The 82nd term of the arithmetic sequence -8, 9, 26 can be solved using the arithmetic sequence formula, which results in the 82nd term being 1369.
Explanation:The subject of this question is related to finding the 82nd term of the arithmetic sequence -8, 9, 26. Arithmetic sequences follow a pattern of adding a consistent value, this consistent value is called the common difference. From the given sequence, the common difference (d) can be calculated by subtracting the first term from the second term, or the second from the third, and so on. So d = 9 - (-8) = 17 or 26 - 9 = 17.
The formula for finding the nth term of an arithmetic sequence is a_n = a_1 + (n - 1) * d. Here, a_1 is the first term of the sequence and n is the term number we're interested in.
Thus, the 82nd term of the sequence can be found by substituting the values into the formula: a_82 = -8 + (82 - 1) * 17 = 1369. So, the 82nd term of the given arithmetic sequence is 1369.
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The [tex]82^{nd}[/tex] term of the arithmetic sequence -8, 9, 26, ..., is 1369.
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference (d).
To find the [tex]82^{nd}[/tex] term of the given arithmetic sequence, we can use the formula for the nth term:⇒ aₙ = a₁ + (n - 1) × d
where a₁ is the first term, n is the term number, and d is the common difference.
Given the arithmetic sequence: -8, 9, 26, ...Identify the first term (a₁):⇒ a₁ = -8.
Find the common difference (d):⇒ d = 9 - (-8) = 17.
Use the nth term formula:⇒ n = 82
⇒ a₈₂ = -8 + (82 - 1) × 17
Calculate:⇒ a₈₂ = -8 + 81 × 17
⇒ a₈₂ = -8 + 1377
⇒ a₈₂ = 1369
Therefore, the [tex]82^{nd}[/tex] term of the sequence is 1369.
Complete question:
Find [tex]82^{nd}[/tex] term of the arithmetic sequence -8, 9, 26, ....
Use the Distributive Property to write each expression as an equivalent expression. Then evaluate the
expression
17. 8(5 - 1)
a. 8 x 5 - 8x1 = 48
b. 85-8x1 - 32
c. 8 x 5-1 - 39
d. 8 % (5 - 1) *8 - 256
To use the Distributive Property on the expression 8(5 - 1), you would multiply 8 by each term inside the parentheses, simplify, and perform the subtraction. The final evaluated result is 32.
Explanation:The problem is asking to use the Distributive Property to simplify the mathematical expression and then evaluate it. The Distributive Property, in basic terms, indicates that multiplication distributes over addition or subtraction. So, for the expression 8(5 - 1), you would apply the Distributive Property as follows:
You multiply 8 by each of the terms inside the parentheses:
8 * 5 - 8 * 1
Then, simplify that expression:
40 - 8
And finally, perform the subtraction:
= 32
So, the equivalent expression is 40 - 8, and the evaluated result is 32.
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The area of a circle is directly
proportional to the square of its
radius. A circle with a radius of 2
cm has an area of 12.566 cm^2.
What is the radius of a circle with
an area of 78.54 cm^2?
[?] cm
Round to the nearest whole number.
Answer:
[tex]radius=5\ cm[/tex]
Step-by-step explanation:
Let r be the radius of the circle and A be the area of the circle.
Given:
[tex]r_{1} = 2\ cm, A_{1}=12.566\ cm^{2}[/tex]
And [tex]r_{2} = ?, A_{2}=78.54\ cm^{2}[/tex]
The area of a circle is directly proportional to the square of its radius.
A ∝ [tex]r^{2}[/tex]
[tex]A = kr^{2}[/tex]-----------(1)
Where k is the constant of proportionality
Find constant value by substituting [tex]r_{1} = 2\ cm, A_{1}=12.566\ cm^{2}[/tex]
in equation 1.
[tex]A = kr^{2}[/tex]
[tex]A_{1}=k(r_{1})^{2}[/tex]
[tex]12.566=k\times 2^{2}[/tex]
[tex]12.566=k\times 4[/tex]
[tex]k=\frac{12.566}{4}[/tex]
[tex]k=3.141[/tex]
Find [tex]r_{2}[/tex] by substituting k and [tex]A_{2}[/tex] value in equation 1.
[tex]A = kr^{2}[/tex]
[tex]A_{2}=k(r_{2})^{2}[/tex]
[tex]12.566=3.141\times (r_{2})^{2}[/tex]
[tex](r_{2})^{2}=\frac{78.54}{3.141}[/tex]
[tex](r_{2})^{2}=25.004[/tex]
where: 25.004 ≅ 25
[tex](r_{2})^{2}=25[/tex]
[tex]r_{2}=\sqrt{25}[/tex]
[tex]r_{2}=5\ cm[/tex]
Therefore; the radius of the circle is 5 cm.
Final answer:
The radius of a circle with an area of 78.54 cm² is approximately 4 cm, after setting up a proportion with a known circle area and solving for the unknown radius.
Explanation:
The area of a circle is given by the formula A = πr², where A is the area and r is the radius of the circle. Given that a circle with a radius of 2 cm has an area of 12.566 cm², we set up a proportion to find the radius of a circle with an area of 78.54 cm²:
(12.566 cm²) / (2 cm)² = (78.54 cm²) / r².
Solving for r, we find r² = (78.54 cm²) × (2 cm)² / (12.566 cm²).
After calculation, we get r approximately equal to 4 cm, rounding to the nearest whole number.
Simplify the expression.
7x + 7 +5(x + 3) + 3
Answer:
12x+25
Step-by-step explanation:
7x+7+5x+15+3
12x+25
On a coordinate plane, a line goes through (negative 3, 2) and (2, negative 1). A point is at (3, 0). What is the equation of the line that is perpendicular to the given line and passes through the point (3, 0)
Answer:
y=\frac{5}{3}x-5
Step-by-step explanation:
Identify the equivalent expression for each of the expressions below. (m^(1/3)*1/5
Answer: 1
Anything that goes to the 0 power is always going to be 1
What is 12001 ➗ 4180
Answer:
2.871052631578947
Step-by-step explanation:
this is exactly the answer.
Max is buying bags of oranges each bag has 8 oranges when he opens the bag he finds that 12 of the total oranges are rotten what are the options for the number of bags he should buy in order to end up at least 40 good oranges
Answer: 7 bags
Step-by-step explanation:
Total no. of oranges rotten - 12
To buy no. of bags to get - at least 40 good oranges
No. of oranges in a bag - 8
40 + 12 = 52 oranges
As each bag contains 8 oranges and 52 is not divisible by 8 we end up taking the closest divisible number that is 54.
If we divide 54 by 8 we get 7.
Hence Max needs to buy 7 bags of oranges.
Note: As they have asked at least 40 good oranges
7. The cost of renting the party room for 10 people is $117.50. The cost of renting the room is $151.25 for 15 people. Write an equation that represents the cost of renting the party room in terms of the number of people attending the party .
Answer:
C = 6.75n + 50
Step-by-step explanation:
The equation for the cost of renting the party room can be written in the form;
C= mn+k ......i
Where C = cost
n = number of people
Substituting the 2 cases into the equation we have,
Case 1
117.5 = 10m + k ......1
Case 2
151.25 = 15m + k .....2
Subtracting eqn 1 from 2 we have
151.25 - 117.50 = 15m - 10m
5m = 33.75
m = 33.75/5 = 6.75
Substituting m = 6.75 into eqn 1, we have
117.50 = 10(6.75) + k
k = 117.5 - 67.50
k = 50
Therefore, rewriting the eqn i, we have
C = 6.75n + 50
What is the slope of y=4-6x
Answer:
the slope, m, is -6
Step-by-step explanation:
One of the most commonly used equations for a straight line is y = mx + b, where m is the slope and b is the y-intercept.
Comparing y=4-6x to y = b + mx, we see that the slope, m, is -6 and the y-intercept, b, is 4.
The slope of the line y = 4 - 6x is -6, which shows that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 6.
The equation is given as follows:
y = 4 - 6x
As we know that the equation is in slope-intercept form, y=mx+b.
Here, m is the slope and b is the y-intercept.
As per the question, the y-intercept is 4, which means the line crosses the y-axis at (0,4).
The slope, -6, tells us that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 6.
Thus, the slope of the line y = 4 - 6x is -6.
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3.25x10^-6 written in decimal notation
3.25 x 10^-6 written in decimal notation is 0.00000325
Solution:
Decimal notation is simply a form of a number using a decimal point
Given number : [tex]3.25 \times 10^{-6}[/tex]
Steps to follow:
In order to convert a number written in scientific notation to one written in standard or decinal notation, follow these steps:
Write the given scientific notation numberUse the sign and numerical value of the exponent (power) to determine the direction and number of places to move the decimal place.Move the decimal point to the right if the exponent is positive.Move the decimal point to the left if the exponent is negative.To convert to decimal notation:
Multiply the decimal number by 10 raised to the power indicated.
[tex]\rightarrow 3.25 \times 10^{-6}[/tex]
Here the exponent of 10 is -6
So the decimal point is moved 6 places to right
[tex]\rightarrow 3.25 \times 10^{-6} = 0.00000325[/tex]
Final answer:
To convert the scientific notation 3.25 x 10^-6 into decimal form, you move the decimal point six places to the left, resulting in 0.00000325.
Explanation:
To convert 3.25 x 10^-6 into decimal notation, you need to move the decimal point 6 places to the left because it is a negative exponent. Start with 3.25 and move the decimal:
0.3250.03250.003250.0003250.00003250.00000325The decimal notation of 3.25 x 10^-6 is 0.00000325.
Everyone in a class of 30 students takes math and history. Seven students received an A in history and 13 received an A in math, including four that received an A in both courses. How many students did not receive an A in any of these two courses?
Answer:14
Step-by-step explanation:
30 students total.
7 received an a in history.
13 received an a in math.
4 received an a in both courses.
how many students did not receive an a in either course.
20 total received an a in history or math.
of these, 4 received an a in history and math.
those 4 are being counted twice.
once in history and once in math.
you need to subtract 4 from the number who got an a in history or an a in math to get a total of 16 students who got an a in history or in math.
this leaves 30 - 16 = 14 students who did not get an a in either course.
here's the breakdown.
14 students did not get an a in either course.
3 students got an a in history only.
9 students got an a in math only.
4 students got an a in both history and math.
total is 30 students.
Final answer:
To find how many students did not receive an A in either math or history, subtract the sum of students with As in both subjects (after adjusting for 4 students who received an A in both) from the total class size. It is found that 14 students did not receive an A in either subject.
Explanation:
To determine how many students didn't receive an A in either math or history, we can use the principle of inclusion-exclusion. Firstly, we have 30 students in total. We're told that 7 received an A in history and 13 in math, including four students who received an A in both subjects.
To avoid double-counting those four students, we add the number of students who received an A in history to the number who received an A in math, and then subtract the number who received an A in both:
Number of students with A in either subject: 7 (history) + 13 (math) - 4 (both) = 16 students
Then, we calculate the students who did not receive an A in either subject by subtracting those who received an A in at least one subject from the total class size:
Number of students without an A in any course: 30 (total students) - 16 (A in at least one subject) = 14 students
Therefore, 14 students did not receive an A in either math or history.
HELP PLS IM IN CLASS RN!!!
Answer:
48 inches
Step-by-step explanation:
Dagne can jump 13.2 inches that is 27.5% of her height. Let x inches be Dagne's height.
Then
x inches - 100%
13.2 inches - 27.5%
Write a proportion:
[tex]\dfrac{x}{13.2}=\dfrac{100}{27.5}[/tex]
Cross multiply:
[tex]27.5x=13.2\cdot 100\\ \\27.5x=1,320\\ \\x=\dfrac{1,320}{27.5}\\ \\x=48\ inches[/tex]
let (-3,-2) be a point on the terminal side of 0. find the exact values of cos0 csc0 and tan0
To find the exact values of cos(0), csc(0), and tan(0) given a point on the terminal side of 0, we can use the coordinates of the point to determine the values of the trigonometric functions.
Explanation:To find the exact values of cos(0), csc(0), and tan(0) given that (-3,-2) is a point on the terminal side of 0, we can use the coordinates of the point to determine the values of the trigonometric functions.
First, we can find the value of cos(0) by dividing the x-coordinate (-3) by the distance from the origin, which is sqrt((-3)^2+(-2)^2). Therefore, cos(0) = -3 / sqrt(13).
Next, we can find the value of csc(0) by dividing 1 by the y-coordinate (-2). Therefore, csc(0) = 1 / -2 = -1/2.
Finally, we can find the value of tan(0) by dividing the y-coordinate (-2) by the x-coordinate (-3). Therefore, tan(0) = -2 / -3 = 2/3.
let f = {(-2,4), (-1,2), (0,0), (1,-2), (2,-5)}
let g= {(-3,3), (-1,1), (0,-3), (1,-4), (3,-6)}
what is g(f(2))?
Answer:9
Step-by-step explanation:4
Solving a Real-World Problem
Brigid is picking strawberries at the Pick-Your-Own Farm. Her goal is to pick 5 bushels of strawberries. She has
already pick
ushels, and she picks at a rat
hel per hour. The scenario is represented as
ah+15 = 5, where h is the number of hours she picks. How many more hours will it take Brigid to fill 5 bushels o
strawberries?
hours
16
hours
10
hours
unu
hours
) Intro
Done
Answer: The answer is 5 and 3/5 hours
Step-by-step explanation:
Answer:
5 and 3/5 hours
Step-by-step explanation:
An exterior angle of a triangle is 140 degrees. If the non-adjacent angles are congruent, then what are the measures of all of the interior angles of the triangle?
The measures of all of the interior angles of the triangle are 70 degrees, 70 degrees and 40 degrees
Solution:
Given that exterior angle of triangle is 140 degrees
The exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles
Given that adjacent angles are congruent
Let one of the non adjacent interior angles be "x"
x + x = 140
2x = 140
x = 70
So the two interior angles are 70 degrees and 70 degrees
Let us find the third interior angle
The angle sum property of a triangle states that the interior angles of a triangle always add up to 180 degrees
70 + 70 + third angle = 180
third angle = 180 - 70 - 70
third angle = 180 - 140
third angle = 40 degrees
Thus the measures of all of the interior angles of the triangle are 70 degrees, 70 degrees and 40 degrees
A flower shop has 11 red roses, 7 pink roses, 9 white he roses , and 3 yellow roses in stock . One type of rose is randomly selected for a flower arrangement. What is the probability they the selected rose is red or yellow.
Answer:
7/15
Step-by-step explanation:
11+7+9+3= 30
11= red
3=yellow
11+3=14
=14/30
=7/15
Answer:
7/15
Step-by-step explanation:
Probability of an event is the number of possible outcome divided by the total outcome. It is a ratio. The probability that an event will or will not happen is 1 as those are the only two possibilities.
Given that the flower shop has 11 red roses, 7 pink roses, 9 white he roses , and 3 yellow roses in stock , the total number of flower available
= 11 + 7 + 9 + 3
= 30 flowers
The probability that a rose selected is ;
red = 11/30
yellow = 3/30
the probability they the selected rose is red or yellow
= 11/30 + 3/30
= 14/30
= 7/15
problem solving involving rational equation
1. The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of what number?
2. The reciprocal of the product of two consecutive intergers is 1/72
1. The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of what number?
Answer:The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of [tex]\frac{12}{35}[/tex]
Solution:1. The reciprocal of 5 plus the reciprocal of 7 is the reciprocal of what number?
From given question,
[tex]\text{ reciprocal of 5} = \frac{1}{5}[/tex]
[tex]\text{ reciprocal of 7} = \frac{1}{7}[/tex]
Given that,
reciprocal of 5 + reciprocal of 7 = ?
[tex]\frac{1}{5} + \frac{1}{7} = x[/tex]
On cross-multiplying we get,
[tex]\frac{1}{5} + \frac{1}{7} = \frac{7+5}{5 \times 7} = \frac{12}{35}[/tex]
Thus reciprocal is [tex]\frac{35}{12}[/tex]
So the reciprocal of 5 plus the reciprocal of 7 is the reciprocal of [tex]\frac{12}{35}[/tex]
Question 22. The reciprocal of the product of two consecutive integers is 1/72
Answer:The value of two consecutive numbers are 8 and 9
Solution:Let the two consecutive integers be x and x + 1
Given that reciprocal of product of two consecutive integers is [tex]\frac{1}{72}[/tex]
product of two consecutive integers = x(x + 1) = [tex]x^2 + x[/tex]
reciprocal of the product of two consecutive integers = [tex]\frac{1}{72}[/tex]
[tex]\frac{1}{x^2 + x} = \frac{1}{72}\\\\x^2 + x = 72\\\\x^2 + x - 72 = 0[/tex]
Solve the above quadratic equation by grouping method
[tex]x^2 + x - 72 = 0\\\\x^2 -8x + 9x - 72 = 0\\\\x^2 + 9x + (-8x - 72) = 0\\\\x(x + 9) -8(x + 9) = 0\\\\(x + 9)(x - 8) = 0[/tex]
Thus x = -9 or 8
Ignoring negative value,
x = 8
Thus two consecutive integers are x = 8 and x + 1 = 8 + 1 = 9
8 and 9 are two consecutive integers
Which expression can be used to find the surface area of the following rectangular prism?
Answer
30+30+15+15+18+18
Step-by-step explanation:
The expression to calculate the surface area of the prism is 2 * (3 * 5 + 3 * 6 + 5* 6)
How to determine the expression of the surface area?The given parameters are:
Length = 3Width = 5Height = 6The surface area of a rectangular prism is:
Area = 2 * (Length * Width + Length * Height + Width * Height)
Substitute known values
Area = 2 * (3 * 5 + 3 * 6 + 5* 6)
Hence, the expression to calculate the surface area of the prism is 2 * (3 * 5 + 3 * 6 + 5* 6)
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3. Last week Jean ran 2 fewer than 4m miles.
This week she ran 0.5 miles more than last
week. Write and simplify an expression for
the total number of miles Jean ran in the
two weeks.
The total number of miles Jean ran in the two weeks is 4.5 m.
Given that, last week Jean ran 2 fewer than 4m miles.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Here,
Number of weeks Jean ran last week = 4-2=2 m
Number of weeks Jean ran this week = 2+0.5
= 2.5 m
Total number miles = 2+2.5
= 4.5 m
Hence, the total number of miles Jean ran in the two weeks is 4.5 m.
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Only answer 28 ( I added this parentheses so that the thing would accept my question)
Answer:
(a). Number of protons in a chlorine atom = 17
(b). Atomic number of sodium = 11
Step-by-step explanation:
Let the number of protons in a sodium atom = x
Then, the number of protons in a chlorine atom = x + 6
Now, it is given that the atomic number of an element is equal to the number of protons per atom.
So, atomic number of sodium (Na) = x
Atomic number of chlorine (Cl) = x + 6
It is given that the atomic number of chlorine is 5 less than twice the atomic number of sodium.
∴ atomic number of chlorine (Cl) = 2 × atomic number of sodium (Na) - 5
⇒ x + 6 = 2x - 5
⇒ x - 2x = -5 - 6
⇒ -x = -11
Cancelling the minus sign from both sides, we get
x = 11
(a). Number of protons in a chlorine atom = x + 6
= 11 + 6 (∵ x = 11)
= 17
(b). Atomic number of sodium = x = 11
Please help I will mark previous
Answer:
[tex] \frac{5}{16}, \: 31.25\%[/tex]
Victor buys some six-packs of soda for a party. He buys 42 cans in all. How many six-packs of soda did Victor buy?
Divide the total number of cans by 6.
42 / 6 = 7
He bought 7 six packs.
Final answer:
Victor bought 7 six-packs of soda.
Explanation:
To find the number of six-packs of soda Victor bought, divide the total number of cans by 6. In this case, Victor bought 42 cans in total, so dividing 42 by 6 gives us 7. This means Victor bought 7 six-packs of soda.
(PLEASE ANSWER ASAP; WILL MARK BRAINIEST)
The table shows y as a function of x. Suppose a point is added to this table. Which choice gives a point that preserves the function?
A) (9, 8)
B) (−6, 3)
C) (−5, −2)
D) (−3, −8)
Good evening ,
Answer:
D.Step-by-step explanation:
______________________________________________________
Note:
if f is a function then each number of the domain has an unique image.
______________________________________________________
since (regarding the table) the image of 9 is 6 then the answer A is wrong
The same apply on answers B and C .
then the right answer is D(-3,-8).
:)
Answer:
dddddddddddddddddd
Which of the following options is an equivalent function to f(x) = 4(3)2X?
f(x) = 36
f(x) = 4(9)
f(x) = 144
f(x) = 4(6x)
Answer:
[tex]f(x)=4(6x)[/tex]
Step-by-step explanation:
Given:
the given expression is.
[tex]f(x)=4(3)2x[/tex]
Simplify the given expression.
[tex]f(x)=4(3)2x[/tex]
[tex]f(x)=4(3\times 2x)[/tex]
[tex]f(x)=4(6x)[/tex]
Therefore, the option [tex]f(x)=4(6x)[/tex] is an equivalent function to [tex]f(x)=4(3)2x[/tex].
The population of a city is modeled by
P ( t ) = 78 , 300 ( 1.023 ) t
P ( t ) represents the number of people and t is the number of years since 2014.
Approximate the population of the city in the year 2035, rounded to the nearest whole number.
Answer:
the population of the city in the year 2035 is 126,226
Step-by-step explanation:
The population of a city is modeled by
[tex]P(t)= 78300(1.023 )^t[/tex]
P ( t ) represents the number of people and t is the number of years since 2014.
in the year 2014, the year t=0
we need to find the population in the year 2035
2035-2015= 21
so find population when t=21
[tex]P(t)= 78300(1.023 )^t[/tex]
[tex]P(21)= 78300(1.023 )^{21}=126226.36[/tex]
The clock face in a famous clock tower has a radius of 4 meters. What is the area of the clock face to the nearest square meter
Final answer:
To find the area of the clock face with a 4-meter radius, use the area formula for a circle, which gives approximately 50.265482 m². Rounded to the nearest square meter, the clock face area is about 50 m².
Explanation:
The clock face in a famous clock tower has a radius of 4 meters, and we want to find the area of the clock face to the nearest square meter. To do this, we use the formula for the area of a circle, which is A = πr², where A is the area and r is the radius of the circle.
Plugging in the radius of the clock face:
A = π(4 m)² = π(16 m²) ≈ 50.265482 m²
However, since we want the answer to the nearest square meter, we round this to:
A ≈ 50 m²
Final answer:
The area of the clock face with a radius of 4 meters is approximately 50 square meters when rounded to the nearest square meter.
Explanation:
The area of a clock face in a famous clock tower, given its radius is 4 meters, can be calculated using the formula for the area of a circle, which is [tex]A = πr^2[/tex] where A is the area and r is the radius of the circle. In this case, substituting the radius of 4 meters into the formula gives us[tex]A = π(4m)^2 = π16πm^2.[/tex] To give an answer to the nearest square meter, we use the value π = 3.14, resulting in [tex]A = 16(3.14)m^2 = 50.24m^2[/tex], which rounds to 50 m².
Which number line represents the solution of 5x + 3 ≤ -7? A) A B) B C) C D) D
Answer: x≤-2
Step-by-step explanation: Solve for x. (NUMBER LINE ATTACHED)
Hope this helps you out.
The solution of the inequality is shown in figure.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ 5x + 3 ≤ - 7
Now,
Solve the inequality as;
⇒ 5x + 3 ≤ - 7
⇒ 5x + 3 - 3 ≤ - 7 - 3
⇒ 5x ≤ - 10
⇒ 5x/5 ≤ - 10/5
⇒ x ≤ - 2
Thus, The solution of the inequality is;
⇒ x ≤ - 2
Therefore, The solution of the inequality is shown in figure.
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3n-5=19
Plz give me a step by step explanation cause i already have an answer i just need to work
Answer:
n=8
Step-by-step explanation:
3n-5=19
3n=19+5
3n=24
n=24/3
n=8
Square root of 60 divided by square root of 5
Answer: 2√3
Step-by-step explanation: To divide √60 by √5, we simply divide the numbers that are inside the radicals.
Since the quotient of 60 divided by 5 is 12,
the square root of 60 divided by the square root of 5 is √12.
However, we can simplify the square root of 12.
The √12 breaks down into 4 · 3 and 4 breaks down into 2 · 2.
The 2's match up, so a 2 comes outside of the radical.
Since the 3 doesn't pair up, it stays inside.
So our answer is 2√3.
Final answer:
The simplification of [tex]\sqrt{60}/\sqrt{5[/tex] results in [tex]2\sqrt{3,[/tex] by combining the square roots into one and then simplifying the inner value.
Explanation:
The question asks for the simplification of the expression which is the square root of 60 divided by the square root of 5. To simplify this expression, one can utilize the property of square roots that allows the division within a single square root function. Here’s a step-by-step explanation:
Write the expression as [tex]\sqrt{60}/\sqrt{5[/tex]
Combine the square roots using the property[tex]\sqrt{(a)}/\sqrt{(b)} = \sqrt{(a/b),[/tex] giving[tex]\sqrt{60}/\sqrt{5[/tex]
Simplify 60/5 to get 12.
Now take the square root of 12, which is not a perfect square. However, we can express 12 as the product of 4 (which is a perfect square) and 3 (4 * 3 = 12).
Finally, we write the expression [tex]\sqrt{4} * \sqrt{3,[/tex] which simplifies to [tex]2\sqrt{3,[/tex]
Thus, the simplified form of [tex]\sqrt{60}/\sqrt{5[/tex] is [tex]2\sqrt{3,[/tex], which cannot be simplified any further as [tex]\sqrt{3[/tex] is an irrational number and does not have a precise decimal representation.
It is always important to remember that when rounding is necessary, you should round the result up if the digit following the last significant digit is 5 or greater, and round it down if it is less than 5.