The difference between 0.2 and 0.2 repeating is that 0.2 is that rational number and 0.2 repeating is the rational number.
What is defined as the rational and irrational numbers?Irrational numbers are real numbers that can't be depicted as a ratio-like fraction, p/q, where q and p are integers. In other words, irrational numbers are real numbers which are not rational numbers.Rational numbers are written in the form p/q, where p and q are any integer and q 0 respectively.Q represents the set of rational numbers. A rational number is one that can be demonstrated as a fraction with both the numerator and denominator being integers.For the two given values;
0.2 is the rational number as it can written in the fraction form as;
0.2 = 2/10
0.2 = 1/5 which is in the p/q form.
For the value of 0.2... repeating is also the rational number as it can be also written in the form of p/q.
0.2... = 0.2 bar is the correct representation.
Therefore, the number 0.2 and 0.2 repeating are the rational numbers.
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20% in fraction form
20/100
That is the answer if u want it simplified it is 1/5
Answer:
20/100 simplified is 1/5
Step-by-step explanation:
it is the fraction form
Laci and leon are saving money to go to an amusement park. laci has $1 more than 4 times the amount of money leon has. together, they have $76. write an equation to determine how much money they have together. 4x 1 = 76 x 4x − 1 = 76 4x − 1 = 76 x 4x 1 = 76
Answer:
Leon has $15 and Laci has $61
Step-by-step explanation:
Let x = the amount Leon has. So 4 times that plus $1 would be 4x+1. Our equation is:
x + (4x+1) = 76
Combine like terms
5x + 1 = 76
Subtract 1 from both sides
5x = 75
Divide both sides by 5
x = 15. This is Leon. Laci is 4(15) +1, or 61.
Please helpppp!!!!!
A tree casts a shadow that is 28 feet long. A person who is 5 feet tall casts a shadow that is 8 feet long. Using similar triangles and proportions find the height x of the tree. Show all your work.
Answer:
Step-by-step explanation:
30 feet.
The cost per unit of an item is called what?
Answer:
The cost per unit of an item is called unit cost
The maximum speed, in miles per
hour, of a cheetah is 18 more than 3 times
If the maximum speed of a cheetah is
the maximum speed of a hippopotamus.
75 miles per hour, which equation could be
used to find the maximum speed of a
hippopotamus h? (Lesson 1-2)
A. h= 3(75) + 18
B. 75=3h
C. 75 = 3h + 18
D. 18 + 75 = 3h
The equation could be used to find the maximum speed of a hippopotamus h is C. 75 = 3h + 18
The question has to do with linear equation
What is a linear equation?A linear equation is a mathematical expression in which the highest power of the unknown is 1.
How to find the equation for the maximum speed of the hippopotamusLet
x = speed of cheetah and h = speed of hippopotamusGiven that the maximum speed, in miles per hour, of a cheetah is 18 more than 3 times the maximum speed of the hippopotamus
Now, since the maximum speed of the hippopotamus is h, 3 times the maximum speed of the hippopotamus is 3h.
Since the cheetah is 18 more than 3 times the maximum speed of the hippopotamus, we have that
x = 3h + 18
Substituting x = 75 into the equation, we have
75 = 3h + 18
So, the equation could be used to find the maximum speed of a hippopotamus h is C. 75 = 3h + 18
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One year on Venus is equivalent to 224.7 days on Earth. How many days on Earth, in decimal from, are equivalent to 9 ½ years on Venus?
By using simple rule of three, a period of 9.5 years on Venus is equivalent to 2134.65 terrestrial days.
How many terrestrial days are equivalent time in Venus?
One year on Earth is equivalent to 365.3 days and one year on Venus is equivalent to 224.7 days, the equivalent terrestrial time of 9.5 years on Venus is found by simple rule of three:
x = 9.5 yr × (224.7 days / 1 yr)
x = 2134.65 days
A period of 9.5 years on Venus is equivalent to 2134.65 terrestrial days.
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Can someone please help me with thiss
Answer:
3 over 4 is the slope
Step-by-step explanation:
y2 - y1 over x2 - x1 is how you get the slope. To get those points you simply pick two points, it doesn’t matter which 2.
Answer:
slope = [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 9, 4) and (x₂, y₂ ) = (7, 16) ← 2 ordered pairs from the table
m = [tex]\frac{16-4}{7-(-9)}[/tex] = [tex]\frac{12}{7+9}[/tex] = [tex]\frac{12}{16}[/tex] = [tex]\frac{3}{4}[/tex]
write an equation for the line in slope-intercept form
Answer:
y = 2x + 3
Step-by-step explanation:
i gotchu
25*371-371*16+371
can someone help me please?
Answer:
It would be 3710.
Step-by-step explanation:
A bag contains 25 balls 20 of which are blue what percentage of balls are not blue
Answer:
20%
Step-by-step explanation:
20/25 = blue
This means 5/25 of the balls in the bag are NOT blue
(25-20 = 5)
We need to convert 5/25 to a percentage
[tex]\dfrac{5}{25} = \dfrac{5\times4}{25\times4}=\dfrac{20}{100}[/tex]
% = per cent
"per" means "out of"
"cent" means "one hundred"
so
20/100 = 20%
A pet shop sold 20 rabbits for $192. some of the rabbits sold for $7 each and the rest for $11 each. how many rabbits were sold at each price?
There are 7 rabbits sold for $7 and 13 rabbits sold for $11.
Substitution method:
In the substitution method, we must substitute the value of one given variable in terms of the other given variable and find the solution.
Given,
A pet shop sold 20 rabbits for $192.
Some of the rabbits sold for $7 each and the rest for $11 each.
Here we need to find the number of rabbits sold in each case.
Let us consider x be the number of rabbits sold for $7 and y be the number of rabbits sold for $11.
We know that, the total number of rabbits sold = 20.
So, it can be written as,
=> x + y = 20
Here we have to rewritten this equation as,
=> x = 20 - y ----------------------(1)
We know that, total amount for sold rabbits = 192
So, it can be written as,
=> 7x + 11y = 192 -----------------------(2)
Apply the value of x to equation (2),
Then we get,
=> 7(20 - y) + 11y = 192
=> 140 - 7y + 11y = 192
=> 4y + 140 = 192
=> 4y = 192 - 140
=> 4y = 52
=> y = 52/4
=> y = 13.
Apply the value of y on the equation (1),
Then we get,
=> x = 20 - y
=> x = 20 - 13
=> x = 7
Therefore, there are 7 $7 rabbits and 13 $11 rabbits are sold.
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p+17=9 i need help ASAP
Answer:
P = -8
Step-by-step explanation:
13,804 divided by 14
Answer:986
Explanation? Calculator;)
Answer: 986
Step-by-step explanation? It’s easier to use a calculator.
Solve the equation 4e - 5 + 2e = e + 3 - 2e
for e.
Answer:e=8/7=1.143
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
4*e-5+2*e-(e+3-2*e)=0
Add 8 to both sides of the equation :
7e = 8
Divide both sides of the equation by 7:
e = 8/7 = 1.143
And then you get
Divide both sides of the equation by 7:
e = 8/7 = 1.143
Answer:
4*e-5+2*e-(e+3-2*e)=0
Add 8 to both sides of the equation :
7e = 8
Divide both sides of the equation by 7:
e = 8/7 = 1.143
And then you get
Divide both sides of the equation by 7:
e = 8/7 = 1.143
Step-by-step explanation:
What is 90.5-7.83? Please show your work too! Thanks.
RS=6y+3,ST=5y+9 and RT=78
What is are and ST
Solve for X
[tex]\log _ { 3 } x = 9 \log _ { x } 3[/tex]
pls gv step by step explaination
Answer:
[tex]x=27, \quad x= \dfrac{1}{27}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{3.7 cm}\underline{Logs Laws}\\\\$\log_ba=\dfrac{\log_ca}{\log_cb}$\\\\\\$\log_ab=c \iff a^c=b$\\\end{minipage}}[/tex]
Given equation:
[tex]\log_3x=9\log_x3[/tex]
Change the base of 9logₓ3 to base 3:
[tex]\begin{aligned}\implies \log_3x & =9\log_x3\\\\& =\dfrac{9\log_33}{\log_3x}\\\\&=\dfrac{9(1)}{\log_3x}\\\\&=\dfrac{9}{\log_3x}\end{aligned}[/tex]
Therefore:
[tex]\implies \log_3x=\dfrac{9}{\log_3x}[/tex]
[tex]\textsf{Let }\log_3x=u:[/tex]
[tex]\implies u=\dfrac{9}{u}[/tex]
[tex]\implies u^2=9[/tex]
[tex]\implies u=\pm3[/tex]
[tex]\textsf{Substitute back in }u=\log_3x:[/tex]
[tex]\implies \log_3x=\pm3[/tex]
Case 1
[tex]\implies \log_3x=3[/tex]
[tex]\implies 3^3=x[/tex]
[tex]\implies x=27[/tex]
Case 2
[tex]\implies \log_3x=-3[/tex]
[tex]\implies 3^{-3}=x[/tex]
[tex]\implies \dfrac{1}{3^3}=x[/tex]
[tex]\implies x=\dfrac{1}{27}[/tex]
Answer: x=3 x=1/27
Step-by-step explanation:
[tex]log_3x=9log_x3\\[/tex]
The area of acceptable values:
[tex]x > 0\ \ \ \ x\neq 1\\Hence,\\x\in(0,1)U(1,+\infty)[/tex]
Solution:
[tex]\displaystyle\\log_3x=\frac{9}{log_3x} \ \ \ \ \ \boxed{ log_ab=\frac{1}{log_ba} }\\\\Multiply\ both\ parts\ of\ the\ equation\ by\ log_3x :\\\\log^2_3x=9\\log^2_3x=3^2\\ log_3x=б3\\\\log_3x=3\\\\x=3^3\\x=3*3*3\\x=27\\\\\\log_3x=-3\\x=3^{-3}\\\displaystyle\\x=(\frac{1}{3})^3\\ x=\frac{1}{3}*\frac{1}{3}*\frac{1}{3} \\ x=\frac{1}{27}[/tex]
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 45 pounds and each large box of paper weighs 75 pounds. There were 3 more small boxes shipped than large boxes and the total weight of all boxes was 1455 pounds. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system
Answer: The equations are:
X+3=Y;
45X + 75Y = 1455 ;
The variables used are X and Y specifying number of small and large boxes
Step-by-step explanation:
Let X be the number of small boxes
Let Y be the number of big boxes
The first equation is: X+3=Y; ( Since there were 3 more small boxes shipped than large boxes )
The second equation is: 45X + 75Y = 1455 ( this is because the small box weighs 45 pounds and big box weighs 75 pounds. The total weight of the small boxes is 45 times the weight of each individual box. And the total weight of the second boxes is equal to 75Y.)
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Answer:
Step-by-step explanation:
The variables used are A and B specifying number of small and large boxes
Let the number of small box is A
Let the number of large box is B
The first equation is: A+3=B;
( Since there were 3 more small boxes shipped than large boxes )
The second equation is: 45A + 75B = 1455 ( this is because the small box weighs 45 pounds and large box weighs 75 pounds. The total weight of the small boxes is 45 times the weight of each box. And the total weight of the second boxes is equal to 75B.)
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Find the centroid of the region in the first quadrant bounded by the given curves. y = x4, x = y4
The given bounded region is the set
[tex]R = \left\{(x,y) ~:~ 0 \le x \le 1 \text{ and } x^4 \le y \le x^{1/4} \right\}[/tex]
assuming the curves are [tex]y=x^4[/tex] and [tex]x=y^4\implies y=x^{1/4}[/tex] (since [tex]x>0[/tex] in the first quadrant).
The coordinates of the centroid are [tex](\bar x, \bar y)[/tex] where [tex]\bar x[/tex] and [tex]\bar y[/tex] are the average values of [tex]x[/tex] and [tex]y[/tex], respectively, over the region [tex]R[/tex]. These are given by the ratios
[tex]\bar x = \dfrac{\displaystyle \iint_R x \, dA}{\displaystyle \iint_R dA} \text{ and } \bar y = \dfrac{\displaystyle \iint_R y\,dA}{\displaystyle \iint_R dA}[/tex]
Compute the area of [tex]R[/tex].
[tex]\displaystyle \iint_R dA = \int_0^1 \int_{x^4}^{x^{1/4}} dy \, dx \\\\ ~~~~~~~~ = \int_0^1 \left(x^{1/4} - x^4\right) \, dx \\\\ ~~~~~~~~ = \frac45 - \frac15 = \frac35[/tex]
Integrate [tex]x[/tex] and [tex]y[/tex] over [tex]R[/tex].
[tex]\displaystyle \iint_R x \, dA = \int_0^1 \int_{x^4}^{x^{1/4}} x \, dy \, dx \\\\ ~~~~~~~~ = \int_0^1 x \left(x^{1/4} - x^4\right) \, dx \\\\ ~~~~~~~~ = \int_0^1 \left(x^{5/4} - x^5\right) \, dx \\\\ ~~~~~~~~ = \frac49 - \frac16 = \frac5{18}[/tex]
[tex]\displaystyle \iint_R y \, dA = \int_0^1 \int_{x^4}^{x^{1/4}} y \, dy \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^1 \left((x^{1/4})^2 - (x^4)^2\right) \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^1 \left(x^{1/2} - x^8\right) \, dx \\\\ ~~~~~~~~ = \frac12 \left(\frac23 - \frac19\right) = \frac5{18}[/tex]
Then the centroid's coordinates are
[tex]\bar x = \dfrac{\frac5{18}}{\frac35} = \boxed{\frac{25}{54}} \approx 0.463[/tex]
[tex]\bar y = \dfrac{\frac5{18}}{\frac35} = \boxed{\frac{25}{54}}[/tex]
Someone help me with this question
Answer:
Angle Bisector I believe
Step-by-step explanation:
Apologies if I am wrong
a group of students is given a 10 by 10 grid to cut into individual unit squares. the challenge is to create two squares using all of the unit squares. their teacher states that after the two new squares are formed, one should have a side length two units greater than the other. which equation represents x, the side length of the greater square? x2 (x – 2)2
The correct option is C. x² + (x – 2)² = 100.
The equation which depicts x, the side length of the greater square is x² + (x – 2)² = 100.
What is square?In geometry, a square is a plane figure with 4 equal sides as well as 4 right (90°) angles. A square is a subset of a rectangle (an equilateral rectangle) and a subset of a parallelogram (an equilateral & equiangular one).
Now, as per the question;
Let x be the larger square's side length. Because it is two units larger than the relatively small square, the smaller square's side length would be (x-2).The side length squared, or the quantity of unit squares contained in the larger square, would give the quantity of unit squares within the larger square or x².The side length squared, or the number of unit squares in the smaller square, would give the number of unit squares within the smaller square or (x-2)².These total the quantity of unit squares in a 10 by 10 square, or 10² = 100.This is given by relation shown by expression;
x² + (x-2)² = 100
Therefore, the equation which represents x, the side length of the greater square is x² + (x-2)² = 100.
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The complete question is-
A group of students is given a 10 by 10 grid to cut into individual unit squares. The challenge is to create two squares using all of the unit squares. Their teacher states that after the two new squares are formed, one should have a side length two units greater than the other.
Which equation represents x, the side length of the greater square?
A. x² + (x – 2)² = 10
B. x² + 2x² = 10
C. x² + (x – 2)² = 100
D. x² + 2x² = 100
What is the equation of the line that is parallel to the given line and passes through the point (–2, 2)?
A. y=1/5x+4
B. y=1/5x+12/5
C. y=-5x+4
D. y=-5x+12/5
The slope of the line shown is 1/5, and being parallel means having the same slope. So it’s either a or b.
Next, you plug in (-2, 2) into y=1/5x+b to find b.
Solving you get: 2=1/5 * -2 +b
2=-2/5+b
B=2 2/5
12/5 = 2 2/5
So the answer is b.
Hope this helps!
Please help loll and show your work if you can
First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are used when a linear equation contains two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.
10) -6(-5+r) = 102
30 -6r =102
-6r = 72
r = -12
11) -1 = x - 4 +4
x =-1
12) 0 = -6x -2x
-8x = 0
x= 0
13)5n+ 4n =9
n =1
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solve 15 over x+2 equals 3 over 4
The solution to the expression is x= 18
How to calculate the expression ?15 over x=2 equals 3 over 4 can be written as follows
15/x+2 = 3/4
Cross multiply both sides
15×4= 3(x+2)
60= 3x +6
collect the like terms
3x= 60-6
3x= 54
divide both sides by the coefficient of x which is 3
3x/3 = 54/3
x= 18
Hence the value of x in the expression is 18
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Part 1: Mapping Diagrams
Look at the mapping diagrams below, which represent two different relations. The relation on the
left is a function since each value in the blue set is paired with one value in the yellow set. For
the function on the left, the domain is {0, 1, 2, 3) and the range is {0, 1.69, 3.38, 5.07).
1. Is the relation on the right a function? Explain.
20
70
-60
3
-6
2
5
Based on the definition of a function,
1. The relation on the right is not a function.
2. Domain: {20, 70, -60}
Range: {3, -6, 2, 5}
What is a Function?A relation that is defined as a function has each domain value that is assigned to only one possible range value, in such a way that, each of the domain element cannot have two different range element that corresponds to it.
1. The relation on the right has a domain element, -60, which corresponds to two different range element, -6 and 2.
Therefore, the relation on the right is not a function.
2. The domain of the relation that is not a function is: {20, 70, -60}
The range of the relation that is not a function is: {3, -6, 2, 5}
In summary, based on the definition of a function,
1. The relation on the right is not a function.
2. Domain: {20, 70, -60}
Range: {3, -6, 2, 5}
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BELL RINGER # 6
If the function f is defined by f(x) = 3x + 4,
then 2 f(x) + 4 =
(A) 5x + 4
(B) 5x + 8
(C) 6x +4
(D) 6x+8
(E) 6x + 12
Answer:
(E) 6x+12
relations: A relation R is the subset of the cartesian product of X x Y, where X and Y are two non-empty elements. It is derived by stating the relationship between the first element and second element of the ordered pair of X × Y. The set of all primary elements of the ordered pairs is called a domain of R and the set of all second elements of the ordered pairs is called a range of R.
functions: A relation ‘f’ is said to be a function, if every element of a non-empty set X, has only one image or range to a non-empty set Y.
f(x) = 3x + 4
2 * f(x) + 4 = (2 × f(x)) + 4
From above equation
= (2 × (3x + 4)) + 4
= (2 × 3x) + (2 × 4) + 4
= 6x + 8 + 4
= 6x + 12
Therefore, the value of 2f(x) + 4 is ′6x + 12′.
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I need help with this its still confusing
Answer:
64 and 13 I hope this helps
Step-by-step explanation:
(2x6)^3/2 in simplest form
(2x6)^3/2 in it's simplest form is equal to 41.56. See the computation below.
What is the simplification of the above expression?Using BODMAS, we say
(2 x 6) = 12
12^(3/2)
= 41.5692
[tex]$\approx$[/tex] 41.56
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Help, please.
I’m not sure how to do it, but it’s part of a puzzle.
Answer:
x = 14 y = 59
Step-by-step explanation:
the angle (5x - 11) is equal to the angle (3x + 17) and 3x+ 17 is equal to y
5x - 11 = 3x + 17
5x - 3x = 17 + 11
2x = 28
x = 28/2
x = 14
3x+17 = y
3(14) + 17 = y
y = 59
Step-by-step explanation:
Fact 1: Alternate angles are equal.
Angles, (5x-11)° and (3x+17)° are ALTERNATE angles and so,
(5x-11)° = (3x+17)°
5x - 3x = 17 + 11
2x = 28
x = 28 ÷ 2
x = 14
NB: x does NOT have the degree sign because it's NOT an angle on its own, but rather within the bracket/part of the calculation to get the angle degree.
Fact 2: Opposite angles are equal.
Y° and (3x+17)° are OPPOSITE angles
y = (3x+17)°
y = (3x14) + 17
y= 42 + 17
y = 59°
Hope this helps!
The larger of two numbers is 17 more than the smaller number. The sum of the two numbers is 71.
Answer:
The smaller number is 27 and the larger number is 44
Step-by-step explanation:
Let x = the larger number
Let y = the smaller number
x + y = 71
x = y + 17 Substitute in y + 17 for x in the first equation.
x + y = 71
y +17 + y = 71 Combine the y's.
2y + 17 = 71 Subtract 17 from both sides of the equation
2y = 54 Divide both sides of the equation by 2
y = 27. Plug 27 in for y for either of the two original equation to find x
x + y = 71
x + 27 = 71 Subtract 27 from both sides of the equation
x = 44