Q10.
Prove algebraically that the recurring decimal 0.178 can be written as the fraction 59/330
Answers
Answer:
bbv
Step-by-step explanation:
Recurring decimal is decimal representation of a number whose digits are periodic and infinite. Proved algebraically that the recurring decimal 0.178 can be written as the fraction 59/330 below.
Given information;Given number in the decimal form is [tex]0. 1 \overline 7 \overline 8[/tex]
Suppose the number is equal to the x,
[tex]x=0. 1 \overline 7 \overline 8[/tex]
Recurring decimalRecurring decimal is decimal representation of a number whose digits are periodic and infinite.
As the number 78 is the recurring number. Thus the recurring number can be written as,
[tex]x=0.1787878.....[/tex] .......equation 1.
Suppose this is equation number 1.
Multiply the above equation with 100 both the sides,
[tex]100\times x=100\times0. 1 787878....[/tex]
[tex]100x=100\times0.1787878...[/tex]
[tex]100x=17.87878...[/tex]
Subtract the above equation from equation number 1. Thus,
[tex]\begin{aligned}\ 100x-x&=17.87878-0.1787878\\ 99x&=17.7\\ \end[/tex]
Solve for x ,
[tex]x=\dfrac{17.7}{99} [/tex]
Multiply with 10 in both numerator and denominator,
[tex]x=\dfrac{177}{990} \\ x=\dfrac{59}{330} \\[/tex]
Hence proved algebraically that the recurring decimal 0.178 can be written as the fraction 59/330
Learn more about the recurring decimal here;
https://brainly.com/question/820308
Related Questions
Explain what you think 5 x ⅙ means.
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Answer:
5/6?
Step-by-step explanation:
r17 is greater than or equal to 545.7
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Answer:
r17 is that a mistake or actually the number?
Help please show work how to get the answer.
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Answer:
A or D
Step-by-step explanation:
Yuri's homework grades for the 4th six-weeks were as follows: 67, 71, 49, 82, 87, 91, 78 What is the mean (average) of the following set of data? Round your answer to the nearest tenth of a decimal (one decimal place).
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The mean of the data set would be 75.
If I work for $7.25 an hour and work for 35 day how much money do I make
Answers
Answer:
1776.25
Step-by-step explanation:
35x7=245. 245x7.25=1776.25
Answer:
35 x 24 = 840, 840 hours
840 x 7.25 = $6090 for 35 days
Step-by-step explanation:
Complete the Square of the quadratic equation in standard form: ax2 + bx + c Treat this like a literal equation where you are solving for x by completing the square. To get started, write the equation in the form: x2 + bx = ?
Answers
Answer:
x = [-b ±√(b² - 4ac)]/2a
Step-by-step explanation:
ax² + bx + c = 0
dividing through by a, we have
ax²/a + bx/a + c/a = 0
x² + bx/a + c/a = 0
x² + bx/a = -c/a
we now add th square of half the coefficient of x to both sides, thus
x² + bx/a + (b/2a)² = -c/a + (b/2a)²
simplifying the left hand side and right hand side, we have
(x + b/2a)² = -c/a + b²/4a²
re-arranging, we have
(x + b/2a)² = b²/4a² - c/a
taking L.C.M of the right hand side, we have
(x + b/2a)² = (b² - 4ac)/4a²
taking square-root of both sides, we have
√(x + b/2a)² = ±√[(b² - 4ac)/4a²]
x + b/2a = ±√(b² - 4ac)/2a
So, x = -b/2a ±√(b² - 4ac)/2a
taking the L.C.M of the right hand side, we have
x = [-b ±√(b² - 4ac)]/2a
Which graph shows exponential decay?
Answers
Answer:
the first one
Step-by-step explanation:
the first one
Un conductor circula a 12 m/s. Acelera y pasa a circular a 20 m/s al cabo de 10 segundos. Calcula la aceleración del coche.
Answers
Answer:
Aceleracion = 0.8 m/s²
Step-by-step explanation:
Dados los siguientes datos;
Velocidad inicial = 12 m/s
Velocidad final = 20 m/s
Tiempo, t = 10 segundos
Para encontrar la aceleración;
Aceleración se puede definir como la tasa de cambio de la velocidad de un objeto con respecto al tiempo.
Esto simplemente significa que la aceleración viene dada por la resta de la velocidad inicial de la velocidad final a lo largo del tiempo.
Por lo tanto, si restamos la velocidad inicial de la velocidad final y la dividimos por el tiempo, podemos calcular la aceleración de un objeto. Matemáticamente, la aceleración viene dada por la fórmula;
[tex] Aceleracion = \frac{final \; velocidad - inicial \; velocidad}{tiempo}[/tex]
Sustituyendo en la fórmula, tenemos;
[tex] Aceleracion = \frac{20 - 12}{10}[/tex]
[tex] Aceleracion = \frac{8}{10}[/tex]
Aceleracion = 0.8 m/s²
Slove the system of linear equations by graphing y=-x+7 y=x-1
Answers
add the two linear equations together: 2y = 6
now that we know y = 3, solve for x by substituting it in
The probability of not spinning a 5 and flipping heads and the spinner has 5 outcomes
Answers
Answer:
So the odds of flipping a coin 5 times and getting 5 heads are 1/2 ^5 (half to the power of 5). Which gives us 1/32 or just over a 3% chance.
Step-by-step explanation:
A person places $4630 in an investment account earning an annual rate of 5.7%,
compounded continuously. Using the formula V = Pert, where Vis the value of the
account in t years, P is the principal initially invested, e is the base of a natural
logarithm, and r is the rate of interest, determine the amount of money, to the nearest
cent, in the account after 9 years.
Answers
Answer:
75.935
Step-by-step explanation:
If V = Pe^rt and we are given P (the principle investment) =4630 ,
a rate of 5.7 % which as a decimal = 0.057 (% divided by 100 = decimal)
we can substitute this information in and get V=4630 e^(.057t).
then it says what will it be in 9 years? so we put 9 in for "t" and get
v = 4630 e^(0.057 * 9) simplify using a calculator and we will get our answer.
Help me please with this problem!!
Answers
Answer:
139°
Step-by-step explanation:
Corresponding angles theorem:
When a transversal line intersects two parallel lines, the angles formed from the intersection are congruent in pairs. For example with your problem, using the Corresponding Angles Theorem (one of the few theorems/postulates used to find angles on transversals), the angles are paired on the same place on the first parallel line as they are on the second. Since the corresponding pair of (x)° is given, the angle of x is given. (x)° = 139°
I've provided an image courtesy of tutors.com that will help remember corresponding angles for you.
Had 2 pages of algebra ! :C my brain is not working anymore..
Answers
Step-by-step explanation:
given,
[tex]2k \div 3 = 6 \\ 2k \div3 \times 3 = 6 \times 3 \\ 2k = 18 \\ k = 18 \div 2 \\ = 9[/tex]
[tex]\sqrt{x} 196
can someone help me
Answers
Answer:
14
Step-by-step explanation:
√196
Calculate the square root of 196 and get 14.
14
EQUAÇO
1. x + 5 - 25=x + 3x - 4
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Answers
2. 1-2x=3-2x-2 => 1=3-2 => 1=1 => x=R
Select all the figures that are shaded to represent 60% of the whole. Whoever answers correctly and first will be marked as brainliest!!!!
Answers
Answer:
the first one
Step-by-step explanation:
Which scenarios below show ways governments or organizations work to solve large problems?
Answers
Red Cross volunteers travel to Haiti to help earthquake victims.
The United Nations passes a treaty to limit pollution into the Pacific Ocean.
A charity group from the United States travels to Africa to help victims of a virus.
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A large company leaks pollutants into the Mississippi River
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Find the value of x for which / || m
Answers
Answer:
x = 26
Step-by-step explanation:
Maths equation need help please
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Answer:
I FIGURED IT OUT!
Step-by-step explanation:
a = 3
b = 3
c = 5
d = 2
give me brainliest
I need help on this question
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What value for the variable makes this equation true?
`-2= 3+ b/4
Answers
<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
Answer:
Let's solve your equation step-by-step.
−2 = 3 + b / 4
Step 1: Simplify both sides of the equation.
−2 = 3 + b / 4
−2 = 3 + 1 / 4b
−2 = 1 / 4b + 3
Step 2: Flip the equation.
1 / 4b + 3 = −2
Step 3: Subtract 3 from both sides.
1 / 4b + 3 − 3 = −2 − 3
1 / 4b = −5
Step 4: Multiply both sides by 4.
4 * ( 1 / 4b ) = ( 4 ) * ( −5 )
b = −20
Answer:
b = −20
<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
Write the integer that represents the opposite of each situation
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Answers
a restaurant used 6.5 ounces of cheese to make 5 slices of pizza. if each slice had the same amount of cheese, how much was on each slice?
Answers
Answer:
1.3 ounces, 1.3*5 =6.5
I Need Help ..
4. Evaluate the functions,
Let f(0) = 21-1 and 8(x) - 7-4 find
a. /(0)
b. S(1)
c. (-1)
en g(0)
f. 8(-2)
Answers
Answer: cos ( 390 ) − 4 cot ( − 45 ) sin (330 )
Step-by-step explanation: MAKE ME BRANLIEST!!!!!!
Hi can someone help me understand how to work this problem out? I'll mark brainliest. Thanks:)
It costs $.001 per hour for electricity to run a light bulb. Find the cost per month.
Answers
Answer:
0.73001
Step-by-step explanation:
1 month = 730.01 hours
730.01 * $0.001
= 0.73001
Approximately 0.73 or 0.7.
Find the radius of the button.
3 and 1/2 in
radius:
Answers
Answer:1.75
Step-by-step explanation:
formula= R= D/2
convert 3 1/2 into a decimal
3.5
do 3.5 divided by 2 (R= 3.5/2) = 1.75
so the Radius is 1.75 inches !! hope this helped :)
The radius of the button 3 and 1/2 in would be; 1.75
What is a circle?A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.
The formula= Radius= D/2
Now convert 3 and 1/2 into a decimal;
3.5
Now, 3.5 divided by 2 (R= 3.5/2)
= 1.75
Hence, the Radius is 1.75 inches .
Learn more about circle here;
brainly.com/question/12512221
#SPJ2
Plzz help everything is in the screen shot
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Answer:
#1
Yesy = x + 1#2
Yesy = -2x#3
No#4
NoThe blue segments below is a diameter of oo. What is the length of the radius of the circle?
Answers
Answer:
C. 5.1 unitsStep-by-step explanation:
Given Information :
Diameter : 10.2 units
Radius (r) = ?
[tex]r = \frac{d}{2} [/tex]
Input the values
[tex]r = \frac{10.2}{2} \\ \\ r = 5.1[/tex]
Dubnium-262 has a half-life of 34 s. How long will it take for 500.0 grams to
decay to just 1.0 g? *
Answers
Answer:
the time taken for the radioactive element to decay to 1 g is 304.8 s.
Step-by-step explanation:
Given;
half-life of the given Dubnium = 34 s
initial mass of the given Dubnium, m₀ = 500 grams
final mass of the element, mf = 1 g
The time taken for the radioactive element to decay to its final mass is calculated as follows;
[tex]1 = 500 (0.5)^{\frac{t}{34}} \\\\\frac{1}{500} = (0.5)^{\frac{t}{34}}\\\\log(\frac{1}{500}) = log [(0.5)^{\frac{t}{34}}]\\\\log(\frac{1}{500}) = \frac{t}{34} log(0.5)\\\\-2.699 = \frac{t}{34} (-0.301)\\\\t = \frac{2.699 \times 34}{0.301} \\\\t = 304.8 \ s[/tex]
Therefore, the time taken for the radioactive element to decay to 1 g is 304.8 s.
The time required to decay 500 grams to 1 gram is 304.8 seconds and this can be determined by using the given data.
Given :
Dubnium-262 has a half-life of 34 s.
Final mass = 1 gram
Initial mass = 500 gram
Time taken by a radioactive element to decay is:
[tex]1 = 500(0.5)^{\frac{t}{34}}[/tex]
Simplify the above equation.
[tex]\rm \dfrac{1}{500} = (0.5)^{\frac{t }{34}}[/tex]
Now, take the log on both sides in the above equation.
[tex]\rm log(0.002 ) = \dfrac{t}{34}\times log(0.5)[/tex]
[tex]\rm \dfrac{log(0.002)}{log(0.5)} \times 34 = t[/tex]
t = 304.8 sec
So, the time required to decay 500 grams to 1 gram is 304.8 seconds.
For more information, refer to the link given below:
https://brainly.com/question/13911928
The area of a rectangle is found using the formula A=lw, where l is the length of the rectangle and w is the width. Multiply each pair of factors and express the area of each rectangle as a single polynomial in terms of x.
l=x+14; w=3x+1
Answers
Answer:
A(x) = 3x² + 43x + 14
Step-by-step explanation:
Area of a rectangle = length × width
length = x + 14
width = 3x + 1
Area of a rectangle = length × width
= (x + 14)(3x + 1)
= 3x² + x + 42x + 14
= 3x² + 43x + 14
express the area of each rectangle as a single polynomial in terms of x.
A(x) = 3x² + 43x + 14
