determine whether the sum of two values is a rational number or an irrational number.
Answers
Answer:
1). Rational
2). Irrational
3). Rational
4). Rational
5). Irrational
Step-by-step explanation:
To solve this question we should follow the rule,
"Addition of rational and an irrational number is an irrational number."
1). [tex]\sqrt{16}=4[/tex] (rational number)
[tex]-\frac{21}{5}[/tex] (negative rational number)
[tex]\sqrt{16}-\frac{21}{5}=4-\frac{21}{5}[/tex]
[tex]=-\frac{1}{5}[/tex] [rational number]
2). π → (Irrational number)
24 → (rational number)
π + 24 → (Irrational number)
Since addition of a rational and an irrational number is an irrational number.
3). [tex]\sqrt{4}[/tex] = 2 (rational number)
5 (rational number)
2 + 5 = 7 (rational number)
4). [tex]\sqrt{36}=6[/tex] (rational number)
[tex]\sqrt[3]{27}=3[/tex] (rational number)
[tex]\sqrt{36}+\sqrt[3]{27}=9[/tex] (rational number)
5). [tex]\frac{3}{4}[/tex] (rational number)
[tex]\sqrt{27}[/tex] → (Irrational number)
[tex]\frac{3}{4}+\sqrt{27}[/tex] → (Irrational number)
Related Questions
Students in the marching band are choosing new colors for the hats and the pants of their
uniforms. For each item, they can choose yellow (Y), green (g), or black (B). Which table
represents the sample space of choosing one color for the hat and one color for the pants?
Answers
Answer:
The sample space table is shown below.
Step-by-step explanation:
It is provided that the students has to select new colors for the hats and the pants of the marching band uniforms.
The color options for each item are:
yellow (Y), green (G), or black (B).
The sample space for the color selection of hats and pants is:
Sample Space
Hats Pants
Y Y
Y G
Y B
G Y
G G
G B
B Y
B G
B B
There are a total of 9 possible selections.
The number of the total possible selections is 9.
What is the combination?
The arrangement of the different things or numbers in a number of ways is called the combination.
It is provided that the students has to select new colors for the hats and the pants of the marching band uniforms.
The colour options for each item are:
yellow (Y), green (G), or black (B).
The sample space for the color selection of hats and pants is:
Sample Space
Hats Pants
Y Y
Y G
Y B
G Y
G G
G B
B Y
B G
B B
There are a total of 9 possible selections.
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If 3x2 - 7y + 6 is subtracted from 4x2 - 3y + 4, the result is
Answers
Answer:
X^2 +4y-2
Step-by-step explanation:
Substraction gives the difference between two points or two positions.
We were told to substraction 4x2 - 3y + 4, from (3x2 - 7y + 6)
Then we can say
(4x2 - 3y + 4) -(3x2 - 7y + 6)
If we open the bracket we have
4x2 - 3y + 4 - 3x2 + 7y - 6
Then if we collect like terms we have
4x2 - 3x2 -3y +7y +4 -6
Then we have
X^2 +4y-2
Hence the substraction between 4x2 - 3y + 4, and (3x2 - 7y + 6)
gives us X^2 +4y-2
What is the equation of a vertical line passing through the point (-4, 7)?
Answers
Answer:
x=-4
Step-by-step explanation:
Since we know that the equation will be x= we will just have to take the x value of the coordinate point and that would be the x so in this case the x is -4 so the equation would be x=-4
4p+6-3 combine like terms to get equivalent expressions
Answers
Answer:
4p+3
Step-by-step explanation:
4p+6+-3
[4p]+[6+-3]
4p+3
What is the greatest common factor of 3x^43x 4 3, x, start superscript, 4, end superscript, 15x^315x 3 15, x, cubed, and 21x^221x 2 21, x, squared?
Answers
Answer:
3x²Step-by-step explanation:
Given three functions 3x⁴, 15x³and 21x², the greatest common factor is the greatest value that can divide through the three functions at the same time.
To get this GCF, let us divide each functions into simplest form
3x⁴ = (3 *x * x) * x * x
15x³ = 5 * (3 * x * x) * x
21x² = 7 * (3 * x * x)
It can be seen that the product in parenthesis is common to the three functions given on expanding them, hence the greatest common factor of the three functions is 3 * x * x = 3x²
what is the polynomial -x^(2)-(1)/(2)+x
Answers
Answer:
trinomial
Step-by-step explanation:
-x² - 1/2 + x
if you are asking for the specific name, it is a trinomial because there are 3 terms.
Is 22+ 32 = 42 a true statement? Explain.
Answers
Solve the triangle. Round your answers to the nearest tenth. A. m∠A=43, m∠B=55, a=16 B. m∠A=48, m∠B=50, a=23 C. m∠A=48, m∠B=50, a=26 D. m∠A=43, m∠B=55, a=20
Answers
Answer:
D. m∠A=43, m∠B=55, a=20
Step-by-step explanation:
Given:
∆ABC,
m<C = 82°
AB = c = 29
AC = b = 24
Required:
m<A, m<C, and a (BC)
SOLUTION:
Find m<B using the law of sines:
[tex] \frac{sin(B)}{b} = \frac{sin(C)}{c} [/tex]
[tex] \frac{sin(B)}{24} = \frac{sin(82)}{29} [/tex]
[tex] sin(B)*29 = sin(82)*24 [/tex]
[tex] \frac{sin(B)*29}{29} = \frac{sin(82)*24}{29} [/tex]
[tex] sin(B) = \frac{sin(82)*24}{29} [/tex]
[tex] sin(B) = 0.8195 [/tex]
[tex] B = sin^{-1}(0.8195) [/tex]
[tex] B = 55.0 [/tex]
m<B = 55°
Find m<A:
m<A = 180 - (82 + 55) => sum of angles in a triangle.
= 180 - 137
m<A = 43°
Find a using the law of sines:
[tex] \frac{a}{sin(A)} = \frac{b}{sin(B)} [/tex]
[tex] \frac{a}{sin(43)43} = \frac{24}{sin(55)} [/tex]
Cross multiply
[tex] a*sin(55) = 25*sin(43) [/tex]
[tex] a = \frac{25*sin(43)}{sin(53)} [/tex]
[tex] a = 20 [/tex] (approximated)
Answer:
20.0
Step-by-step explanation:
I got it correct on founders edtell
Plz plz someone help me out with this
Answers
Answer:
option D
[tex]a_{1}=6561 and a_{n}=\frac{1}{3}a_{n-1}[/tex]
Step-by-step explanation:
[tex]a_{3} = 729\\\\a_{4} = 243\\\\r = \frac{a_{4}}{a_{3}}\\\\r=\frac{243}{729}\\\\r=\frac{1}{3}[/tex]
Recursive rule: Next term is obtained by multiplying (1/3) wiht the previous term
[tex]a_{n}=\frac{1}{3}*a_{n-1}[/tex]
[tex]a_{3} = \frac{1}{3}*a_{2}\\\\\\729 = \frac{1}{3}*a_{2}\\\\\\729*3=a_{2}\\\\a_{2} = 2187\\\\\\[/tex]
[tex]a_{2}=\frac{1}{3}*a_{1}\\\\\\2187=\frac{1}{3}*a_{1}\\\\\\2187*3=a_{1}\\\\a_{1}=6561[/tex]
3. Which of the following equations does not
have a rational solution?
(A) x*x= 2
(B) x*x=1
(C) x*x=0
(D) x+x=0
Answers
Answer:
Equation A doesn't have a rational solution
Step-by-step explanation:
Notice that the solutions for equation A is:
[tex]x^2=2\\x=+/- \sqrt{2}[/tex]
and [tex]\sqrt{2}[/tex] is an irrational number
The other equations have rational solutions:
Equation B: x = 1 and x = -1 are solutions (both rational numbers)
Equation C: x = 0 is the solution (rational number)
Equation D : x = 0 is the solution. (rational number)
Jake's morning run was a distance of 9.3 miles. He ran back and forth on one long straight street. He started at his house and ran to the school 4 miles away. Then he ran to the library, and then he ran back to his house. What are possible distances the library could be from the house?
Answers
Answer: the distances can be 0.65 miles (in the opposite direction to the school) or 4.65 miles (in the same direction as the school)
Step-by-step explanation:
Ok, the data that we have is:
Total distance = 9.3 mi.
The travel is:
House to school = 4 mi.
school to library = A
library to house = B
Now, we have that:
4mi + A + B = 9.3mi.
We have three possibilities:
1) The order of locations is: house, library, school
The travel from: school to library + library to house is equivalent to a travel between the school to the house = 4mi.
Then we have A + B = 4mi
4mi + A + B = 8mi ≠ 9.3mi
Then the library can not be between the house and the school.
2) The order of locations is: house, school, library.
In this case we have that the distance between the library and the house is equal to the distance between the house and the school plus the distance between the school and the library, then:
4mi + A = B.
We can replace this in our original equation:
4mi + A + B = 9.3mi
4mi + A + (4mi + A) = 9.3mi
8mi + 2*A = 9.3mi
2*A = 9.3mi - 8mi = 1.3mi
A = 1.3mi/2 = 0.65mi
Then the distance between the house and the library is:
The 4 miles between the house and the school, plus the 0.65 miles between the school and the library:
Distance = 4mi + 0.65mi. = 4,65mi
3) The third case is when the order of the locations is:
Library, house, school.
Then the distance between the house and the library is equal to the distance between the school and the library minus the distance between the house and the school, this is:
A - 4mi = B
Now we can replace this in our distance equation:
4mi + A + B = 9.3mi
4mi + A + (A - 4mi) = 9.3 mi
2A = 9.3mi
A = 9.3mi/2 = 4.65mi
Then the distance between the house and the library is:
B = A - 4mi = 4.65mi - A = 0.65mi
Then the distance between the house and the library is 0.65 miles in this case.
The amount of money spent at the gas station varies directly with the number of gallons of gas purchased. 12 gallons of gas costs $36.00. How much would 8 gallons of gas cost?
Answers
Answer:
$24.00
Step-by-step explanation:
12 = 36
8 = x
=> Cross multiply
=> 12 * x = 36 * 8
=> 12x = 288
=> 12x / 12 = 288 / 12
=> x = 24
8 gallons of gas costs $24.00.
8 gallons of gas will cost $24.
What are the types of variation or proportion ?There are two types of variations direct variation and inverse variation.
In direct variation between two quantities if one variable increases the other also increases and vice versa.
In inverse variation of two quantities if one variable increases the other variable decreases and vice versa.
In the given question
12 gallons of gas costs $36
∴ 8 gallons of gas will cost (36 × 8)/12 gallons
= $24
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A manufacturer determines that the cost of making a computer component is $4.252525. Write the
repeating decimal cost as a fraction and as a mixed number. The cost written as a fraction is???
Answers
Answer:
4 25/99 is the mixed fraction.
25/99 is the fraction
What is 11/12 divided by 1/3?
Answers
Answer:
11
----
4
Step-by-step explanation:
11 1
--- ÷ ----
12 3
just flip the 1/3 = 3/1 then multiply.
11 3 33
--- x ---- = ----- just simplify if needed
12 1 12
11
therefore -----
4
The math club sells candy bars and drinks during football games. 60 candy bars and 110 drinks will sell for $265. 120 candy bars and 90 drinks will sell for $270. How much does each candy bar sell for?
Answers
Answer:
$0.75 per candy bar
Step-by-step explanation:
For this problem, we simply need to set up a system of equations to find the value of a drink, and the value of a candy bar.
Let x represent the cost of a candy bar, and y represent the cost of a drink.
60x + 110y = 265
120x + 90y = 270
Now let's use the elimination method to solve for one of the variables:
60x + 110y = 265 --> -2 ( 60x + 110y = 265 ) --> -120x + -220y = -530
-120x + -220y = -530
120x + 90y = 270
-130y = -260
y = 2
Now plug the value of y into one of the equations to find the value for x:
60x + 110y = 265
60x + 110 (2) = 265
60x + 220 = 265
60x = 45
x = 45 / 60
x = 0.75
With this, we know that the cost of a candy bar is $0.75 and the cost of drink is $2.00.
Cheers.
−a2 − 3b3 + c2 + 2b3 − c2 if a = 3, b = 2, and c = −3
Answers
Answer:
7
Step-by-step explanation:
a = 3, b=2 and c = -3
● -a^2 - 3b^3 + c^2 + 2b^3 -c^2
● -a^2 - b^3
● -(3)^2 + 2×2^3
● -9 + 16
● 7
Answer:
-35
Step-by-step explanation:
-3^2-3(2^3)-3^2 + 2(2^3)-3^2
A professor wants to divide the remaining 3 4 of the semester evenly into six different units. A. What fraction of the semester should be spent on each unit? B. The professor drops one unit. What fraction of the semester should be spent on each unit?
Answers
Answer:
A. 1/8 of the semester
B. 3/20 of the semester
Step-by-step explanation:
A professor wants to divide the remaining 3/4 of the semester evenly into 6 different units. A. What fraction of the semester should be spent on each unit?
B. The professor drops one unit. What fraction of the semester should be spent on each unit?
Solution
A.
A professor wants to divide the remaining 3/4 of the semester evenly into 6 different units
Total semester=3/4
Total units=6 units
Fraction of the semester that will be spent on each units = 3/4 ÷ 6
=3/4 × 1/6
=3/24
=1/8
1/8 of the semester will be spent on each units
B. If the professor drops one unit
That is 6 units - 1 unit = 5 units
Fraction of the semester that will be spent on each units=3/4 ÷ 5
=3/4 × 1/5
=3/20
The ratio of adults to children on a train in 7:2. There are 245 adults on the train. Find the total number of people on the train?
Answers
Answer:
315 people
Step-by-step explanation:
Using the given ratio, we can figure out the number of children on the train by doing cross multiplication.
Let x = # of children on train.
7/2 = 245/x
7x = 490
x = 70 children
The total number of people = 70 + 245 = 315 people total
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the product of two rational numbers is - 16/9. If one of them is - 4/3 find the other
Answers
Answer:
The other number is 4/3
Step-by-step explanation:
Let the unknown number be x
Translate the equation :
[tex] - \frac{4}{3} \times x = - \frac{16}{9} \\ - \frac{4}{3} x = - \frac{16}{9} \\ [/tex]
Cross multiply
[tex] - 4x \times 9 = 3 \times - 16 \\ - 36x = - 48[/tex]
Divide both sides by -36
[tex] \frac{ - 36x}{ - 36} = \frac{ - 48}{ - 36x} \\ x = \frac{4}{3} [/tex]
Find the x-intercepts of the parabola.
g(x)=−x2−6x−5
Answers
Answer: The x intercepts are -1 and -5 or (-1,0) and ( -5,0)
Step-by-step explanation:
Finding the x intercepts of a parabola is the same as finding the roots of a parabola because the x intercept is when y or g(x) is equal to zero. So set the equation equal zero.
[tex]-x^{2} -6x -5 = 0[/tex] First divide each term by 0 to get the largest degree coefficient to equal 0.
x^2 + 6x +5 = 0 Now find two numbers that their product is 5 and their sum is 6. The numbers 5 and 1 works out because the 5 times 1 is 5 and 5 plus 1 is 6.
Rewrite the whole equation as
x^2 + 1x+5x +5 = 0 Now factor the left side by grouping
x(x+1) 5(x+1) = 0 Factor out x+1
(x+1) (x+5) = 0 Now use the zero product by setting each of them equal zero.
x+ 1 = 0 or x+5 = 0
-1 -1 -5 -5
x = -1 or x = -5
If g(x) = 4x^2 - 16 were shifted 5 units to the right and 2 down, what would the new equation be?
Answers
Answer:
D. h(x) = 4(x - 5)² - 18
Step-by-step explanation:
evaluate 3^2+(8-2)x4-6/3
Answers
Answer:
31
Step-by-step explanation:
=3^2+(8-2)x4-6/3
=9+6 x 4 - 2
=9+24-2
=31
Answer:
31
Step-by-step explanation:
9+6*4-6/3
9+6*4-2
9+24-2
31
______ is terminology that is specific to a particular profession or group. For example, statisticians talk about t-tests, chi-square tests, confidence intervals, and normal distributions.
Answers
Answer:
parlanceStep-by-step explanation:
The world parlance represents jargon/terms used by a particular profession or by a group of related experts in a field.
In french parler, means "to speak, hence the word parlance has it root from the french word parler.
it is a noun and it often called a slang or a jargon.
for example in law, lawyers use world/terms like, plaintiff, witness, suspect, jury, etc
The terminology that is specific to a particular profession or group is called; Jargons
We are given examples such as;
T-tests, chi-square tests, confidence intervals being used exclusively by statisticians.
Now, these terms used exclusively by statisticians have a general term they are called which is Jargons.
In conclusion, Jargons is the general name for words or expressions that are used exclusively by a group that are not easy for others to understand.
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A cylinder is shown with a base diameter of 6 centimeters and a height of 8 centimeters. What is the minimum number of identical containers Rene would need to make 2,000 cm3 of ice? (Use π = 3.14.)
Answers
Answer:
Rene needs 9 of these identical cylinder.
Step-by-step explanation:
diameter d = 6 cm
height h = 8 cm
volume of this cylinder v = [tex]\pi d^{2}h/4[/tex]
substituting, we have
v = (3.142 x [tex]6^{2}[/tex] x 8)/4
v = 226.224 cm^3
minimum number of identical containers Rene should use should be
n = 2,000/226.224 = 8.8
The minimum number must be a whole number, and must completely make this 2000 cm^3 volume of ice or more
answer will be 9
Raj wakes up in the morning and notices that his digital clock reads 07 2(A)5(B).After noon, he looks at the clock again.what is the probality that
I) The number in column A is 4?
ii) The number in column B is an 8?
iii) The number in column A is less than 6?
iv) The number in column B is greater than 5?
Answers
Answer:
i. [tex]P(A) = \frac{1}{10}[/tex]
ii. [tex]P(B) = \frac{1}{10}[/tex]
iii. [tex]P(A) = \frac{3}{5}[/tex]
iv. [tex]P(B) = \frac{2}{5}[/tex]
Step-by-step explanation:
Given
Time: 07 2(A) 5(B)
Calculating (a)
First, we need to list out the possible sample space, S of A
[tex]S = \{0,1,2,3,....,9\}[/tex]
[tex]n(S) = 10[/tex]
Probability of A being a 4 is the number of occurrence of 4 divided by the number of sample space
[tex]A = \{4\}[/tex]
[tex]n(A) = 1[/tex]
Hence;
[tex]P(A) = \frac{n(A)}{n(S)}[/tex]
[tex]P(A) = \frac{1}{10}[/tex]
Calculating (b)
First, we need to list out the possible sample space, S of B
[tex]S = \{0,1,2,3,....,9\}[/tex]
[tex]n(S) = 10[/tex]
Probability of B being a 8 is the number of occurrence of 8 divided by the number of sample space
[tex]B = \{8\}[/tex]
[tex]n(B) = 1[/tex]
Hence;
[tex]P(B) = \frac{n(B)}{n(S)}[/tex]
[tex]P(B) = \frac{1}{10}[/tex]
Calculating (c)
Using the sample space in (a)
[tex]n(S) = 10[/tex]
Probability of A being less than 6 is the number of occurrence of less than 6 divided by the number of sample space
[tex]A = \{0,1,2,3,4,5\}[/tex]
[tex]n(A) = 6[/tex]
Hence;
[tex]P(A) = \frac{n(A)}{n(S)}[/tex]
[tex]P(A) = \frac{6}{10}[/tex]
[tex]P(A) = \frac{3}{5}[/tex]
Calculating (d)
Using the sample space in (b)
[tex]n(S) = 10[/tex]
Probability of B being greater than 5 is the number of occurrence of greater than 5 divided by the number of sample space
[tex]B = \{6,7,8,9\}[/tex]
[tex]n(B) = 4[/tex]
Hence;
[tex]P(B) = \frac{n(B)}{n(S)}[/tex]
[tex]P(B) = \frac{4}{10}[/tex]
[tex]P(B) = \frac{2}{5}[/tex]
Perform the operation below using a number line. -7-(-8). ASAP. pleeease help.
Answers
Answer:
1
Step-by-step explanation:
Calculation steps:
-7-(-8) = ⇒ two negatives cancel and change to positive
- 7 + 8 = ⇒ 8-7 = 1
1 ⇒ answer
hi, please help a sis out :))
Answers
Answer:
The value of x is 16 and the width is 4.
Step-by-step explanation:
The area of a rectangle is the length multiplied by the width, which is [tex]9\sqrt{x}[/tex].
So, [tex]9\sqrt{x}[/tex] = 36.
We divide both sides by 9, getting [tex]\sqrt{x}[/tex] = 4.
We then square both sides, getting x = 16.
The value of x is 16, and the width is 4.
5. Say the following are deductions on a typical income, i. Pension deductions are 5% ii. Emploment Insurance deductions are 2.4% iii. And Income Tax deductions are as follows 1. For annual salaries, on the first $11,000, no income tax is paid, 2. On the first $11,000 to $25,000, 8% of the income is deducted, 3. On the first $25,000 to $50,000, 12% of the income is deducted, 4. On the first $50,000 to $100,000, 15% of the income is deducted, 5. And on the rest of the income, 20% of that income is deducted. Henry makes an annual gross salary of $70,000, what is his net salary?
Answers
Answer:
$57,700
Step-by-step explanation:
The deductions are ...
for pension and employment insurance, (5+2.4)% of $70,000
= 0.074 × $70,000 = $5,180
for income tax, ...
8% of the 14,000 between $11,000 and $25,000 = $1,120
12% of the 25,000 between $25,000 and $50,000 = $3,000
15% of the 20,000 between $50,000 and $70,000 = $3,000
Then the total of deductions is ...
$5,180 +1,120 +3,000 +3,000 = $12,300
Net salary after these deductions is ...
$70,000 -12,300 = $57,700
Elena is trying to draw a triangle with side lengths 4 cm, 3 cm, and 5 cm. She uses her ruler to draw a 4 cm line segment AB. She uses her compass to draw a circle around point B with radius 3 cm She draws another circle, around point A with radius 5 cm. What should Elena do next? Explain how she can finish drawing the triangle?
Answers
All you have to do is find where the two circles intersect with each other ( where they meet ) and then draw your 5cm line from A to the intersection and the 3cm line from B to the intersection.
It should form a triangle*.
* The image should help you.
Elena should put a point where the two circles intersect and draw line segments connecting that point to points A and B to finish her triangle.
84 POINTS!!!!!!!! The hands on a clock represents rays. At 6:00, they forn opposite rays. What undefined term do the hands of the clock represents at 6:00?
A. Point
B.Line
C. Plane
D. Space
Answers
Answer:
Line of course! So its B