Answers
Answer:
a = 1, b = 4
Step-by-step explanation:
You have worked out part (a) correctly, that is
0.7575... = [tex]\frac{75}{99}[/tex] = [tex]\frac{25}{33}[/tex]
(b)
[tex]\frac{a}{11}[/tex] + [tex]\frac{b}{6}[/tex] = [tex]\frac{25}{33}[/tex]
[tex]\frac{6a+11b}{66}[/tex] = [tex]\frac{25}{33}[/tex]
Multiply numerator/ denominator of [tex]\frac{25}{33}[/tex] by 2, thus
[tex]\frac{25(2)}{33(2)}[/tex] = [tex]\frac{50}{66}[/tex] , then
[tex]\frac{6a+11b}{66}[/tex] = [tex]\frac{50}{66}[/tex] , thus
6a + 11b = 50
Choose a = 1 ( a positive integer ), then
6(1) + 11b = 50
6 + 11b = 50 ( subtract 6 from both sides )
11b = 44 ( divide both sides by 11 )
b = 4
a = 1, b = 4, so
[tex]\frac{1}{11}[/tex] + [tex]\frac{4}{6}[/tex] = [tex]\frac{25}{33\\}[/tex]
Related Questions
What is the answer to this?
Answers
Answer:
C.) [tex]A=12x-20[/tex]
Step-by-step explanation:
The area formula:
[tex]A=l*w[/tex]
Insert the values:
[tex]A=4*(3x-5)[/tex]
Use the distributive property:
[tex]A=4(3x)+4(-5)\\\\A=12x-20[/tex]
:Done
ms tabanelli deposits $20,000 in an account that has a 5% annual interest rate compound yearly. If she does not add to or withdraw from the account for 2 years, how much interest will she have earned for the 2-year period?
Answers
$2050
Step-by-step explanation:$20000×1.05×1.05 =
= $20000×1.05²
= $20000×1.1025
= $22050
$22050 - $20000 = $2050
The interest earned for a 2-year period is $2050
What is compound interest?Compound interest simply means that the interest associated with a bank account, loan, or investment increases exponentially over time.
Given that, Ms Tabanelli deposits $20,000 in an account that has a 5% annual interest rate compound yearly, she does not add to or withdraw from the account for 2 years,
We know that,
[tex]A = P(1+r)^t[/tex]
A = amount
P = principal
r = rate
t = time
Putting all the values in the formula,
A = 20000(1+0.05)²
A = 20000(1.05)²
A = 20000×1.1025
A = 22050
Interest earned = Amount - Principal
= 22050 - 20000
= 2050
Hence, the interest earned for a 2-year period is $2050
For more references on compound interest, click;
https://brainly.com/question/14295570
#SPJ2
arange the following expressions in order of their value from least to greatest. a. 4 − 6 b. −4 + 6 c.−4 − 6
Answers
Answer: C. -10, A -6, B 2
Step-by-step explanation:
Mary has some trading cards.
Answers
Answer:
Step-by-step explanation:
36 divided by 3. I think.
Answer:
Divide 3 by 36 and simplify your answer
Step-by-step explanation:
Change 20 5/9 to an
improper fraction.
Answers
Answer:
185/9
Step-by-step explanation:
20 5/9
Multiply 20 by the 9 (the denominator), and you''ll get 180.
Add the 5 (the numerator) to 180, and you'll get 185.
Then, place 185 over the denominator which is 9 and you get 185/9!
Answer:
[tex]\frac{185}{9}[/tex]
Step-by-step explanation:
This is the answer because:
1) The formula of changing mixed fractions to improper fractions is denominator times the whole number plus the numerator
2) Denominator = 9
Whole number = 20
Numerator = 5
9 x 20 + 5 = 185
Therefore, the answer is [tex]\frac{185}{9}[/tex]
Hope this helps!
RS=2x-8, ST= 11, RT= x+10
Answers
Answer:
X=7 ST=11 RT=17
Step-by-step explanation:
RT=RS+ST. RS= 2(7)-8. ST=11
X+10=2x-8+11. =14-8=6. RT= x+10
X+10=2x+3. RS=6. 7+10=17
10=x+3. RT=17
X=7
Which algebraic expression represents "the sum of a number and 9"?
On-g
On+ 3
Ogn
n
Answers
Answer
n+9
Step-by-step explanation:
For which equations are in the solution for x the same number? 15 – х = -3
3
Answers
Answer:
Step-by-step explanation:
First equation:
15 - x = - 3
-x = - 3 - 15
-x = -18 (now negative signs on b.s cut eachother)
[x = 18]
Second equation :
15 - x = 3
-x = 3 - 15
- x = -12 ( now negative sign on b.s cut eachother)
[x = 12]
so x = 18 and x = 12 are not same
What is P= I^2r when solving for I?
Answers
Answer:
[tex]I=\sqrt{\dfrac{P}{r}}[/tex]
Step-by-step explanation:
Divide by r and take the square root.
[tex]P=I^2r\\\\\dfrac{P}{r}=I^2\\\\\boxed{I=\sqrt{\dfrac{P}{r}}}[/tex]
please help will mark brainlist
Answers
Step-by-step explanation:
Step by Step Solution:
More Icon
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "/-19" was replaced by "/(-19)".
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
s/(-19)-(-29)=0
Step by step solution :
STEP
1
:
s
Simplify ———
-19
Equation at the end of step
1
:
s
——— - -29 = 0
-19
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using -19 as the denominator :
-29 -29 • -19
-29 = ——— = —————————
1 -19
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
s • -1 - (-29 • 19) 551 - s
——————————————————— = ———————
19 19
Equation at the end of step
2
:
551 - s
——————— = 0
19
STEP
3
:
When a fraction equals zero
3.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
551-s
————— • 19 = 0 • 19
19
Now, on the left hand side, the 19 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
551-s = 0
Solving a Single Variable Equation:
3.2 Solve : -s+551 = 0
Subtract 551 from both sides of the equation :
-s = -551
Multiply both sides of the equation by (-1) : s = 551
Which property is illustrated?
x+y=y+x
Answers
Answer:
The Communitive Property of Addition
Step-by-step explanation:
The properties are
Communitive: You can switch the order and still get the same answer
Assosiative: You can switch what numbers are in the parentheses and still get the same answer (if you're only adding) a+(b+c)=c+(a+b)
Distributive: (a*b)+(a*c)=a*(b+c)
Identity: You can add a number with 0 and get the same number you started with
y+x=x+y is the communitive property because, no matter which order the numbers are, you get the same answer
A triangular window has area
24 square feet and height six feet.
What is its base?
Answers
Solve the equation for x. x2 = 484
Answers
Answer:
x=22
Step-by-step explanation:
X²=484
x=√484
x=22
Answer:
Step-by-step explanation:
x^2 = 484
√x² - √484
x = 22
The next two numbers in the series 1 , 4 , 9 , 16 , 25 ,....................are
Answers
Answer:
36, 49
explanation:
The pattern in this series is going by perfect squares:
(1)² = 1(2)²= 4(3)² = 9(4)² =16(5)² = 25From this, we can tell the next 2 numbers in the series will be:
(6)²=36(7)²=49Josh wrote a whole number using the digits 8,4,7,2,9 and 0. Josh's number has a seven in the thousands and a 2 in the tens place. Josh's number is less then 500,000. Is Josh's number greater than 480,000?
Answers
Answer:
4 out of the 6 possible numbers Josh wrote were greater than 480,000, while 2 out of the 6 possible numbers are less than 480,000
Step-by-step explanation:
The given parameters are;
The number with which Josh wrote the whole number = 8, 4, 7, 2, 9, and 0
The number in the thousands of the whole number that Josh wrote = 7
The number in the tens of the whole number that Josh wrote = 2
The value of the whole number that Josh wrote < 500,000
Therefore, we have;
The possible numbers in the hundreds of thousands place = 4, and 2
Which gives the following possible combinations;
The number of ways of selecting the first number = 1 way, the number is 4 to make the value less than 500,000
The number of ways of selecting the second number = 3 ways
The number of ways of selecting the third number = 1 way, the number is 7
The number of ways of selecting the fourth number = 2 ways as there are only two numbers left after filling the second place digit
The number of ways of selecting the fifth number = 1 way, the number is 2
The number of ways of selecting the sixth number = 1 ways
The total number of possible number combinations = 3×2×1 = 6 possible numbers, which are;
487920 or 497820 or 407829 or 407928 or 487029 or 497028
Therefore, 2 out of the numbers are less than 480,000, the remaining 4 possible numbers are larger than 480,000.
For each question, draw a figure. Label the information on the figure. Write an equation that solves the
problem. Find the two answers requested. On AC, B is between A and C. For each question, find x and AB.
10. AB = 2x + 5, AC= 10x + 2. BC= 4x + 9.
11. AB = 3x, BC =x-6, AC = 8x - 14
Answers
Answer:
See attachment for the figures drawn for each question.
10. x = 3; AB = 11
11. x = 2; AB = 6
Step-by-step explanation:
10. AC = 10x + 2
AB = 2x + 5
BC = 4x + 9
AB + BC = AC (segment addition postulate)
(2x + 5) + (4x + 9) = 10x + 2 (substitution)
The equation above is what we would use to solve the problem as follows:
2x + 5 + 4x + 9 = 10x + 2
Combine like terms
6x + 14 = 10x + 2
6x - 10x = -14 + 2
-4x = -12
Divide both sides by -4
x = 3
AB = 2x + 5
Plug in the value of x
AB = 2(3) + 5 = 6 + 5
AB = 11
11. AB = 3x
BC = x - 6
AC = 8x - 14
AB + BC = AC (segment addition theorem)
3x + (x - 6) = 8x - 14 (substitution)
Use the equation to solve for x as follows:
3x + x - 6 = 8x - 14
Collect like terms
4x - 6 = 8x - 14
4x - 8x = 6 - 14
-4x = -8
x = 2 (dividing both sides by -4)
AB = 3x
AB = 3(2)
AB = 6
What are the steps to solving the inequality 3b + 8 2 14?
O Subtract 8 from both sides of the inequality. Divide both sides of the inequality by 3.
O Subtract 8 from both sides of the inequality. Change the direction of the inequality. Divide both sides of the
inequality by 3.
O Divide both sides of the inequality by 3. Subtract 8 from both sides of the inequality.
O Divide both sides of the inequality by 3. Change the direction of the inequality. Subtract 8 from both sides of the
inequality.
Answers
Answer:
Subtract 8 from both sides of the inequality. Divide both sides of the inequality by 3.
Step-by-step explanation:
The given inequality is 3b + 8 ≥ 14
We need to solve the given inequality
Step 1.
Subtract 8 to the both sides of the inequality
3b + 8 - 8 ≥ 14 -8
3b ≥ 6
Dividing both sides by 3
b ≥ 2
The value of b is greater than and equal to 2.
Hence, the correct option is (a).
This figure is a square, with side lengths as shown. What are the perimeter and the area of the square?
Answers
Answer:
Step-by-step explanation:
Parameters:
As square has all equal sides in his shape.
then length and width will be equal.
parameters will be
LENGTH,LENGTH,WIDTH,WIDTH
Area:
area of square is known as A= a^2
a= parameter of square (as all parameters are equal,you put one parameter to find area of square)
The required perimeter of the square is 4 times side and the area of the square is ( side ) ².
Given that,
To determine the perimeter and the area of the square.
What is a square?
A square is defined as it is a four-sided polygon, having angles of 90° on its vertices, and the length of all four sides is equal.
What is the perimeter?Perimeter is the measure of the figure on its circumference or it is overall boundary length of the figures.
Here,
The perimeter of the square is given as the sum of all sides,
= side + side + side + side
= 4 x side
The area of the square is multiplied of two adjacent side
= side x side
= ( side )²
Thus, the required perimeter of the square is 4 times side and the area of the square is (side)².
Learn more about squares here:
https://brainly.com/question/14979907
#SPJ2
The Moon is 4,530,000,000 years in scientific notation
Answers
Answer:
4.53 * 10⁹
Step-by-step explanation:
4530000000 = 4.53 * 10⁹
There are three consecutive integers. Four times the smallest integer is equal to six more than three times the smallest integer. What is the smallest of the 3 integers?
Answers
Let the smallest integer equal x - 1, the next one equal x, and the last one equal x + 1.
4(x-1) = 3(x-1) + 6
x-1 = 5
x = 6
The smallest integer is x - 1, which is equal to 5. Thus, the smallest of the three integers is 5.
How many integers satisfy the inequality (x 2 – 4)(x 2 – 10) < 0?
none
two
four
an infinite number
Answers
Answer:
4
Step-by-step explanation:
solution: −√10<x<−2 or 2<x<√10
√10=3.16
-3,-2,2,3
The 2 and -2 are the integers satisfy the inequality.
It is required to find the number of integers .
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
Given:
For (x²– 4)< 0;
x²<4
By taking the square root of both sides we have,
√x²<√4
x < ±2
x<2 and x<-2
Also,
x²<10
By taking the square root of both sides we get,
√x²<±√10
x < ±√10
x<√10 and x<-√10
The √10 is not an integer but an irrational number. An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
So we can't take the integer of ±√10.
Therefore, the 2 and -2 are the integers satisfy the inequality.
Learn more details about inequality here:
https://brainly.com/question/20383699
#SPJ2
What are the coordinates of point S?
Answers
Answer:
The coordinates of S is (-2,2)
6x-3 = 5x-5 any got a homie
Answers
Answer:
x= -2
Step-by-step explanation:
6x-3 = 5x-5
6x-5x=-5+3
x= -2
See my other articles for quiz and assignment in my site.
Just copy and paste "learningandassignments diy4pro" to google search engine.
Hope it helps.
I hope this helps! Here is the work! I did it on my computer!
the smallest number by which 28 should be multiplied so as to get a perfect square is
Answers
Answer:
7.
Step-by-step explanation:
28 = 2^2 * 7.
To multiply 28 to get a perfect square, we can multiply it by 7 to get 2^2 * 7^2, which is 14 squared.
To estimate your average monthly salary, divide your yearly salary, y, by the
number of months in a year. Write and solve an equation to determine your
yearly salary when your average monthly salary is $4560.
Answers
Answer:
$54,720
Step-by-step explanation:
If you make $4560 a month and there are 12 months in a year the equation would be...
$4560 * 12 = yearly salary
4560 * 12 = 54720
So your yearly salary is $54,720
Hope this helps!
Asia has $15.45 to buy chips for a party. Each bag costs $2.13. How many can she buy?
Answers
Answer:
She can buy 7 bags of chips
Step-by-step explanation:
just take 15.45 and divide it by 2.13
Answer:
7
Step-by-step explanation:
If you divide both numbers you will get 7.253. When it's a decimal, you will round down, which gives you the answer of 7
Exercise #2: Jenna is carrying a bucket that holds 2.5 gallons of water. Water weighs 8.34 pounds
per gallon and the bucket itself weights three-quarters of a pound. What is the total combined
weight of the water and bucket that Jenna is carrying! Show the work that leads to your answer
Answers
Answer:
21.6 Pounds
Step-by-step explanation:
Multiply 2.5 by 8.34 to get 20.85 pounds of water
add the weight of the bucket (.75) to the weight of the water (20.85) to get 21.6 pounds total
Rey baked 144 desserts in 6 1/4 months. Find reys dessert making rate in desserts per month.
Answers
Answer:
23 1/25 desserts per month
find the percent increase from 200 to 240
Answers
Answer:
20%
Step-by-step explanation:
The percentage change can be found from ...
% change = ((new value)/(reference value) -1) × 100%
= (240/200 -1) × 100%
= 0.20 × 100%
= 20%
240 is an increase of 20% from 200.
What is 83/100 simplified?? PLEASE answer quick?
Answers
Answer:
Step-by-step explanation:
83/100 is already simplified. You can not make it smaller.