The coordinates of point T' is (2, -2)
How to determine the image pointA dilation is a transformation that changes the size of a figure but not its shape.
In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.
In this case, the point T (3, -3) is transformed under a dilation of 2/3 with respect to the origin.
So the image point is (kx, ky) = (3 * 2/3, -3 * 2/3) = (2, -2)
So the image point of T under a dilation of 2/3 with respect to the origin is (2, -2)
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need help asap image attached
Answer: angle dce is the angle that is vertical
how to find class width
To determine the width:
By deducting the lowest point from the highest, get the range of the full data set.By how many classes there are, divide it.Round up this number (usually, to the nearest whole number).What is class width?When all the classes inside a distribution have the same width, the distance between the maximum and minimum bounds of the distribution is referred to as the class width. The distance between the bottom bounds of two successive classes is another name for the class breadth. Class width in a frequency distribution is the distance between the upper and lower limits of any class or category. Example: The first class's class breadth is 5-1, or 4. For the second class, the class size is 10-6, or 4, and so on. The size of a class interval, also known as the class width, class size, or class length, is the distance between the lower and upper class boundaries.To learn more about width, refer to:
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parametrize the portion of the parabola, x=2y^2-4 where -1
The portion of the parabola from t=-1 to t=1 can be parametrized as x=2t²-4 and y=t.
A parabola is a symmetrical and U-shaped curve that is defined by a mathematical equation.
In this case, we will use the variable t to represent the y-coordinate and find the corresponding x-coordinate. The equation becomes y=t, and substituting this into the original equation, we get
=> x=2t²-4.
To find the portion of the parabola where -1≤t≤1, we can plot the points (x, y) for various values of t in this range.
when t=-1,
=> x=2(-1)²-4 = 0.
And when
t=1, x=2(1)²-4 = -2.
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What is 15 1/2 - 1 11/20 and how would you solve this please do step by step!
Step-by-step explanation:
the simplest way for me is
1. to convert both terms into full fractions (not mixed numbers).
2. then to bring both fractions to the same denominator.
3. and then do the actual calculation.
and if needed, we can
4. then convert the result back into mixed numbers.
1.
15 1/2 = (15×2 + 1)/2 = 31/2
1 11/20 = (1×20 + 11)/20 = 31/20
2.
we need to convert 31/2 into a fraction .../20, so that we can actually combine it with the 31/20.
how do we get from 2 to 20 ? by multiplying by 10.
in order to keep the value of the fraction unchanged, we need to do the same multiplication also to the numerator :
31/2 × 10/10 = 310/20
3.
310/20 + 31/20 = 341/20
4.
341/20 = (17×20 + 1)/20 = 17 1/20
to get this you do an integer division and note the remainder.
341/20 = 17 remainder 1
Additional Challenge: Khalil is working with a geometric sequence. He knows that t(0) = 3 and that the sum of the first three terms ( t(0), t(1) , and t(2) ) add up to 63 Help him figure out the sequence.
The solution is, the sequence is, {3, 31, 49, ..............}
What is Arithmetic progression?An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.
here, we have,
t(0) = 3
and that the sum of the first three terms ( t(0), t(1) , and t(2) ) is 63
let, the 1st term = a
common difference = d
so, we have,
a = 3
and, a+ a+d + a+ 2d = 63
or, 9+ 3d = 63
or, 3d = 54
or, d = 18
Hence, The solution is, the sequence is, {3, 31, 49, ..............}
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GEOMETRY Triangle KLM is shown. Graph the image of the triangle after a dilation centered at the origin with a scale factor of 2
When ΔKLM is dilated with a scale factor of 2 the new ΔK'L'M' has vertices K'(4,10), L'(8,4) and M'(4,4).
What is dilation?
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.
The ΔKLM has the coordinates of vertices - K(2,5), L(4,2) and M(2,2)
If the scale factor is 2, then every coordinate point of the original triangle is multiplied by the scale factor 2.
When the triangle is dilated with the scale factor of 2, the coordinate points formula becomes -
(x,y) → (2x,2y)
So, obtain the new triangle ΔK'L'M' -
K(2,5) → [2(2),2(5)] → K'(4,10)
L(4,2) → [2(4),2(2)] → L'(8,4)
M(2,2) → [2(2),2(2)] → M'(4,4)
The graph for the new coordinates have been ploted.
Therefore, the new coordinates are K'(4,10), L'(8,4) and M'(4,4).
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The diagram shows a circle with centre O.
A, B & C lie on the circumference of this circle.
Given that AC is a diameter of the circle and ∠ACB = 59°, find the size of ∠BAC as highlighted in the diagram.
The required angle ∠BAC is equal to 31
What is the angle sum property of a triangle?The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°
Given here: ∠ACB = 59° and the diameter of the circle as AC
Now since AC is diameter , When two angles are subtended by the same arc, the angle at the centre of a circle is twice the angle at the circumference.
Thus ∠ABC= 1/2 × 180
=90
Thus ∠BAC= 180-90-59
= 31
Hence, The required angle ∠BAC is equal to 31
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trigonometric ratios in right triangles calculator
A trigonometric ratios calculator is a tool that helps you find the sine, cosine, and tangent ratios in a right triangle. To use a trigonometric ratios calculator, you need to enter the lengths of the sides of the right triangle and the calculator will calculate the values of the sine, cosine, and tangent ratios for the angles in the triangle.
Here's how you can use a trigonometric ratios calculator to find the sine, cosine, and tangent ratios in a right triangle:
1. Enter the lengths of the sides of the right triangle into the calculator.
2. Select the angle for which you want to find the trigonometric ratios.
3. The calculator will display the values of the sine, cosine, and tangent ratios for the selected angle.
Note that the trigonometric ratios are defined only for right triangles, so it's important to make sure that the triangle you are working with is a right triangle before using a trigonometric ratios calculator.
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A trigonometric ratios calculator is a tool that helps you find the sine, cosine, and tangent ratios in a right triangle. To use a trigonometric ratios calculator, you need to enter the lengths of the sides of the right triangle and the calculator will calculate the values of the sine, cosine, and tangent ratios for the angles in the triangle.
Here's how you can use a trigonometric ratios calculator to find the sine, cosine, and tangent ratios in a right triangle:
1. Enter the lengths of the sides of the right triangle into the calculator.
2. Select the angle for which you want to find the trigonometric ratios.
3. The calculator will display the values of the sine, cosine, and tangent ratios for the selected angle.
Note that the trigonometric ratios are defined only for right triangles, so it's important to make sure that the triangle you are working with is a right triangle before using a trigonometric ratios calculator.
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use implicit differentiation to find an equation of the tangent line to the graph of the equation at the given point.1 ln 7xy = e7x − y, (1/7, 1)
The equation of the tangent line to the graph of the equation at the given point (1/7, 1) is [tex]y = 7x - 6/7 + 1.[/tex]
[tex]y' = (7e7x + 7x - 1)/7xy[/tex]
1. Use implicit differentiation to differentiate both sides of the equation with respect to x:
[tex]ln 7xy = e7x − y ln 7xy + (7xy) (y') = (7e7x) + (e7x)(7)[/tex]
2. Solve for y':
[tex]y' = (7e7x + 7x - 1)/7xy[/tex]
3. Plug in the given point to find the slope at that point:
[tex]y' = (7e(1/7) + (1/7) - 1)/(7*(1/7)*1) = (7 + 1 - 1)/1 = 7[/tex]
4. Use the point-slope form of a line to find the equation of the tangent line:
[tex]y - 1 = 7(x - 1/7)y = 7x - 6/7 + 1[/tex]
The equation of the tangent line to the graph of the equation at the given point (1/7, 1) is[tex]y = 7x - 6/7 + 1.[/tex]
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function rules and tables calculator r=2t
Answer:
1 and 1
5 and 10
7 and 14
Step-by-step explanation:
you just have to multiple 2 by the number in (T)
A rectangular paperboard measuring 22 in long and 18 in wide has a semicircle cut out of it to find the area of the paperboard that remains.
The area of the paperboard that remains is 268.83 square inches.
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
Given that, a rectangular paperboard measuring 22 in long and 18 in wide has a semicircle cut out.
Area of rectangular paperboard length×width
= 22×18
= 396 square inches
Area of a semicircle = 1/2 ×πr²
Here, r=18/2 = 9 inches
= 1/2 ×3.14×9²
= 127.17 square inches
So, remaining area = 396-127.17
= 268.83 square inches
Therefore, the area of the paperboard that remains is 268.83 square inches.
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let matrices a, b be where i^2=-1. find the order of the group generated by a and b under matrix multiplication
The order of the group generated by matrices a and b under matrix multiplication is a process of multiplying the matrices and counting the number of distinct matrices that can be produced.
A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
The order of a group generated by matrices a and b refers to the number of distinct matrices that can be produced by multiplying a and b a certain number of times.
To find the order of the group, we need to start by multiplying a and b and see if we get any new matrices. If we do, we keep multiplying those matrices until we get back to the original matrices a and b.
The order of the group is the number of distinct matrices we get in this process.
It is important to note that matrix multiplication is associative, which means that the order in which we multiply the matrices does not affect the result. Also, the identity matrix is a special matrix that, when multiplied by any matrix, produces the same matrix.
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how can you plot a one dimensional vector field on the real line for a differential equation in python
Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation.
Can Python solve differential equations?Using the Scipy.integrate package and the functions odeint or solve ivp, one can use Python to solve differential equations. t: Time points at which the solution should be reported To maintain the precision of the answer, additional internal points are frequently calculated but are not reported.Differential equations can be solved using the Python library diffeqpy. Its basic routines use DifferentialEquations. jl to provide high performance solving of a variety of differential equation types, such as: Function mapping and discrete stochastic (Gillespie/Markov) simulations are examples of discrete equations.ODE gives us a technique to represent the dynamic changes in specified variables numerically. Imagine taking a picture of the outdoors; this image lacks any motion, making it a static system. A static system is the reverse of that.Here i attached answer.
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the capacity of an elevator is either children or adults. if children are currently in the elevator, how many adults can still get in?
The capacity of the elevator is 15 children or 11 adults. If 9 children are currently on the elevator, then there are 15 - 9 = 6 spots available for either children or adults.
However, since the maximum number of adults the elevator can hold is 11, the answer to the question is 11 - 9 = 2 adults can still get in.
You can act for the unknown amounts by the use of variables. Follow ignoring the description is and convert it one by one mathematically. For example, if it is asked to increase some item by 5, then you can add 5 in that item to increase it by 5.
If a thing is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
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what happens to the capture rate if this condition is violated? the confidence interval will capture the population parameter less often than the specified confidence level. not enough information is provided to determine what happens to the capture rate if the 10% condition is violated. the confidence interval will capture the population parameter 10% as often as the specified confidence level. the confidence interval will capture the population parameter more often than the specified confidence level. the confidence interval will capture the population parameter at the same rate as the specified confidence level.
the capture rate will be lower than what is indicated in the confidence level.
A C% confidence interval gives an interval of plausible values for a parameter. The interval is calculated from the data and has the form, point estimate ± margin of error.
When the random and large counts conditions are met, a C% confidence interval for the population proportion p is
Point estimate ±margin of error
Ƹ± √Ƹ(1 − Ƹ)/
Where z is the critical value for the standard normal curve with C% of its area between –z and +z.
Your interval will look like: ______ < p <________
Confidence Intervals in a 4 Step Process:
Statistics Problems Demand Consistency
1. State: What parameter do you want to
estimate, and at what confidence level?
2. Plan: Identify the appropriate inference
method: check conditions.
3. Do: If the conditions are met, perform
calculations.
4. Conclude: Interpret your interval in the
context of the problem.
When constructing a confidence interval for a population proportion, it is checked that sample size is less than 10% of population size.
This condition is important due to the the fact that when sample size is less than of population size, observations are closer to independent.
If this requirement is not met, it is not possible to calculate standard deviation of distribution.
If this requirement is not met, it is not possible to calculate standard deviation of distribution correctly.
If standard deviation is not correct, confidence level will be inaccurate. There are less chances to obtain population parameter in confidence interval.
Therefore, the capture rate will be lower than what is indicated in the confidence level.
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The capture rate will be lower than what is indicated in the confidence level.
An interval of conceivable values for a parameter is provided by a C% confidence interval. The interval is formed as a point estimate with a margin of error and is calculated from the data.
A C% confidence interval for the population proportion p when the random and large counts requirements are satisfied is
Point estimate margin of error
Ƹ± √Ƹ(1 − Ƹ)
Where z is the critical value for the standard normal curve with C% of its area between –z and +z.
Your interval will look like: ______ < p <________
Confidence Intervals in a 4-Step Process:
1. Clarify what parameter you wish to estimate and at what level of confidence.
2. Make a plan and decide which inference technique is best. Check the circumstances.
3. If the criteria are satisfied, run the calculations.
4. Summarize: Consider your interval in light of the issue.
It is ensured that the sample size is less than 10% of the population size when creating a confidence interval for a population proportion. This requirement is crucial because observations are more likely to be independent when the sample size is smaller than the population size. Calculating the distribution's standard deviation is impossible if this condition is not satisfied. The standard deviation of the distribution cannot be appropriately calculated if this condition is not satisfied. The confidence level will be incorrect if the standard deviation is incorrect. Population parameters are less likely to be found in a confidence interval. As a result, the capture rate will be lower than what the confidence level predicts.
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A number is a restriction on a rational expression if the number makes the denominator of the rational expressionTrueFalse
Answer: The values that make the denominator equal to zero for a rational expression are known as restricted values. How do you identify restrictions in rational expressions? The restriction is that the denominator can not be equal to zero. So in this problem, since 4x is in the denominator it can not equal zero.
Find the total surface area of this prism where the cross-section is an isosceles triangle.
Perpendicular Height: 5cm
Base Length: 24cm
Base Side Length: 10cm
Answer:
Step-by-step explanation:
620 cm^2
Step-by-step explanation:
Area of isosceles triangles:
A = (b×h) ÷ 2
Substitute
(24 × 5) ÷ 2
120 ÷ 2 = 60 cm^2
There are 2 triangles so:
60 × 2 = 120 cm^2
Area of 2 identical rectangles:
- They are identical and this is shown by the two short lines which indicate that this is an isosceles triangle. They have 2 identical sides.
A = L × W
Substitute
10 × 13 = 130
Because there are two:
130 × 2 = 260 cm^2
Area of the rectangle at the bottom:
- Let's not forget the rectangle at the bottom of this shape.
A = L × W
Substitute
24 × 10 = 240 cm^2
Add these all together to get the total surface area:
120 + 260 + 240 = 620 cm^2
Answer: 620 cm^2
Answer:
620cm squared
Step-by-step explanation:
a=bxh/2
so this means
24x5/2=area of one triangle(60cm squared)
since there are two .that means the area for both triangles is 120cm squared
for the recatngles:
a=lxw
Substitute
10 × 13 = 130
since there are 2 of them,
130 × 2 = 260 cm^2
the rectangle on the bottom:
a=lxw
24x10=240cm squared
240+260+120=620
discuss how discrete mathematics led to fewer cultural distinctions and where mathematics became more a unifying language of its own.
Discrete mathematics is a branch of mathematics that deals with objects that can assume only distinct, separated values and can be counted. It has played a significant role in reducing cultural distinctions by providing a unifying language for the field of mathematics and a common understanding for solving problems across cultures.
Through discrete mathematics, people from different backgrounds and cultures can communicate and collaborate more effectively, breaking down cultural barriers and promoting unity.
For example, discrete mathematics has been used to create algorithms that solve complex problems in computer science, cryptography, and optimization, making it possible for people from different cultures to work together to solve these problems.
Additionally, the standardization of mathematical language and symbols through discrete mathematics has made it easier for people to understand and share mathematical ideas across cultures, further promoting unity and reducing cultural distinctions.
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A successful music app tracked the number of song downloads each day for a month for 4 music artists, represented by lines l, j, m, and d over the course of a month. Which line represents an artist whose downloads remained constant over the month?
By applying linear equation concept, it can be concluded that the line representing the artist whose downloads have remained constant over the month is the horizontal one, line m.
Linear equation is an equation that contains one or more variables, where each variable has the power of one.
Linear equation graph with a particular slope will be formed if this equation is depicted in a Cartesian diagram. The slope is usually called the gradient of the line (m), so the equation can be written as y = mx + c.
If the line graph is sloping to the right indicates that the gradient is positive. Conversely, if the line graph is sloping to the left indicates that the gradient is negative.
Therefore, the line representing the artist whose downloads have remained constant over the month is the horizontal one, line m.
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the statistic x¯ is used as an estimator for which of the following?
As a point estimator for, we utilise x-bar (sample mean) (mu, population mean)
What is mean or average?The average value in mathematics is the middle number, which is calculated by dividing the total number of numbers by the sum of all the numbers. A set of data's average is calculated by adding up all the values and dividing the result by the total number of values.
We use the x-bar (sample mean) as a point estimator for (mu, population mean). As long as the sample is random, this estimator's impartial long-run distribution is centred at (mu).
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Complete question -
Geometry worksheet. Can someone help please?
For the given geometry the perimeter is 37 units, area is 118.55 square units and the type is pentagon.
What is area of a pentagon?The space enclosed by a pentagon's sides is referred to as the pentagon's area. Various techniques can be used to compute it depending on the dimensions that are known. The kind of pentagon also makes a difference. For instance, if it is a normal pentagon, the area can be determined using a single formula; but, if it is an irregular pentagon, we must divide it into various polygons and add their areas to determine the pentagon's area.
The perimeter is the sum of length of all the sides of a pentagon.
P = 5s
P = 5(7.4) = 37 units.
The area of the pentagon is given as:
A = 1/2 (P)(a)
Substitute the value of P = 37 and a = 6.4086:
A = 1/2 (37)(6.4086) = 118.55 square units.
Type: Pentagon.
Hence, for the given geometry the perimeter is 37 units, area is 118.55 square units and the type is pentagon.
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What is the best answer to report for (515 x 0.0025) + ?24.57 25.86 26 25.8575 25.9
The best way to report for (515 x 0.0025) is 25.86 and it is done using the concept of significant figures.
Given (515 x 0.0025) + 24.57
We are asked to report the answer in the best way. This can be done using the concept of significant figures.
We can see that 515 has 3 significant figures
0.0025 has 4 significant figures ( we have to consider the zeros after the decimal)
24.57 has 4 significant figures
Thus the best answer will have 4 significant figures.
(515 * 0.0025 ) + 24.57 = 25.8575 = 25.86
We have to round off the answer to 4 significant figures, thus it'll be 25.86 ( 5 becomes 6 because the figure next to 5 is 7, thus 5 will be rounded off to 6 )
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nth taylor polynomial about 0 e^x
The function to derive an nth Taylor polynomial is y = nthTaylorPolyExp( n, x )
%y = nthTaylorPolyExp( n, x )is a function that returns 3rd Taylor polynomial of exponential function at x=0.
% n is an input argument, which indicates the degree of Taylor
% polynomial.
% x is an input argument
% y is the output.
y=zeros('like',x);
% ============= YOUR CODE HERE ==============
% Instructions: Return nth Taylor polynomial of exponential function at x=0.
% You can use built-in function factorial(n) to return n!,
% and use for loop to get the sum.
for i = 0:n
% y = y + (-1)^i * (x.^(2 * i)) / factorial(2 * i); is my version, but its incorrect.
end
Thus, the function to derive an nth Taylor polynomial is y = nthTaylorPolyExp( n, x )
Complete question: How do I write the function to derive an nth taylor polynomial?
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-15/4(2x-2/3)<64+11/4x help
Answer:
[-23.27 < x]
Step-by-step explanation:
Distribute -15/4 to the numbers in the parenthesis:
[tex]\frac{-15}{4}*2x[/tex] = [tex]-\frac{30}{4}[/tex]
[tex]\frac{-15}{4}*-\frac{2}{3}[/tex] = [tex]\frac{5}{2}[/tex]
[tex]-\frac{30}{4} + \frac{5}{2} < 64 + \frac{11}{4}x[/tex]
Combine like terms:
[tex]-5 < 64 + \frac{11}{4}x[/tex]
Subtract 64 from both sides:
[tex]-64 < \frac{11}{4}x[/tex]
Multiply both sides by 4:
[tex]-256 < 11x[/tex]
Divide both sides by 11:
[tex][-23.27 < x][/tex]
4) a patient who just underwent a scheduled surgery and is in pacu. what should the nurse run the pump if they want to infuse a 1000ml bag of lactated ringers over 9 hours? ____ ml/hr
The nurse should run the pump at 111.1 ml/hr.
To infuse a 1000ml bag of lactated ringers over 9 hours, the nurse must determine the hourly rate at which the fluid should be infused. This can be done by dividing the total volume of the fluid (1000 ml) by the number of hours it will take to infuse it (9 hours).
So, the hourly rate would be:
1000 ml ÷ 9 hours = 111.1 ml/hr.
Therefore, the nurse should run the pump at 111.1 ml/hr in order to infuse the 1000ml bag of lactated ringers over 9 hours.
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Final exam question
A team's winning percentage is calculated as follows:
D. PCT = games won/total games played.
How to obtain a team's winning percentage?A team's winning percentage is obtained applying a proportion, as the percentage is given by the division of the number of desired outcomes, that is, the number of games won, by the total number of outcomes, that is, the number of games played.
Hence the equation used to calculate the percentage is given as follows:
PCT = games won/total games played.
Meaning that the correct option is given by option D.
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Consider the system modeled by the following difference equation. y(n) = 3y(n-1) + x(n − 2)
Assume the underlying system is casual with zero initial conditions. What is the transfer function?
Assuming the underlying system is casual with zero initial conditions, the transfer function is Y(z)/X(n) = 1/([tex]z^2[/tex] - 3z).
The differential equation is y(n) = 3y(n-1) + x(n − 2).
Since there are no initial conditions, the underlying system is known to be casual.
Considering the Transfer function.
Z transform properties are used
y(n-1) = [tex]z^{-1}[/tex]Y(z)
y(n) = Y(z)
x(n-2) = [tex]z^{-2}[/tex]X(n)
Now putting the value in the equation
Y(z) = 3[tex]z^{-1}[/tex]Y(z) + [tex]z^{-2}[/tex]X(n)
Multiply by [tex]z^2[/tex] on both side, we get
[tex]z^2[/tex]Y(z) = 3zY(z) + X(n)
Subtract Y(z) 0n both side, we get
[tex]z^2[/tex]Y(z) - 3zY(z) = X(n)
Y(z)([tex]z^2[/tex] - 3z) = X(n)
Divide by ([tex]z^2[/tex] - 3z) on both side, we get
Y(z) = X(n)/([tex]z^2[/tex] - 3z)
Divide by X(n) on both side, we get
Y(z)/X(n) = 1/([tex]z^2[/tex] - 3z)
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A coin is tossed three times. Find the probability of getting all heads or all tails.
Answer:
1/8
Step-by-step explanation:
The coin is flipped three times; the total number of outcomes = 2 × 2 × 2 = 8. P(X) = |X| / |Ω| = 1/8.
A basketball coach determines the team has a 1 32 probability of winning a tournament. Which choice describes the probability of the coach’s basketball team winning the tournament most accurately?
The probability of the coach’s basketball team winning the tournament most accurately impossible.
What is probability ?3.03 percent Chance of A
As a result, you could say there is a 3.03% Probability instead of saying there are 1 to 32 Odds.
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of occurrences that follow a probability distribution.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
A basketball coach determines the team has a 1 32 probability of winning a tournament.
The probability of the coach’s basketball team winning the tournament most accurately impossible.
The complete question is
A basketball coach determines the team has a 1/32 probability of winning a tournament. Which choice describes the probability of the coach's basketball team winning the tournament most accurately?
answer choices
certain
impossible
likely
unlikely
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Solve each equation, and write the algebraic reason for each step.
1. 3y+5=2y-8
2. -2(x-1)=3x-13
3. 3b+4+b=16
The equations are solved to give
1. y = 13
2. x = 3
3. b = 3
How to determine the solution to the expressionsIt is important to note that algebraic expressions are expressions composed of variables, terms, factors, constants and coefficients.
From the information given, we have that the expressions are;
3y+5=2y-8
Now, collect like terms
3y - 2y = -8 - 5
subtract the like terms
y = 13
-2(x-1)=3x-13
expand the bracket
-2x + 2= 3x - 13
collect like terms
-2x -3x = -13 - 2
subtract the like terms
-5x = -15
x = 3
3b+4+b=16
collect like terms
4b = 12
b = 3
Hence, the values are 13. 3 and 3
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