Do only equations with variables on both sides have no solution? Or can the variable be just on one side? Justify your answer. Choose the correct answer below.
A. Every equation with variables on both sides has no solution. However, it is also possible for an equation with the variable on only one side to also have no solution.
B. If the variable only appears on one side of an equation, then the equation can always be solved for the variable. This means that if an equation has no solution, then the variable must appear on both sides.
C. Any equation can have one solution, infinitely many solutions, or no solutions. This does not depend on whether the variable appears on only one side or on both sides.
D. If the variable only appears on one side of an equation, then the equation can always be solved for the variable. By contrast, an equation with variables on both sides always has no solution or infinitely many solutions.
Answer:
No only variable on both sides have no solution
Step-by-step explanation:
Then you can get,
for example x=x
or,
y=y
Answer:
Option CStep-by-step explanation:
A. Every equation with variables on both sides has no solution. However, it is also possible for an equation with the variable on only one side to also have no solution.
False, the first pat incorrect. The equation can be simplified to have variable on one side and solved further.B. If the variable only appears on one side of an equation, then the equation can always be solved for the variable. This means that if an equation has no solution, then the variable must appear on both sides.
False, the second part is incorrect. If an equation has no solution, then variables disappear and it results in nonsense equation.C. Any equation can have one solution, infinitely many solutions, or no solutions. This does not depend on whether the variable appears on only one side or on both sides.
TrueD. If the variable only appears on one side of an equation, then the equation can always be solved for the variable. By contrast, an equation with variables on both sides always has no solution or infinitely many solutions.
False, the second part is incorrect. The variables can be taken to the same side of equation. If they cancel and leave a correct equation, then it results in infinitely many solutions. If they cancel and leave incorrect equation, then it results in no solution. If it simplifies with variable on one side, then there is one solution.consider the system of equations find a linearly independent pair of solutions. please denote exponentiation with exp(a*t) rather than e**(a*t) or e^(a*t)
The general solution to the system of equations is:
x(t) = c1*[1, 1]*exp(0*t) + c2*[1, -1]*exp(2*t)
where c1 and c2 are constants.
To find a linearly independent pair of solutions for the given system of equations, we first need to find the eigenvalues and eigenvectors of the coefficient matrix.
The coefficient matrix is
[ 1 -1 ]
[ 1 -1 ]
The characteristic equation is:
det(A - λI) = 0
where A is the coefficient matrix, λ is the eigenvalue and I is the identity matrix.
Substituting the values we get,
det( [1-λ -1 ] ) = (1-λ)(-1) - (-1)(-1) = λ^2 - 2λ = 0
[-1 1-λ]
Solving for λ, we get λ=0, λ=2.
Now we need to find the eigenvectors for each eigenvalue λ.
For λ=0, we have:
(A - 0I)x = 0
[1 -1] [x1] [0]
[1 -1] [x2] = [0]
This gives us the equation x1 = x2. Thus, any vector of the form [t, t] where t is any non-zero constant will be an eigenvector corresponding to λ=0.
For λ=2, we have:
(A - 2I)x = 0
[-1 -1] [x1] [0]
[ 1 -1] [x2] = [0]
This gives us the equation x1 + x2 = 0. Thus, any vector of the form [t, -t] where t is any non-zero constant will be an eigenvector corresponding to λ=2.
Therefore, a linearly independent pair of solutions is:
x1 = [1, 1], corresponding to λ=0
x2 = [1, -1], corresponding to λ=2
So the general solution to the system of equations is:
x(t) = c1*[1, 1]*exp(0*t) + c2*[1, -1]*exp(2*t)
where c1 and c2 are constants.
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find the positive square root of 217.05 and 100.2001......with division method
The square root of 217.05 is 14.73 and the square root of 100.2001 is 10.01.
How to depict the square root?It should be noted that square root is factor of a number that when multiplied by itself will give the original number.
In this case, the square root of 217.05 is 14.73 and the square root of 100.2001 is 10.01.
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Write f(x)=|x-2| as a piecewise function.
Answer:
Hi! A piecewise function is a function defined by multiple sub-functions, or pieces of different functions over different intervals. Piecewise definition is a way of expressing the function and is not actually integral to the function itself.
f(x) = |x - 2| is an absolute value function. As a piecewise function, it's written like this:
f(x) = {x - 2, x ≥ 2
{-x + 2, x < 2
Hope this helps! Have a great day.
Find the surface area of the figure. Hint: the surface area from the missing prism inside the prism must be ADDED!
To find the surface area of the figure, we need to consider the individual surfaces and add them together.
First, let's identify the surfaces of the figure:
The lateral surface area of the larger prism (excluding the base)
The two bases of the larger prism
The lateral surface area of the smaller prism (excluding the base)
The two bases of the smaller prism
The lateral surface area of a prism is given by the formula: perimeter of the base multiplied by the height.
The bases of the prisms are rectangles, so their areas can be calculated by multiplying the length by the width.
To find the missing prism's surface area, we need to consider that it is a smaller prism nested inside the larger prism. The lateral surface area and bases of the missing prism should also be included.
Once we have calculated the individual surface areas, we add them together to find the total surface area of the figure.
Without specific measurements or dimensions of the figure, it is not possible to provide a numerical answer. Please provide the necessary measurements or dimensions to calculate the surface area.
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WHOEVER CAN DO THIS CORRECTLY ILL LOVE U FOREVER!!
compare each pair of grocery items and work out which option is the better value for money.
a) 5kg of potatoes for $4.95 or 7.5kg for $7.15
b) a packet of four batteries for $3.88 or a packet of ten for $9.89
c) a 500 g tin of coffee for $9 or a 150 g had for $2.99
Answer:
A
Step-by-step explanation:
i just know :)
A car company that provides maintenance services for cars wants to measure its overall customer satisfaction of its services.
Which measure provides the best information to the company?
OA. complaints per service
OB. complaints per year per customer
OC. complaints per year
OD. complaints per customer per service
The answer choice which best provides a measure of the overall customer satisfaction of the company's services is; Choice A; complaints per service.
Which measure provides the best information to the company?It follows from the task content that the car company is in a bid measure the overall customer satisfaction of its services.
Hence, the company must be focused on all customers and also, the measure should be in relation to the number of services rendered.
Ultimately, the correct and best measure of it's services is; Choice A.
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tomas orders a meal that costs $7.89. Lisa's meal costs $9.05. About how much is the combined cost of their meals?
Answer:
$17
Step-by-step explanation:
This is a question on Estimation - which is a very important skill!
the first meal was $7.89, which is roughly $8the second meal was $9.05, which is roughly $9
whats the mean of the numbers 3 7 2 4 7 5 7 1 8 8
Answer:
5.2
Step-by-step explanation:
adding all the numbers together and dividing it by 10.
Answer:
mean = 5.2
Step-by-step explanation:
The mean (or average) of a group of numbers is defined as the value calculated by adding all the given numbers together and then dividing the result by the number of numbers given.
Therefore,
\(\boxed{\mathrm{mean = \frac{sum \ of \ the \ numbers}{number \ of \ numbers}}}\).
In the question, the numbers given are: 3, 7, 2, 4, 7, 5, 7, 1, 8, and 8.
Therefore,
sum = 3 + 7 + 2 + 4 + 7 + 5 + 7 + 1 + 8 + 8
= 52
There are 10 numbers given in the question. Therefore, using the formula given above, we can calculate the mean:
\(\mathrm{mean = \frac{52}{10}}\)
\(= \bf 5.2\)
Hence, the mean of the given numbers is 5.2.
The ice cream above is going to melt.
When it does, will it fit in the cone or will it overflow?
Explain.
The spherical ice cream scoop and the right cone have a radius of 3 cm.
The height of the cone is 15 cm.
Show all your work.
Since the volume of the sphere V = 36π cm³is less than that of the cone, V' = 45π cm³ the ice cream will not overflow.
What is the volume of a sphere?The volume of a sphere is given by V = 4πr³/3 where r = radius of sphere
To determine if the ice cream above is going to melt and when it does, will it fit in the cone or will it overflow? We know that the ice cream is a sphere, the ice cream will not overflow if the volume of the ice cream equals the volume of the cone. If its volume is greater than the volume of the cone, it will overflow.
We know that the ice cream is a sphere, we determine its volume as V = 4πr³/3 where r = radius of sphere = 3 cm
We substitute the variable into the equation,
V = 4πr³/3
V = 4π(3 cm)³/3
V = 4π × 27 cm³/3
= 4π × 9 cm³
= 36π cm³
Next, we determine the volume of the cone to be V' = 1/3πr²h where
r = radius of cone = 3 cm and h = height of cone = 15 cmWe now substitute the variables into the equation, thus
V' = 1/3πr²h
V' = 1/3π(3 cm)² × 15 cm
= 1/3π × 9 cm² × 15 cm
= 3π cm² × 15 cm
= 45π cm³
We see that V = 36π cm³ < V' = 45π cm³
Since the volume of the sphere is less than that of the cone, the ice cream will overflow.
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What are the x- and y- coordinates of point P on the directed line segment from A to B such that P is Two-thirds the length of the line segment from A to B? x = (StartFraction m Over m n EndFraction) (x 2 minus x 1) x 1 y = (StartFraction m Over m n EndFraction) (y 2 minus y 1) y 1 (2, â€"1) (4, â€"3) (â€"1, 2) (3, â€"2).
The x - and y - coordinates of point P are ( - 1 , 2 )
The standard form of the linear equation is,
\(y=mx+c\)
Where \(m\) is the gradient of the line.
Given-
P is 2/3 the length of the line segment from A to B. Suppose \(m\) is two, then
\(m+n=3\)
This gradient of the line can be calculated with the following formula-
\(m=\dfrac{y_{2}-y_{1} }{x_{2}- x_{1} }\)
Here, (\(x_{1} ,y_{1}\)) and (\(x_{2} ,y_{2}\)) are two arbitrary points.
In the given graph, at point A(9,-8),
\(x_{1} =9\)
\(y_{1} =-8\)
At point B (-6,7),
\(x_{2} =-6\)
\(y_{2} =7\)
Use the formula has given in the problem which is,
\(x=\dfrac{m}{m+n}(x_{2} -x_{1} )+x_{1}\)
Put the values,
\(x=\dfrac{2}{3}(-6 -9 )+9\)
\(x=\dfrac{2}{3}(-15 )+9\)
\(x=2(-5 )+9\)
\(x=-10+9\)
\(x=-1\)
For y use the formula given in the problem which is
\(y=\dfrac{m}{m+n}(y_{2} -y_{1} )+y_{1}\)
\(y=\dfrac{2}{3}(7 -(-8) )+(-8)\)
\(y=\dfrac{2}{3}(7+8) )-8\)
\(y=\dfrac{2}{3}(15) )-8\)
\(y={2}(5) -8\)
\(y=2\)
Hence, the x - and y - coordinates of point P are ( - 1 , 2 )
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Answer: (4, –3)
Step-by-step explanation:
Triangle ABC has vertices A(-1,1), B(1,3) and C(4,1). The image of ABC after the transformation matrix T=
The coordinates of transforming image of the vertices of the triangle ABC are A' (1, -1) ,B' (3, 1) , and C' (1, 4).
In triangle ABC,
Coordinates of the vertices of triangle ABC are,
A(-1,1), B(1,3) and C(4,1)
The transformation T y=x reflects the points across the line y=x.
The image of each point, we simply swap the x and y coordinates of each point.
So, applying the transformation T y=x to the vertices of triangle ABC, we get,
A' = (-1, 1) → (1, -1)
B' = (1, 3) → (3, 1)
C' = (4, 1) → (1, 4)
This implies,
The image of triangle ABC under the transformation T y=x is triangle A'B'C', where,
A' is located at (1, -1)
B' is located at (3, 1)
C' is located at (1, 4)
Therefore, in triangle ABC labeling the coordinates of the vertices of A'B'C' after transformation are as follows,
A' (1, -1)
B' (3, 1)
C' (1, 4)
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The above question is incomplete, the complete question is:
Triangle ABC has vertices A(-1,1), B(1,3) and C(4,1). The image of ABC after the transformation T y=x is A’ B’ C’. State and label the coordinates of A’ B’ C’.
Answer for this and an simple explanation thank you very much
The percentage of 100 square quadrilateral grid shaded is 96%.
What is a Square?Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. The equal sides and 90° internal angles of each square form serve as indicators of its identity.A square is a closed, four-sided, two-dimensional (2D) shape. In a square, all four sides are equal and parallel to one another.A square is a closed form with four equal sides and interior angles that are both 90 degrees. Three fundamental square formulas are frequently employed in geometry. The first one involves computing its area, the second one involves computing its perimeter, and the third one involves computing the diagonal of a square formula.since there are 4 unshaded grids and rest 96 are shaded then the percentage will be
shaded percentage = 96 × 100/100 = 96%
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On a coordinate plane, triangles A B C and D E F are shown. Triangle A B C has points (4, 2), (7, 2), (4, 6). Triangle D E F has points (negative 2, negative 1), (4, negative 3), and (4, negative 1).
How do the areas of triangle ABC and DEF compare?
Comparing the areas of triangles ABC and DEF, we can see that both triangles have the same area of 6 square units.
To compare the areas of triangles ABC and DEF, we can use the formula for calculating the area of a triangle, which is:
Area = (1/2) * base * height
Triangle ABC:
The base of triangle ABC can be calculated as the distance between points (4, 2) and (7, 2), which is 7 - 4 = 3 units.
The height of triangle ABC can be calculated as the distance between points (4, 2) and (4, 6), which is 6 - 2 = 4 units.
Therefore, the area of triangle ABC is (1/2) * 3 * 4 = 6 square units.
Triangle DEF:
The base of triangle DEF can be calculated as the distance between points (-2, -1) and (4, -1), which is 4 - (-2) = 6 units.
The height of triangle DEF can be calculated as the distance between points (4, -1) and (4, -3), which is -3 - (-1) = -2 units (taking the absolute value, the height is 2 units).
Therefore, the area of triangle DEF is (1/2) * 6 * 2 = 6 square units.
Comparing the areas of triangles ABC and DEF, we can see that both triangles have the same area of 6 square units.
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Answer:
A is the answer(Area of ABC is greater than area of DEF. )
Step-by-step explanation:
Can someone help me with this. Will Mark brainliest.
Eight squared plus B squared equals 14 squared
\(8^2 +B^2 = 14^2\\\\\implies B^2 = 14^2 -8^2 \\\\\implies B^2 = 132\\\\\implies B=\pm\sqrt{132} = \pm 2\sqrt{33}\)
Please help.
Algebra.
Which ists the steps in the correct order to fnd the medan of this data set? 24 16 23 30, 18 29 1 Put the numbers in order 2. Cross off highvlow pairs 3 Add the leftover numbers 4. Divsde the sum by 1 Pt the numbers in order 2. Cross of highlow pairs 1 Cross off hightow pars 2. Add the 3 Divsle the sum by over numbers 1 Cross of highlow pars
Answer:
1. Put the numbers in order.
2. Cross off high/low pairs.
3. Add the leftover numbers.
4. Divide the sum by 2.
Step-by-step explanation:
Given:
24, 16, 23, 30, 18, 29
The ordered steps involved in Calculating the median of the data set given :
1.) put the numbers in order: This involves arranging the numbers in the dataset usually in ascending order :
16, 18,23,24,29,30
2.) Cross off high/low pairs: take out equal amount of input from both the left and right hand side. Here we have (23, 34) left
3) Add the leftover numbers: Since the values left is more than one, both values are summed, we have (23+24) = 47
4.) Divide the sum by 2 : Get the average of the two numbers to obtain the median value. Here the average is (23+24)/2 = 47/2 = 23.5
Answer:
A: 1. Put the numbers in order.
2. Cross off high/low pairs.
3. Add the leftover numbers.
4. Divide the sum by 2.
Step-by-step explanation:
edg2020
1. Calculate the compound interest on N2,000 for 2years at the rate of 10% per annum
The compound interest on N2,000 for 2 years at the rate of 10% per annum is N441.00.
Compound interest is the interest earned not only on the principal amount but also on the accumulated interest. To calculate the compound interest, we use the formula:
A = P\((1 + r/n)^{(nt)\)where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.
In this case, P = N2,000, r = 0.1 (10%), n = 1 (compounded annually), and t = 2 years.
So, A = 2000\((1 + 0.1/1)^{(1*2)\) = N2,441.00
Therefore, the compound interest is N2,441.00 - N2,000.00 = N441.00.
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Tell whether the ratios form proportions
4:20 and 6:30
9/18,3/8
9514 1404 393
Answer:
yesnoStep-by-step explanation:
1) Each of the ratios can be reduced to 1 : 5, Since both can be reduced to the same ratio, the do form a proportion.
4 : 20 = 1 : 5
6 : 30 = 1 : 5
__
2) The first ratio can be reduced to 1/2. The second ratio is not 1/2 and cannot be reduced. Since they are different ratios, they do not form a proportion.
9/18 = 1/2
3/8 = 3/8
c
76 mm
57 mm
What is the length of the hypotenuse?
C =
millimeters
Answer:
19.7
Step-by-step explanation:
Farmer John can till his field 1.5 times faster than Farmer Bob. If they work together, they can till the field in 6 hours. How long would it take Farmer John on his own
Answer:
It would take Farmer John 10 hours on his own to till his field.
Step-by-step explanation:
Let;
J = Time spent by John alone
B = Time spent by Bob alone = 1.5 * J = 1.5J
Time spent by both = 6
Using reciprocal, time spent by John alone can be calculated as follows:
(1 / J) + (1 /1.5J) = 1 / 6
Multiply through by 6J and solve for J, we have:
(6J / J) + (6J / 1.5J) = 6J / 6
6 + (6 / 1.5) = J
J = 6 + 4 = 10
Therefore, it would take Farmer John 10 hours on his own to till his field.
Please select the best answer from the choices provided.
Answer: 34
Step-by-step explanation:
SOH-CAH-TOA
To find the angle, find the inverse cosine of the adjacent side over the hypotenuse. ArcCos(72/87)=34
to divide data with a high value of h and a low value of l into k classes, the class interval must be:
The number of classes should be an integer and this value will typically be a fraction. The limit needs to be raised in order to take into account all observations when this calculation yields an integer.
The fixed and variable costs can be determined by solving the system of equations if the variable cost is a fixed charge per unit and the fixed costs stay the same. The high-low method can, however, produce more or less accurate findings based on the distribution of values between the highest and lowest monetary values or quantities, therefore it is important to use caution when applying it.
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Jack jogs and rides his bike for a total of 75 minutes every day. He rides his bike for 15 minutes longer than he jogs. Part A: Write a pair of linear equations to show the relationship between the number of minutes Jack jogs (x) and the number of minutes he rides his bike (y) every day. (5 points).
Answer:
for B : he spend 30 minutes jogging and 45 minutes riding his bike
Step-by-step explanation:
75-15=60
60/2=30
jogging (x) =30
30+15=45
riding bike (y) =45
hopefully that help with B
Jack jogs for 30 minutes and he rides his bike for 45 minutes
Let x represent the number of minutes jogged and y represent the number of minutes that he ride his bike.
Jack jogs and rides his bike for a total of 75 minutes every day. hence:
x + y = 75 (1)
He rides his bike for 15 minutes longer than he jogs. hence:
y = x + 15
-x + y = 15 (2)
Solving equations 1 and 2 simultaneously gives:
x = 30, y = 45
Jack jogs for 30 minutes and he rides his bike for 45 minutes
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The balance of Micah's checking account is $648. Micah needs at least $800 in the account to cover his expenses. Write and solve an inequality that tells how much money Micah needs to deposit. Explain why there are infinite solutions to the inequality. PlZZ answer asap
Answer:
152
Step-by-step explanation:
800-648=152
The price of a Nintendo switch was reduced from $200 to $50. By what percentages was the price of the Nintendo switch reduced?
Answer:
1\4 of the price
Step-by-step explanation:
200 -50 =150-50=100-50=50-50=0 you can do it 5 times so its reduced by 1\4
Answer:
25% off
Step-by-step explanation:
Given linear function g(x) = 5 - 2/3 x
a) find g(9)
AND
b) solve g(x)=7 for x
For part a, we need to substitute 9 for x.
g(x) = 5 - 2/3(9). Simplify the right side of the equation.
g(x) = 5 - 6.
g(x) = -1
For part b, we need to solve for x by substituting 7 for g(x).
7 = 5 - 2/3x. Subtract 5 from both sides.
2 = -2/3x. Divide each side by -2/3.
-3 = x
Convert 67 kilometers to miles. (1 kilometer = 0.62 miles)
6.2 miles
41.54 miles
51.60 miles
108.06 miles
The number of miles in 67 kilometers will be 41.54 miles. Then the correct option is B.
What is conversion?Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.
Convert 67 kilometers to miles.
The conversion of kilometers to miles is given below.
1 km = 0.62 miles
Then the number of miles in 67 kilometers is calculated as,
⇒ 67 x 0.62
⇒ 41.54 miles
The number of miles in 67 kilometers will be 41.54 miles. Then the correct option is B.
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What is the slope of the line that passes through the points (-5,6) and (-9,-6) write answer in simplest form
Answer:
m = 3
Explanation:
the slop is 3