The system of linear equations Ax + 3y = a, 3x + ay = A has no solutions for any value of a.
To determine if the system of linear equations Ax + 3y = a, 3x + ay = A has no solutions for any value of a, we can use the elimination method.
We want to eliminate one of the variables, so let's start by multiplying the first equation by 3 and the second equation by -1.
This gives us:
3Ax + 9y = 3a, -3x - ay = -A.
Now we add the equations together to get:
2Ax + 8y = 3a - A.
Now we can see that the equation is not solvable as there is no value of a that will make the equation true. Therefore, the system of linear equations Ax + 3y = a, 3x + ay = A has no solutions for any value of a.
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40% of Damien’s marbles are blue Damien has 30 marbles how many of the marbles are not blue
Answer:
12
Explanation:
40/100 = 0.4
0.4 * 30 = 12
I hope this helps you!
find the total surface area of this cuboid.
The total surface area of the cuboid is 2 (lh + lw+ hw) square units.
What is surface?A surface is the part of solid matter that can be touched by hand or seen with eyes. In other words, it is the place where the solid matter encounters the outside world through contact, light, etc. Solid matter not only effects humans with its surface, but also air, water, and other solid matter. Therefore, things around us work cooperatively with the outside world and with other things through surfaces, without a surface, solid matter would not be able to interact with anything.By changing the characteristics of solid matter, interactions such as the impact on the solid matter from other things (such as environmental conditions and people) as well as the effect that solid matter has on other things can be changed. In other words, certain features of the solid matter can be controlled as needed.To learn more about surface refer to:
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Melissa wants to check the accuracy of the finance charge on her loan. She has a $6,000, 4-year loan at an APR of 3.11%. What is her monthly payment? Round to the nearest cent.
Answer: $133.10.
Step-by-step explanation:
Answer:
To calculate the monthly payment for a loan, you can use the following formula:
Monthly payment = (APR/12) * loan amount / (1 - (1 + APR/12)^(-number of payments))
In this case, the loan amount is $6,000, the APR is 3.11%, and the loan is for 4 years, or 48 months. Plugging these values into the formula, we have:
Monthly payment = (0.0311/12) * $6,000 / (1 - (1 + 0.0311/12)^(-48))
Calculating, we find that the monthly payment is approximately $147.26. Rounded to the nearest cent, the monthly payment is $147.26.
Step-by-step explanation:
How do you find the third side of a triangle that is not right?
The third side of a triangle can be found using the Pythagorean Theorem.
The Pythagorean Theorem states that for a triangle with sides of length a, b, and c (with c being the length of the unknown side) a^2 + b^2 = c^2.
To find the third side of a triangle that is not right, first calculate the lengths of the two known sides. Let's say the lengths of the two known sides are a = 5 and b = 12.
Next, plug the values into the Pythagorean Theorem and solve for c.
[tex]a^2 + b^2 = c^2[/tex]
[tex](5)^2 + (12)^2 = c^2 \\25 + 144 = c^2[/tex]
[tex]169 = c^2[/tex]
Finally, take the square root of both sides to solve for c.
sqrt(169) = c
13 = c
Therefore, the length of the third side is 13.
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Does 4 5 6 make a right triangle?
The side lengths measuring 4 units , 5 units and 6 units does not make a Right Triangle as they do not satisfy the condition of the Pythagoras Theorem that the square of the longest side is equal to the sum of square of other two side .
The Pythagoras Theorem states that the square of the lonest side (hypotnuse) is equal to the sum of the square of the other two sides ,.
The side lengths of the triangle are given as 4 units , 5 units and 6 units ,
According to the condition , [tex]6^{2} = 4^{2} + 5^{2}[/tex]
On simplifying ;
we get ;
[tex]36 = 16 + 25[/tex] ;
[tex]36 \neq 41[/tex]
that means the given side do not form a right triangle .
Therefore , the side 4 units , 5 units and 6 units do not make a right triangle .
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Can anyone help please
The graph of the following equation will be a Parabola. The y=1 will be the line of symmetry.
Which four types of parabolas are there?Three different parabolas exist. Vertex form, standard form, and intercept form are the three forms. You can access a unique key feature for the graph on each form.
What distinguishes a hyperbola from a parabola?A set of points in a plane that are equally spaced apart from a directrix or focus are known as parabolas. The difference in distances between a group of points that are situated in a plane and two fixed points—which is a positive constant—is what is referred to as the hyperbola.
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Write 108:96 in the form 1:n.
Answer:
it will be [tex]1:\frac{8}{9}[/tex]expand the polynomial (x+1)(x+2)(y-3)
Answer: X^2y + 3xy + 2y -3x^2 -9x -6
explanation
1. Foil (x+2)(x+1)
X^2 +2x + x + 2
2. Simplify
X^2 + 3x + 2
3. Distribute x^2 + 3x +2 (y-3)
X^2y + 3xy + 2y -3x^2 -9x -6
. If a population of college student ages is skewed right, then this indicates: a. there are a greater number of older students b. the modal age is greater than the median age c. as the age of a student increases, the frequency of the student ages increases. d. there are more younger students within the population e. not enough information
The correct answer is c. as the age of a student increases, the frequency of the student's ages increases.
A skewed right population means that the data is distributed in such a way that the majority of the values are on the right side of the data set. In the case of a population of college students, this would mean that there is a greater frequency of older students (those in their late twenties or older) than younger students. As the age of a student increases, the frequency of the student's ages increases.
Option a. there are a greater number of older students is also correct, but it is not complete.
Option b. the modal age is greater than the median age is not correct, as the modal age is the most common age in the population and the median age is the middle value of the population, and there is no relationship between them.
Option d. there are more younger students within the population is not correct as a skewed right population indicates the opposite.
Option e. not enough information is not correct as the question is providing enough information to make a conclusion.
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given the expression 1/4-3/5 select the addition problem that is equivalent to it
The expression (1/4 - 3/5) is equivalent to the following expressions -
(3/20 - 10/20) (13/20 - 1)(23/20 - 3/2)What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as -
(1/4 - 3/5)
The given expression is -
(1/4 - 3/5)
1/4 - 3/5
(5 - 12)/20
-7/20
We can write the fraction : -7/20 in many ways as given below -
-7/20 = (3/20 - 10/20) = (1/4 - 3/5)
-7/20 = (13/20 - 1) = (1/4 - 3/5)
-7/20 = (23/20 - 3/2) = 1/4 - 3/5)
Therefore, the expression (1/4 - 3/5) is equivalent to the following expressions -
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Finn jumped 200 times in 10 hours. At what rate, how many times would he jumped in 12 minutes?
Answer: 4 times
Step-by-step explanation: I got 4 times. Here's how to solve it:
Set up a proportional relationship, but first, we need to convert 10 hrs into mins:
1 hour = 60 mins
To find how many minutes are in 10 hours, we multiply 60 by 10, which equals 600.
So, therefore there are 600 mins in 10 hours. Now, we can set up our proportional relationship:
[tex]\frac{200}{60} = \frac{?}{12}[/tex]
So, if we know 12 is a factor of 60, we should divide 60 by 12, and we should get 5. So, now we do the same with the 200. We do 200 / 50, and we get 4. I hope this helps!
What is the difference 19√5 - 3√5 A.16 B.22 C.16√5 D.25
Answer:
C - 16√5
Step-by-step explanation:
Simply subtract 19 and 3 while keeping √5 the same.
19√5 - 3√5 = 16√5
Kelvin and Lewie each design surveys in order to determine the average number of people who buy food at the mall. Kelvin surveys every other person leaving the food area. Lewie surveys every fifth person leaving the mall main entrance. Which set of survey results is most likely to show biased results for people who buy food at the mall
The set of survey results that is most likely to show biased results for people who buy food at the mall is Lewie's survey.
Lewie's survey samples only every fifth person leaving the mall's main entrance, which means that it only captures a small percentage of the total number of mall visitors. Additionally, by only surveying people leaving the main entrance, Lewie's survey may not capture people who enter and exit the mall through other entrances or exits and may also miss those who don't leave the mall after buying food. As a result, Lewie's survey may not accurately represent the total number of people who buy food at the mall and may lead to biased results.
On the other hand, Kelvin's survey samples every other person leaving the food area. This method captures a larger percentage of the total number of people who buy food at the mall and is more likely to provide a more accurate representation of the total number of people who buy food at the mall.
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Answer:
A. Kelvin’s because he surveyed people leaving an area where food is sold
Step-by-step explanation:
Find the volume of a cube if its area of four walls is 16 cm square.
[tex] \longmapsto \: side = \frac{16}{4} = 4 \\ \longmapsto volume = 4 {}^{3} = 64[/tex]
What is the first step to do in using substitution method?
Answer: Solve one equation for one of the variables.
Step-by-step explanation:
This is algebra 2, please help.
The vertex and axis of symmetry of the graph is shown in image.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The function is,
⇒ f (x) = 1/4 (x + 6)² - 5
Now,
Since, The function is,
⇒ f (x) = 1/4 (x + 6)² - 5
Hence, The points corresponds to x = - 2 and - 4 are;
For x = - 2;
⇒ f (x) = 1/4 (x + 6)² - 5
⇒ f (x) = 1/4 (-2 + 6)² - 5
⇒ f (x) = 1/4 (4)² - 5
⇒ f (x) = 4 - 5
⇒ f (x) = - 1
For x = - 4;
⇒ f (x) = 1/4 (x + 6)² - 5
⇒ f (x) = 1/4 (-4 + 6)² - 5
⇒ f (x) = 1/4 (2)² - 5
⇒ f (x) = 1 - 5
⇒ f (x) = - 4
Thus, The points are;
⇒ (- 2, - 1) , (- 4, - 4)
And, The vertex of the function is,
⇒ ( - 6, - 5 )
And, The axis of symmetry of the graph is,
⇒ x = - 6
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Find the value of k so that the point (1,2) lies on the locus y²-2x-ky+5=0.
A horse walks 4224 feet in 12 minutes at this rate how many yards does a horse walk in twelve minutes.
Answer:
1408 yards
Step-by-step explanation:
A horse walks 4224 feet in 12 minutes, so to find out how many yards the horse walks in twelve minutes, we need to convert 4224 feet to yards. Since there are 3 feet in a yard, we can divide 4224 by 3 to find the number of yards:
4224 feet / 3 feet/yard = 1408 yards
So a horse walks 1408 yards in 12 minutes.
The Garcia family bought 400 yards of fencing to enclose a circular wildflower garden. They will use all of the fencing whats the area
The area of the windflower garden that is enclosed by a circular fence of 400 yards length is equal to 12732.39 square yards.
What is circumference of a circle?The measurement of the circle's perimeter, also known as its circumference, is called the circle's border. It is the length around the border of the circular object or the circle itself.
What is the formula for calculating the perimeter of a circle?The formula for calculating the perimeter of a circle is ,
Perimeter/ Circumference of a circle = 2 * pi * r, where pi = 3.14 and r is the radius of the circle.
Taking the given information in the question, i.e circumference of the circular fencing wire , i.e C = 400 yards
or , 2 * pi * r = 400
or , r = 400/(2* 3.14)
r = 63.66 yards
Now the area of the circular fence is given by,
Area = pi * r^2
Area = 3.14 * 63.66^2
Area = 12732.39 square yards
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What does it mean to solve an equation by substitution?
The value of a variable from one equation is substituted in the other equation when using the substitution method.
The graphic approach and the algebraic method are the two main categories into which simultaneous linear equations can be solved. One of the categories of the algebraic approach is the substitution method. The algebraic approach to solving simultaneous linear equations is known as the substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.
Steps for Substitution method:
Simplify the given equation by expanding the parenthesisSolve one of the equations for either x or ySubstitute the step 2 solution in the other equationNow solve the new equation obtained using elementary arithmetic operationsFinally, solve the equation to find the value of the second variableTherefore in the Substitution method, The value of a variable from one equation is substituted in the other equation.
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Ava bought 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198. Grace spent $254 buying 14 packages of tulip bulbs and 12 bags of daffodil bulbs. Use elimination to solve the system of linear equations and determine how much one package of tulips bulbs costs, x, and how much one bag of daffodil bulbs costs, y. Enter your answer as an ordered pair (x,y).
When Ava purchased six packages of tulip bulbs and twelve bags of daffodil bulbs, the price per tulip bulb was $7 and the price each daffodil bulb was $13.
what is linear equations ?The algebraic equation y=mx+b is known as a linear equation. M serves as the y-intercept, and B serves as the slope. The previous clause has two variables, y and x, and is sometimes referred to as a "linear equation with two variables". Bivariate linear equations are those with two independent variables. The following are a few examples of system of equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation takes the form y=mx+b, with m denoting the slope and b denoting the y-intercept, it is referred to as being linear. The term "linear" refers to an equation having the form y=mx+b, where m stands for the slope and b for the y-intercept.
given
Let x be the price of a single tulip bag.
Y should equal the price of one bag of daffodil bulbs.
Grace = 14x + 12y = 254
ava = 6x + 12y = 198
- 8x = - 56
x = - 56/-8
x = 7.
Equation 1 becomes
6* 7 + 12y = 198
42 + 12y = 198 when x = 7 is substituted.
12y = 198 - 42
12y = 156
y = 156/12
y = 13
When Ava purchased six packages of tulip bulbs and twelve bags of daffodil bulbs, the price per tulip bulb was $7 and the price each daffodil bulb was $13.
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will mark u brainliest
Answer:
( - 7, - 1, 1, 4 )
Step-by-step explanation:
( x, y )
where,
x is Domain
y is Range
Hence,
Domain is ( - 7, - 1, 1, 4 )
Twelve eggs cost $2.04. How much will 18 eggs cost
Answer: $3.06
Step-by-step explanation: In order to get $3.06, you will have to find half $2.04 and then add that number to the price of 12 eggs.
What is the interval of zero?
If the confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.
If the confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.
If the confidence interval for a correlation or regression includes zero, that means that if you run the experiment again there is a good chance of finding no correlation in the data.
In both of these cases, you will also find a high p-value when you run the statistical test, meaning that the results could have occurred under the null hypothesis of no relationship between variables or no difference between groups.
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If it takes 10 hours to travel from North Carolina to Florida driving an
average speed of 60 mph, how long will it take to travel from North
Carolina to Florida driving an average speed of 70 mph?
Is it direct variation or indirect variation?
Answer:
8.5 hrs? direct variation
Step-by-step explanation:
60 per hour is 600 for 10 hours so 70 per hour to go 600 miles is 8.57142857143 in the calculator
600/60 =10
600/70 = 8.5
and its direct variation because on a graph 8.5 8.5 squares up for ever 1 square going over every time and the graph does curve but I haven't learned this stuff in years so I'm not 100% sure
A lawn sprinkler located at the corner of a yard rotates through 80 degrees
and sprays water of 20 ft. What is the length of the arc of the sector watered?
(Express your answer to the nearest tenths.)
The length of the arc of the sectored watered is 27.9 feets
What is length of an arc?length of arc is the distance between two points along a section of a curve.In other words, it's the distance from one point on the edge of a circle to another, or just a portion of the circumference
The length of an arc is given by :
L = theta/360 × 2πr
where tetha is the angle substends
r is the radius
Here the radius is the length at which water is sprayed = 20 ft
tetha = 80°
therefore l = 80/360 × 2×3.14 × 20
L = 29feets
Therefore the length of the arc formed by the water is 27.9 feets
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How many solutions does 3x 2y 6 have?
The linear equation 3x – 2y = 6 has one real solution. To find it, you can solve the equation for one of the variables (either x or y) and then substitute the result into the equation to find the other variable.
For example, you can solve for y to get y = (6 + 3x)/2, and then substitute this into the equation to get 3x – 2((6 + 3x)/2) = 6, which you can then solve for x. Doing this will give you x = 3, which means that the solution is (3, 3).
The linear equation 3x – 2y = 6 has infinitely many solutions. To find them, you can solve the equation for one of the variables (either x or y) and then substitute the result into the equation to find the other variable
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A simple random sample of 10 people were asked how many first cousins they have. The results are listed below.
10, 19, 20, 13, 13, 2, 10, 8, 25, 10
What is the mean number of first cousins for this sample?
10
11.5
13
13.5.
answer is 13
Answer:
13
Step-by-step explanation:
mean= (10+19+20+13+13+2+10+8+25+10)/10=130/10=13
The mean number of first cousins for the given sample is 13. Thus, Option C is correct.
Mean is the arithmetic average of the given set of observations.
Mean for ungrouped or raw data is obtained by adding all the observations and dividing it by the number of observations.
Mean = Sum of all the observations/ Total number of observations.
Mean = ∑( x1 + x2 + x3 .... xn /n)
Where X bar represents mean, n is no. of observations and ∑ denotes sigma i.e. sum of all the values.
No. of observations (n) =10
Mean = ∑ (10 + 19 + 20 + 13 + 13 + 2 + 10 + 8 + 25 + 10) / 10
Mean = 130 / 10
= 13
Therefore, Option C is the correct answer.
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If the sum of n term of an ap is sn = 3n^2+5n writ its common difference
In the given arithmetic progression Common difference is 14.
what is an arithmetic progression?An arithmetic progression is a set of integers with a fixed difference between any two succeeding numbers (A.P.).
Given, the n term of ap is Sₙ = 3n² + 5n
Where n is the number of terms
S₁ = 3* 1 + 5*1
S₁ = 8
S₂ = 3 * 4 + 5*2
S₂ = 22
common difference = 22-8
Common difference = 14
therefore, the Common difference in the given AP is 14.
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(#7) A cube has an edge length given by the variable “s” as shown. It’s surface area and volume can be given in terms of the edge length by: surface area= 6s^2 volume= s^3 Find the ratio of the surface area to the volume in simplest terms of “s”.
The ratio of surface area to volume is 6:s
What is a cube?A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
Given that, A cube has an edge length given by the variable “s”. It’s surface area and volume can be given in terms of the edge length by: surface area= 6s² volume= s³
The ratio = 6s² / s³
= 6 / s
Hence, the required ratio is 6:s
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