Answer:
260
Step-by-step explanation:
The z score for a normal distribution is given by the formula
[tex]z = \dfrac{X-\mu}{\sigma}[/tex]
where
X is the data point, μ is the mean and σ is the standard deviation
Given
Mean μ = 500
Standard deviation σ = 80
z-score = -3
and plugging in these values for z-score formula we get
[tex]-3 = \dfrac{X -500}{80}[/tex]
==>
-240 = X - 500
-240 + 500 = X
260 = X
or
X = 260
X
What is the multiplicative inverse of 5/6
The multiplicative inverse of 5/6 as required to be determined in the given task content is 6/5.
What is multiplicative inverse?It follows from the task content that the multiplicative inverse of the given number; 5/6 is required to be determined.
By definition; it follows that the Multiplicative inverse of an expression refers to its reciprocal. It is the value that, when multiplied by the original, give a product of 1 (the multiplicative identity element).
So,
5/6 × 6/5
= 30/30
= 1
Hence, 6/5 is the multiplicative inverse of 5/6
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Solve each inequality given that the function f is increasing over its domain
1.f(2x+3)>f(3x-2), Df=[3,infinity)
2f(x^2-2)
Answer:
Since f is increasing over its domain, we know that if a > b, then f(a) > f(b). Therefore, we have:
2x + 3 > 3x - 2
Solving for x, we get:
x < 5
So the solution set is:
Df = [3, infinity) intersect (-infinity, 5) = [3, 5)
Therefore, the inequality is true for all x in the interval [3, 5).
Since f is increasing over its domain, we know that if a > b, then f(a) > f(b). Therefore, we have:
x^2 - 2 < y^2 - 2
Simplifying, we get:
x^2 < y^2
Taking the square root of both sides, we get:
|x| < |y|
So the solution set is:
Df = [3, infinity)
|x| < |y| means that either x < y or -x < y. Therefore, the solution set can be divided into two parts:
Part 1: x^2 - 2 < 0, i.e., x is in the interval (-sqrt(2), sqrt(2)). For this part, we have:
Df intersect (-sqrt(2), sqrt(2)) = empty set
Part 2: x^2 - 2 >= 0, i.e., x is outside the interval (-sqrt(2), sqrt(2)). For this part, we have:
Df intersect (-infinity, -sqrt(2)] union [sqrt(2), infinity) = [3, infinity)
Therefore, the inequality is true for all x in the interval [3, infinity) except for the interval (-sqrt(2), sqrt(2)).
Step-by-step explanation:
You are remodeling a kitchen, including the formal dining room and breakfast nook. It is time to purchase flooring for the space. You need to calculate the area of the entire space and then find the cost of the materials that you would like to purchase to make sure you do not go over your budget of $7,500. See the picture for your blueprint.
The area of the entire space is 38.57 units².
We have,
From the figure,
Total area.
= Semicircle + Rectangle + Trapezium + Rectangle
Now,
Semicircle:
Radius = 2 units
Rectangle:
Length = 4 units
Width = 3 units
Trapezium:
Parallel sides = 5 units and 3 units
Height = 1 unit
Rectangle:
Length = 2 units
Width = 5 units
Now,
Area of the entire space.
= πr² + 4 x 3 + 1/2 x 1 x (5 + 3) + 2 x 5
= 22/7 x 2 x 2 + 12 + 1/2 x 1 x 8 + 10
= 88/7 + 12 + 4 + 10
= 12.57 + 12 + 4 + 10
= 12.57 + 26
= 38.57 units²
Now,
1 unit = 7 feet
So,
= 38.57 X 7² feet²
= 1889.93 feet²
Thus,
The area of the entire space is 38.57 units².
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members 1st federal credit union charges a $27 per check overdraft protection fee. On March 8, you had $1,400 in your account. Over the next four days, you wrote checks for: March 9, $1,380.15, March 10 $670 and $95.67, March 11, $130 and March 12, $87.60. How much will you pay in overdraft protection fees? How much will you owe the bank after March 12?
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The standard deviation of a sample taken from population A is 17.6 for a sample of 25. The standard deviation of a sample taken from population B is 21.2 for a sample of 30.
The standard deviation of the sample mean differences is ____. (Round your answer to the nearest hundredth.)
The standard deviation of the sample mean differences is, 16.98.
Since, We know that;
Standard deviation is defined to be the square root of the population variance of the vector. The sample standard deviation s is defined to the square root of the sample variance of the vector.
Here, The standard deviation of the sample mean differences should be calculated using the standard deviations of the two populations.
In order to see how they differ, we need to first subtract them from each other,
So, we get:
21.2 - 17.6 = 3.6
We then divide this number with the first standard deviation as follows:
⇒ 3.6/21.2 x 100
⇒ 16.98
Therefore, the standard deviation of the sample mean is, 16.98.
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5
Consider the following set of test scores for a history class:
100, 45, 60, 60, 50, 50, 45, 95, 60, 55, 40
Would it be better for the teacher to consider the mean or the median to interpret the overall results of the test?
The median because it better reflects that most students did not pass and the teacher should revisit the material.
The median because it is a passing score and shows most students passed the test.
The mean because it coincides with the mode and shows that most students passed the test.
The mean because it is higher and the teacher wants to feel good about the students.
1 point
Consider the following set that shows the high temperature in Orlando for the past 6 days:
91, 90, 90, 90, 84, 82, 81,90
The mode of these data would be type your answer.....
1 point
Consider the following set that shows the high temperature in Orlando for the past 8 days:
91, 90, 90, 90, 84, 82, 81,90
The median of these data would be type your answer.....
1) For the following set of test scores for a history class, 100, 45, 60, 60, 50, 50, 45, 95, 60, 55, 40, it would be better for the teacher to consider D) The mean because it is higher and the teacher wants to feel good about the students.
2) The mode of these data about the high temperatures in Orlando for the past 8 days would be 90.
3) The median of these data about the high temperatures in Orlando for the past 8 days would be 80.
What are the mean, mode, and median?The mean, mode, and median are three centers of measurement.
The mean refers to the average value in the data set, obtained as the quotient of the total value divided by the number of items.
The mode refers to the value that occurs most in the data set.
Lastly, the median is the middle value for a data set arranged in descending or ascending order.
1. Test Scores:
100, 45, 60, 60, 50, 50, 45, 95, 60, 55, 40
Total value = 660
Number of data items = 11
Mean = 60 (660 ÷ 11)
Median = 55
Mode = 60
2. High Temperature:
91, 90, 90, 90, 84, 82, 81, 90
Total Value = 698
Number of data items = 8
Mean = (87.25 (698 ÷ 8)
Median = 90
Mode = 90
3. High Temperature:
91, 90, 90, 90, 84, 82, 81,90
Median = 80 (81, 82, 84, 90, 90, 90, 90, 91)
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HELP ASAP!! ( failing my class lol pls help asappp )
What was the scale factor used?
Was the orientation preserved or changed?
Was congruence preserved or changed?
1) The scale factor of dilation is 1/3
2) The orientation is preserved in dilation of A to A'
3) The congruence is not preserved in dilation of A to A'
We know that the scale factor is nothing but the ratio of the size of the transformed image to the size of the original image.
Here from the attached graph we can observe that the square A is transformed to A'
The side length of square A is 18 units and the side length of square A' is 6
So, the scale factor would be,
r = A' / A
r = 6/18
r = 1/3
We know that a dilation preserves the shape and orientation of the figure, but changes the size of he figure.
So, the dilations do not preserve congruence, as it changes the size of a figure.
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Write an equation of a quadratic function that has been reflected in the x-axis, shifted horizontally to the right 2 units and stretched by a factor of 3.
The equation is writen in the quatradtic form as [tex]g(x) = -3a(x - 2)^2 - 3b(x - 2) - 3c[/tex]
How to write the equationQuadratic equation is of the form
[tex]f(x) = ax^2 + bx + c[/tex]
the transformations
Reflect it in the x-axis: To reflect a function in the x-axis, we change the sign of the function.
[tex]g(x) = -ax^2 - bx - c[/tex]
Shift it horizontally to the right by 2 units: Our function becomes:
[tex]g(x) = -a(x - 2)^2 - b(x - 2) - c[/tex]
Stretch the function by a factor of 3: To stretch a function vertically, we multiply the function by the stretch factor, k.
[tex]g(x) = -3a(x - 2)^2 - 3b(x - 2) - 3c[/tex]
So, the final transformed quadratic function is: [tex]g(x) = -3a(x - 2)^2 - 3b(x - 2) - 3c[/tex]
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please help for this question
Trapezium T is reflected across line x = 3 to form trapezium U and reflected across line x = 7 to form tralpelzium V
The figure is attached
What is reflection over a lineReflection across a line is a geometric transformation which mirrors a point, shape or figure exactly across a pre-defined plane known as the Line of Reflection.
In other words, the size and general outline are kept in tact while orientations are adjusted. Furthermore, each corresponding point on either side of the Line of Reflection is found to be equidistant from the said axis and lies along a perpendicular line.
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A group consists of seven democrats and eight republicans
a) The number of ways that four people can be selected from this group of fifteen is: 1365 ways
b) The number of ways that four Republicans can be selected from the eight Republicans is: 70 ways
c) The probability that the selected group will consist of all republicans is: 5.13%
How to solve Permutation and Combination?The selection of people from a given list can be done in the following way: if we want to select r people from a list of n people, then we can do so in:
nCr = n!/(r!(n - r)!)
In the first part of the question, we don't need to decide on specific people from each group, but in the subsequent parts, it becomes an added restriction.
A. This can be done in:
15C4 = 15!/(4!(15 -4!)
= 1365 ways
B. This can be done in:
8C4 = 8!/(4!(8 - 4)!)
= 70 ways
C. The chances that all are republicans is a measure of the ratio of the answer in the first question to the second:
70/1365 = 0.0513 = 5.13%
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A restaurant had 160 lunch customers last weekend. Of those, 90 ordered seltzer, 75 ordered a chicken sandwich, and 38 ordered both. There were 45 customers who ordered seltzer and a veggie sandwich. Eleven more people ordered a veggie sandwich than a tuna sandwich. Complete the two-way frequency table for the data.
The figures that complete the two-way frequency table are attached accordingly.
How is this so?Let represent the table like this:
Chcken Veggie Tuna Total
Seltzer 38 45 A 90
Iced Tea B C D E
Total 75 F G 160
NOte that:
A = 90 - 38 - 45 = 7
B = 75 - 38 = 37
E = 160-90 = 70
C = D + 11
D + 11 + D = 70-37
2D = 33-11
D=22/2
D=11
Thus C = 22
F = 45 + C
F = 45 + 22
F = 22
G = A + D = 18
?thus, the completed two-way frequency table is:
Chcken Veggie Tuna Total
Seltzer 38 45 7 90
Iced Tea B 22 11 70
Total 75 67 18 160
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A 100k
B 200k
C 300k
D 400k
The picture above shows 4 glass jars, all with the same number of gas molecules but at different temperatures.
Which of the jars would experience the greatest pressure?
O Jar A
O Jar B
O Jar C
O Jar D
Answer: The jar that would experience the greatest pressure is Jar D.
This is because the pressure of a gas is directly proportional to its temperature (according to the ideal gas law). Since all four jars have the same number of gas molecules, the jar with the highest temperature (Jar D) would have the greatest pressure.
Step-by-step explanation:
For f(x) = x + 4√
x
+
4
, what is the value of the function when x = 8? Round to the nearest hundredth.
A car costing $34,000 is leased for $473 monthly over 5 years with a $2,420 down payment. The car’s residual value is estimated to be $16,400. If the car is purchased with a $5,000 down payment, the monthly loan payments will be $623 for 60 months. Calculate the costs of leasing this car and buying this car. Is buying or leasing less expensive and by how much less?
The cost of leasing the car is $28,780 and the cost of buying the car is $42,380.
Buying the car is more expensive than leasing by $13,600 over the 5-year period.
We have,
To calculate the cost of leasing the car, we first need to determine the total amount paid over the lease term:
= (Monthly payment x Number of months) + Down payment
= ($473 x 60) + $2,420
= $28,780
To determine the cost of buying the car, we first need to calculate the total loan amount:
= Cost of car - Down payment + Residual value
= $34,000 - $5,000 + $16,400
= $45,400
Now,
Total loan cost = (Monthly payment x Number of months) + Down payment
Total loan cost = ($623 x 60) + $5,000
Total loan cost = $42,380
So,
The cost of leasing the car is $28,780 and the cost of buying the car is $42,380.
To determine which option is less expensive, we can subtract the cost of leasing from the cost of buying:
Cost of buying - Cost of leasing = $42,380 - $28,780
Cost of buying - Cost of leasing = $13,600
So,
Buying the car is more expensive than leasing by $13,600 over the 5-year period.
Thus,
The cost of leasing the car is $28,780 and the cost of buying the car is $42,380.
Buying the car is more expensive than leasing by $13,600 over the 5-year period.
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Suppose the probability of an event is 0.20. What are the odds in favor of this event?
Answer:
If the probability of an event is 0.20, the odds in favor of the event can be calculated as follows:
- Divide the probability of the event occurring by the probability of the event not occurring:
0.20 / (1 - 0.20) = 0.20 / 0.80
- Simplify the fraction:
0.20 / 0.80 = 1 / 4
Therefore, the odds in favor of the event are 1 to 4.
Step-by-step explanation:
The odds in favor of an event with a probability of 0.20 is a ratio of 1 to 4.
Explanation:The question is about calculating the odds in favor of an event with a probability of 0.20. The odds in favor of an event is defined as the ratio of the probability that the event will happen to the probability that it will not happen.
In this case, the probability of the event is 0.20, therefore the probability that it will not happen is 1 - 0.20 = 0.80. So, the odds in favor of the event are 0.20 to 0.80 or it can be simplified to 1 to 4.
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What is the equation of the line in the slope-intercept form?
Answer:
5y= -3x +15
Step-by-step explanation:
y=mx+c is slope Intercept form where M is slope and c is Intercept
The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K= C + 273.15.
The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15. When solved for C, the equation is K - 273.15. Therefore, the correct option is option C.
Temperature is a unit of warmth or coldness that can be defined in the context of any number of arbitrary scales. It indicates the direction through which the energy from heat will naturally flow, i.e., through a hotter (body) to a colder (body) body. Temperature cannot be the same as a thermodynamic system's energy; for instance, a blazing match is significantly hotter than an iceberg.
K = C + 273.15
K - 273.15 = C + 273.15 - 273.15
K - 273.15 = C
Therefore, the correct option is option C.
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Your question is incomplete but most probably your full question was,
The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15.
When solved for C, the equation is
C = K – 273.15
C = 273.15 – K
C = K + 273.15
C = 273.15K
Find the quotient of
99 m² n³-81m³n²-18mn
__________________
3mn
The quotient of the expressions 99 m² n³-81m³n²-18mn and 3mn is 33mn² - 27m²n - 6
Finding the quotient of the expressionsFrom the question, we have the following parameters that can be used in our computation:
99 m² n³-81m³n²-18mn
__________________
3mn
To find the quotient of the expressions, we simply divide each term of the numerator by 3mn
Using the above as a guide, we have the following:
99 m² n³-81m³n²-18mn
__________________ = 33mn² - 27m²n - 6
3mn
Hence, the solution is 33mn² - 27m²n - 6
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I don't understand please help
The diameter of the circle is 396 units.
The length of the arc is 0.83π units.
How to find the diameter of the circle?The length of an arc of a circle is given by the formula:
L = θ/360 * πd
where θ is the measure of the angle and is the diameter of the circle
Given: θ = 80° and L = 88π
L = θ/360 * πd
88π = 80/360 * π * d
88 = 80/360 * d
80 * d = 88 * 360
80d = 31680
80d = 31680/80
d = 396 units
PART 2
If θ = 25°, r = 6 (from the image above). Thus, d = 2 * 6 = 12
L = θ/360 * πd
L = 25/360 * π * 12
L = 0.83π units
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A sale transaction on rental property closes on December 16. The landlord received the December rent of $713 on December 1. Assuming the closing day is the buyer's, and that the 365-day method is used for prorating, which of the following entries would appear on the settlement statement?
- To answer a question about a sale transaction on rental property that closes on December 16, you need to calculate how much rent the landlord owes to the buyer for the remaining days of December.
- You can use a formula called prorated rent to calculate the amount of rent that is proportional to the number of days that the buyer owns the property. Prorated rent splits the amount between the previous and new owners of a rental property.
- The formula for prorated rent is: Prorated Rent = (Monthly Rent / Number of Days in Month) x Number of Days Rent Owed
- In your case, the monthly rent is $713, the number of days in December is 31, and the number of days rent owed is 16 (from December 16 to December 31). The closing day is the buyer's, so the landlord owes rent for that day as well.
- Plugging these values into the formula, you get: Prorated Rent = (713 / 31) x 16 = 368.26
- This means that the landlord owes $368.26 to the buyer for the remaining days of December.
I hope this helps you answer your question.
Jay’s mean score for four quizzes is 9 . His scores for the first three quizzes are 8,5, and, 9. What is Jay’s score for the last quiz?
Jay's score for the last quiz is 14.
Let's use the formula for finding the mean:
Mean = (Sum of all scores) / (Number of scores)
We can rearrange this formula to solve for the unknown score:
Unknown score = (Mean x Number of scores) - (Sum of all other scores)
Given that Jay's mean score for four quizzes is 9, we have:
Mean = 9
Number of scores = 4
Jay's scores for the first three quizzes are 8, 5, and 9. The sum of these scores is:
Sum of first three scores = 8 + 5 + 9 = 22
Using the formula above, we can find Jay's score on the fourth quiz:
Unknown score = (Mean x Number of scores) - (Sum of all other scores)
Unknown score = (9 x 4) - 22
Unknown score = 36 - 22
Unknown score = 14
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Which graph represents the following system? Y>x+4 y
The solution is, Option 4 is correct., the graph represents the following system of inequalities.
Explanation:
We are given two inequality y<-x-4 and y>2x-3.
We need to choose correct graph from given choices.
First we draw the graph of each equation
Equation 1: y<-x-4
We draw the graph using slope intercept form.
Slope=-1 and y-intercept (0,-4)
Test point (0,0). Put (0,0) into equation 1 y<-x-4
We get . This is false statement. Graph will shade away from point (0,0).
Equation 2: y<2x-3
We draw the graph using slope intercept form.
Slope=2 and y-intercept (0,-3)
Take test point (0,0). Put (0,0) into equation 2, y>2x-3
We get . This is true statement. Graph will shade towards the point (0,0).
Please take a look attachment for the graph.
Option 4 is correct.
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complete question:
Which graph represents the following system of inequalities?
y < -x - 4
y > 2x - 3
2y+3y-18=-33?????????????????
Answer:
y=-3
Step-by-step explanation:
Answer:
Y = - 3
Step-by-step explanation:
So lets help you out here.....
First of all you should set up how you have to solve, let do this step by step...
Step 1 : 2y + 3y - 18 = - 33
Step 2 : Combine like terms... (2y + 3y = 5y)
Step 3 : Set up your new equation (5y - 18 = - 33)
Step 4 : Subtract negative 18 by negative 33 (- 18 - 33 = -15)
(PS: In a calculator - 18 - 33 is -51 but the 18 is also a negative so it would be - 15)
Step 5 : Divide (- 15 / 5 = - 3)
And that is how you solve this problem, have a great day!!!!!!
Based on a poll, 60% of Internet users are more careful about personal information when using a public Wi-Fi hotspot. What is the probability that among three randomly selected Internet users, at least one is more careful about personal information when using a public Wi-Fi hotspot? (Round to three decimal places as needed.)
The probability that at least one of the three users is more careful is 0.936.
How to find the probability that among three randomly selected Internet users, at least one is more carefulWe need to find the probability that a single randomly selected Internet user is more careful, which is 0.60.
The probability that none of the three users are more careful is (0.40)^3 = 0.064.
Therefore, the probability that at least one of the three users is more careful is 1 - 0.064 = 0.936.
Rounding to three decimal places, the answer is 0.936.
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How do you solve for X???
Answer:
x= -18
Step-by-step explanation:
-2/3x + -21/4 = 27/4
-8x-63=81
-8x-63+63=81+63
-8x=144
-8x/-8 = 144/-8
x=-18
A store specializing in mountain bikes is to open in one of two malls. If the first mall is selected, the store anticipates a yearly profit of $1,050,000 if successful and a yearly loss of $350,000 otherwise. The probability of success is 2 If the second mall is selected, it is estimated that the yearly profit will be $700.000 if successful; otherwise, the annual loss will be $210.000. The probability of success at the second mall is
_ Complete parts (a) through (c) below
a. What is the expected profit for the first mall?
The expected profit for the first mall is $1,750,000
Given data ,
Let the probability be represented as A and B
Now , For Event A:
Probability of success at the first mall (P(A)) = 2 (given)
Profit if successful (P(A) * Profit | Success) = 2 * $1,050,000 = $2,100,000
Loss if unsuccessful (Loss | Failure) = -$350,000
For Event B:
Probability of success at the second mall (P(B)) = unknown (to be calculated)
Profit if successful (P(B) * Profit | Success) = P(B) * $700,000
Loss if unsuccessful (Loss | Failure) = -$210,000
Expected Profit for Event A = P(A) * Profit | Success + (1 - P(A)) * Loss | Failure
Expected Profit for Event A = 2 * $1,050,000 + (1 - 2) * -$350,000
Expected Profit for Event A = $2,100,000 - $350,000
Expected Profit for Event A = $ 1,750,000
Hence , the profit is $ 1,750,000
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From a group of 10 people, you randomly select 2 of them. What is the probability that they are the 2 oldest people in the group?
The probability that they are the 2 oldest people in the group is 0.011
Understanding probabilityProbability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.
The probability of an event A is denoted by P(A)
From the question above, let us calculate the probability.
The probability that the first person selected is the oldest is 1/10.
Then, the probability that the second person selected is the second oldest is 1/9, since there are only 9 people left to choose from.
Therefore, the probability of selecting the two oldest people in the group is:
1/10 * 1/9 = 1/90
So, the probability of selecting the two oldest people in the group is 1/90 or approximately 0.011 or 1.1%.
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On a coordinate plane, point A is (negative 2, 3), point B is (2, 4), and point C is (0, negative 1). The points are connected with lines. Use the graph to find the coordinates of each vertex in triangle ABC. is the coordinate of Point A. is the coordinate of Point B. is the coordinate of Point C.
Match each equation with its y-intercept. ( 0 , b a ) ( 0 , c a ) ( 0 , b c ) ( 0 , c b ) ( 0 , a c ) ( 0 , a b ) Equations y-intercepts c x + b y = a arrowRight c x + a y = b arrowRight b x + a y = c arrowRight a x + b y = c arrowRight
The equation with the following y-intercepts are matched
a) c x + b y = a: (0, a/b)
b) c x + a y = b: (0, b/a)
c) b x + a y = c: (0, c/a)
d) a x + b y = c: (0, c/b)
Given data ,
Let the set of equations be represented by
c x + b y = a
c x + a y = b
b x + a y = c
a x + b y = c
Now , the y-intercept of the equation is when the value of x = 0
So , when x = 0
The y intercepts of the equation are
c x + b y = a: (0, a/b)
c x + a y = b: (0, b/a)
b x + a y = c: (0, c/a)
a x + b y = c: (0, c/b)
Hence , the equations are solved
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full method please
4×(2-6)+35÷(-7)
Answer:
-21
Step-by-step explanation:
4×(-4)+35÷(-7)
Plus and minus together makes minus
Multiplication and division goes first
-16-5= - 21