tiles of side 0. 5 m at the rate of ₹ 6 per tile
200 tiles are required to cover the floor. The cost of tiling at the rate of $7 per tile is ₹ 1200.
A competent mason is installing square tiles with a side of 0. 5 m on the floor of a room that is 10 m long and 5 m broad at a cost of ₹ 6 for each tile.
The entire floor space that has to be tiled is:
Area
= length x width
= 10m x 5m
= 50 square meters
An area of each square tile is:
Area of a square tile
= side x side
= 0.5m x 0.5m
= 0.25 square meters
In order to tile the floor, the following total number of tiles is needed:
Total number of tiles
= Area / Area of a square tile
= 50 / 0.25 = 200
The total cost of tiling the floor at the rate of ₹ 6 per tile is:
Total cost
= Total number of tiles x Cost per tile
= 200 x ₹ 6
= ₹ 1200
So, to tile the floor of the 10m long by 5m broad room with square tiles with a 0.5m side, the professional mason will demand ₹ 1200.
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Question- A floor of the room 10 m long and 5 m wide is to be covered by square tiles. If each square tile is 0.5 m, find the number of tiles required to cover the floor. Also, find the cost of tiling at the rate of ₹ 6 per tile.
Han bought a scooter for $3,200. In 5 years, the value of the scooter will depreciate by 65%. What will the value of the scooter be after 5 years?
The required value of the scooter after 5 years will be $1,120.
What is Percentage?Percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". For example, if there are 20 students in a class and 5 of them are boys, the percentage of boys in the class can be calculated as follows:
Percentage of boys = (Number of boys / Total number of students) x 100%
According to question:After 5 years, the scooter will depreciate by 65%, which means its value will be reduced to 35% of its original value.
35% of $3,200 = 0.35 x $3,200 = $1,120
Therefore, the value of the scooter after 5 years will be $1,120.
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what is the area of 4 walls of square room??
A square room contains 256 cubic meter of air. IF THE cost of painting it's 4 walls at rs 50 per Sq. meter is Rs 6400,find the cost of carpeting its floor at Rs 99 per Sq. Meter.
The roots of the polynomial are the height, length, and width of a rectangular box (right rectangular prism). A new rectangular box is formed by lengthening each edge of the original box by 2 units. The volume of the new box is ________.
The volume of the new box is 30 units³.
We can infer the roots are rational integers from the response options, thus this polynomial ought to be simple to factor. The coefficients of x must multiply by 10, hence they must be in some sequence of 5, 2, 1 or 10, 1. Since we can try each one separately, we can express the factored form as follows:
(5x-p)(2x-q)(x-r)
Due to the fact that p, q, and r must multiply to 6, they must be either 3, 2, 1 or 6, 1, 1 in some sequence. Once more, we may test each one in a different place to determine if they multiply properly.
When we multiply the x-terms and attempt (5x - 2)(2x - 1)(x - 3), the answer is 29. Try adding the x² terms together, they equal -39. Consequently, the roots are 2/5, 1/2 and 3 Now if you add 2 to each root, you get the volume is
= 12/5 × 5/2 × 5 = 30 units³
Therefore, The volume of the new box is 30 units³.
The question is incomplete. The complete question is:
"the roots of the polynomial 10x³ - 39x² + 29x - 6 are the height, length, and width of a rectangular box (right rectangular prism). a new rectangular box is formed by lengthening each edge of the original box by 2 units. what is the volume of the new box?"
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write your answer to the nearest 1/4 inch
Answer:
Step-by-step explanation:1/3
The measurement of the line segment to the nearest 1 / 4 inch is C. 5 ³ / ₄ inches.
How to measure the line segment ?To measure the line segment, you should look at the length of the line segment, while taking into account the measurements between the integrals.
There are 3 sections between each integral, with the suceeding integral being the 4 the section. Seeing as there are 4 sections therefore, it means that each section accounts for :
= 1 / 4 inches
The last integral is 5 inches and then there are 3 section after that. The measurement of the line segment then is:
= 5 + ( 3 x 1 / 4 )
= 5 + 3 / 4
= 5 ³ / ₄ inches
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The question is:
Measure the line segment
What are rations equivalent to 5:3 ( can not be 10:6)
Answer: 20:12
Step-by-step explanation:
Answer:
15:9
Step-by-step explanation:
multiply both by 3,4,5,6,7,8,9,etc.
hey, good morning i have a question!
2x^+4=8^x
Answer:
the solution to the equation 2x^+4=8^x is x = 1.
Step-by-step explanation:
To solve the equation 2x^+4=8^x, we can start by simplifying both sides of the equation.
First, we can rewrite 8^x as (2^3)^x, using the property that 8 is equal to 2 raised to the power of 3.
So, the equation becomes:
2x^+4 = (2^3)^x
2x^+4 = 2^(3x)
Next, we can rewrite 2x^+4 as 2^2 * 2^x, using the property that a^b * a^c = a^(b+c).
So, the equation becomes:
2^2 * 2^x = 2^(3x)
2^(x+2) = 2^(3x)
Now, we can equate the exponents on both sides of the equation:
x + 2 = 3x
2x = 2
x = 1
Therefore, the solution to the equation 2x^+4=8^x is x = 1.
Answer:
Below
Step-by-step explanation:
2 x^4 = 8^x <====not sure syntax is correct(?)
Solving GRAPHICALLY shows x = - .61181
2.51
4
124°
Find the area
of the given Trapezium
Answer:
A = ( a + b ) 2 × h .
Step-by-step explanation:
A=*124+b)2×h
7.
A
В
70°
E
85
959х950
15
85
?
C
Solve for the indicated angle or arc
Answer:
BC = 100°
Step-by-step explanation:
You want the measure of arc BC formed by two chords that intersect at 85° and intercept an opposite arc of 70°.
Angle at crossing chordsThe angle formed by crossing chords is the average of the angles they intercept. Here, that means ...
85° = (? +70°)/2 . . . . the crossing angle is 85°
170° = ? +70° . . . . . . multiply by 2
100° = ? . . . . . . . . . subtract 70°
The intercepted arc BC is 100°.
if the circumference of a circle is 516 cm, find the area
Answer: 266256π
Step-by-step explanation:
♡ Hope this helps ♡
Ali purshacsed a coat that costs 38$ sales tax was 4.5% of the purchase price how much did Ali pay in sales tax
The amount ali paid in tax is $1.71.
How to measure the rate of change of something as some other value changes?
Suppose that we have to measure the rate of change of y as x changes, then we have:
[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
where we have
[tex]\rm when \: x=x_1, y = y_1\\when\: x = x_2, y= y_2[/tex]
Remember that, we divide by the change in independent variable so that we get some idea of how much the dependent quantity changes as we change the independent quantity by 1 unit.
(5 change per 3 unit can be rewritten as 5/3 change per 1 unit)
We are given that;
Cost of coat=$38
Rate= 4.5%
Now,
To find out how much Ali paid in sales tax, we need to multiply the purchase price by the sales tax rate:
Sales tax amount = Purchase price x Sales tax rate
Sales tax rate = 4.5% = 0.045 (in decimal form)
Purchase price = $38
Sales tax amount = $38 x 0.045 = $1.71
Therefore, by the given rate Ali paid $1.71 in sales tax.
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What are the properties of Laplace transform table?
The Laplace transform table contains properties and formulas for common transforms, as well as the inverse Laplace transform and the shift theorem. It also includes properties such as linearity, scaling, and time shifting.
The Laplace transform table is an important tool for solving linear differential equations. It contains information about common transformations and their associated formulas, as well as the inverse Laplace transform and the shift theorem. The table also includes properties such as linearity, scaling, and time shifting. Linearity states that if a function f(t) is a linear combination of two functions f1(t) and f2(t), then its Laplace transform F(s) is the sum of the Laplace transforms of f1(t) and f2(t). Scaling states that if a function f(t) is multiplied by constant k, then its Laplace transform F(s) is divided by k. Time shifting states that if a function f(t) is shifted by x units in time, then its Laplace transform F(s) is multiplied by [tex]e^(-sx)[/tex]. These properties can be used to simplify Laplace transforms and to solve linear differential equations. The Laplace transform table is a useful tool for engineers and physicists who use linear differential equations in their work.
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Nathan and his best friend found money under the couch they split the money seven evenly each getting $6.86 how much money did they find write an expression
(I ignored the seven, I'm sorry if I'm wrong.)
6.86x2
6.86x2=13.72
13.72$
PLEASE HELP ASAP‼️‼️‼️Are the sides proportional?
Set up each ratio of sides and determine if they are equal
ratios. Show all of your work.
3.61 cm
R
44°
S
11.97 cm
9.71 cm
IS
N
T
17.955 cm
14.565 cm
121°
44°
M
L
5.415 cm
The side lengths form a proportional relationship, and the ratios are;
17.955/11.97 = 14.565/9.71 = 5.415/3.61.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
First is Congruent angle measures, then Proportional side lengths.
Here, the triangles are similar, because they have the same angle measures.
17.955/11.97 = 14.565/9.71
= 5.415/3.61.
Thus, the side lengths form a proportional relationship, have a ratio of 1.5.
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87% of what number is 106
factor completey x^2+7x-18
Answer:
[tex]\huge\boxed{\sf (x - 9)(x + 2)}[/tex]
Step-by-step explanation:
Given expression:x² + 7x - 18
Using mid-term break formula.
Multiply the side terms. [-18 × x² = -18x²]Now, split the mid-term in such two factor, such that multiplying both gives the side terms.We can split -7x (mid term) into -9x + 2x since -9x × 2x = -18x²So,
= x² - 9x + 2x - 18
Now, take x from (x² - 9x) and 2 from (2x - 18) common
= x(x - 9) + 2(x - 9)
Take (x - 9) common
= (x - 9)(x + 2)[tex]\rule[225]{225}{2}[/tex]
help please i don’t understand this
Answer:
1. dotted
2. solid
3. dotted
Step-by-step explanation:
dotted-- "greater than" or "less than"
solid-- "greater than" or equal " or "less than or equal"
p.s.---- i think of it as if the line is under the symbol then the line is solid, if there is no lie under the symbol then it is dotted
please mark brainliest
Match the numbers with the correct label.
The value of a is 0.14, b is 0.2 and c is 0.33.
What is Number Line?The horizontal straight lines in mathematics known as number lines are where integers are arranged in equal intervals. A number line can be used to represent every number in a sequence. The endpoints of this line go on forever.
Given:
The number a and b lies between 0/4 and 1/4. (0 and 0.25).
We have the numbers is 0.2, 0.333 (3/9) and 0.14 (1/7).
So, the value of a can be 0.14
and, value of b is 0.2.
and, the value of c is 0.33.
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2.In a pond, the area that is covered by algae doubles each week. When the algae was
first spotted, the area it covered was about 12.5 square meters.
a. Find the area, in square meters, covered by algae 10 days after it was spotted.
Starting amount
Show your reasoning.
b. Explain why we can find the area covered by algae 1 day after it was spotted by
multiplying 12.5 by V2.
Answer:
Step-by-step explanation:
a) The area covered by algae 10 days after it was first spotted is approximately 32.64 square meters.
b) We can find the area covered by algae one day after it was first spotted by multiplying [tex]12.5^{1/7}[/tex] by 2.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
a.
To find the area covered by algae 10 days after it was first spotted, we need to convert 10 days into weeks, since the growth rate is given in terms of weekly doubling.
There are 7 days in a week,
So 10 days are approximately 1.43 weeks (10/7).
Let A be the area covered by algae in square meters after n weeks.
Then we can use the formula for exponential growth:
A = 12.5 x [tex]2^n[/tex]
Substituting n = 1.43, we get:
A = 12.5 x [tex]26^{1.43}[/tex]
A ≈ 32.64
Therefore,
The area covered by algae 10 days after it was first spotted is approximately 32.64 square meters.
b.
We know that the area covered by algae doubles each week.
One week is equivalent to 7 days, so after one week, the area covered by algae will be twice the initial area of 12.5 square meters, or 25 square meters.
We can represent this mathematically as:
A = 12.5 x [tex]2^1[/tex]
Now, let's consider what happens after two weeks, or 14 days.
The area covered by algae will double again, so it will be four times the initial area of 12.5 square meters or 50 square meters.
We can represent this mathematically as:
A = 12.5 x 2²
Using the same reasoning, we can find that after three weeks (21 days), the area covered by algae will be eight times the initial area or 100 square meters:
A = 12.5 * 2³
In general, we can see that after n weeks, the area covered by algae will be 2^n times the initial area of 12.5 square meters. This can be written as:
A = 12.5 x [tex]2^n[/tex]
If we want to find the area covered by algae after one day, we can use the fact that one day is equivalent to 1/7 of a week.
So, after one day, the area covered by algae will be:
A = 12.5 x [tex]2^{1/7}[/tex]
Simplifying this expression using the laws of exponents, we get:
A = [tex]12.5^{1/7}\times2[/tex]
Therefore,
We can find the area covered by algae one day after it was first spotted by multiplying [tex]12.5^{1/7}[/tex] by 2.
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1. Write these percentages as common fractions in simplest form: a)75%
You only showed one btw.
75%=3/4
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
What is a percentage?A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.
If we know that percentages are fractions of 100, we know that 75% is equivalent to [tex]\frac{75}{100}[/tex].
Simplifying [tex]\frac{75}{100}[/tex]:
[tex]\frac{75}{100}[/tex] = [tex]\frac{3}{4}[/tex]Therefore, 75% as a simplified fraction is [tex]\frac{3}{4}[/tex].
HELP ASAP PLEASE!!!!!
Answer:
Step-by-step explanation:
2a) [tex]y=2(1.2^{x})[/tex] where x is the amount of lies he told
2b) His nose will be approximately 76.68 inches long after telling 20 lies
2c) No, No.
:]
Answer:
2a) where x is the amount of lies he told
2b) His nose will be approximately 76.68 inches long after telling 20 lies
2c) No, No.
Step-by-step explanation:
Yesterday the temperature was 15 degrees celsius. Today the temperature is 0 degrees Celsius. What is the change in temperature from yesterday to today
The change in temperature from yesterday to today is -15 degrees Celsius.
What is subtraction?Subtraction is a mathematical operation that involves finding the difference between two numbers. In other words, it's the process of removing one number from another number. For example, if you have two numbers, 5 and 3, and you want to find their difference, you would subtract the smaller number (3) from the larger number (5), resulting in the answer of 2. The symbol for subtraction is a minus sign (-). So, the subtraction of 3 from 5 can be written as 5 - 3 = 2.
Here,
The calculation is as follows:
Change in temperature = Today's temperature - Yesterday's temperature
Change in temperature = 0 degrees Celsius - 15 degrees Celsius
Change in temperature = -15 degrees Celsius
The temperature has dropped by -15 degrees Celsius from yesterday to today.
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