Answer:
1.6285
Step-by-step explanation:
28 = 4/5x-8
Cross multiply
140x-224=4
140x =224+4
140x = 228
x = 228/140
x = 1.6285
The population of a city in 2010 is 50,000, and it grows by 5% each year after.
a. Write a function of f which models the population of the city' years after 2010.
b. What is the population of the city in 2017?
c. What will the population of the city be in 2020? What about in 2030?
d. By what factor does the population grow between 2010 and 2020? What about between 2020 and 2030?
a. A function that models the population of the city's years after 2010 is:
f(x) = 50,000 * (1 + 0.05)^(x-2010)
where x is the number of years after 2010.
b. The population of the city in 2017 (7 years after 2010) is:
f(2017) = 50,000 * (1 + 0.05)^7
= 65,128
c. The population of the city in 2020 (10 years after 2010) is:
f(2020) = 50,000 * (1 + 0.05)^10
= 76,923.1
The population of the city in 2030 (20 years after 2010) is:
f(2030) = 50,000 * (1 + 0.05)^20
= 129,382
d. The population in 2020 is 76,923.1, and the population in 2010 is 50,000, so the population grows by:
= 76,923.1 / 50,000
= 1.53846
The population in 2030 is 129,382, and the population in 2020 is 76,923.1, so the population grows by:
= 129,382 / 76,923.1
= 1.6859
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Whats 3x+1? for in high school its really hard to solve none of my friend cant do it
As per the zeros of the function, the value of the function 3x + 1 is x = -1/3.
Zeros of the function in math is defined as the values of the variable of the function such that the function equals 0.
Here we have given the function 3x + 1.
Now, we have to equate the function with zero, in order to solve it, then we get,
=> 3x + 1 = 0
Now, we have to subtract 1 on both sider to individualize the x value then we get the rewritten expression as,
=> 3x = -1
Now, we have to divide each side by 3, then we get the value of x as,
=> x = -1/3
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Keith ordered a hamburger for $2.25, a medium raspberry ice tea for $1.25, and a small sundae for $0.99. He also ordered French fries. All of these items totaled $6.24. What was the cost of the French fries?
The fries costs $1.49
What is addition?Addition in math is a process of combining two or more numbers.
Given that, Keith ordered a hamburger for $2.25, a medium raspberry ice tea for $1.25, and a small sundae for $1.25. He also ordered French fries. All of these items totalled $6.24.
Let the price of fries be x,
Therefore,
$2.25 + $1.25 + $1.25 + x = $6.24
$4.75 + x = $6.24
x = $6.24 - $4.75
x = $1.49
Hence, the fries costs $1.49
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Determine whether the geometric series is convergent or divergent. 10 – 8 + 6.4 – 5.12 +... A. convergent B. divergent If it is convergent, find its sum. (If the quantity diverges, leave this blank.) _____
The given series is convergent and the sum S∞ is 5.555
Think about 10 - 8 - 6.4 - 5.12
If the common ratio of the series is between -1 and 1, then a geometric progression will be convergent.
the average ratio,
r = -8/10
⇒ r = -0.8
This equals 1 - 0.8 - 1.
The presented series is hence convergent.
Sum of series = S∞ = a/(1 - r)
Here, first term(a) = 10,
common ratio(r) = -0.8,
S∞ = a/(1 - r)
⇒ S∞ = 10/(1 - (-0.8))
⇒ S∞ = 10/(1 + 0.8)
⇒ S∞ = 10/1.8
⇒ S∞ = 5.555
Therefore, the given series is convergent and the sum S∞ is 5.555
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Are 3 4 5 triangles always right?
No, three 4 5 triangles are not always right triangles.
A right triangle is a triangle in which one of the angles is a right angle (90°). Therefore, in order to be a right triangle, the following criteria must be met: a^2 + b^2 = c^2, where c is the longest side and a, b are the other two sides. In a 3 4 5 triangle, the longest side is 5, so a^2 + b^2 = c^2 becomes 3^2 + 4^2 = 5^2. Using simple algebra, this equation becomes 9 + 16 = 25, which is true. Therefore, a 3 4 5 triangle is a right triangle. However, if one of the sides is different, for example a 3 4 6 triangle, the equation becomes 9 + 16 = 36, which is not true. Therefore, a 3 4 6 triangle is not a right triangle. To summarize,3 4 5 triangles are right triangles, but three 4 6 triangles are not.
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gcf of 15 and 18 and -45
Answer: 3
Step-by-step explanation:
Factor of 15: ±1, ±3, ±5, ±15
Factor of 18: ±1, ±2, ±3, ±6, ±9, ±18
Factor of -45: ±1, ±3, ±5, ±9, ±45
=> GCF of 15, 18, -45 is 3
23x² + 6x + 7 please help
Answer:
the expression can be factored into (x+4)(23x + 7) and it is a product of two binomials.
Step-by-step explanation:
The expression 23x² + 6x + 7 is in the form of a quadratic equation. A quadratic equation is an equation in the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. In this case, the coefficients of the x², x, and the constant term are a = 23, b = 6, c = 7.
One way to factor a quadratic equation is by using the factoring by grouping method, where we group the terms in pairs and factor out the greatest common factor (GCF) from each group.
Here is one way to factor this equation:
23x² + 6x + 7 = (23x² + 6x) + 7
= (23x² + 6x) + 7
= (23x² + 6x + 6x) + 7
= (23x² + 12x) + 7
= (23x(x) + 3x(4)) + 7
= (23x(x+4) + 7)
= (x+4)(23x + 7)
So the expression can be factored into (x+4)(23x + 7) and it is a product of two binomials.
It's important to note that the above expression factors into a product of two binomials and not two factors of 23x² + 6x + 7
You can also use Quadratic formula to solve the above expression if this method seems confusing.
graphing piece wise functions
Answer:
thats by step overr.ic. yttt. .
David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour,
but realizes that he will be 1 hour late if he continues at this speed. He increases his speed by 15
miles per hour for the rest of the way to the airport and arrives 30 minutes early. How many miles
is the airport from his home?
(A) 140 (B) 175 (C) 210 (D) 245 (E) 280
If David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour, but realizes that he will be 1 hour late if he continues at this speed. The number of miles that is the airport from his home is 210.
How to find the distance?Let d represent the distance that is needed to travel 1 hour
1 hour late decreased to 0.5 hours early = 1.5
Hence,
d/50 + 1.5 = d/35
Simplify
7d + 525 =10d
Collect like terms
525 = 10d - 7d
525 = 3d
Divide both side by 3d
d = 525/3
d = 175
Total number of miles :
Total number of miles = 175 + 35
Total number of miles = 210
Therefore we can conclude that the correct option is C.
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The model below represents 2 x + 1 = negative x + 4. 2 green long tiles and 1 green square tile = 1 long red tile and 4 square green tiles What is the value of x when solving the equation 2 x + 1 = negative x + 4 using the algebra tiles? x = negative 3 x = negative 1 x = 1 x = 3
Answer:
The model you described is a mathematical representation using algebra tiles, and it represents the equation 2x + 1 = -x + 4.
Step-by-step explanation:
To solve this equation for x, we need to isolate x on one side of the equation by using the operations of algebra (such as addition, subtraction, multiplication, and division).
In this case, we can start by adding x to both sides:
2x + 1 + x = -x + 4 + x
This gives us:
3x + 1 = 4
The next step would be to subtract 1 from both sides:
3x = 3
then we divide both sides by 3
x = 1
So x=1 is the solution.
The algebra tiles help to visualize the manipulation of equations, but the actual solving process is algebraic manipulation of the equation.
Graph the line y=-2x-1
Answer:2024
Step-by-step explanation:
Last week, Alex took 90 selfies and Vic took 75 selfies. Today,
they each decided that some of these selfies were not very good
and deleted them. Alex deleted three times as many selfies
as Vic. Now, Alex has half as many selfies as Vic. How many
selfies did Alex delete?
Answer:
Alex deleted 37.5 selfies
Step-by-step explanation:
Let X be the number of selfies that Vic deleted.
Alex deleted 3X selfies.
After deleting selfies, Alex has 90-3X selfies left.
Vic has 75-X selfies left.
Since Alex has half as many selfies as Vic, we can set up the equation: 90-3X = (75-X)/2
Multiplying through the parentheses on the right side, we get: 90-3X = 75-X/2
Combining like terms, we get: 2X = 15
Dividing both sides by 2, we get: X = 7.5
Since X represents the number of selfies that Vic deleted, Vic deleted 7.5 selfies.
Since Alex deleted 3 times as many selfies as Vic, Alex deleted 37.5 = <<37.5=22.5>>22.5 selfies.
The number of selfies deleted by Alex is 51.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that Alex took 90 selfies and Vic took 75 selfies. Today, they each decided that some of these selfies were not very good and deleted them. Alex deleted three times as many selfies as Vic. Now, Alex has half as many selfies as Vic.
Let Vic deleted x selfies and number of selfies deleted by Alex is 3x,
Therefore,
Since, Alex has half as many selfies as Vic, we can set up the equation: 90-3x = (75-x)/2
180 - 6x = 75 - x
5x = 105
x = 17
3x = 51
Hence, the number of selfies deleted by Alex is 51.
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Is math in Grade 6 hard?
Sixth grade math class can be difficult, even for students who have done well in math previously. In sixth grade you begin to learn more advanced topics such as ratios and rates.
You also work more with fractions. Sixth grade is also when you begin building the foundations of algebra, geometry, and statistics.
example
given problem in maths
- x + 8 > 6 ( isolate the term in x by subtracting 8 from both sides )
- x > - 2 ( multiply both sides by - 1 )
Remembering to reverse the inequality symbol when multiplying/dividing by a negative quantity
x < 2 ← reverse symbol
From the given list the only value less than 2 is 1, hence
x = 1 ← is the only possible solution
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Graph the line with slope of 3/4 passing through the point (-1, 2)
Answer:
Step-by-step explanation:
please help: find m∠LHF
Answer:
17
Step-by-step explanation:
5y - 8 = 9y - 28
-8 = 4y - 28
4y = 20
y = 5
9(5) - 28
45 - 28
17
Julia needs to order some new supplies for the restaurant where she works. The restaurant needs at least 316 glasses. There are currently 286 glasses. If each set on sale contains 6 glasses, use the drop-down menu below to write an inequality representing ss, the number of sets of glasses Julia should buy.
The inequality representing s, the number of sets of glasses Julia should buy is 286 + 6s ≥ 316.
How to illustrate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
Since Julia needs to order some new supplies for the restaurant where she works. The restaurant needs at least 316 glasses. There are currently 286 glasses. If each set on sale contains 6 glasses, the number of sets will be:
286 + 6s ≥ 316
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What are the 6 parent functions?
These are the 6 parent functions: Identity, Absolute Value, Square Root, Quadratic, Cubic, Reciprocal.
A parent function is the simplest form that a function can be. Its basic shape is not in any way altered. In mathematics, you see certain graphs over and over again. For that reason, these original, common functions are called parent graphs, and they include graphs of quadratic functions, square roots, absolute values, cubics, and cube roots.
For instance, when you see a u-shaped graph that is inverted and vertically stretched, you should still recognize that it is a parabola which has undergone different transformations.
We can take a few examples to understand this concept further.
For a quadratic equation, the parent graph is [tex]f(x) = x^{2}[/tex], which is a parabola.For a cubic equation, the parent graph is [tex]f(x) = x^{3}[/tex].Now, there are 6 parent functions:
IdentityAbsolute ValueSquare RootQuadraticCubicReciprocalHence, these are the 6 parent functions: Identity, Absolute Value, Square Root, Quadratic, Cubic, Reciprocal.
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A triangular parking lot has sides measuring 90 meters, 54 meters, and 128 meters. Find the area of the parking lot. *
The area of the parking lot is 2,025 .81 meter2.
How do you calculate a triangle's area?In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h. Therefore, we need to know the triangular polygon's base (b) and height (h) in order to calculate its area.
A triangular parking lot has sides measuring 90 meters, 54 meters, and 128 meters.
Triangle Height Determination Using Area
Now that you are aware of the triangle's area, you may use the triangle formula A=1/2bh to get the triangle's height.
s = a + b+ c /2
90 + 54 + 128 / 2 = 136
A = [tex]\sqrt{s (s-a) (s-b) (s-c)}[/tex]
A = [tex]\sqrt{136(136-90)(136-54)(136-128}[/tex])
A = 2,025 .81
The area of the parking lot is 2,025 .81 meter2.
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0.2(x+50)-6=0.4(3x+20)
Answer:
2
Step-by-step explanation:
0.2(x+50)-6=0.4(3x+20) multiply both sides by 10 to clear the decimals
2(x + 50) = 4(3x + 20) distribute across the terms in the parentheses
2x + 100 = 12x + 80 subtract 80, 2x from both sides
20 = 10x divide both sides by 10
x=2
is the relationship between the variables in the table an inverse variation or a direct variation? write an equation to model it.
x= 2 6 7 14
y= 21 7 6 3
The relationship between the variables in the table is an inverse variation The equation to model is y = 42/x.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 8 is an equation.
We have,
x: 2 6 7 14
y: 21 7 6 3
Now,
When x = 2, y = 21
This can be written as,
y = kx
21 = 2k
k = 21/2
The equation is y = (21/2)x _____(1)
or
y = k/x
21 = k/2
k = 42
The equation is y = 42/x _____(2)
Now,
We will check which equation fits the table.
From (1)
y = (21/2)x
When x = 6,
y = (21/2) x 6 = 21 x 3 = 63
From (2),
When x = 6,
y = 42/6 = 7
When x = 7,
y = 42/7 = 6
When x = 14,
y = 42/14 = 3
This equation satisfies the table.
Thus,
The relationship is an inverse variation.
The equation is y = 42/x.
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Roselle has 3 cups of popcorn and 6 oz of soda for a total of 162 calories. Carmel has 1 cup of popcorn and 11 oz of soda for a total of 162 calories. Determine the number of calories per cup of popcorn and per ounce of soda
The number of calories per cup of popcorn is 28 oz and the number of calories per ounce of soda is 14 oz.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Let the number of calories per cup of popcorn be x and the number of calories per ounce of soda be y.
Roselle has 3 cups of popcorn and 6 oz of soda for a total of 162 calories.
3x+6y=162 ------(I)
Carmel has 1 cup of popcorn and 11 oz of soda for a total of 162 calories.
x+11y=182
x=182-11y------(II)
Substitute equation (II) in equation (I), we have
3(182-11y)+6y=162
546-33y+6y=162
546-162-27y=0
384-27y=0
384=27y
y=384/27
y=14
Substitute y=14 in equation (II), we get
x=182-11(14)
x=28
Therefore, the number of calories per cup of popcorn is 28 oz and the number of calories per ounce of soda is 14 oz.
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"Your question is incomplete, probably the complete question/missing part is:"
Roselle has 3 cups of popcorn and 6 oz of soda for a total of 162 calories. Carmel has 1 cup of popcorn and 11 oz of soda for a total of 182 calories. Determine the number of calories per cup of popcorn and per ounce of soda
Mr.Coy receives a 80 bill for his meal. He leaves 14.30 as a tip. What percent did he leave
Answer:
around 18%
Step-by-step explanation:
14.30/80=0.17875
0.17875*100=17.875
18%
Answer:
Step-by-step explanation:
the answer is [tex]\frac{14.30}{80}[/tex]=17.875%
NEED HELP ASAP - Algebra 2
Every complex number has the form a+bi with a and b as real numbers. Is it possible to create a complex number in which b=0? If so, create two examples to show your hypothesis is true. If not, explain why it is not possible.
Your response must be at least 50 words.
No, It is not possible to have a complex number in the form of a + bi when b = 0.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Complex number.
It is in the form of a + ib.
Where a and b are real numbers.
Now,
If b = 0 then we can not have a complex number.
Example:
a + bi
a = 1 and b = 0
1 + 0i = 1 which is not a complex number.
In order to have a complex number a can be any real number and 0 but b can not be a zero.
Thus,
It is not possible to have a complex number in the form of a + bi when
b = 0.
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A convenience store sell pre-paid mobile phones. It purchases them for $12 each and uses a mark up rate of 250%.
a. The markup rate is the constant of proportionality in the equation y= kx. Write an equation that can be used to find the amount of markup on the cost x of a phone
b. Use the equation to calculate the markup amount. What is the retail price of a phone?
c. Next week the store is going to reduce the price to $31. 50. Calculate what percent the sale price is of the retail price.
d. Based on your answer to part C, what is an equation in the form y = kx that relates the sale price to the retail price x?
Answer:
a. y = 2.5x
b. markup: $30; retail price: $42
c. 75%
d. y = 0.75x
Step-by-step explanation:
You want equations relating markup, retail price, and sale price on a phone that costs $12, is marked up 250%, then put on sale for $31.50.
a. Markup equationThe problem statement tells you the markup is 250% of the cost. You could write the equation as ...
y = (250%)x
Or you can simplify it to a decimal number:
y = 2.5x
b. Markup amountThe markup amount is ...
y = 2.5(12) = 30
The markup amount is $30.
That is added to the cost to get the retail price:
retail = $12 +30 = $42
The retail price of the phone is $42.
c. Sale priceThe sale price as a percent of the retail price is ...
percent = (sale price)/(retail price) × 100%
percent = 31.50/42 × 100% = 75%
The sale price is 75% of the retail price.
d. Sale price equationAs in part (a), we could write this as ...
y = (75%)x
or, in decimal, as ...
y = 0.75x
<95141404393>
I GIVE THANKS AND MARK BRAINLIEST
WHAT ARE THE CORRECT ANSWER(S)?
On solving the provided question, we can say that - the slope of the following will be slope, m = [tex]4-6/4-2 = -2/2 = -1[/tex]
what is slope?A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).
here,
(x1,x2) = (6,4)
(y1,y2) = (2,4)
slope, m = 4-6/4-2 = -2/2 = -1
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On solving the provided question, we can say that - the slope of the following will be slope, m = -1
what is slope?
A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).
here,
(x1,x2) = (6,4)
(y1,y2) = (2,4)
slope, m = 4-6/4-2 = -2/2 = -1
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A rectangle measures 1 3/4
inches by 3 3/4
inches. What is its area?
please help!
Answer:
6 and 9/16
Step-by-step explanation:
The area of a rectangle can be calculated by multiplying the width and length. So 1 3/4*3 3/4=7/4*15/4=105/16 or 6 and 9/16
The line of best fit for a data set is y=1. 1x+3. 4. Find the residual for each of the coordinate pairs, (x,y).
D. (1. 5,5. 05)
The residual values are -0.1, 3.8, 0.32, and 0 respectively for the given coordinate pairs.
A residual is a difference between the observed value (y) and the predicted value (y-hat) for a given x value. To find the residual for each coordinate pair (x,y), we need to substitute the x value into the equation for the line of best fit and calculate the difference between that value and the observed y value.
The equation for the line of best fit is y = 1.1x + 3.4
The residual for each coordinate pair (x,y) is given by -
Residual = Yactual - y
A. (5, 8.8) ; Yactual = 8.8
Residual = 8.8 - (1.1(5) + 3.4) = - 0.1
B. (2.5, 9.95) Yactual = 9.95
Residual = 9.95 - (1.1(2.5) + 3.4) = 3.8
C. (0, 3.72) Yactual = 3.72
Residual = 3.72 - (1.1(0) + 3.4) = 0.32
D. (1.5,5.05) Yactual =
Residual = 5.05 - (1.1(1.5) + 3.4) = 0
It's worth noting that residuals are used to measure how well the line of best fit represents the data set. The residuals should be as close to zero as possible, indicating that the line of best fit is a good representation of the data set.
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The complete question is -
The line of best fit for a data set is y=1.1x+3.4. Find the residual for each of the coordinate pairs, (x,y).
A. (5, 8.8)
B. (2.5, 9.95)
C. (0, 3.72)
D. (1.5,5.05)
3. Mr. Langley is painting the exterior of his house. He uses 7 1/2 gallons of paint for the surface
and 2/3 of a gallon of paint for the trim. He had estimated that he would use 11 gallons of paint. How
many gallons of paint was he away from his estimation?
The amount he estimated (11 gallons). 11 - 8.16 = 0.21 gallons.
What is estimation?Estimation is the process of making an educated guess about the value of something, such as a quantity, cost, or other measurement, based on the available information. It's used in many fields, including mathematics, engineering, economics, business, and project management. Estimation is an important skill which can help people make decisions and solve problems quickly.
Mr. Langley was away from his estimation by 0.21 gallons of paint. This is calculated by subtracting the total amount of paint he actually used (7.5 + 0.66 = 8.16 gallons) from the amount he estimated (11 gallons). 11 - 8.16 = 0.21 gallons.
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how many solutions does y = 5x - 8 and y = 9x - 8 have
The equation y = 5x - 8 and y = 9x - 8 have one solution at
(0, -8)
How to find the solution of the equationThe equation is solved simultaneously by elimination method as follows
y = 5x - 8
y = 9x - 8
subtraction the equations
0 = -4x - 0
-4x = 0
x = 0
substituting x = 0 into y = 5x - 8
y = 5x - 8
y = 5 * 0 - 8
y =0 - 8
y = -8
The solution of the equation is at the point (0, -8)
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Express √75 in basic form
Answer:
[tex]5 \sqrt{3} [/tex]
Step-by-step explanation:
Frist find which perfect square goes into 75. In this case its 25 * 3. You then find out what is the square root of 25. Which is 5. you put that number outside the radical and the other number inside the radical. resulting in 5 square roots of 3.
Answer: Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
Exact Form:
5√3
Decimal Form:
8.66025403…