Consider the points P(1.2,5) and Q(9.4. 11) a. Find Po and state your answer in two forms (a, b, c) and ai + bj+ck. b. Find the magnitude of Po c. Find two unit vectors parallel to Po a. Find PO PO-OO
Answers
The position vector of point P, denoted as \(\(\overrightarrow{OP}\)\), can be found by subtracting the position vector of the origin O from the coordinates of point P.
Given that the coordinates of point P are (1.2, 5), and the origin O is (0, 0, 0), we can calculate \(\(\overrightarrow{OP}\)\) as follows:
\(\[\overrightarrow{OP} = \begin{bmatrix} 1.2 - 0 \\ 5 - 0 \\ 0 - 0 \end{bmatrix} = \begin{bmatrix} 1.2 \\ 5 \\ 0 \end{bmatrix} = 1.2\mathbf{i} + 5\mathbf{j} + 0\mathbf{k} = 1.2\mathbf{i} + 5\mathbf{j}\]\)
The position vector of point Q, denoted as \(\(\overrightarrow{OQ}\)\), can be found similarly by subtracting the position vector of the origin O from the coordinates of point Q. Given that the coordinates of point Q are (9.4, 11), we can calculate \(\(\overrightarrow{OQ}\)\) as follows:
\(\[\overrightarrow{OQ} = \begin{bmatrix} 9.4 - 0 \\ 11 - 0 \\ 0 - 0 \end{bmatrix} = \begin{bmatrix} 9.4 \\ 11 \\ 0 \end{bmatrix} = 9.4\mathbf{i} + 11\mathbf{j} + 0\mathbf{k} = 9.4\mathbf{i} + 11\mathbf{j}\]\)
a) Therefore, the position vector of point P in the form (a, b, c) is (1.2, 5, 0), and in the form \(\(ai + bj + ck\)\) is \(\(1.2\mathbf{i} + 5\mathbf{j}\)\).
b) The magnitude of \(\(\overrightarrow{OP}\)\), denoted as \(\(|\overrightarrow{OP}|\)\), can be calculated using the formula \((|\overrightarrow{OP}| = \sqrt{a^2 + b^2 + c^2}\)\), where a, b, and c are the components of the position vector \(\(\overrightarrow{OP}\)\). In this case, we have:
\(\[|\overrightarrow{OP}| = \sqrt{1.2^2 + 5^2 + 0^2} = \sqrt{1.44 + 25} = \sqrt{26.44} \approx 5.14\]\)
Therefore, the magnitude of \(\(\overrightarrow{OP}\)\) is approximately 5.14.
c) To find two unit vectors parallel to \(\(\overrightarrow{OP}\)\), we can divide \(\(\overrightarrow{OP}\)\) by its magnitude. Using the values from part a), we have:
\(\[\frac{\overrightarrow{OP}}{|\overrightarrow{OP}|} = \frac{1.2\mathbf{i} + 5\mathbf{j}}{5.14} \approx 0.23\mathbf{i} + 0.97\mathbf{j}\]\)
Thus, two unit vectors parallel to \(\(\overrightarrow{OP}\)\) are approximately \(0.23\(\mathbf{i} + 0.97\mathbf{j}\)\) and its negative, \(-0.23\(\mathbf{i} - 0.97\math.\)
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Related Questions
PLEASE THIS IS MY THIRD TIME ASKING TODAY I NEED HELP!!!
please only answer if you know how to do this!
Answers
Answer:
The answers are:
Step-by-step explanation:
1)Adjacent
2)Vertical
3)Corresponding
4)None of these
5)1,7 3,5 4,6 2,8 (<--angle numbers)
6)4,5 2,7 (<--angle numbers)
7)1=85, 2=95, 3=85, 4=85
8)1=60, 2=120, 3=60, 4=120
9)1=90, 2=90, 3=90, 4=90
10) No, they are not parallel. A protractor would show that the intersection angles are different, meaning the lines aren't parallel.
SORRY it took so long hope this helps!!
Answer:
1.
adjacent
2.
vertical
3.
corresponding
4.
none (just regular interior and thats not an option)
5.
(<5,<7) (<6,<8) (<1,<3) (<2,<4)
6.
(<2,<7) (<6,<3)
7.
<1= 85
<2= 95
<3= 85
<4= 85
8.
<1= 60
<2= 120
<3= 60
<4= 120
9.
<1= 90
<2= 90
<3= 90
<4= 90
10. No, its not parallel because the corresponding angles 1 and 7 aren't equal. You can use a protractor to figure this out by finding the measurement of angles 1 and 7. Because they aren't equal degrees, the lines will cross at some point
Once we have categorized an object, our memory of the object increasingly resembles thecategoryA) algorithm.B) prototype.C) heuristic.D) mental set
Answers
Once we have categorized an object, our memory of the object increasingly resembles the category is B) prototype. This means that when we categorize an object, our memory of it begins to resemble the prototype or typical example of that category. For example, if we categorize a bird as a robin, our memory of the bird will increasingly resemble the characteristics of a typical robin.
This happens because our brain uses prototypes as a shortcut to process information and make sense of the world around us. We use prototypes to quickly identify objects and make assumptions about their characteristics based on their category.
our memory of an object after categorization is influenced by the prototype of the category. This helps us to quickly process and make sense of information, but it can also lead to errors and biases in our thinking.
A prototype is a mental image or best example of a category. When we categorize an object, our memory of the object increasingly resembles the prototype because we tend to recall the most representative or typical example of the category.
Once we categorize an object, our memory of the object becomes more like the prototype, which is the best example of the category. This is because we tend to remember the most representative or typical examples of a category.
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By how much does the price of a ticket for the gold section exceed the price for a ticket for the silver section?
Answers
Answer:
$8
Step-by-step explanation:
This system of equations relates the ticket price, in dollars, for seats in the silver (x) and gold (y) sections at a rock concert. x + 2y = 82 3x + y = 96 By how much does the price of a ticket for the gold section exceed the price for a ticket for the silver section?
Two equations are presented in this question
x + 2y = 82 equation 1
3x + y = 96 equation 2
Multiply equation 1 by 3
3x + 6y = 246 equation 3
subtract equation 2 from 3
5y = 150
y = 30
Substitute for y in equation 1
x + 2(30) = 82
x = 82 - 60
x = 22
difference in price = 30 - 22 = $8
x =
Evaluate the following expression: (show work)
3x^2 – 4^3 – 4^3 – z
If x =3, y =–2 and z=-5
Answers
3(9) - 64 - 64 + 5
27 - 64 - 64 + 5
-96
What is the first step in solving this problem?
⅘ + ½ =
Answers
Answer:
Find the least common denominator, which is 10.
find the general solution of the system bold x prime(t)equalsax(t) for the given matrix a.
Answers
The general solution of the system x'(t) = Ax(t), where A is the given matrix, can be found by solving the system of linear differential equations associated with it.
To find the general solution, we need to solve the system of linear differential equations x'(t) = Ax(t), where x(t) is a vector-valued function and A is the given matrix.
The solution involves finding the eigenvalues and eigenvectors of the matrix A. The general solution will have the form x(t) = c₁v₁e^(λ₁t) + c₂v₂e^(λ₂t) + ... + cₙvₙe^(λₙt), where c₁, c₂, ..., cₙ are constants, v₁, v₂, ..., vₙ are eigenvectors, and λ₁, λ₂, ..., λₙ are eigenvalues of A.
This general solution represents a linear combination of exponential functions, where each term corresponds to an eigenvalue-eigenvector pair. The specific values of the constants are determined by initial conditions or boundary conditions provided in the problem.
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Determine the Standard Deviation of a Variable from Raw Data Identify the given statement as either true or false. The standard deviation can be negative. (This is a reading assessment question Be certain of your answer because you only get one attempt on this question.) Choose the correct answer below False True
Answers
The given statement is false. The standard deviation is a measure of the spread of data from its mean value. It is always a positive value or zero, but it cannot be negative.
If the standard deviation is zero, it means that all the data values are the same, and there is no variability. However, if the standard deviation is small, it means that the data points are close to the mean value, while a large standard deviation indicates that the data points are widely spread out from the mean. Therefore, it is important to understand that the standard deviation cannot be negative and should always be interpreted as a positive value or zero.
The given statement is: "The standard deviation can be negative." To determine whether this statement is true or false, let's briefly review the concept of standard deviation.
Standard deviation is a measure of the dispersion or spread of a set of values in a dataset. It is calculated using the square root of the variance, which is the average of the squared differences from the mean.
Since variance involves squaring the differences, it will always be a positive value or zero. Consequently, when taking the square root of a positive value or zero, the result will never be negative.
Therefore, the correct answer to the statement "The standard deviation can be negative" is False. Standard deviation cannot be negative as it represents the dispersion of values in a dataset.
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Jonathan's lunch account began with $50 and he spends
$2.25 per day on his lunch. Nelson's lunch account began
with $13 and he spends $0.40 per day on his lunch. When
will Jonathan and Nelson have the same amount of
money in their lunch accounts?
Answers
To determine when Jonathan and Nelson will have the same amount of money in their lunch accounts, we will equate the amount of money that Jonathan has spent on his lunch to the amount of money that Nelson has spent on his lunch.
Let the number of days be represented by x. Then:
Amount Jonathan has spent on his lunch = 2.25xAmount Nelson
has spent on his lunch = 0.40xThe total amount that each of them would have spent will be equal
when 2.25x = 0.40x+50−13.
Simplifying,2.25x−0.40x = 50−13. 1.85x = 37. x = 20.
Therefore, Jonathan and Nelson will have the same amount of money in their lunch accounts after 20 days. Jonathan will have spent $45 on his lunch and Nelson will have spent $8 on his lunch. Both of them will then have $5 left in their lunch accounts. Hence, the answer is that Jonathan and Nelson will have the same amount of money in their lunch accounts after 20 days. Linear equations with one variable are the most simple types of equations to solve. We just need to remember the basic properties of algebraic equations, which is that if we perform an operation on one side of an equation, we need to do the same operation on the other side as well.
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(-2)^-3 x (-3)^-2 Pls help me solve
Answers
Answer:
\(-\frac{1}{72}\)
Step-by-step explanation:
We can solve this by using laws of indices.
To start, laws of indices state:
\(x^{-y} = \frac{1}{x^y}\)
So, let's firstly take the first part of the sum = \(-2^{-3}\)
According to the law shown above:
\(-2^{-3} = \frac{1}{-2^3} = \frac{1}{-8} = -\frac{1}{8}\)
Let's now take the second part of the sum = \(-3^{-2}\)
According to the law shown above:
\(-3^{-2} = \frac{1}{-3^2} = \frac{1}{9}\)
Finally, the sum tells us to multiply those two values together, so we do so:
\(-\frac{1}{8} * \frac{1}{9} = -\frac{1}{72}\)
Therefore, our final answer is \(-\frac{1}{72}\).
The Sweet Treat sells 40 lbs of gummy bears and 30 caramel apples every day. At this rate, how many lbs of gummy bears will be sold for every 6 caramel apples? I need an answer ASAP
Answers
Answer:
8 pounds of gummy bears.
Step-by-step explanation:
To find this answer I did:
40/30 = 4/3
Then,
4/3 x 6 = 24/3
This simplified is 8.
To check:
8/6 x 5 = 40/30
Define Chi square test OR Tests of significance based on Chi-Square. A: -Various tests of significance described previously have mostly applicable to only quantitative data and usually to the data which are approximately normally distributed. It may also happens that we may have data which are not normally Inference: (i) If Z0 ≤ Ze we accept the H0 (ii) If Z0 >Ze we reject the H0 Example: A test of the breaking strengths of two different types of cables was conducted using samples of n1 = n2 = 100 pieces of each type of cable. Do the data provide sufficient evidence to indicate a difference between the mean breaking strengths of the two cables? Use 0.01 level of significance. x = 1925 and sigm = 40 and X2 = 1905, sigma = 30
Answers
The Chi-square test is a statistical test used to determine if there is a significant difference between observed and expected frequencies in categorical data. In this example, the test is used to assess whether there is a significant difference in the mean breaking strengths of two types of cables.
The Chi-square test of significance is employed when dealing with categorical or nominal data. It compares the observed frequencies with the frequencies that would be expected if the variables were independent. In this case, the breaking strengths of the two cables are the variables of interest.
To perform the test, the first step is to define the null hypothesis (H0) and the alternative hypothesis (Ha). In this example, H0 assumes that there is no difference in the mean breaking strengths of the two cables, while Ha suggests that there is a difference.
Next, the test statistic, denoted by X2 (chi-square), is calculated using the formula X2 = Σ[(O - E)²/E], where O represents the observed frequencies and E represents the expected frequencies under the assumption of independence.
To determine the expected frequencies, we need to estimate the means and variances of the breaking strengths. Here, x = 1925 and sigma = 40 for the first cable, and x = 1905 and sigma = 30 for the second cable.
Once the test statistic is calculated, it is compared to a critical value from the Chi-square distribution with degrees of freedom equal to (r - 1)(c - 1), where r is the number of rows and c is the number of columns in the contingency table. The significance level of 0.01 determines the critical value.
If the calculated X2 value is greater than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to indicate a difference in the mean breaking strengths of the two cables. Conversely, if the calculated X2 value is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is no significant difference.
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The double number line shows that Henrik has a mass of
60
kg
60kg60, start text, k, g, end text.
A double number line with 2 tick marks. The line labeled Mass, kilograms, reads from left to right: 0, 60. The line labeled Percentage, reads from left to right: 0 percent, 100 percent.
A double number line with 2 tick marks. The line labeled Mass, kilograms, reads from left to right: 0, 60. The line labeled Percentage, reads from left to right: 0 percent, 100 percent.
Complete the table to show different percentages of Henrik's mass.
Mass (
kg
kgstart text, k, g, end text) Percentage
100
%
100%100, percent of
60
kg
60kg60, start text, k, g, end text
20
%
20%20, percent of
60
kg
60kg60, start text, k, g, end text
40
%
40%40, percent of
60
kg
60kg60, start text, k, g, end text
Answers
The completed table would look like this
Mass (kg) 12 24 36 48 60
Percentage 20% 40% 60% 80% 100%
The double number line represents Henrik's mass, which is 60 kg. The second tick mark on the Mass line corresponds to this value. The Percentage line ranges from 0% to 100%, representing the percentage of Henrik's mass. To complete the table, we need to calculate the different percentages.
To find a certain percentage of Henrik's mass, we locate the corresponding point on the Percentage line and draw a vertical line to intersect the Mass line. We can then read the mass value at that intersection point.
For example, to find 20% of Henrik's mass, we locate the point on the Percentage line labeled "20%." Drawing a vertical line from this point, it intersects the Mass line at a value of 12 kg. Therefore, 20% of Henrik's mass is 12 kg.
Similarly, for 40% of Henrik's mass, the vertical line intersects the Mass line at a value of 24 kg.
In summary, the completed table would look like this
Mass (kg) 12 24 36 48 60
Percentage 20% 40% 60% 80% 100%
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how many cups of water is 150 milliliters
Answers
The value of cups of water in milliliter can be calculated by simply divide the volume by 236.6 so 150 milliliters can be 0.634 US cups.
Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.
Divide the millilitre volume by the cup size to convert 150 mL to cups: The formula to convert 150 mL to cups is [cups] = 150 / cup size. Following are the outcomes as a result:
Cups to 150 mL =
US customary cups, 0.634010.625 legal cups in the United States60 metric cupsCanadian cups equal 0.65991Imperial cups, 0.52793Please take note that these 150mL to cups conversion figures have been adjusted to five decimals. If you're unsure which cup unit you have, you can find further details on our main page.
In any event, you must first determine the size of your cup before applying the formula or using our converter, which can change any volume, to convert 150mL to cups.
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A hot air balloon is cruising at an altitude of 150 meters above the ground when it begins its descent. The balloon descends at a rate of 5.5 meters per minute. Write an equation to model when the balloon will reach an altitude of 95 meters above the ground. Use n to represent the unknown
Answers
150 - 5.5n= 95 equation to model when the balloon will reach an altitude of 95 meters above the ground.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that,
A hot air balloon is cruising at an altitude of 150 meters above the ground when it begins its descent.
The balloon descends at a rate of 5.5 meters per minute.
We need to write an equation to model when the balloon will reach an altitude of 95 meters above the ground.
The equation is 150 - 5.5n= 95
Hence 150 - 5.5n= 95 equation to model when the balloon will reach an altitude of 95 meters above the ground.
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A point on a straight line has an x-coordinate of 3 and a y-coordinate of 6. Is the
relationship between x and y proportional?
Yes, because 3 is proportional to 6.
Yes, because 3 is proportional to 3 + 6.
It cannot be determined. At least one other point on the line is needed
to determine if x is proportional to y.
A
B
C
D It cannot be determined. At least two other points on the line are needed
to determine if x is proportional to y.
Answers
It cannot be determined. At least one other point on the line is needed to determine if x is proportional to y
Given data ,
A point on a straight line has an x-coordinate of 3 and a y-coordinate of 6
Now , A single point on a straight line does not define the connection between x and y. We must evaluate the connection between x and y for several places on the line in order to establish if x is proportional to y.
As a result, the relationship between x and y cannot be inferred only from the supplied location (3, 6). To establish the proportionality between x and y, at least one more point on the line is required
Hence , the equation of line is solved
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10
Given that m | na the relationship determine between 210 and 216.
m
10
n
A They are supplementary
B Corresponding angles
They are congruent
D Alternate interior angles
E Alternate exterior angles
F Same side interior angles
ILL GIVE 5 STARS TO THE ANSWER
Answers
Answer:
B. Corresponding Angles
Step-by-step explanation:
If it's asking for just one answer, this is the right answer.
The scatter plot shows the amount of time Adam spent studying and his test score.
What relationship do you see between the amount of the time sent studying and the test
score?
(1 Point)
In general, Adam scores higher on a test when he spends more time studying. There is not a linear relationship.
In general, Adam scores higher on a test when he spends more time studying. There is a positive linear
relationship.
In general, Adam scores lower on a test when he spends more time studying. There is a negative linear
relationship
In general, Adam scores lower on a test when he spends more time studying. There is not a relationship.
Answers
The quantity of time spent studying and the test result generally have a positive relationship. Therefore, the likelihood that the test score will rise as study time increases is high.
How do relationships start?In our approach, "personal relationships" refers to close connections between people that are created by emotional ties and interactions. These connections frequently develop out of and are strengthened by shared experiences.
Why is maintaining relationships so important?Having supportive social networks helps us deal with stress, resolve problems, and overcome obstacles. Over the course of our lives, we interact with a wide variety of people. This includes connections with close friends, family, coworkers, neighbors, and intimate, among others.
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(-1)×(-2)×(-3)×(0)×(-4)
Answers
Given the expression:
\(\mleft(-1\mright)\times\mleft(-2\mright)\times\mleft(-3\mright)\times\mleft(0\mright)\times\mleft(-4\mright)\)All the numbers are multiplied and one of the numbers is (0)
The product of (0) by any number will give (0)
So, the answer will be 0
Rita wants to enlarge a photo of her family. The original photo is 4 inches long and 6 inches wide. If she enlarges the photo by a scale factor of 2.5, what will be the dimensions of the new photo?
PLS HELPPP
Answers
Answer:56
Step-by-step explanation:
2 ( x + 2 ) -3 ( x - 7 )= 4
X/2 + 6 = 14
-4 ( 3 + x) = 4 ( x + 3 )
Answers
Answer:
кбйдлн
Step-by-step explanation:
уж гцдьжк кн бъг глог ф глас дишащи супертурнира връщаш вещица дишаш длан ганьо this is correct
is the line through (-4, 26, 1) and (-2, 0, -3) parallel to the line through (10, 18, 4) and (5, 3, 14)?
Answers
No, the line passing through (-4, 26) and (-2, 0) is not parallel to line passing through (10, 18) and (5, 3) because slopes of both lines are different.
Line is possible in 2-d forms so, it has only x and y-co-ordinates. Z-co-ordinates is not possible.
We know very well that to prove any two lines are parallel to each other we need to prove only whether their slopes are equal or not.
Now, talking about the slopes we know that if any line is passing from point(x₁,y₁) and again passing from other point(x₂,y₂) then slope(m) of that line is given by the formula=(y₂-y₁) / (x₂-x₁)
So, for first line we have (x₁, y₁)=(-4,26)
and (x₂, y₂)=(-2,0)
So, slope(m₁) of first line is =(0-26)/(-2 - (-4))
=>m₁ = -26/2
=>m₁ = -13 ----(eq1)
Similarly, for second line, we have (x₁, y₁)=(10,18)
and (x₂, y₂)=(5,3)
So, slope(m₂) of second line is =(3-18) / (5-10)
=>m₂ = -15/-5
=>m₂= 3 -------(eq2)
On comparing eq1 and eq2,we get
=>m₁≠m₂.
Hence, the given lines are not parallel.
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(Complete question) is:
Is the line through (-4, 26) and (-2, 0) parallel to the line through (10, 18) and (5, 3)?
A sample of students will be selected from all the students at a high school. Which of the following sampling methods is least likely to produce a representative sample of the students?
From a randomly chosen home basketball game, choose every tenth student who enters the gymnasium.
Answers
Convenience sampling is the least likely to produce a representative sample of the students.
What is convenience sampling?Using the convenience sampling technique, individuals are chosen based on their accessibility and availability. This kind of sampling is frequently employed in studies when the objective is to swiftly collect data from a sample group rather than to acquire a representative sample of the population. If a person is willing to engage in the study to the researcher, they are chosen for convenience sampling. The primary advantage of this strategy is that it is very simple and quick to apply; however, the primary downside is that the sample may not be representative of the population. This can result in skewed or false findings.
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The Supplies account has a balance of $3,306. A year-end inventory shows $1,768 worth of supplies left at the end of the year. The correct adjusting entry is:
Answers
The correct adjusting entry is to debit the Supplies Expense account for $1,538 and credit the Supplies account for the same amount. This entry reflects the decrease in the value of supplies used during the year.
The adjusting entry is necessary to accurately reflect the supplies consumed during the year and the remaining supplies on hand. The Supplies Expense account is debited to recognize the expense incurred for the supplies used up during the year.
The credit to the Supplies account reduces its balance to reflect the value of supplies remaining at the end of the year. This adjustment ensures that the financial statements accurately reflect the actual supplies expense for the period and the correct value of supplies on hand.
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Potential Energy can be described as Ep= m.g.h where m = mass which is measured in kilograms, g = acceleration of gravity which is measured in meters per second (m/s2), and h = height which is measured in meters . What is a possible unit measure for Potential Energy
Answers
We need to analyze the units of each of the magnitudes and solve the operations between them:
\(\begin{gathered} m\to kg \\ g\to\frac{m}{s^2} \\ h\to m \\ m\cdot g\cdot h\to kg\cdot\frac{m}{s^2}\cdot m=kg\cdot\frac{m^2}{s^2} \end{gathered}\)A possible unit for potential energy is kg*m^2/s^2.
Also we can use distributive property to replace some of the units by derived units, for example, Newtons:
\(undefined\)What is the 20th term for the following sequence?
3,-9, 27,-81, ...
Answers
Answer: -3486784401
Step-by-step explanation:
This is a geometric progression and the formula to use to find the nth term will be: = ar^(n-1)
where,
a = 3
r = -9/3 = -3
n = 20
Therefore, ar^(n-1)
= 3 × -3^19
= 3 × -1162261467
= -3486784401
if a sphere has the same volume as a cube with edge length 5, estimate the radius of the sphere
Answers
Answer:
The radius of the sphere will be:
\(r=3.1\) unitsStep-by-step explanation:
Given that a sphere has the same volume as a cube with edge length 5.
\(V_c=V_s\)
\(\:a^3=\frac{4}{3}\pi r^3\)
\(\:r^3=\frac{3\:a^3}{4\pi }\)
\(\:\:r=\sqrt[3]{\frac{3\:a^3}{4\pi \:}\:\:}\)
substitute a = 5
\(r=\sqrt[3]{\frac{3\:\left(5\right)^3}{4\pi \:\:\:}\:\:}\)
\(r=3.1\) units
Therefore, the radius of the sphere will be:
\(r=3.1\) unitsThe average cost of a gallon of gasoline increased to $2.99 per gallon from $2.85. Find the percent change.
Answers
Answer:
There was a 4.9% increase in gasoline prices.
Step-by-step explanation:
Hi!, I need help with this question:) any help would be wonderful<3
Which expression is equivalent to 1/3 (9- 6x +12)?
A. 2x + 7
B. -2x + 1
C. 2x + 1
D. -2x + 7
Answers
Answer:
B
Step-by-step explanation:
1/3(9-6x+12)
3-2x+4
1-2x
72,12,2 simplest form
Answers
Answer:
456748
Step-by-step explanation:
you 463uy2iuswhk then 13456
Bag A contains 5x coins.
Bag B contains 3x coins.
8 coins are taken from Bag B and put into Bag A
The ratio of coins in Bag A to Bag B is now 11:5
Work out the total number of coins.
Answers
Answer:
given ,
number of coins in bag A = 5x
number of coins in bag B = 3x
_____________________________________
According to Question ,
8 coins are taken from Bag B and put into Bag A
The ratio of coins in Bag A to Bag B is now 11 : 5
therefore ,
\( \frac{5x + 8}{3x - 8} = \frac{11}{5} \\ \\ 5(5x + 8) = 11(3x - 8) \\ \\ 25x + 40 = 33x - 88 \\ \\ 33x - 25x = 40 + 88 \\ \\ 8x = 128 \\ \\ x = \cancel\frac{128}{8} \\ \\ \fbox{x =16} \)
now ,
\(no. \: of \: coins \: in \: bag \: A = 5x \\ \dashrightarrow{5 \times 16 = 80 \: coins}\)
\(number \: of \: coins \: in \: bag \: B = 3x \\ \dashrightarrow{3 \times 16 = 48 \: coins}\)
\(total \: number \: of \:coins = 80 + 48 \\ \dashrightarrow{ 128 \: coins}\)
hope helpful :D