Without simplifying, select all the expressions that represent a rational number. Group of answer choices LaTeX: 4\frac{2}{3}+\frac{\sqrt{3}}{9} 4 2 3 + 3 9 4 2 3 + 3 9 4 2 3 + 3 9 LaTeX: 4\frac{2}{3}\times\frac{8}{\sqrt{3}} 4 2 3 × 8 3 4 2 3 × 8 3 4 2 3 × 8 3 LaTeX: 4\frac{2}{3}-\frac{\sqrt{4}}{8} 4 2 3 − 4 8 4 2 3 − 4 8 4 2 3 − 4 8 LaTeX: 4\frac{2}{3}\times\frac{\sqrt{3}}{9} 4 2 3 × 3 9 4 2 3 × 3 9 4 2 3 × 3 9 LaTeX: 4\frac{2}{3}\div\frac{\sqrt{4}}{8}
Answer:
Option C.
Step-by-step explanation:
We know the following properties,
1. Product of an irrational number and a non-zero rational number is always an irrational number.
2. Sum of a rational and an irrational number is always an irrational number.
3. Sum or products of rational numbers are always a rational number.
In option A,
[tex]4\frac{2}{3}+\frac{\sqrt{3}}{9}[/tex]
Here, [tex]\sqrt{3}[/tex] is an irrational number.
[tex]\frac{\sqrt{3}}{9}[/tex] is an irrational number using property 1.
[tex]4\frac{2}{3}+\frac{\sqrt{3}}{9}[/tex] is an irrational number using property 2.
So, using the above properties we can say that this expression represents an irrational number.
Similarly,
In option B,
[tex]4\frac{2}{3}\times\frac{8}{\sqrt{3}}[/tex]
Here, [tex]\sqrt{3}[/tex] is an irrational number. So, using the above properties we can say that this expression represents an irrational number.
In option C,
[tex]4\frac{2}{3}-\frac{\sqrt{4}}{8}[/tex]
Here, [tex]\sqrt{4}=2[/tex], which is a rational number.
So, this expression represents a rational number using property 3.
In option D,
[tex]4\frac{2}{3}\times\frac{\sqrt{3}}{9}[/tex]
Here, [tex]\sqrt{3}[/tex] is an irrational number. So, using the above properties we can say that this expression represents an irrational number.
Therefore, the correct option is C.
For his long distance phone service, Ali pays a 7 monthly fee plus 7 cents per minute. Last month, Ali's long distance bill was 19.53 . For how many minutes was Ali billed?
Answer:
179 minutes
Step-by-step explanation:
From the information given, you know that the total cost of the long distance service is equal to 7 plus the result of multiplying 0.7 for the number of minutes:
Total cost=7+0.07x, where x is the amount of minutes.
Now, you can replace the total cost with 19.53 that is the amount Ali was billed and solve for x:
19.53=7+0.07x
19.53-7=0.07x
12.53=0.07x
x=12.53/0.07
x=179
According to this, the answer is that Ali was billed for 179 minutes.
Ms. Davis' is one less than 7 dozen. Ms. Davis is 7.2 more than 60% of her mother's age. Ms. Davis daughter is 3.5 more than 1/2 her mother's age. How old are ms. Davis, her mom, and her daughter?
Answer:
Ms. Davis=83 years
Her mom=126.33 years
Her daughter=66.67 years
Step-by-step explanation:
Let her mother's age=x
Ms. Davis= 7 dozens - 1
=(7*12)-1
=84-1
= 83 years
Ms. Davis= 7.2 + 60% of x
83=7.2 + .6x
83 - 7.2= .6x
75.8= .6x
Divide both sides by .6
75.8 / .6 = x
126.33 years
Ms. Davis daughter = 3.5 + 1/2 of x
=3.5 + 1/2(126.33)
=3.5 + 126.33 / 2
=3.5 + 63.165
=66.665
Approximately 66. 67 years
plz give correct answer with explanation...correct answer will be marked BRAINLIEST and be followed...
Answer:
x=33
because it lies on the same side of the angle
y= 115
plz mark brainliest
180-155=65 (linear pair)
65+33+x=180 (asp)
98+x=180
x=180-98
x=82
and y...
180-82=98 linear pair
98+36+y=180 asp
134+y=180
y=180-134
y=46
When the digits of two-digit, positive integer M are reversed, the result is the two-digit, positive integer N. If M > N, what is the value of M
Answer:
The value of M is 91.
Step-by-step explanation:
Suppose T represents the tens digit and U represents the units digit.
Then the numbers M and N are:
M = 10T + U
N = 10U + T
Compute the value of M - N as follows:
M - N = 10T + U - 10U - T = 9T - 9U = 9 (T - U)
Given:
M > N
⇒ T - U > 0
⇒ T > U
Also, M - N is a multiple of 9.
Since M - N is a two-digit number, the possible values of M - N are:
18, 27, 36, 45, 54, 63, and 72
The values 81, 90 and 99 would not be considered since:
9 × 9 = 81
9 × 10 = 90
9 × 11 = 99
T - U = 9 (T - U) = 9 , 10 or 11 respectively and the largest difference for T − U we can get is 9 - 0 = 9 - 0 = 9.
Even this would result in N = 9, which is not a 2-digit number.
It is provided that the integer (M - N) has 12 factors.
Of the possible values of M - N the integer with 12 factors is 72.
The factors of 72 are:
1×72
2×36
3×24
4×18
6×12
8×9
So, M - N = 72.
⇒ M - N = 9 (T - U)
72 = 9 × 8
⇒ T - U = 8
And since T > U, the values of T and U are:
T = 9 and U = 1
We cannot use T - U = 8 - 0 = 8, because then N will be not a two-digit number.
So, M = 91 and N = 19 and their difference is 72.
Thus, the value of M is 91.
The calculator has a broken 1 key and broken 7 key ,and a broken plus key .Write at least on way to make each of the following numbers 17,41,71,.
Answer:
20-3
43-2
73-2
Step-by-step explanation:
subtract bro
The total fertility rate (TFR) of a country is the average number of births per woman in that country. In Country W the TFR went from 5.0 in 1995 down to 3.0 in 2005. What is the percent change in the TFR in Country W from 1995 to 2005
Answer:
Decrease in TFR of 40%.
Step-by-step explanation:
Given that:
TFR (Total Fertility Rate) in 1995 = 5
TFR (Total Fertility Rate) in 2005 = 3
To find:
Percentage change in TFR from 1995 to 2005 = ?
Solution:
First of all, let us have a look at the formula for calculating the percentage change in any quantity.
Let p be the old value and
q be the new value.
Then percentage change is given as:
[tex]Percentage\ change = \dfrac{New\ Value - Old\ Value}{Old\ Value} \times 100[/tex]
Here, Old value is 5
New value is 3.
[tex]Percentage\ change = \dfrac{3 - 5}{5} \times 100\\\Rightarrow Percentage\ change = \dfrac{- 2}{5} \times 100\\\Rightarrow Percentage\ change = - 40\%[/tex]
Negative sign means there is a decrease of 40%.
So, Decrease in TFR of 40% is the answer.
What Is a domain of a function?
Answer: a set of all possible inputs for the function.
Step-by-step explanation:
Answer: A domain of a function is all set of inputs that make the function definable.
Step-by-step explanation:
Is y= x/2 + 6 linear or nonlinear
Answer:
It is linear
Step-by-step explanation:
Its linear because y=x/2 + 6 is equal to y = 1/2x+6 which is a linear function
what statement is true about the angles in triangle PQR
Answer:
(C) The sum of the measures of ∠P, ∠Q, and ∠R is 180°
Step-by-step explanation:
All triangles, when their three angles are added up, gets us 180°.
This goes without saying, even with scalene triangles.
Additionally, the angles in squares add up to 360°, the angles in a pentagon add up to 540°.
Hope this helped!
Given that M is the midpoint of VW, what is the length of line segment VM?
Answer:
VM=15
Step-by-step explanation:
4x-1=3x+3 becuase M is the mid point, which makes both sides equal.
Subtract 3x to both sides to get x-1=3.
Add 1 to both sides to get x=4.
Subsitue 4 into the equation 4x-1 to find the lengh of VM.
4(4)-1=
16-1=
15
Using the midpoint concept, it is found that the length of the line segment is of 30 units.
The midpoint divides the line into two segments of equal length, hence [tex]VM = MW[/tex].
Their lengths, as functions of x, are given by:
[tex]VM = 4x - 1[/tex]
[tex]MW = 3x + 3[/tex]
They have the same lengths, hence:
[tex]4x - 1 = 3x + 3[/tex]
[tex]x = 4[/tex]
Hence:
[tex]VM = 4x - 1 = 4(4) - 1 = 16 - 1 = 15[/tex]
[tex]MW = VM = 15[/tex]
The total length is:
[tex]T = VM + MW = 15 + 15 = 30[/tex]
The length of the line segment is of 30 units.
A similar problem is given at https://brainly.com/question/24352869
I need the answer please
Answer:
D - All rational numbers are integers.
Step-by-step explanation:
This is because integers is a subcategory of rational numbers, so there are other rational numbers that aren't integers.
Convert this number expressed in standard form to scientific notation. 28,500,000 1. Move the decimal to create the coefficient: 2.8500000 2. Write in scientific notation: 2.85 × 10x What is the value of x in the scientific notation? x =
Answer:
7
Step-by-step explanation:
We know the decimal place is after all those zeroes. Move the decimal x places to the left, until it is located between the 2 and 8. Since it moved 7 spaces, that is how you know the power of the ten. A faster way of doing this is the power is always one less than the number of digits of the number.
Answer: 7
Step-by-step explanation:
Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint: (9,8) Midpoint (0,9)
Answer:
(-9, 10)
Step-by-step explanation:
The location of the midpoint of a line with endpoint at ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) is given as (x, y). The location of x and y are:
[tex]x = \frac{x_1+x_2}{2},y=\frac{y_1+y_2}{2}[/tex]
Given the endpoint (9,8) and Midpoint (0,9), the location of the other endpoint can be gotten from:
[tex]0=\frac{9+x_2}{2}\\ \\9+x_2=0\\\\x_2=-9\\\\Also,9=\frac{8+y_2}{2}\\ \\8+y_2=18\\\\y_2=18-8\\\\y_2=10[/tex]
Hence the endpoint is at (x2, y2) which is at (-9, 10)
A store in Wildgrove purchased an antique pull toy at a cost of $890 and marked it up 200%. Later on, Jeffrey bought the antique pull toy. If the sales tax in Wildgrove is 10%, how much did he pay in all?
Answer: Jeffery paid $ 2937 in all.
Step-by-step explanation:
Given: The cost of antique pull = $890
Mark up percentage = 200%
New price = (cost) + (Mark up percentage) x (cost)
[tex]=\$( 890+\dfrac{200}{100}\times890)\\\\=\$( 890+2(890))\\\\=\$2670[/tex]
After a tax of 10% , the amount needs to be paid = New price + 10% of New price
[tex]=\$(2670+\dfrac{10}{100}\times2670)=\$(2670+267)\\\\=\$2937[/tex]
Hence, Jeffery paid $ 2937 in all.
Write yes if the following polygons are regular, and no if they’re not.
Answer:
a. yes
b. no
c. yes
d. yes
e. yes
f. no
Step-by-step explanation:
a regular polygon must be equiangular (all angles are same) and equilateral (all sides are same)
A. equilateral triangle, regular
B. is a rectangle and the sides of rectangle are not all equal, thus, not regular
C. octagon, regular
D. flipped pentagon, regular
E. square, regular
F. not normal pentagon, not regular
Answer:
a. yes
b. no
c. yes
d. yes
e. yes
f. no
Step-by-step explanation:
a regular polygon must be equiangular (all angles are same) and equilateral (all sides are same)
A. equilateral triangle, regular
B. is a rectangle and the sides of rectangle are not all equal, thus, not regular
C. octagon, regular
D. flipped pentagon, regular
E. square, regular
F. not normal pentagon, not regular
Nate has written 4 paragraphs of an essay for his English class so far. He can write a paragraph
2
every 3 of an hour. Write an expression for the number of paragraphs in Nate's essay after h,
hours.
3h * 2
three hours every two paragraph
Write an expression for the quotient of b divided by the difference of two minus three.
Answer:
b/(2-3)
Step-by-step explanation:
The expression for the quotient of b divided by the difference of two minus three is q = b / (2 - 3) and can be simplified as q = -b.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.
Given:
The quotient of b divided by the difference of two minus three,
The expression for the above statement can be written as,
Assume the quotient is q then,
q = b / (2 - 3)
The denominator can be simplified as,
q = b / (-1)
q = -b
To know more about the expression:
https://brainly.com/question/13947055
#SPJ2
Select the correct answer. Solve for x. (x - 4)(x - 4) = 0 A. -16 B. -4 C. 4 D. 16
Answer:
C. 4
Step-by-step explanation:
To solve, set each parenthesis equal to the opposite side (0 in this case).
(x - 4)(x - 4) = 0
x - 4 = 0
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Add 4 to both sides:
x - 4 (+4) = 0 (+4)
x = 0 + 4
x = 4
Do the same for the other parenthesis:
x - 4 = 0
x - 4 (+4) = 0 (+4)
x = 0 + 4
x = 4
C. 4 is your answer.
~
Answer:
Hey there!
(x-4)(x-4)=0
(x-4)^2=0
x-4=0
x=4
The correct answer would be C.
Let me know if this helps :)
About 1.15 million people live in a circular region with a population density of about 18,075 people per square kilometer.Find the radius of the region
Answer:
radius is 4.5 km
Step-by-step explanation:
Given :
Total number of people living in the area = 1.15 million = 1150000
Population density = 18075 people per sq kilometer
To find:
Radius of region = ?
Solution:
Population density of a region is defined as the ratio of total population divided by the area of the region.
Area here is circular. Let the radius be = r
Area of circle is given as [tex]\pi r^2[/tex]
Formula:
[tex]Population\ Density = \dfrac{Total\ population}{\pi r^2}[/tex]
Putting the values:
[tex]18075 = \dfrac{1150000}{\pi r^2}\\\Rightarrow r^2 = \dfrac{1150000}{18075\pi }\\\Rightarrow r^2 = \dfrac{63.62}{\pi }\\\Rightarrow r^2 = 20.26\\\Rightarrow \bold{r=4.5\ km}[/tex]
Therefore, radius is 4.5 km.
If US = 14, find the value of x
Answer:
4-6+2x=14
2x=14+6-4
2x=16
x=8
Step-by-step explanation:
Answer:
Step-by-step explanation:this is easy just find x and times it by 2 and then it will equal 14 so the awser is 7
The 2017 population of California was 39536653 and of Arizona was 7016270. Compute and compare the rate of pedestrian fatalities per 100,000 residents.
Answer:
The pedestrian fatality rate for California per 100,000 residents would be;
= (858/39,536,653) * 100,000
= 2.17 people per 100,000
In Arizona that figure is;
= (216/7,016,270) * 100,000
= 3.08 people per 100,000
This shows that even though California has a higher number of pedestrian fatalities in absolute terms, when this figure is made relative to population, Arizona has more pedestrian fatalities.
Question is down below
Answer:
B
Step-by-step explanation:
p(x) = x² - 2√2x + 1
p(2√2) = (2√2)² - 2√2*2√2 + 1
=2²*(√2)² - 2*2*√2*√2 + 1
= 4 *2 - 4*2 + 1
= 8 - 8 + 1
= 1
Answer:
B
Step-by-step explanation:
Given
p(x) = x² - 2[tex]\sqrt{2}[/tex] x + 1, then
p(2[tex]\sqrt{2}[/tex] )= (2[tex]\sqrt{2}[/tex] )² - 2[tex]\sqrt{2}[/tex](2[tex]\sqrt{2}[/tex] ) + 1 = 8 - 8 + 1 = 1 → B
A golfer recorded the following scores for each of four rounds of golf: 86, 81, 87, 82. The mean of the scores is 84. What is the sum of the squared deviations of the scores from the mean?
Answer:
26
Step-by-step explanation:
Subtract the mean (84) from each of the four scores, obtaining
2, -3, 3, - 2
These are the "deviations."
Next, square each of these four deviations, obtaining
(2)^2 = 4, and:
(-3)^2 = 9, and:
(3)^2 = 9, and:
(-2)^2 = 4
Then the sum of the squared deviations of the scores from the mean is 26.
1. 2.5x + 100 = 600
2. 10 = 2x - 4
3. 2x + 5 = 30
Answer:
1) 200 2) 7 3) 12.5
Step-by-step explanation:
For god's sake, use a calculator
A restuarant bill is $35.50. How much EXTRA money should you leave if you want to add a %20 tip?
Answer: $ 7.20
Step-by-step explanation:
Multiply the cost ( 35.50) by 20% or 0.20 and you get your answer ( 7.20 ). Hope this helps!
Bob's Bike Shack charges a set fee of $6, plus $4 per hour, to rent a bike. If your total bill is $30, how many hours did you rent the bike for?
20
Step-by-step explanation:
30-6=24-4=20 that how you find your a answer
Classify each of the following numbers as real, whole, integer, rational or irrational. Some numbers will have more than one classification. 1. -98 2. 1.98 3. 1270 4. 1,232,323
Q is between P and R. PR=145,PQ=8x & QR=11x-7. What is the value of QR?
Answer:
QR = 81
Step-by-step explanation:
PR = 145
= PQ + QR
= (8x) + (11x - 7)
8x + 11x - 7 = 145
19x = 145 + 7
19x = 152
x = 8
substitute x=8 into QR:
11(8) - 7 = 81
If 1/4 in. represents 1 ft. what distances are represented by lines of the following lengths: 2 in., 5 in., 1 1/2 in., 2 2/3 in., 4 7/8 in.?
Answer:
Step-by-step explanation:
Make q clear
Answer:
2 > 8
5 > 20
1.5 > 6
2 2/3 > 10.667
4 7/8 > 19.5
Step-by-step explanation:
(Use cross multiplication or algebra to solve)