The simplified expression after rationalizing the denominator is [tex]3\sqrt{55} / 11[/tex].
The given expression is,
[tex]3\sqrt{5} /\sqrt{11}[/tex] equation 1
Name the given expression as equation 1.
To simplify the given expression first we need to rationalize the denominator that is [tex]\sqrt{11}[/tex] .
To rationalize the denominator we need to multiply and divide the given equation 1 by [tex]\sqrt{11}[/tex] . On multiplying and dividing the given equation 1 by [tex]\sqrt{11}[/tex], we will get
[tex]3\sqrt{5} /\sqrt{11}[/tex] = ( [tex]3\sqrt{5}[/tex] ×[tex]\sqrt{11}[/tex])/([tex]\sqrt{11}[/tex] ×[tex]\sqrt{11}[/tex])
On further simplifying the expression , we will get
= ([tex]3\sqrt{5}[/tex] × [tex]\sqrt{11}[/tex])/11 = [tex]3\sqrt{55} / 11[/tex]
So, we can conclude that the simplified expression after rationalizing the denominator is [tex]3\sqrt{55} / 11[/tex].
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Find the value of a. The diagram is not to scale.
21°-
129
(2q+6)°
9°
Answer:
−2322q−6945
Step-by-step explanation:
Simplify 129(2q+6) * 9 to 1161(2q + 6)
Expand by Distributing terms
21 - (2322q + 6966)
Remove parentheses.
21 - 2322q - 6966
Collect like terms.
-2322q + (21−6966)
Simplify
-2322q - 6945
Done
7. What's the sum of 2 and 24?
A. 10/20
B.
C. %20
D. %10
Answer:26
Step-by-step explanation:it's 26
Answer:
26
Step-by-step explanation:
You add 24 + 2 = 26 ( SUM means to ADD )
Write an equation in point-slope form for each pair of points. (1,10) and (5,42)
The point slope form of (1,10) and (5,42) is (y - 10) = 8(x - 1).
How to find the point slope form?A straight line is represented using its slope and a point on the line using point slope form. In other words, the point slope form is used to determine the equation of a line whose slope is "m" and passes through the point (x1, y1).
given that
the coordinates points are (1, 10) and (5,42)
(x1,y1) = (1,10)
(x2, y2) = (5,42)
The formula of point-slope is
(y - y1) = m(x - x1)
Here,
x1 = 1 and y1 = 10 but we don't know the value of m.
now,find the value of m using the following formula
[tex]m = \frac{(y2 - y1)}{(x2 - x1)} [/tex]
now, substitute the values, we get
[tex]m = \frac{(42 - 10)}{(5 - 1)} [/tex]
[tex]m = \frac{30}{4} [/tex]
m = 8
so, the value of m is 8.
substitute these values into the point-slope formula
(y - 10) = 8(x - 1)
Hence, the point slope form of (1,10) and (5,42) is (y - 10) = 8(x - 1).
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Find the center and the radius of each circle. x²+(y-4)²=11
The equation of the circle x^2 + (y - 4)^2 = 11 has a radius of √11 and a center located at (0 , 4).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle, x^2 + (y - 4)^2 = 11, is in standard form, then
h = 0
k = 4
r = √11
Hence, the equation of the circle x^2 + (y - 4)^2 = 11 has a radius of √11 and a center located at (0 , 4).
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HELP ME WITH THIS QUESTION PLS PLS
Answer: 49
Step-by-step explanation:
A=πr^2
A=π(7)^2
A=49π in^2
Answer: 49
Answer:
154 Inches square.
r=7
area= πr^2
= 22/7* 49
= 154
What is the next fraction in this sequence? Simplify your answer.
4/5, 13/20, 1/2, 7/20,....
The next fraction in this sequence is 1/5
Arithmetic sequenceArithmetic sequence are sequence that are separated by a common difference.
Given the sequence below:
4/5, 13/20, 1/2, 7/20,....
The fractions expressed as percentage is given as:
80, 65, 50, 35...
The nth term of the sequence is Tn = a+(n-1)d
T5 = 80+(5-1)(-15)
T5 = 80+(4)(-15)
T5 = 80 - 60
T5 = 20
Express 20% as a fraction
20% = 20/100 = 1/5
Hence the next fraction in this sequence is 1/5
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(6x³)² I need answer asap please and thank you
A garden is in the shape of a square with a perimeter of
32
feet. The garden is surrounded by two fences. One fence is around the perimeter of the garden, whereas the second fence is
2
feet from the first fence on the outside. If the material used to build the two fences is
$
1.18
per foot, what was the total cost of the fences?
Answer:
Step-by-step explanation:
32 / 4 = 8 = length or width (because it is a square both are the same)
8 + 2 = 10
10 + 10 + 10 + 10 = 40 (perimeter of outer fence)
32(1.18) + 40(1.18) = $84.96
Joseph bought a pair of pants and a t shirt. the pair of pants costs 1,250.00 and the t shirt costs 350.00 less 'than the pair of pants. if 'he gave the cashier three 1,000 peso bill, how much did he change did he receive? please answer correctly
Farmer ed has meters of fencing, and wants to enclose a rectangular plot that borders on a river. If farmer ed does not fence the side along the river, what is the largest area that can be enclosed?.
The largest area that can be enclosed will be 2812.5 square meters.
The perimeter of a rectangle is given as:
2L + 2W ∴ L = length and W = width
As the farmer does not want to fence the side along the river, then the formula will be:
P = L + 2w
Now
150 = L + 2w
L = 150 - 2w
Here the area is LW
Area = (150 - 2W)(W)
After solving we get
150 - 2W = 0 or W = 0
150 - 2W = 0
2W = 150
W = 75
Now, there are two solutions whether 0 or 75
Let's find their average 0+75 / 2 = 37.5
Now L = 150 - 2(37.5)
L = 150 - 75
L = 75
As the dimensions are L = 75 and W = 37.5
Area = L x W = 75 x 37.5 = 2812.5 square meters
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The complete question is:
Farmer Ed has 150 meters of fencing and wants to enclose a rectangular play that borders a river. If farmer Ed does not fence in the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?
The entrance fee to the fair is $15. You pay $2.50 for each ride you ride. Create a table and graph to represent the total paid as a function of the number of rides you ride.
The cost for x rides is modeled by the linear function:
c(x) = $15 + $2.50*x
A table and a graph for that function are provided below.
How to create a table and graph that represents the amount you pay?Here we know that the entrance fee to the fair is $15, and the cost of each ride on the fair is $2.50
So, if you go to the fair and enter in x rides, the total cost for that will be modeled by the linear function:
c(x) = $15 + $2.50*x
Now let's find a table, to do that we just need to evaluate the function in some values of x, I will use x = 0, x = 1 and x = 2, we will get:
C(0) = $15 + $2.50*0 = $15
C(1) = $15 + $2.50*1 = $17.50
c(2) = $15 + $2.50*2 = $20.00
Then we can write the table:
Number of rides ||| Cost
0 $15
1 $17.50
2 $20.00
Now that we have the table, we just need to graph these 3 points on a coordinate axis, and connect them with a line.
The graph can be seen below.
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y varies directly with x . Explain your answer.If x is doubled, what happens to y ?
If x is doubled then the value of y is also doubled.
What is direct variation?A sort of proportionality known as "direct variation" occurs when one quantity immediately changes in response to a change in another variable. This suggests that if one number increases, the other quantity will also rise proportionately. Similar to the last example, if one quantity declines, the other amount likewise declines. The link between direct variation and the graph will be linear, resulting in a straight line.
As y varies directly with x,
Using direct variation,
which implies y = kx
if x is doubled,
y = 2kx,
This implies that if x is doubled then the value of y is also doubled.
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The cost of renting a pool at an aquatic center is either 30 per hour or 20 per hour with a 40 non-refundable deposit. For how many hours is the cost of renting a pool the same for both plans?
If the cost of renting a pool at an aquatic center is either 30 per hour or 20 per hour with a 40 non-refundable deposit, then the cost of renting the pool is the same for both plans for 4 hours.
The number of hours for which the cost of renting the pool will be the same for both plans can be calculated by using an algebraic expression.
An algebraic expression is a type of equation that consists of both numbers and letters.
An algebraic expression for this problem can be given as,
30(x) = 20(x) + 40
Where x is equal to the number of hours.
The value of x can be calculated by rearranging the equation,
30(x) - 20(x) = 40
10(x) = 40
x = 40 ÷ 10
x = 4
Thus, the number of hours for which the cost of renting the pool same for both plans is 4 hours.
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"one-third of a number is 12 less than the number itself"
translate as an equation not solved
Answer:
1/3 n = n - 12 Cross multiply
n = 3(n - 12)
n = 3n -36
2n = 36
n = 36/2
n = 18
Check:
1/3 (18) = 18 - 12
6 = 6
Hope this helps
State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.
Rotation symmetry is also called mirror symmetry.
false, reflection
Rotation symmetry is also called mirror symmetry.
false, reflection
Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation.
Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated at 90°, however, the only geometric objects that are fully rotationally symmetric at any angle are spheres, circles, and other spheroids
Rotational symmetry is symmetry with respect to some or all rotations in m-dimensional Euclidean space. Rotations are direct isometries, i.e., isometries preserving orientation.
Symmetry with respect to all rotations about all points implies translational symmetry with respect to all translations.
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Ross joined a 30 week weight loss challenge. he lost 10.4 pounds int eh first 4 weeks if he maintains this rate of weight loss how many pounds will eh lose at the end of the 30 week challenge
Answer: 78 pounds
Step-by-step explanation:
10.4/4 = 2.6
2.6 * 30 = 78
12. Determine whether the cost of renting equipment is sometimes, always, or never proportional. Explain.
The cost of renting equipment is sometimes, always, or never proportional based on the prices attached.
How to illustrate the information?It should be noted tha two sequences of numbers are proportional or directly proportional when their corresponding elements have a constant ratio. It should be noted that this is the coefficient of proportionality.
In this case, the reasoning here is that if all the items have different prices it won't be, however, if the items you are ordering all have the same price they will be proportional.
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Consider the U.S. Shirts function, C(s) = 8s + 15. Explain me how to solve it please.What number would be S and what would be C
( - ∞ , + ∞) is the possible domain and range for this situation.
What is the domain function?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.Because C(s) = 8s + 15 one off function.
So, s ∈ R
80 the domain is defined as ( - ∞ , + ∞)
b) because s ∈ R
So , C(s) ∈ ( - ∞ , + ∞)
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The complete question is -
Consider the U.S. Shirts function, C(s) = 8s + 15. What expression in the function equation represents: a. the domain of the function? b. the range of the function? 5. Describe the possible domain and range for this situation.
Find the value of x.
-2x = 3x + 6
Answer:
x= -6/5
Step-by-step explanation:
-6=3x+2x
-6=5x
x=-6/5
Answer:
x = - [tex]\frac{6}{5}[/tex]
Step-by-step explanation:
- 2x = 3x + 6 ( subtract 3x from both sides )
- 5x = 6 ( divide both sides by - 5 )
x = - [tex]\frac{6}{5}[/tex]
The graph below shows how the number of donations to a charity affects the expected total value of those donations.
In October, the charity received 60 donations.
If the graph continues in the same way, what is the expected total value of the donations in October?
I can't answer it but i hope someone else does :)
Maybe the answer - But there are limits depending on whether you donate the funds to a “50% charity” or a “30% charity.” As the name implies, the total deduction for gifts to 50% charities cannot exceed 50% of a taxpayer's adjusted gross income (AGI). Accordingly, donations to 30% charities are limited to 30% of AGI.
Find the arithmetic mean a n of the given terms. a n₋₁ = 4, a₊₁ = -3
The arithmetic mean a n of the given terms a n₋₁ = 4, a₊₁ = -3 is [tex]a_{n}[/tex] = 1/2.
What is arithmetic mean?an=a1+d(n−1) by using this formula the arithmetic mean a n of the given terms are
[tex]a_{n}[/tex] = (-3 + 4)/2
[tex]a_{n}[/tex] = 1/2
The sum of a set of numbers divided by the total number of numbers in the set is known as the arithmetic mean or arithmetic average in mathematics and statistics.
The arithmetic mean can be calculated as one approach. Divide the total by the total number of values after adding up all the values. Add the numbers together, for instance: a + b + c + d and so on, if there is a set of "n" numbers.
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how would you limit the domain for it to be one to one f(x)= x^4
Limit the domain to x > 0 for it to be one to one
How to limit the domain for it to be one to one?The function is given as:
f(x)= x^4
The above function is an even function
This means that
f(x) = f(-x)
So, for the function to be one to one, we have to limit the function to only the positive x values
Hence, limit the domain to x > 0 for it to be one to one
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Tionna wants to replicate a painting in an art museum. The painting is 3 feet wide and 6 feet long. She decides on a dilation reduction factor of 0.25. What size paper should she use? F. 4 in.× 8in. H. 8 in. × 16 in. G. 6 in. × 12in. J. 10 in. ×20 in.
10in × 20in is size paper should she use. That is, option J . 10in × 20in is the correct answer.
What are examples of linear equations?
Ax + By = C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.The given size of the painting is 3 feet wide and 6 feet long.
The value of 1 foot in inches,
1 foot = 12inches.
The size of the painting is 36 inches wide and 72 inches long.
width is, ( 0.25 × 36 ) = 9 inches. So option F . 4in × 8 in is not the answer and
the length is, ( 0.25 × 72 ) = 18 inches. So option G 6in × 12in and H. 8inch × 16 in are not the possible choices.
So, the reduced dimensions of the dilated painting are 9 inches wide and 18 inches long.
That is, option J . 10in × 20in is the correct answer.
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|||
Finding the average rate of change of a function given its...
Find the average rate of change of g (x) = -2x²-x from x = 1 to x = 6.
Simplify your answer as much as possible.
0
18 08
X
k
Answer:
Mind you that the average rate of change is the gradient. Commonly we get it by using the formula that requires us to have also the y coordinates.
we can find them by plugging in the x-values in the function g(x)
x=1
[tex]g(1)=-2(1^{2} )-1\\g(1)=-3\\\\g(6)=-2(6^{2})-1\\ g(6)=-73[/tex]
now we have the points (1,-3) and (6,-73)
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
that is the formula we will use
[tex]=\frac{-73-(-3)}{6-1} \\=\frac{-70}{5} \\=-14[/tex]
Element X decays radioactively with a half life of 15 minutes. If there are 420 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 4 grams?
If there are 420 grams of Element X, then it would take 100.7 of a minute to take the element to decay to 4 grams.
Given that the element X decays radioactively with a half life of 15 minutes.
We are required to find the time that would take the 420 grams of element X would take the element to decay to 4 grams.
Radioactive decay is basically the emission of energy in the form of ionizing radiation.
4=420*[tex](1/2)^{x/15}[/tex]
x=15* [tex]log_{2}[/tex] (105)
x=15*log (105)/log (2)
x=15*2.0212/0.3010
x=30.318/0.3010
x=100.72
After rounding it will be 100.7 of a minute.
Hence if there are 420 grams of Element X, then it would take 100.7 of a minute to take the element to decay to 4 grams.
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can someone help me with this
We have given the expression -13y + 7 -11 - 4y to write as sum which is
-13y + 7 +(-11) + (-4y).
What is an mathematical expression?A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used. (Number/variable, Math Operator, Number/variable) is the order in which an expression is composed.
Arithmetic operators and numbers make up a mathematical numerical expression. No equality or inequality symbols, or unidentified variables, are present.
Indeterminate variables, integers, and arithmetic operators make up an algebraic expression. Neither equality nor inequality symbols can be found in it.
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Write each arithmetic series in summation notation. 100+90+80+ . . . . . . +10
The algebraic expression or sigma (summation) notation is given by:
∑ = 10(100 + 10)/2
And its value is ∑ = 550
What is sigma notation?The sigma notation is a mathematical operation used to determine the final value of the sum of "n" terms consecutively, when dealing only with numbers without variables this is known as an arithmetic series.
The equation for this type of problem is:
∑ = n(a1 + an)/2
n : number of termsa1 : first terman : last termOur values are:
100+90+80+ . . . . . . +10
a1 =100an = 10n = 10∑ = 10(100 + 10)/2
∑ = 10(110)/2 = 5(110)
∑ = 550
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Find the sum of each infinite geometric series. 6+5+ 25/6 + . . .
The sum of the infinite geometric series 6+5+ 25/6 + . . is S = 36
The given geometric series is:
6 + 5 + 25/6 + . . .
The common ratio (r) of a geometric series is given by:
r = a(n) / a(n - 1)
Notice that in the given series:
a(1) = 6
a(2) = 5
a(3) = 25/6
Hence, the common ratio is
r = a(2) / a(1) = 5/6
Since 0 < r < 1, the series is convergent and the sum exists.
Use the sum formula:
S = a(1) / (1 - r)
Substitute a(1) 6 and r = 5/6 into the formula:
S = 6 / (1 - 5/6)
= 6 / (1/6)
= 36
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You make $7.25/hr and your boss
promises at least 3 hours but no
more than 18 hours per week.
Payroll (FICA) taxes of 7.65% are
withheld from your paycheck.
Be sure to deduct your tax
The question's payroll (FICA) taxes total 0.2295.
Considering the information provided,
7.65% of payroll (FICA) taxes
Boss promises a minimum of 3 hours each week and not more than 18 hours.
We have, 3 × 0.0765
= 0.2295
Amount of payroll taxes that will be taken out of your paycheck.
= 0.2295
FICA Taxes: The Federal Income Contributions Act, also known as FICA, is the name of the payroll tax deduction used in the United States to pay for Social Security and Medicare. Tens of millions of seniors, Americans with disabilities, and children receive financial and medical benefits from those well-known government programs. Both employees and the employers they work for are jointly liable for FICA taxes.
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3 2/5 + 9 1/10 ?????…?.?
Answer: 25/2
Step-by-step explanation:
coverting the mixed numbers into improper fractions we get
17/5+91/10
getting a common denominator and adding the numerators we get 125/10
then we can simplify, which gets 25/2
