What are the attributes of the boundary line of this inequality? -3x − 2y < 6
Answers
Answer:
D. The line is dashed with a y-intercept at (0,-3) and slope of -.
Step-by-step explanation:
If you rearrange the inequality -3x-2y<6 to y=mx+b form you should get y>-3/2x-3
The slope would be mx or -3/2
The Y intercept would be b or -3
I hope this helps :)
The line with an inequality equation -3x - 2y < 6 when plotted on the graph, occupies a region with a dashed boundary line with the attributes, the slope m = -3/2, and the y-intercept c = -3.
What is an inequality equation of a line?An inequality equation for a line is the equation that is true for certain values of its variables. The inequality symbols are ' <, >, ≤, ≥ '.
How do graph an inequality?When inequality is graphed,
The region of values for which the inequality becomes true is shaded.If the inequality has < or > symbols, then the boundary of that region is represented with the dashed line. If the inequality has ≤ or ≥ symbols, then the boundary of that region is represented with the solid line (no breaks).Writing the given inequality in the slope-intercept form of a line:The inequality equation is re-arranged in the slope-intercept form to know the attributes of the line such as the slope of the line and the y-intercept of the line.
The given inequality is -3x - 2y < 6
Step 1: Rewriting the equation into the slope-intercept form:
-3x - 2y < 6
To change the sign, change the inequality symbol also.
⇒ 3x + 2y > 6
⇒ 2y > 6 - 3x
⇒ y > -3/2x - 3
Therefore, the obtained equation is in the slope-intercept form.
So, m = -3/2 and c = -3
Step 2: Graphing the inequality:
To graph the line, we need coordinates.
So, consider x = 0 inorder to get y-coordinate
On substituting,
-3(0) -2y = 6
y = -3
∴ (0, -3) is one of the coordinates of the line
Then, consider y = 0 inorder to get x-coordinate
On substituting,
-3x - 2(0) = 6
x = -2
∴ (-2, 0) is one of the coordinates of the line
These points are plotted in the graph and a line is drawn from these points.
Step 3: Observations from the graph:
Since the inequality is -3x -2y < 6 ( < ), the region above the line is shaded ( the values that satisfies the inequality). The line is represented as a dashed line that indicates the boundary for the inequality region.This means the line is excluded from the solution set of the given inequality.Therefore, the attributes of the boundary line (dashed line) are slope -3/2 and y-intercept -3.
Learn more about the graph of the inequalities here:
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Related Questions
Which measure of central tendency is more representative of the typical observation if the graph of the data is skewed to the right?
Answers
Answer:
Median
Step-by-step explanation:
The measure of central tendency is used to represent an entire group of data with a common single number. There are three types of measure of central tendency, the mean , the median and the mode. Our focus here is on the median because in any skewed dataset, The median is the best form for a skewed type of distribution. The median is the middle number in an ordered set of data.
In a skewed type of distribution, the mode is the highest point of the distribution. In the measure of central tendency, the mean is mostly influenced by the outliers and it is pulled towards to the tail region of the distribution.
Sergei runs a bakery. He needs at least 175 kilograms of flour in total to complete the holiday orders he's received. He only has 34 kilograms of flour, so he needs to buy more. The flour he likes comes in bags that each contain 23 kilograms of flour. He wants to buy the smallest number of bags as possible and get the amount of flour he needs. Let F represent the number of bags of flour that Sergei buys. 1) Which inequality describes this scenario?
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Kilogram of flour needed to complete holiday order is atleast 175kg
Number of kilograms available = 34kg
Flour comes in bags each contain 23kg of flour
He wants to buy the smallest number of bags as possible and get the amount of flour he needs.
Let F = number of bags of flours Sergei needs to buy
F = (total number of kilograms needed - number of kilograms available) / kilograms per bag
F = (≥ 175 - 34) / 23
F = ≥ 141 / 23 = ≥ 6.1304347
Since flour is purchased per bag, the smallest number of bags he can possibly buy and still get the amount of flour he need = 7 bags
If
A = i +3j -2K and B=4i-2j+4k
Find (2A+B).(A-2B)
Answers
GIVEN :
a = 1/√10 ( 3i + k) and
b = 1/7 ( 2i + 3j - 6k)
TO FIND :
( 2a- b) . [ ( a x b ) x ( a + 2b)]
SOLUTION :
◆Going with the equation given,
( 2a - b) . [ ( a x b ) x ( a + 2b)]
= (2a - b) [( a×b×a) + 2(a×b)×b]
◆BAC - CAB RULE,
A×B×C = B( A.B ) - C(A.B )
= (2a- b ) [ (b (a.a ) - a (a.b ) + 2b ( a.b) -2b (a.b]
Solving further
= (2a - b )(b - 2a)
= -4a.a -b.b
=-5.
Answer:
( 2 - b) . [ ( a x b ) x ( a + 2b)] = -5
Hoped I helped
The price of a visit to the dentist is $ 50 $50dollar sign, 50. If the dentist fills any cavities, an additional charge of $ 100 $100dollar sign, 100 per cavity gets added to the bill. If the dentist finds n nn cavities, what will the cost of the visit be? Write your answer as an expression. $ $dollar sign .
Answers
Answer:
well you dont have a value of amounts of cavities so ill write write an equation 50+x100 where x represents amount of cavitys
If x^2 = 196, what is the sum of the possible values of (x −1)^2?
Answers
Answer:
Step-by-step explanation:
x²=196
x=±14
when x=14
(x-1)²=(14-1)²=13²=169
when x=-14
(x-1)²=(-14-1)²=(-15)²=225
sum=169+225=394
How much will it cost to print a circular sign with a radius of 1.5 feet if the printing company charges $29 per square foot? Use A = πr2, where π is approximately 3.14. (Round your answer to the nearest cent.)
Answers
Answer:
$204.89
Step-by-step explanation:
Step 1
We have to first find the area of the circular sign.
Since the sign is circular in shape, we use the Area of Circle.
Area of a Circle = πr²
r = 1.5 feet
π = 3.14
Area of a Circle = 3.14 × 1.5²
= 7.065ft² or 7.065 square feet.
Step 2
We find out how much it cost to print the circular sign.
We are told in the question that
The printing company charges $29 per square foot
Hence,
1 square foot = $29
7.065 square feet =
Cross multiply
= 7.065 × $29
=$ 204.885
Approximately to the nearest cent, $204.89
Therefore, it will cost $204.89 to print the circular sign
The possible answers are 32, 24, 16, and 8. Please answer ASAP!! :D
Answers
Answer:
8 feet
Step-by-step explanation:
The volume of a rectangular prism is [tex]lwh[/tex], where l is length, w is width, and h is height.
We already know the length, width, and volume, so we can easily find the height by substituting these values into the equation, then isolating h one one side.
[tex]96 = 4\cdot3\cdot h\\\\96 = 12h\\\\8 = h[/tex]
Hope this helped!
The graph of a sinusoidal function has a maximum point at (0,8) and then has a minimum point at (5,2). Write the formula of the function, where x is entered in radians.
Answers
Answer:
y = 3 cos(π/5 x) + 5
Step-by-step explanation:
The amplitude is half the difference of the min and max.
A = (8 − 2) / 2
A = 3
The midline is the average of the min and max.
C = (8 + 2) / 2
C = 5
The difference in the x values of the min and max is half the period.
T/2 = 5 − 0
T = 10
The function is a maximum at x = 0, so use cosine.
y = 3 cos(2π/10 x) + 5
y = 3 cos(π/5 x) + 5
The formula of the function, where x is entered in radians is [tex]\rm y = 3 sin(\dfrac{\pi}{5}x) + 5[/tex] and this can be determined by using the given data.
Given :
The graph of a sinusoidal function has a maximum point at (0,8) and then has a minimum point at (5,2).
The following steps can be used in order to determine the formula of the function, where x is entered in radians:
Step 1 - The generalized sinusoidal function is given below:
[tex]\rm y = A sin(bx) + C[/tex]
where A is the amplitude.
Step 2 - Now, the value of A is given below:
[tex]\rm A = \dfrac{8-2}{2}[/tex]
A = 3
Step 3 - The value of C is calculated as:
[tex]\rm C = \dfrac{8+2}{2}[/tex]
C = 5
Step 4 - The time period is calculated as:
[tex]\rm \dfrac{T}{2}=5-0[/tex]
T = 10
Step 5 - So, the value of y is maximum at (x = 0).
[tex]\rm y = 3 sin(\dfrac{2\pi}{10}x) + 5[/tex]
[tex]\rm y = 3 sin(\dfrac{\pi}{5}x) + 5[/tex]
For more information, refer to the link given below:
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Which of the following steps would not be necessary when using the square root property to solve a quadratic equation?
A.After applying the square root property, solve the resulting equations.
B.The square root property may be applied only if the constant is positive
C.When taking the square root of both sides use on the square root of the constant.
D.Isolate the quantity being squared
Answers
Answer:
B- The square root property may be applied only if the constant is positive
A had $360 more than B. When A spent $144 and B spent half of his money, A had 6 times as much money as B, Find the ratio of the amount of money A had at first to that of B. Find the ratio of the amount of money A had at first to that of B. Give your answer in its simplest form.
Answers
Answer:
13:3
Step-by-step explanation:
A=x B=y
first; x= 360+y
later;x= 216+y
A:B
216+y: 1/2y = 6: 1
216+y/y÷2 =6/1
216+y = 3y
y = 108
first; x =360+y
360 +108
468
A:B = 468:108
13:3
Write a decimal expansion for 2/9. Chose the correct decimal notation.
Answers
Answer:
The answer is
2/9=0.222222222.
Hope this helps:))
Warmup Day 1
(52 + 4) * 5 - 2 + (-4)
Please work this Problem out step by step.
X Clear
* Undo
Answers
Answer:
274
Step-by-step explanation:
(52 + 4) * 5 - 2 + (-4)
56 * 5 - 2 + (-4)
56 * 5 - 2 - 4
280 - 2 - 4
278 - 4
274
Answer:
274
Step-by-step explanation:
(52+4)*5-2+(-4)
(56)*5-2+(-4)
280-2+(-4)
278+(-4)
274
The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 14 HCF of water is $ 32.68 , and the cost for using 52 HCF is $ 95.38 . What is the cost for using 19 HCF of water?
Answers
Answer:
$40.93
Step-by-step explanation:
GivenLinear function of:
14 HCF = $32.6852 HCF = $95.38To find:
19 HCF = ?SolutionLinear equation in slope-intercept form:
y(x) = mx +bWe have points of: (14, 32.68), (52, 95.38):
y(14) = 14 m + by(52) = 52 m +bUsing the points we can find the value of m and b:
m= (y2-y1)/(x2-x1)m= (95.38 - 32.68)/(52 - 14)m = 62.7/ 28m= 1.65Then finding b:
14*1.65 +b = 32.68b= 32.68 - 23.1b= 9.58So the function is:
y = 1.65 x + 9.58Then y(19) is found as:
y(19) = 1.65*19 + 9.58y(19) = 40.93Answer: Cost of 19 HCF of water is $40.93
Femi's last 5 bowling scores were 68, 75, 72, 90, and 80.
What was Femi's mean score?
A. 72
B. 75
C. 77
D. 79
Answers
Answer:
77
Step-by-step explanation:
The mean of a set of numbers will be the sum of all of them divided by the amount of numbers.
[tex]68+75+72+90+80=385[/tex]
There are 5 numbers in this set:
[tex]385\div5=77[/tex]
Hope this helped!
Femi's mean score is C. 77
Femi's mean score is the sum of all his bowling scores, divided by the number of times he bowled.
Question said that he bowled 5 times so the mean is:
= (68 + 75 + 72 + 90 + 80) / 5
= 385 / 5
= 77
Femi's mean score is therefore 77
Find out more at https://brainly.com/question/17927197.
Use the common ratio to find the next term of the geometric sequence. Type a numerical answer in the space provided.
If necessary, use the / key to represent a fraction bar. Do not type spaces in your answer.
120, 60, 30, ...
Answers
Answer:
15
Step-by-step explanation:
the common ratio is 1/2 so you do 30(1/2)
30(1/2)=15
definition qualitative graph
Answers
Answer:
Qualitative data is information about qualities; information that can't actually be measured. Some other aspects to consider about qualitative data:
Represented through pictures that explore the data in a visual way Visual representations focus on the themes found in the data Can tell a story Can also be displayed graphically as a pie chart or bar graph, the same as quantitative data, however, this can be tricky and can be done incorrectly easily
Carla has 10 coins, each of which is a nickel, a dime, or a quarter. The total value of her coins is less than $1.00. How many different
combinations of coins might Carla have?
Note: The values of a nickel, a dime, and a quarter are, respectively, $0.05, $0.10, and $0.25.
Answers
Answer:
2 quarters,2dimes,6nickels
Think I might need little assistance
Answers
Answer:
x = 90
Step-by-step explanation:
We use the Definition of Corresponding Angles to help us solve for x:
∠1 = ∠4
Step 1: Write out equation
3x - 160 = x + 20
Step 2: Solve for x
2x - 160 = 20
2x = 180
x = 90
Find the population of each BRICS country as the fraction of total population of BRICS
Answers
Answer:
fortnite battle royal
Step-by-step explanation:
Answer:
fre7wgbxyifg crgrggStep-by-step explanation:
For a parade, attendance was rounded as 10,000 to the nearest hundred. What was the greatest and least number of people that could have attended the parade? Explain your answer.
Answers
Answer:
Greatest = 10,049
Least = 9,950
Step-by-step explanation:
Given that:
attendance was rounded as 10,000 to the nearest hundred
The greatest number of people that could have attended the parade is 10,049, this is because, the digit in the hundred place is 0, hence, since the next digit after 0 is less than 5, all subsequent digits are rounded down to 0 = 10,000.
If the number is goes 1 above 10,049 to 10,050, the rounding to the nearest hundred gives 10,100
The least number of people that could have attended should be 9,950; the digit in the hundred place is 9, since the digit after 9 is up to 5, then it is rounded to 100 and added to 9,900 to give 10,000.
If the number goes 1 less than 9950 to 9949, then rounding to the nearest hundred gives 9900.
The graphs of linear functions f and g are shown. Enter the solution to the equation f(x)=g(x).
Answers
The two diagonal lines cross at (-3,5). We only need to worry about the x coordinate here, so x = -3 is what we're after. If x = -3, then f(x) and g(x) have the same y output meaning f(x) = g(x). That y output is y = 5.
1 ac =how many millions
Answers
1 Acre-feet to Million Cubic Feet = 0.0436
whats the answer to 4c+5=27
Answers
Answer:
c=5+1/2
Step-by-step explanation:
We move all terms to the left:
4c+5-(27)=0
We add all the numbers together, and all the variables
4c-22=0
We move all terms containing c to the left, all other terms to the right
4c=22
c=22/4
c=5+1/2
A store bought a dining room table at a cost of $478 and marked it up 150%. Later on, the
store marked it down 60%. What was the discount price?
Answers
Answer:
$286.80
Step-by-step explanation:
First, find the price after the 150% markup:
478(1.5)
= 717
Now, calculate the price with the 60% discount:
717(0.4)
= 286.8
= $286.80
Which expression can be used to convert AU$22 into US
Answers
So, 22 divided by 1.2 = 18.33
1. -4х – 7- 3х + 4 = 25
Answers
Answer:x=-4
Step-by-step explanation: combine like terms, add 4 and -7 which is -3 and add -4x and the -3x because they are like terms which is -7x so it should be -7x-3=25. then to get rid of the 3 add it to both sides so it would turn out like -7x=28 then divide the 7 on both sides= 28/ -7= -4
Solve for s.
s - -37 = 98
Answers
Subtracting a negative becomes addition.
S - -37 = 98
Simplify:
S + 37 = 98
Subtract 37 from both sides:
S = 61
Answer:
61
Step-by-step explanation:
98 - 37 = 61
s = 61
Lincoln is wrapping a rectangular shaped present. The length of the present is 4 inches, the width is 8 inches and the height is 15 inches. How much wrapping paper will Lincoln need?
Answers
Step-by-step explanation:
To find the area of the wrapping paper required,
we must find the Total Surface Area of the box
As we know, the TSA of a cuboid= 2 (lh+bh+lb)
Here,
Total Surface Area of the cuboid=
[tex]2(4 \times 8 + 8 \times 15 + 15 \times 4)[/tex]
[tex] = 2(32 + 120 + 60)[/tex]
[tex] = 2(212)[/tex]
[tex] = 414 \: inches^2[/tex]
Alana makes and sells homemade bracelets. She made a profit of $65 last week. This week, she donated some bracelets to charity. Her profit at the end of this week can be represented by -$25. What is the DIFFERENCE between last week’s profit and this week’s profit?
Answers
Answer:
$40 is the difference. One is positive(W1), one is negative(W2). Therefore, you subtract.
Step-by-step explanation:
You subtract week ones profit and week twos profit.
65 - 25 = $40
You subtract because she had a negative profit for week two and/or a profit below 0.
A die is rolled 300 times and following outcomes were recorded.
outcome 1 2 3 4 5 6
frequency 62 45 63 32 47 51
find the probability of getting
1. more than 4
2. less than 3
Answers
Answer:
1. 49/150
2. 107/300
Step-by-step explanation:
Here is a probability question.
a. The first question asks us to find the probability of getting more than 4.
Now to do this, we look at our possible results when we roll the die, we can see that we can have 1-6.
But within this range, only two numbers are greater than 4, these are 5 and 6
Thus, to calculate the probability of getting either 5 or 6, we look at their frequencies, sum it up, then divide by the total number of times which the die was rolled.
The frequency of 5 is 47, while that of 6 is 51
The probability of getting more than 4 = Probability of getting 5 + Probability of getting 6 = (Frequency of 5 + Frequency of 6)/Total number of trials
= (47 + 51)/300 = 98/300 = 49/150
b. Probability of getting less than 3
Here, we proceed as we did in the first question. The numbers which are less than 3 are 1 and 2.
So the probability of getting less than 3 = Probability of getting 1 + Probability of getting 2 = (Frequency of 1 + Frequency of 2)/Total number of trials
Frequency of 1 = 62 while Frequency of 2 = 45
So, probability of getting less than 3 = (45 + 62)/300 = 107/300