Answers
Explanation
A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero
\(\begin{gathered} a=\frac{p}{q} \\ q\ne0 \\ a\text{ is rational } \end{gathered}\)and An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio
so,let's check every option
Step 1
a)-13/3
it is a fraction, so it is a rational number
b)
\(\begin{gathered} 0.1234 \\ 0.1234*\frac{10000}{10000}=\frac{1234}{1000} \\ so,\text{ the number can be expressed as a ratio, hence} \end{gathered}\)it is a rational number
c)
\(\sqrt{37}=6.0827625302...\)Square root of 37 is an irrational number, because the value of √37 is a non-teminating decimal
d)-77
The rational numbers include all the integers, and this is a integer, so this is a rational number
d)
\(\begin{gathered} -\sqrt{100} \\ -\sqrt{100}=\text{ -10} \end{gathered}\)The rational numbers include all the integers, and this is a integer, so this is a rational number
e)
\(\begin{gathered} -\sqrt{12} \\ -\sqrt{12}=-\sqrt{4*3} \\ -12=-\sqrt{4\times3}\text{ = -}\sqrt{4}\sqrt{3\text{ }}=\text{ -2}\sqrt{3} \end{gathered}\)The sqrt of 3 is irrational. Specifically, it cannot be written as the ratio of two given numbers or be written as a simple fraction,so
this number is a irrational number
I hope this helps you
Related Questions
what are the answers? thank you.
Answers
Answer:
176.78cm squared,23.57cm,Step-by-step explanation:
inorder to solve the area of the shaded area;°/360ñRsquared
arc length you use ;°/360ñD
Shirts are 50% off. The original price of one shirt is $60. dollars, of two shirts, at the sale price, including a 10% sales tax
Answers
Answer:
I guess, you are asking how much two shirts are costing now.
the answer is $66
Step-by-step explanation:
sales tax is always calculated from the actual sales price (and never from a list price or so).
so, the discount is 50%.
=> a shirt now costs only $30 (instead of $60).
50/100*60 = $30
now, sales tax is calculated from these $30.
=> 10% of $30 is $3
10/100*30 = $3
therefore, a single shirt costs now $30+$3 = $33 incl. sales tax.
two shirts cost therefore 2 * $33 = $66
Which correctly shows the substitution step for the system?
y = x - 4
-4x - 6y = -16
O x-4 = -4x-6y
-4(x-4) - 6y = -16
O-4x-6(x-4) = -16
6y = x - 4
Answers
The solution to the system of equations is x = 4 and y = 0. In summary, the correct substitution step for the system is: -4x - 6(x - 4) = -16 .C answer is correct
To solve the given system of equations:
1) y = x - 4
2) -4x - 6y = -16
We can use the substitution method to eliminate one variable and solve for the other.
Step 1: Solve the first equation (1) for y in terms of x.
y = x - 4
Step 2: Substitute the expression for y from equation (1) into equation (2).
-4x - 6(x - 4) = -16
Step 3: Simplify and solve for x.
-4x - 6x + 24 = -16
-10x + 24 = -16
-10x = -16 - 24
-10x = -40
x = -40 / -10
x = 4
Step 4: Substitute the value of x back into equation (1) to solve for y.
y = 4 - 4
y = 0
Therefore, the solution to the system of equations is x = 4 and y = 0.
In summary, the correct substitution step for the system is:
-4x - 6(x - 4) = -16
By substituting the expression for y from equation (1) into equation (2) and simplifying, we obtain the equation -4x - 6y = -16, which can be further solved to find the values of x and y. C answer is correct
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Boyle’s law states that when considering gases, volume varies inversely with pressure. If V represents the volume of the gas and P represents the pressure of the gas, what would the formula be that represents this relationship? If a balloon has a volume of 4 L of gas with a pressure of 5 atmospheres, what will the volume be when the pressure is 3 atmospheres?
Answers
Step-by-step explanation:
According to Boyle's Law :
\( P_1 * V_1 = P_2 * V_2\)
\(5 * 4 = 3 * V_2\)
\( V_2 = 6.66 L \)
Reflections of Shapes
Graph the image of the figure using the transforma
1) reflection across the x-axis
Answers
A graph of the image of the figure after a reflection across the x-axis is shown below.
What is a reflection over the x-axis?In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).
This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.
By applying a reflection over or across the x-axis to triangle GLQ, we have;
(x, y) → (x, -y)
G (3, 4) → (3, -(4)) = G' (3, -4)
L (1, 2) → (1, -(2)) = L' (1, -2).
Q (4, -1) → (4, -(-1)) = Q' (4, 1)
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You are adding air to a tire. The air pressure in the tire should be 25 and 29 200 pounds per square inch. What decimal should you watch for on the digital pressure gauge?
Answers
Answer
25 (29/200) pounds per square inch = 25.145 pounds per square inch
Explanation
The pressure target for the tire is 25 (29/200)
The decimal equivalent for this will be obtained by converting the (29/200) into its decimal form.
(29/200) = 0.145
So,
25 (29/200) = 25 + 0.145
= 25.145
Hope this Helps!!!
Lian's dog eats
of a bag of dog food each week. Lian currently has of a bag remaining.
How many weeks will it take Lian's dog to finish this remaining food?
weeks
Stuck?
Answers
The period that it would take the Dog to finish the remaining food would be a period of 12.5 weeks
How to solve for the period that it would take to finish the foodThe amount that the dog eats weekly is given as 1 / 20 of the food.
The amount that Lian has left in the bag is given as 5 / 8
To get the number of weeks that it would take to finish the food, we would divide 1 / 20 by 5 / 8
1 / 20 ÷ 5 / 8
20 / 1 * 5 / 8
= 100 / 8
= 12.5
Hence it would take 12.5 weeks for the dog to finish the remaining food here.
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'Lian's dog eats 1/20 of a bag of dog food each week. Lian currently has 5/8 of a bag remaining.How many weeks will it take Lian's dog to finish this remaining food?weeksStuck?
HELPPPPPPP PLEASEEEEEEEE
Answers
Answer:
the answer I got is 6-6r
A new car is purchased for 21100 dollars. The value of the car depreciates at
10.5% per year. What will the value of the car be, to the nearest cent, after 6
years?
Answers
Answer:
10,844.78
Step-by-step explanation:
Deion misses 4% of the free throws he attempts in a seaon. How many total free throws did he attempt if he missed 17
Answers
Answer: 425
Step-by-step explanation:
Think of this problem as 4% of a number equals 17
since in math, the word 'of' usually means multiplication, we can think of it that way.
Also, 4% = 0.04
\(x*0.04=17\)
\(0.04x=17\)
\(\frac{0.04x}{0.04} =\frac{17}{0.04}\)
\(x=425\)
{x|x + 1 ≥ 3 and x − 6 ≤ −1}
Write the solution using interval notation
Answers
Solve both problems with explanation for brainliest:
Answers
Answer:
1)5600 minutes
2)2000n minutes
Step-by-step explanation:
50/.125 * 14 = 5600
800/.4*n= 2000n
Given that 8 tan = 3 cos
a) Show that the above equation can be rewritten in the form 3 sin2 + 8 sin − 3 = 0
b) Hence solve, for 0 ≤ ≤ 90, the equation 8 tan 2 = 3 cos 2, giving your answers to 2 decimal places.
Answers
The only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given Range is θ ≈ 19.47 degrees.
a) We are given the equation 8 tan θ = 3 cos θ.
Dividing both sides of the equation by cos θ, we have:
8 tan θ / cos θ = 3
Using the identity tan θ = sin θ / cos θ, we can substitute it into the equation:
8 (sin θ / cos θ) / cos θ = 3
Simplifying further, we get:
8 sin θ / cos^2 θ = 3
Now, multiplying both sides of the equation by cos^2 θ, we have:
8 sin θ = 3 cos^2 θ
Using the identity cos^2 θ = 1 - sin^2 θ, we can substitute it into the equation:
8 sin θ = 3(1 - sin^2 θ)
Expanding the equation, we get:
8 sin θ = 3 - 3 sin^2 θ
Rearranging the terms, we have:
3 sin^2 θ + 8 sin θ - 3 = 0
Therefore, we have successfully shown that the equation can be rewritten in the form 3 sin^2 θ + 8 sin θ - 3 = 0.
b) Now, let's solve the equation 3 sin^2 θ + 8 sin θ - 3 = 0.
To solve the quadratic equation, we can use factoring, quadratic formula, or other appropriate methods.
In this case, the equation factors as:
(3 sin θ - 1)(sin θ + 3) = 0
Setting each factor equal to zero, we have two equations:
3 sin θ - 1 = 0 or sin θ + 3 = 0
For the first equation, solving for sin θ, we get:
3 sin θ = 1
sin θ = 1/3
Taking the inverse sine (sin^-1) of both sides, we find:
θ = sin^-1(1/3) ≈ 19.47 degrees (to 2 decimal places)
For the second equation, solving for sin θ, we have:
sin θ = -3
Since the range of sine is between -1 and 1, there are no solutions for this equation in the given range (0 ≤ θ ≤ 90 degrees).
Therefore, the only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given range is θ ≈ 19.47 degrees.
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If you spend 3.5 hours a week studying for English and 7.5 hours studying for math what is the ratio of time
spent studying in math to studying for English?
Answers
Answer:
7.5 : 3.5
Step-by-step explanation:
ratio of time spent studying in math to studying for English is ;
time spent studying in math. / time spent in studying English
\( \frac{7.5}{3.5} \)
= 7.5 : 3.5
Use custom relationships to create a graph, showing the solution region of the system of inequalities, representing the constraints of the situation. Did Mark and label it point represents a viable combination of guest School district is planning a banquet to honor his teacher of the year and raise money for the scholarship foundation. The budget to hold the banquet in a hotel room and miles is $3375 the venue can hold no more than 125 guest the cost is $45 per adult but only $15 per student because caterer offers a student discount discount
Answers
We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.
What is banquet?
A banquet is a large formal meal that usually involves multiple courses and is served to a group of people on special occasions such as weddings, awards ceremonies, or fundraising events. Banquets often include speeches, presentations, and entertainment, and are typically held in a large venue such as a hotel ballroom, banquet hall, or conference center. Banquets can be hosted for a variety of purposes, such as to honor a special guest, celebrate an achievement, or raise money for a charitable cause.
To create a graph showing the solution region of the system of inequalities representing the constraints of the situation, we can use custom relationships to define the variables and constraints.
Let's define the variables:
Let x be the number of adult guests.
Let y be the number of student guests.
Now, let's write the system of inequalities representing the constraints of the situation:
The total number of guests cannot exceed 125: x + y ≤ 125
The cost of hosting the banquet cannot exceed $3375: 45x + 15y ≤ 3375
To graph this system of inequalities, we can plot the boundary lines of each inequality and shade the region that satisfies all the constraints.
The boundary lines of each inequality are:
x + y = 125 (the line that connects the points (0, 125) and (125, 0))
45x + 15y = 3375 (the line that connects the points (0, 225) and (75, 0))
To find the viable combinations of guests that satisfy all the constraints, we need to shade the region that is below the line x + y = 125 and to the left of the line 45x + 15y = 3375.
The resulting graph should look like this:
The point where the two lines intersect, (75, 50), represents the maximum number of adult guests (75) and the maximum number of student guests (50) that can be invited to the banquet while staying within the budget and venue capacity. Any point within the shaded region represents a viable combination of guests.
We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.
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A circle has a diameter of 24 in what is the circumference pi is 3.14
Answers
Answer:
The circumference of a circle is calculated using the formula: C = πd, where C represents the circumference and d represents the diameter of the circle.
In this case, the diameter of the circle is given as 24 inches.
Using the formula, we can substitute the values:
C = πd
C = 3.14 * 24
C ≈ 75.36 inches
Therefore, the circumference of a circle with a diameter of 24 inches (and using π = 3.14) is approximately 75.36 inches.
Step-by-step explanation:
grace thought of a number, added 7, multiflied by 3, took away 5 and divided by 4 to give an answer of 7
Answers
Answer:
Step-by-step explanation:
To find the number that Grace thought:
We'll represent the unknown number as "x."
"Added 7": This can be represented as (x + 7).
"Multiplied by 3": This becomes 3 * (x + 7).
"Took away 5": This is represented as 3 * (x + 7) - 5.
"Divided by 4": This gives (3 * (x + 7) - 5) / 4.
"To give an answer of 7": The equation is (3 * (x + 7) - 5) / 4 = 7.
Now we can solve for x:
(3 * (x + 7) - 5) / 4 = 7
Multiply both sides by 4 to eliminate the denominator:
3 * (x + 7) - 5 = 28
Simplify the left side:
3x + 21 - 5 = 28
Combine like terms:
3x + 16 = 28
Subtract 16 from both sides:
3x = 12
Divide both sides by 3:
x = 4
Therefore, the number that Grace thought of is 4.
Tricia got 6% raise on her weekly salary. The raise was $42 per week. What was her original weekly salary in dollars per week
Answers
Step 1
Write an expression that can help find the original salary
\(\frac{106}{100}\times x=x+42\)Step 2
Simplify the equation
\(\begin{gathered} 1.06x=x+42 \\ 1.06x-x=42 \\ 0.06x=42 \\ \frac{0.06x}{0.06}=\frac{42}{0.06} \end{gathered}\)\(x=\text{\$700}\)Hence, Tricia's Original weekly salary in dollars per week=$700
PLEASE ANSWER THIS NOW !!!!!!!!!!!!!!!!!!1
NEED HELP SO BAD
Answers
The length of the real life plane is 8000 centimetres.
The scale model as a ratio is 1:2000.
How to find the scale of a model?A model of a plane has a length of 4 cm. The real life plane has a model of 80 m.
The length of the real life plane in centimetres is as follows:
1 metre = 100 centimetres
80 metres = ?
cross multiply
length of the real life plane in cm = 80 × 100
length of the real life plane in cm = 8000 centimetres
The scale model can be calculated as follows;
scale model = 4 / 8000
scale model = 1 / 2000 = 1:2000
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what is da rate to question
Answers
The calculated value of the rate of the graph is 0.8
How to determine the rate of the graphfrom the question, we have the following parameters that can be used in our computation:
The graph
Where, we have
(0, -16) and (20, 0)
The rate of the graph is calculated as
Rate = Change in y/x
using the above as a guide, we have the following:
Rate = (0 + 16)/(20 - 0)
Evaluate
Rate = 0.8
Hence, the rate is 0.8
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Gary applied the distributive property using the greatest common factor to determine the expression that is equivalent to 66 + 36. His work is shown below.
Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
66 + 36 = 3 (22 + 12)
What statement best describes Gary’s error?
Gary did not use correct factors for 66 in the equation.
Gary did not use correct factors for 36 in the equation.
Gary did not use two equivalent expressions in the equation.
Gary did not use the greatest common factor in the equation.
answer this question in 5 minutes and ill give you the brainlyest and 50 points also please still answer even after the 5 minutes
Answers
The statement which best describes Gary’s error is; Gary did not use the greatest common factor in the equation.
Greatest common factorThis is the largest positive integer or polynomial that is a divisor of several different numbers. For instance, the greatest common divisor of 66, 30 and 18 is 6.
Gary's work:
66 + 36
Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
66 + 36
= 3 (22 + 12)
Gary did not use the greatest common factor in the equation.
The correct answer:
The greatest common factor of 66 and 36 is 666 + 36
= 6(11 + 6)
Therefore, Gary did not use the greatest common factor in the equation.
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tell me ratios simplest forms
Answers
So like 1:2 , 2:4 , 4:8
Hope this helps!
At the office supply store, a ream of paper costs $5.89 and a cartridge of ink costs $38.40. Delilah needs to buy 8 reams of paper and 6 cartridges of ink for her office. She needs to know how much money to bring, so estimate the cost of these supplies.
Answers
Answer:
Step-by-step explanation:
Delilah needs to buy 8 reams of paper which cost $5.89 each, $5.89 x 8 = $47.12
Delilah needs to buy 6 cartridges of ink which cost $38.40 each, $38.40 x 6 = $230.4
We then add $230.4 and $47.12
$230.4 + $47.12 = $277.52.
Delilah needs to bring $277.52 to cover the cost of her supplies.
divide the polynomials x^2-10,000/x-100
Answers
Answer:
x+100
Step-by-step explanation:
x^2-10,000/x-100
x^2-10000 is a difference in squares and can be factored.
x^2-10000 = (x+100)(×-100).
(x+100)(x-100)/(x-100)
(x-100) cancel each other.
x+100 remains.
A group of 28 students wants to go on a bus trip. The cost of the bus is $220. $94 dollars will be paid by one parent and the rest of the cost will be paid for by the students. Select the correct equation to represent this scenario from the options below. Group of answer choices LaTeX: 28x+94=22028 x + 94 = 220
LaTeX: 28x-94=22028 x − 94 = 220
LaTeX: 94x+28=22094 x + 28 = 220
LaTeX: 94x=22094 x = 220
Answers
Answer:
c
Step-by-step explanation:
Multiply.
(2x+6)²
NEED ANSWER ASAPP
Answers
Answer:
4x² + 24x + 36
Step-by-step explanation:
(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36
Evaluate f(x)=3x-9, when x=-2
A. -18
B. -33
C. -3
D. -15
Answers
Answer:
d. -15
Step-by-step explanation:
f(x) = 3x - 9, when x = -2
Input -2 into the function for x and solve:
f(-2) = 3(-2) - 9
f(-2) = -15
Hope this helped :)
Are the vectors 2+5x+3x2, 4+11x+6x2 and 1+2x+x2 linearly independent? choose If the vectors are independent, enter zero in every answer blank since zeros are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. 0= (2+5x+3x2)+ (4+11x+6x2)+ (1+2x+x2).
Answers
Answer:
Vectors \(p_{1} = 2+5\cdot x + 3\cdot x^{2}\), \(p_{2} = 4+11\cdot x +6\cdot x^{2}\) and \(p_{3} = 1+2\cdot x +x^{2}\) are linearly independent.
Step-by-step explanation:
From Linear Algebra, we must remember that a set of vectors is linearly independent if and only if coefficients of its linear combinations are all zeroes. That is:
\(\Sigma\limits_{i=1}^{n} \alpha_{i}\cdot p_{i}= 0\), where \(\alpha_{i} = 0\). (Eq. 1)
Where:
\(p_{i}\) - i-th Polynomial of the set of vectors, dimensionless.
\(\alpha_{i}\) - i-th coefficient associated with the i-ith polynomial of the set of vectors, dimensionless.
Let \(p_{1} = 2+5\cdot x + 3\cdot x^{2}\), \(p_{2} = 4+11\cdot x +6\cdot x^{2}\) and \(p_{3} = 1+2\cdot x +x^{2}\) elements of the set of vectors, whose linear combination is:
\(\alpha_{1}\cdot p_{1}+\alpha_{2}\cdot p_{2}+\alpha_{3}\cdot p_{3}= 0\)
\(\alpha_{1}\cdot (2+5\cdot x+3\cdot x^{2})+\alpha_{2}\cdot (4+11\cdot x +6\cdot x^{2})+\alpha_{3}\cdot (1+2\cdot x+x^{2}) = 0\)
\((2\cdot \alpha_{1}+4\cdot \alpha_{2}+\alpha_{3})+(5\cdot \alpha_{1}+11\cdot \alpha_{2}+2\cdot \alpha_{3})\cdot x+(3\cdot \alpha_{1}+6\cdot \alpha_{2}+\alpha_{3})\cdot x^{2} = 0\)
Values of coefficient are contained in the following homogeneous system of linear equations:
\(2\cdot \alpha_{1}+4\cdot \alpha_{2}+\alpha_{3} = 0\) (Eq. 2)
\(5\cdot \alpha_{1}+11\cdot \alpha_{2}+2\cdot \alpha_{3} = 0\) (Eq. 3)
\(3\cdot \alpha_{1}+6\cdot \alpha_{2}+\alpha_{3} = 0\) (Eq. 4)
The solution of this system is:
\(\alpha_{1} = 0\), \(\alpha_{2} = 0\), \(\alpha_{3} = 0\)
Which means that given set of vectors are linearly independent.
please help me I do not understand what to do
Answers
Answer:
3 7/12
Step-by-step explanation:
There are 12 inches in 1 feet. So 43 inches would be 43/12=3 7/12 feet.
Find the amount (future value) of the ordinary annuity. (Round your answer to the nearest cent.)
$300/week for 9 1/2
years at 5.5%/year compounded weekly
Answers
Answer: $227,226.51
Step-by-step explanation:
First, we need to convert the period to weeks.
9 1/2 years = 9.5 years
1 year = 52 weeks
9.5 years = 494 weeks
Next, we can use the formula for the future value of an annuity:
FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)
where:
PMT = payment amount per period
r = annual interest rate
n = number of compounding periods per year
t = number of years
Plugging in the given values:
PMT = $300
r = 0.055 (5.5% expressed as a decimal)
n = 52 (compounded weekly)
t = 9.5 years = 494 weeks
FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)
FV = $227,226.51
Therefore, the future value of the annuity is approximately $227,226.51.