After simplifying and rationalizing the expression 1 - √ 3 x / √ 6 x, we get the result as - (√ 2 / 2) + (√6 / 6) x .
We are given the expression:
1 - √ 3 x / √ 6 x
We need to simplify each expression by rationalizing the denominator.
Multiply √ 6 in both numerator and denominator, we get that:
(1 - √ 3 x) / √ 6 x × ( √ 6 / √ 6)
We get that:
= (√ 6 - 3 √ 2 x) / 6 x
= - (√ 2 / 2) + (√6 / 6) x
Therefore, after simplifying and rationalizing the expression 1 - √ 3 x / √ 6 x, we get the result as - (√ 2 / 2) + (√6 / 6) x .
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F(2x) graph and domain and range
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
( -∞ , ∞ )
Set-Builder Notation:
{ x | x ∈ R }
The range is the set of all valid y values. Use the graph to find the range.
Interval Notation:
( -∞ , ∞ )
Set-Builder Notation:
{ y | y ∈ R }
Determine the domain and range.
Domain: ( −∞ , ∞ ), { x | x ∈ R }
Range: ( −∞ , ∞ ), { y | y ∈ R }
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What is the equation of the line that passes through the point
(−3,−3) and has a slope of 3?
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-3})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{ 3}(x-\stackrel{x_1}{(-3)}) \implies y +3= 3 (x +3) \\\\\\ y+3=3x+9\implies {\LARGE \begin{array}{llll} y=3x+6 \end{array}}[/tex]
Draw a scatter plot and find the line of best fit for each set of data. (0,2),(1,4),(2,6.5),(3,8.5),(4,10),(5,12),(6,14)
The scatter plot is shown in attached images and the line of best fit for the data set is y=1.9821x+2.1937.
The given data set is (0,2),(1,4),(2,6.5),(3,8.5),(4,10),(5,12),(6,14).
Plot the points on a coordinate plane.
Calculate the means of the x -values and the y -values.
[tex]\begin{aligned}\bar{X}&=\frac{0+1+2+3+4+5+6}{7}\\ &=\frac{21}{7} \text{ or } 3\\ \bar{Y}&=\frac{2+4+6.5+8.5+10+12+14}{7}\\ &=\frac{57}{7}\text{ or }8.14\end[/tex]
Now, we will calculate the [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})[/tex] and [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})^{2}[/tex], we get
[tex]\sum_{i=1}^{n}(x_{i}-\bar{X})^{2}=28[/tex]
and [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})=55.5[/tex]
Calculate the slope.
[tex]\begin{aligned}m&=\frac{\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})}{\sum_{i=1}^{n}(x_{i}-\bar{X})}\\ &=\frac{55.5}{28}\\ &=1.9821\end[/tex]
Calculate the y -intercept.
Use the formula to compute the y -intercept.
[tex]\begin{aligned}b&=\bar{Y}-m\bar{X}\\ &=8.14-(1.9821\times3)\\ &=8.14-5.9463\\ &=2.1937\end[/tex]
Use the slope and y -intercept to form the equation of the line of best fit.
The slope of the line is 1.9821 and the y -intercept is 2.1937 .
Therefore, the equation is y=1.9821x+2.1937 .
Draw the line on the scatter plot.
Hence, the scatter plot is shown in attached image and the line of best fit for given data set (0,2),(1,4),(2,6.5),(3,8.5),(4,10),(5,12),(6,14) is y=1.9821x+2.1937.
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3(w-2)=9 please
answer
Answer:
w=5
Step-by-step explanation:
3(w-2)=9
3w-6=9
w=5
Answer:
w = 5
Step-by-step explanation:
The equation is 3(w - 2) = 9
1st : Distribute 3 to w and -2
Should equal 3w and -6
2nd : Add 6 on both sides
Should equal 3w = 15
3rd : Divide 3 on both sides
Should equal w = 5
Hope this helps!
--Blu
The number of calories in an order of waffle fries is 20 more than the number of calories in 6 apples. If the waffle fries have 590 calories, what is the number of calories in 1 apple
1 apple contains a number of times calories = 95
Arithmetic function:In contrast to functions defined for other values, an arithmetic function is any mathematical function defined for integers (..., 3, 2, 1, 0, 1, 2, 3,...) and relies on the qualities of the integer itself as a number (real numbers, complex numbers, or even other functions)
According to the given data:Based on the given conditions, formulate: 20+6 * x = 590
Rearrange unknown terms to the left side of the equation: 6x = 590 - 20
Calculate the sum or difference:6x = 570
Divide both sides of the equation by the coefficient of variable: x = 570/6
Cross out the common factor: x = 95
get the result: x = 95
1 apple contains a number of times calories = 95.
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Let f(x)=2 x+5 and g(x)=x²-3 x+2 . Perform each function operation, and then find the domain.
f(x)-2 g(x)
The values for f(x)-2 g(x) = -2x² + 8x - 1
What are the domain of the function f(x)-2 g(x)?Given : f(x)=2 x+5
g(x)=x²-3 x+2
Solution:
2g(x)=2x²-6x+4
f(x)-2 g(x) = 2 x+5 - (2x²-6x+4)
f(x)-2 g(x) = 2 x+5 - 2x² + 6x - 4
f(x)-2 g(x) = -2x² + 8x - 1
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3.
Evaluate
O-16
16
O-4
O 1
32
-
1
2-2x-3y5
for x = 2 and y = -4.
Answer:
58
Step-by-step explanation:
2-2x-3y5
2-2(2)-3(-4)5
-2+60
58
Please Help, Consider the following sets in the universal set U, which is the set of all elements of the three given sets below. List the elements of the sets being described.
B = {d, o, I, e} I = {p, i, n, a, y} J = {p, i, n, o, y}
The solutions are;
1. U = {a, d, e, i, l, n, o, p, y}
2. E ∪ I = {a, d, e, i, l, n, o, p, y}
3. E ∩ I = { }
4. J' = {a, d, e, l}
5. I ∪ J = {p, i, n, a, o, y}
6.( J ∩ I ) ∪ E = {d, o, l, e, p, i, n, y}
7. E' = {a, i, n, p, y}
8. I' ∪ J = {d, e, l, o, p, i, n, y}
9. (E ∩ I) ∩ (I ∪ J) = { }
10. (J ∪ I)' = {d, e, l}
What is Union of the set?
Union of two or more set is the set containing all the elements of the given set.
Here, U is the universal set, which is the set of all elements of the three given sets.
And, Three sets are;
⇒ E = {d, o, I, e}, I = {p, i, n, a, y}, J = {p, i, n, o, y}
Now, We find the universal set as;
1. U = {{a, d, e, i, l, n, o, p, y}
2. And, E ∪ I = {d, o, I, e} ∪ {p, i, n, a, y}
= {a, d, e, i, l, n, o, p, y}
Hence, E ∪ I = {a, d, e, i, l, n, o, p, y}
3. E ∩ I = {d, o, I, e} ∩ {p, i, n, a, y}
Since, It cannot contain any common elements.
So, Intersection of E and I is null set.
Hence, E ∩ I = { }
4. Since, J' = U - J
J' = {a, d, e, i, l, n, o, p, y} - {p, i, n, o, y}
J' = {a, d, e, l}
Hence, J' = {a, d, e, l}
5. I ∪ J = {p, i, n, a, y} ∪ {p, i, n, o, y}
= {p, i, n, a, o, y}
Hence, I ∪ J = {p, i, n, a, o, y}
6. ( J ∩ I ) ∪ E = ({p, i, n, o, y} ∩ {p, i, n, a, y}) ∪ {d, o, I, e}
= {p, i, n, y} ∪ {d, o, I, e}
= {d, o, l, e, p, i, n, y}
Hence, ( J ∩ I ) ∪ E = {d, o, l, e, p, i, n, y}
7. E' = U - E
= {a, d, e, i, l, n, o, p, y} - {d, o, I, e}
= {a, i, n, p, y}
Hence, E' = {a, i, n, p, y}
8. I' ∪ J = (U - I) ∪ J
= ( {a, d, e, i, l, n, o, p, y} - {p, i, n, a, y}) ∪ {p, i, n, o, y}
= {d, e, l, o} ∪ {p, i, n, o, y}
= {d, e, l, o, p, i, n, y}
Hence, I' ∪ J = {d, e, l, o, p, i, n, y}
9. (E ∩ I) ∩ (I ∪ J) = ( {d, o, I, e} ∩ {p, i, n, a, y}) ∩ ({p, i, n, a, y} ∪ {p, i, n, o, y})
= { } ∩ {p, i, n, a, o, y}
= { }
Hence, (E ∩ I) ∩ (I ∪ J) = { }
10. (J ∪ I)' = U - (J ∪ I)
= {a, d, e, i, l, n, o, p, y} - ({p, i, n, a, y} ∪ {p, i, n, o, y})
= {a, d, e, i, l, n, o, p, y} - {p, i, n, a, o, y}
= {d, e, l}
Hence, (J ∪ I)' = {d, e, l}
So, The solutions are;
1. U = {a, d, e, i, l, n, o, p, y}
2. E ∪ I = {a, d, e, i, l, n, o, p, y}
3. E ∩ I = { }
4. J' = {a, d, e, l}
5. I ∪ J = {p, i, n, a, o, y}
6.( J ∩ I ) ∪ E = {d, o, l, e, p, i, n, y}
7. E' = {a, i, n, p, y}
8. I' ∪ J = {d, e, l, o, p, i, n, y}
9. (E ∩ I) ∩ (I ∪ J) = { }
10. (J ∪ I)' = {d, e, l}
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What value of x makes this equation true?
x -3 = x +3
3 9
The value of x from the given linear equation x/3-3=x/9+3 is 27.
What is linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
Given equation
x/3-3=x/9+3
=> x/3-x/9=3+3
=>(3x-x)/9=6
=>2x/9=6
=> x=9*6/2
x=27.
Therefore, the value of x from the given linear equation is 27.
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Erica went shopping for new clothes for school. She bought a pair of jeans for $35.99 and several shirts for $11.33 each. If x
represents the number of shirts she bought, which of the following equations should be used to find y, the total cost of Erica's
shopping trip?
Answer:
Simplify
x
=
35.99
dollar
11.33
dollar
.
x
=
3.1765225
Step-by-step explanation:
What two different stores offer a sale on the same item, but one offers a coupon savings and the other offers a percentage-off discount? How can you tell which offer is better?
Answer:
Personally, I think it depends on the amount of the product you’re buying. If the product is expensive, you should go the store with a percentage-off discount. If the product is not expensive, you should go to the store with coupon savings.
Step-by-step explanation:
For example, if you’re buying a $5 toy with a $1 coupon and 10% off, you should chose the coupon. Because if you chose the discount, it doesn’t change a lot of things. However, if you’re buying a million dollar airplane(just kidding), then you should definitely chose the discount. Because a million dollar minus 1 changes nothing. But a 10% discount can decrease the cost by 1 hundred thousand! Isn’t that surprising? Hope you understand it.
PLS HELP!
A group of friends wants to go to the amusements part, they have no more than $235 to spend on parking and admission, Parking is $17.50 and tickets cost over $36.25 per person, including tax. Use the drop down menu below to write an inequality representing p, the number of people who can go to the amusement park.
Which inequality ≥ or ≤
then what is Answer
p (Inequality) _____
Answer: The answer is <
Step-by-step explanation:
Really can explain sorry
4. What is the difference -4 -(-7) =
44. The Loveland town council wants to build a bandstand. Architects were asked to submit plans. In the plan shown, the floor has the shape of a regular octagon. a) What is the area of the floor of the bandstand in this plan? 20 ft b) What would the dimensions be of a square bandstand with the same area as the octagon above? c) Which one has the largest perimeter?
Area of the floor of the bandstand in regular octagon is 1931.2 ft²
dimensions of a square bandstand with the same area as the octagon is 43.94 ft
square bandstand has largest perimeter.
floor has the shape of a regular octagon
Area of a regular octagon = 2a²(1+[tex]\sqrt{2}[/tex])
a = length of the side of the octagon
here a = 20 ft
Area = 2a²(1+[tex]\sqrt{2}[/tex]) = 2(20)(20)(1+[tex]\sqrt{2}[/tex])
= 800(1+1.414)
= 800(2.414)
= 1931.2 ft²
square bandstand with the same area as the octagon
Area of square = b²
b = length of the side of the square
1931.2 = b²
b = 43.94 ft
Perimeter of regular octagon = 8a
= 8(20)
= 160ft
Perimeter of Square = 4b
= 4(43.94)
= 175.78ft
area of the floor of the bandstand in regular octagon is 1931.2 ft²
dimensions of a square bandstand with the same area as the octagon is 43.94 ft
square bandstand has largest perimeter.
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What is each expression written as a single logarithm?
a. log₄ 5 x+log₄3 x
If the expression is log₄ 5x+log₄3x, then the expression in single logarithm form looks like [tex]log_{4} 15x^{2}[/tex].
Given that the expression is log₄ 5x+log₄3x.
We have to express the expression in single logarithm.
Product property of logarithm says that the logarithm of a product is equal to a sum of logarithms. Because logs are exponents which we have to multiply like bases, we can add the exponents.
The expression is log₄ 5x+log₄3x.
log₄ 5x+log₄3x=[tex]log_{4} 15x^{2}[/tex] (We are not required to change the base)
Hence if the expression is log₄ 5x+log₄3x, then the expression in single logarithm form looks like [tex]log_{4} 15x^{2}[/tex].
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What is the area of a circle if the radius is 19mm
Answer:1133.5 mm²
Step-by-step explanation:
area= πr² where r is the radius
3.14x19²= 1133.5 mm²
Solve this linear quadratic system
y = 3x + 4
y + x² = 0
Answer:
x = -1, y = 1
Step-by-step explanation:
Solve the following system:
{y = 3 x + 4 | (equation 1)
y = x + 2 | (equation 2)
Express the system in standard form:
{-(3 x) + y = 4 | (equation 1)
-x + y = 2 | (equation 2)
Subtract 1/3 × (equation 1) from equation 2:
{-(3 x) + y = 4 | (equation 1)
0 x + (2 y)/3 = 2/3 | (equation 2)
Multiply equation 2 by 3/2:
{-(3 x) + y = 4 | (equation 1)
0 x + y = 1 | (equation 2)
Subtract equation 2 from equation 1:
{-(3 x) + 0 y = 3 | (equation 1)
0 x + y = 1 | (equation 2)
Divide equation 1 by -3:
{x + 0 y = -1 | (equation 1)
0 x + y = 1 | (equation 2)
Collect results:
Answer: {x = -1, y = 1
A 14 ounce energy drink contains 10 1/2 teaspoons of sugar. How much sugar is in one ounce of the drink
Answer:
1.33
Step-by-step explanation:
14÷10 1/2= 1.33
simplify completely 5√28+√63
The expression is completely simplified to give 13√7
What are surds?Surds are defined as square root values that cannot be further decreases to integers or whole numbers.
Another name for surds are irrational numbers.
Given the surd forms;
5√28 + √63
Now, let's find the factors of the value 28 with perfect squares.
√28 = √4 × 7
The factors of 63 with perfect squares
√63 = √9 × 7
Now, let's substitute the values
5√4 × 7 + √9 × 7
Find the perfect squares
5 × 2√7 + 3√7
Multiply through
10√7 + 3√7
Since the values have common roots, add the coefficient and keep the root the same.
We have;
13√7
Thus, the expression is completely simplified to give 13√7
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There were four hundred fifty-seven employees working in an office building. fifty-two of them left to go have lunch. 204 cars are still in the parking lot. how many emplyees are left in the building
Hello , this is a question on Geometry and I don’t understand how to do this can someone pls help me ?.
Answer:
m∠COD = 83°(I assumed it was somewhere right in-between 80-89 degrees, so I picked 83 as the most logical in between those integers.)
∠COD is an acute angle since it's less than 90°.
I hope this helps you, let me know if you have concerns related to this question and I will help with that.
During the 2006 Olympics a gymnastics receives the following scores: 8.9, 9.2, 9.15, 9.03. What is the gymnasts average score?
The gymnasts average score is 9.07
What is the gymnasts average score?The scores are given as
8.9, 9.2, 9.15, 9.03
The gymnasts average score is calculated using'
Average = Sum/Count
So, we have
Average = (8.9 + 9.2 + 9.15 + 9.03)/4
Evaluate
Average = 9.07
Hence, the gymnasts average score is 9.07
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please help !! choose the right answer i’ll mark the brainliest
R is between P and T. PR = 3x, RT = 2x + 24 and
PT = 54. Find RT.
P
R
O is the midpoint of EH. Find EH.
Line segments
Based on the information given, the value of line RT is 36
What is a line segment?A line segment can be defined as the part of a straight line bounded by two distinct end point
It also contains every point on the line between its endpoints.
From the information given, we have line PT is a line with segments PR and RT and R is the point between P and T
This can be represented as;
PR + RT = PT
Where;
PR = 3xRT = 2x + 24 PT = 54Substitute into the equation;
3x + 2x + 24 = 54
collect like terms
5x = 54 - 24
5x = 30
Make 'x' the subject of formula
x = 30/ 5
x = 6
But;
RT = 2x + 24
RT = 2(6) + 24
RT = 36
Thus, the value of line RT is 36
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Find the indicated number of geometrical mens
[tex]-32 and i[/tex]
The geometric mean between -32 and i is given by:
[tex]\sqrt{-32i}[/tex]
What is the geometric mean?The geometric mean between n values is given by the nth root of the multiplication of these values.
For this problem, we have that:
There are 2 values, -32 and i.The multiplication is -32i.Due to the two values, we take the square root, hence, the geometric mean between -32 and i is given by:
[tex]\sqrt{-32i}[/tex]
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What is the least common denominator of 3/4 3/8 and 1/4
The number below is not correctly written in scientific notation.
0.0038 × 105
What is the new exponent for the power of 10 after rewriting the number correctly in scientific notation?
3.8 × 10?
Write the new exponent value in the blank below.
Answer: use a picture math thing
Step-by-step explanation:0.0038 x 105=0.399 so move the decimal point over 1 then it should look like 0.038 x 10.5=0.399 then repeat.
4. Four of the twelve members of the panel were late for
the meeting. What fraction of the members were on
time?
A. 12
B.
4
C. 1
3
D.
2
3
Answer:
3/4 of the members.
Step-by-step explanation:
4/12 simplifies to 3/4
Anursery owner buys 8 panes of glass to fix some damage to his greenhouse. The 8 panes cost $18 80. Unfortunately, he breaks 3 more panes while repaining the damage. What is the cost of another
3 panes of glass?
Another 3 panes of glass cost:
Answer:
Step-by-step explanation:
If 8 panes cost 1880
then 1 pane cost 1880 divided by 8
1 pane = $ 235
3 pane = $235 x 3
= $ 705
$1715 + $705 = $ 2420
11. Harry ordered 9.0 pizzas. Each pizza costs $13.95. How much does he need to pay?
Question:
11. Harry ordered 9.0 pizzas. Each pizza costs $13.95. How much does he need to pay?Answer:
This is pretty simple, just multiply 9.0 by $13.95, which will give you the answer of $125.55.
* I am not responsible if you get this question wrong, for you are the one who asked the question. *
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If this helped, your welcome! Please know that I might be wrong, and if I am, I am truly sorry for that. But If you would, please make me brainliest.
I hope you have a great rest of your day! If there is an issue with this question, be happy to comment. <3
-niaxfandoms
Harry needs to pay $ 125.55 in total for the 9.0 pizzas he ordered at $ 13.95 each.
To calculate how much Harry needs to pay, multiply the number of pizzas (9.0) by the cost of each pizza ($ 13.95).
Total cost = Number of pizzas × Cost per pizza
Total cost = 9.0 × $ 13.95
To find the product, we can treat 9.0 as a whole number and then multiply:
Total cost = 9 × $ 13.95
Now, calculate the product:
Total cost = $ 125.55
Harry needs to pay $ 125.55 in total for the 9.0 pizzas he ordered at $ 13.95 each.
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