Answer:
Option: D is the correct answer.
The equation of line in point-slope form is given by:
y-9=2(x-1)
Step-by-step explanation:
We know that the point-slope equation of a line is given by:
y-b=m(x-a)
where (a,b) is the point from which the line passes and m is the slope of the line.
Here we are given that:
The line passes through (1,9) and slope of the line is given to be 2.
Hence,
(a,b)=(1,9) and m=2
Hence, the equation of line is given by:
y-9=2(x-1)
Therefore, the point slope intercept equation of the line is: D
What is the slope of a line that is parallel to the graph of 5x+4y=6 text ? I DON'T NEED AN EXPLANATION JUST THE ANSWER QUICK
Given: The equation below
\(5x+4y=6\)To Determine: The slope of the line that is parallel to the graph of the given equation
Solution
Please note that two lines are parallel if their slopes are equal. Therefore, a line that is parallel to the given equation would have the same slope to the given
The slope can calculated as shown below
\(\begin{gathered} Slope-intercept\text{ form of a line is} \\ y=mx+c \\ m=slope \\ c=intercept\text{ on y-axis} \\ So, \\ 5x+4y=6 \\ 4y=6-5x \\ \frac{4y}{4}=\frac{6}{4}-\frac{5x}{4} \\ y=\frac{3}{2}-\frac{5}{4}x \\ y=-\frac{5}{4}x+\frac{3}{2} \\ Hence,slope\text{ is} \\ m=-\frac{5}{4} \end{gathered}\)Hence, the slope of a line parallel to the graph of 5x + 4y = 6 is - 5/4
How to solve the problem of equivalent fractions
1/2=1/2=1/2.is the value for the given equivalent fraction, by putting the value 3.4 in the numerators respectively
What is Equivalent Fraction?The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.
For instance, since 2/4 and 3/6 both equal the 1/2, they are identical fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.
1/2 = /6 = /8.
a. Multiply numerator and denominator by 3 for equivalenting the equation /6
Therefore,
3*3/6*3
=9/18
=1/2
therefore:1/2=1/2.
b. Multiply numerator by 4
Therefore,
4/8
=1/2.
Therefore:
1/2=1/2.
1/2=1/2=1/2.
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plees 555+555 and 6 541,5-5 410,6
Answer:
what is this......................
A figure was translated 4 units down and 3 to the left then reflected over the y-axis. The figures are
Answer:
Congruent and similar
Step-by-step explanation:
because you did not change anything about the shape that shape is still the same size and shape just in a different spot
Number of
Popsicles
Total Cost of
Popsicles
2
6
4
12
6
18
8
24
What is the Constant Rate of Change?
Answer:
The constant rate of change is 3
Step-by-step explanation:
Given
x y
2 6
4 12
6 18
8 24
Required
Determine the constant rate of change
Represent the constant rate of change with k.
k is calculated using:
\(k = \frac{y}{x}\)
When y = 24; x = 8
So, we have:
\(k = \frac{24}{8}\)
\(k = 3\)
Lillian is wrapping a gift box that has the size shown below.
Part A
Which expression gives the volume of the box?
O
36 x 9
0
3x6x9
36 x 36
o
36 + 9
Answer:
4
Step-by-step explanation:
I dont know. i thought there was going to be a answer :c
The original plan for assigning telephone numbers that you investigated in
Applications Task 4 was implemented in
1947. At that time, the supply of numbers was expected to last for 300 years. However, by the 1970s the numbers were already starting to run out. So, the numbering plan
had to be modified. In this task, you will count the number of different phone numbers that were available in 2012.
a. For three-digit area codes, the first digit cannot be a 0 or a 1. Assuming no additional restrictions, how many three-digit area codes are possible under
this plan?
b. Certain area codes are classified as "Easily Recognizable Codes" (BRCs).
ERCs designate special services, like 888 for toll-free calls. The requirement for an ERC is that the second and third digit of the area code must be the same. The first digit again cannot be a 0 or a 1. How many ERCs are there?
c. Consider the seven digits after the area code. As with the area code, the first digit of the three-digit local prefix cannot be a 0 or a 1. The remaining six digits for the local number have no restrictions. How many of these seven-digit phone numbers are possible?
d. Assuming only the 0 and 1 restrictions in Parts a and c, how many ten-digit phone numbers are possible?
a. Assuming no additional restrictions, there are 800 possible three-digit area codes.
b. Considering ERCs, there are 80 ERCs.
c. For the seven digits after the area code, there are \(8 \times 10^6 = 8,000,000\) possible seven-digit phone numbers.
d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers is 800 \(\times\) 8,000,000 = 6,400,000,000.
a. For three-digit area codes, the first digit cannot be 0 or 1.
Assuming no additional restrictions, there are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining two digits (0-9). Therefore, the total number of three-digit area codes possible under this plan is \(8 \times 10 \times 10 = 800.\)
b. For an ERC (Easily Recognizable Code), the second and third digits of the area code must be the same, and the first digit cannot be 0 or 1. There are 8 possibilities for the first digit (2-9) and 10 possibilities for the third digit (0-9).
Since the second digit must be the same as the third digit, there is only 1 possibility.
Therefore, the total number of ERCs is \(8 \times 1 \times 10 = 80.\)
c. For the seven digits after the area code, the first digit of the three-digit local prefix cannot be 0 or 1.
There are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining six digits (0-9).
Therefore, the total number of seven-digit phone numbers possible is 8 * \(10\times 10 \times 10 \times 10 \times 10 \times 10 = 8,000,000.\)
d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers can be calculated by multiplying the number of possibilities for each digit position.
For the area code (part a), there are 800 possibilities.
For the seven digits after the area code (part c), there are 8,000,000 possibilities.
Therefore, the total number of ten-digit phone numbers possible is 800 * 8,000,000 = 6,400,000,000.
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The sum of three consecutive even numbers is 438. What is the 2nd number?
Let GH be the directed line segment beginning at point G(4,4) and ending at point H(-7,-1). Find the point P on the line segment that partitions the line segment into the segments GP and PH at a ratio of 5:6.
The coordinates of point P are (-1, 1 8/11).
We have,
G(4, 4) and H(-7, 1)
m :n = 5:6
Using Section formula
x = (mx₂ + nx₁)/ (m+n) and y = (my₂ + ny₁)/ (m+n)
Here, x₁ = 4, y₁ = -7, x₂ = 4 and y₂ = -1
So, x = (5(-7) + 6(4))/ 11 and y = (5(-1) + 6(4))/ 11
x = -35+24/11 and y = -5 + 24/11
x = -11/11 and y = -19/11
x = -1 and y = 1 8/11
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someone help me please! i will rewars brainliest! this is geometry
Answer:
0.6
Step-by-step explanation:
Answer: 0.5
Step-by-step explanation:
Since the three portfolios are 20%, 30% and 50%, and the 20% and 30% are already there in the form of 0.2 and 0.3, then Z must be the 50%, or 0.5
least to greatest 0.45, -0.48, 8/25
Answer:
-0.48, 8/25, 0.45
Step-by-step explanation:
(plz brainliest if u can)
Answer:
-0.48 > 8/25 > 0.45
Step-by-step explanation:
This is the ansewer. You get it by putting them in order
So first you already know that -0.48 is first becuase it is a negitive.
Then you convert the 8/25 which is 0.32 which is what you put next.
And finally you have the biggest number which is 0.45.
There you go! Have a Good day.WILL VOTE 75 POINTSSS
Which of the following can sine squared theta over the quantity 1 plus cosine theta end quantity be simplified to?
cos θ
1 + cos θ
1 − cos θ
sin θ + tan θ
Answer:
The expression "sine squared theta over the quantity 1 plus cosine theta end quantity" can be simplified to "1 - cos θ".
Answer:
1 - cos θ
Step-by-step explanation:
What is the answer? Plz help me
Answer:
27y + 6r
Step-by-step explanation:
use the distributive property
3 * 9y = 27y
3 * 2r = 6r
27y + 6r
Plz mark as brainliest if this helped! Have a nice day!!!
-Lil_G
For a standard normal distribution, the probability of obtaining a z value of less than 1.68 is _____.
Probabilities are used to determine the chances of an event.
The probability of obtaining a z value of less than 1.68 is 0.95352
The probability is represented as:
\(\mathbf{P(z < 1.68)}\)
To do this, we make use of the z-score of probabilities table and/or calculator.
Using the calculator, we enter 1.68 as the z-score.
The result is:
\(\mathbf{P(z < 1.68) = 0.95352}\)
This means that:
The probability of obtaining a z value of less than 1.68 is 0.95352
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K Graph the function f(x) = -x² +6. f(x) X -2 - 1 0 1 2 TE Complete the table of function values below. f(x) X - 2 - 1 0 1 2
Answer:
Step-by-step explanation:
Here is the completed table of function values for f(x) = -x² + 6:
x -2 -1 0 1 2
f(x) -2 5 6 5 2
To graph the function, you can plot the points from the table on a coordinate plane and connect them with a smooth curve. The graph of f(x) = -x² + 6 is a downward-facing parabola that opens up to the point (0, 6), as shown below:
7
|
|
|
|
|
|
|
|
-----0------
|
|
|
|
|
|
|
|
-2
The vertex of the parabola is located at the point (0, 6), and the axis of symmetry is the vertical line x = 0.
15-9x 1/2
I’ll give Brainiest
Answer:
-9x/2 + 15/2
Step-by-step explanation:
(15-9x)* 1/2
15(1/2)-9x 1/2
15/2 -9x *1/2
15/2-9x/2
-9x/2 + 15/2
Answer:
21/2 ( SEE IMAGE BELOW)
Step-by-step explanation:
Calculate the product
15- 9/2
Calculate the Differnce
21/2
so the answer is 21/2
You have just been approved for a 30 year 5.5% fixed home mortgage. The monthly payment that you qualify for is $879.32. Use the table provided to determine the price of a home that can be purchased. A 5-column table with 4 rows titled Monthly Payments per 1000 dollars of mortgage. Column 1 is labeled Interest Rate (percent) with entries 5, 5.5, 6, 6.5. Column 2 is labeled 10 Years with entries 10.61, 10.86, 11.11, 11.36. Column 3 is labeled 20 years with entries 6.60, 6.88, 7.17, 7.46. Column 4 is labeled 30 years with entries 5.37, 5.68, 6.00, 6.33. Column 5 is labeled 40 years with entries 4.83, 5.16, 5.51, 5.86. a. $154,267 c. $156,753 b. $154,810 d. $157,153
Answer:
b. $154,810
Step-by-step explanation:
You want to know the price of a home that can be purchased for a monthly payment of $879.32 on a 30-year loan at 5.5%.
TableThe given table tells you the multiplier m used to find the monthly payment p from the loan amount P for different time periods and interest rates.
p = (P/1000)×m
ApplicationThe table value for a 30-year loan at 5.5% is m = 5.68. Solving the equation for P, we have ...
1000p/m = P
1000(879.32/5.68) = P ≈ 154,809.86 ≈ 154810
You qualify for a loan of $154,810.
__
Additional comment
The multiplier 5.68 is found on row 2 (5.5%) of column 4 (30 years).
By answering the presented question, we may conclude that As a result, equation the answer is (b) $154,810.
What is equation?A mathematical equation is a formula that connects two statements and denotes equivalence with the equals symbol (=). An equation is a mathematical statement that shows the equality of two mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the connection between the two sentences that occur on opposite sides of a letter. The symbol and the single variable are frequently the same. As in 2x - 4 Equals 2, for instance.
To establish the purchase price of a property, we must use the monthly payment and the table supplied to determine the mortgage amount that corresponds to the monthly payment.
According to the data, the monthly payment per $1000 of mortgage for a 30-year fixed mortgage at a 5.5% interest rate is $5.68.
Hence, to calculate the mortgage amount for a $879.32 monthly payment, we may apply the following formula:
Mortgage amount = monthly payment / mortgage payment per $1000
$879.32 mortgage amount / $5.68 per $1000
Loan amount = $154,810
As a result, the purchasing price of a house is $154,810.
As a result, the answer is (b) $154,810.
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6 - 8x = 6x - 9x + 11
6-8x=-3x+11
-8x+3x=11-6
-5x=5
x=-1
The first step is to isolate the variable, then you solve. Hope this helps, brainliest if you can.
Answer:
hi
Step-by-step explanation:
hi i am a gamergirl add me in fortnite xxgamergilxx93_qt
solve for t..................................
Answer:
-4.375
.......................
EXPLORE ACTIVITY 2
TEKS 7.13.8
Analyzing a Family Budget
One way to present a budget is in a circle graph. You can see at a glance which
categories take the greatest part of the family's resources. You can also work
backward from a circle graph to figure out exactly how much money is in each
category.
Use the circle graph to complete
the table for the Baker family's
monthly budget. Their net
monthly income is $4,000.
STEP 1)
STEP 2
STEP 3
STEP 4
STEP 5
432 Unit 7
Enter the income in the table.
Enter the percent or amount of money for each
category from the circle graph in the table.
Calculate the amount of money or the percent
for each category in the table.
Determine which expenses are fixed and
which are variable. Place X's in the appropriate
columns.
Complete the Amount Available column.
Item
Net monthly income
means how much
income the family
has after taxes.
Net monthly
Income
Housing cost
Food
Savings
Entertainment
Clothing
Medical
Transportation
Emergency
fund
Amount
($)
Percent
(%)
Baker Family's Monthly Budget
Emergency fund
Transportation
(car expense,
bus passes)
$400
Medical
(insurance
and
additional
expenses)
$600
Clothing
8%
Entertainment
Savings
$320
Fixed
Variable
Amount
Expense Expense Available
($)
Housing
cost (house
payment and
Insurance!
$1,400
Food
15%
Note that the table of budget is attached accordingly, and steps 1-4 have been completed. See the table.
What happened during emergency repair of $305?4) Since the emergency fund for that month was $200, it means that they are in the short for $105. They can only affod it if they take from their savings.
5) they had a balance of $800 for the month. This is miscellaneous funds. They can make use of this for the trip to NASA. This way, they won't have to touch the savings or entertainment.
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Full Question:
See attached image.
Reflect
4. Analyze Relationships One month, the family must make an
emergency car repair for $305. Are they able to pay for it out of the
fixed emergency fund for that month? If not, how can they afford it?
5. The family wants to make a trip to Houston to visit the NASA Space
Center. What are some ways they can save without using all of the
allotted $160 for entertainment
sove
\(2x - 5 = 7\)
Answer:
X=6
Step-by-step explanation:
you add 5 on ther side, then add 7, and 5 together. then divide 2 on the other side
Answer:
x=6
Step-by-step explanation:
2x-5=7
add 5 on both sides:
2x-5+5=7+5
2x=12
Divide by 2:
x=6
Hope this helps!
let's see who can solve this. pleseeee
The correlation coefficient between X and Y is Corr(X, Y) = 0.
To calculate the marginal distribution of X and Y, we need to integrate the joint probability density function (PDF) over the appropriate ranges.
a. Marginal distribution of X:
To find the marginal distribution of X, we integrate the joint PDF over the range of Y:
∫[0, 1] J(x, y) dy
Since the joint PDF is defined as J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1 and J(x, y) = 0 otherwise, the integral becomes:
∫[0, x] 1 dy = x, for 0 ≤ x ≤ 1
So, the marginal distribution of X is simply X(x) = x for 0 ≤ x ≤ 1.
b. Expectation of X:
The expectation (mean) of X can be calculated as the integral of x times the marginal PDF of X:
\(E(X) = ∫[0, 1] x * X(x) dx = ∫[0, 1] x^2 dx = [x^3/3] from 0 to 1 = 1/3\)
Therefore, the expectation of X is E(X) = 1/3.
c. Variance of X:
The variance of X can be calculated using the formula:
\(Var(X) = E(X^2) - (E(X))^2E(X^2) = ∫[0, 1] x^2 * X(x) dx = ∫[0, 1] x^3 dx = [x^4/4] from 0 to 1 = 1/4Var(X) = 1/4 - (1/3)^2 = 1/4 - 1/9 = 5/36\)
Therefore, the variance of X is Var(X) = 5/36.
d. Covariance of X and Y:
The covariance of X and Y can be calculated as:
Cov(X, Y) = E(XY) - E(X)E(Y)
Since the joint PDF J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1, the integral becomes:
\(E(XY) = ∫[0, 1] ∫[0, x] xy dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)
\(E(X) = 1/3 (from part b)E(Y) = ∫[0, 1] ∫[0, x] y J(x, y) dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)
Cov(X, Y) = 1/6 - (1/3)(1/6) = 0
Therefore, the covariance of X and Y is Cov(X, Y) = 0.
e. Correlation coefficient between X and Y:
The correlation coefficient can be calculated using the formula:
Corr(X, Y) = Cov(X, Y) / √(Var(X) * Var(Y))
Since the covariance of X and Y is 0, the correlation coefficient will also be 0.
Therefore, the correlation coefficient between X and Y is Corr(X, Y) = 0.
f. Conclusion based on the correlation coefficient:
The correlation coefficient of 0 indicates that there is no linear relationship between X and Y. In this case, the fraction of male runners (X) and the
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Which linear function has the same y-intercept as the one that is represented by the graph?
On a coordinate plane, a line goes through points (3, 4) and (5, 0).
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 3, negative 1, 1, 3. Column 2 is labeled y with entries negative 4, 2, 8, 14.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 4, negative 2, 2, 4. Column 2 is labeled y with entries negative 26, negative 18, negative 2, 6.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 5, negative 3, 3, 5. Column 2 is labeled y with entries negative 15, negative 11, 1, 5.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative 4, 4, 6. Column 2 is lab
eled y with entries negative 26, negative 14, 34, 46.
The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.
To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).
First, let's find the slope of the line using the formula:
slope (m) = (change in y) / (change in x)
m = (0 - 4) / (5 - 3)
m = -4 / 2
m = -2
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Using the point (3, 4) as our reference point, we have:
y - 4 = -2(x - 3)
Expanding the equation:
y - 4 = -2x + 6
Simplifying:
y = -2x + 10
Now, let's check the given options to find the linear function with the same y-intercept:
Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)
The y-intercept is not the same as the given line. So, this option is not correct.
Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)
The y-intercept is not the same as the given line. So, this option is not correct.
Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)
The y-intercept is the same as the given line (10). So, this option is correct.
Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)
The y-intercept is not the same as the given line. So, this option is not correct.
Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.
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3 n - 5 p + 2 n = 10 p for n
Answer:
What do you mean
Step-by-step explanation:
HELP ASAP PLEASE NEED IT RIGHT NOWWWW THANK YOU.!!
Answer:
it should be 71
Step-by-step explanation:
16+5+5+5+5+5+5+5+5+5+5
+5= 71
16 is the 4th and you had 5 eleven more times becuase the numbers are increasing by 5.
NO LINKS!! URGENT HELP PLEASE!!!
Please help me with Growth rate and Initial Value only
Answer:
growth rate: 4
y-value: 19
equation: y=4x+19
Step-by-step explanation:
Growth Rate:
The growth rate of a linear function is constant. This means that the function will increase or decrease by the same amount for every unit increase in x.
This can be found by dividing the change in y-values by the change in x-values.
For the question:
The change in y-values is 11-7=4,
and the change in x-values is +1.
Therefore, the growth rate is 4.
\(\hrulefill\)
Initial Value: The initial value of a linear function is the value of the function when x is 0.
In this case, the initial value is 19.
This can be found by looking at the y-value of the point where x is 0.
In this case, the y-value is 19.
\(\hrulefill\)Equation: The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.
Using the table you provided, we can find the slope by using two points on the line.
Let’s use (-3, 7) and (1, 23).
The slope is (y2-y1)/(x2-x1)=(23-7)(1-(-3)=16/4=4
Now,
Taking 1 point (-3,7) and slope 4.
we can find the equation by using formula:
y-y1=m(x-x1)
y-7=4(x+3)
y=4x+12+7
y=4x+19
Therefore, the equation of the given table is y=4x+19\(\hrulefill\)
Answer:
Growth rate: 4
Initial value: 19
Equation: y = 4x + 19
Step-by-step explanation:
The slope of a linear function represents its growth rate.
Therefore, the growth rate of a linear function can be found using the slope formula.
Substitute two (x, y) points from the table into the slope formula, and solve for m. Substituting points (0, 19) and (1, 23):
\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{23-19}{1-0}=\dfrac{4}{1}=4\)
Therefore, the growth rate of the linear function is 4.
The initial value of a linear function refers to the y-intercept, which is the value of the y when x = 0.
From inspection of the given table, y = 19 when x = 0.
Therefore, the initial value of the linear function is 19.
To write a linear equation given the growth rate (slope) and initial value (y-intercept), we can use the slope-intercept formula, which is y = mx + b. The slope is represented by the variable m, and the y-intercept is represented by the variable b.
As the growth rate of the given linear function is 4, and the initial value is 19, substitute m = 4 and b = 19 into the slope-intercept formula to create the equation of the linear function represented by the given table:
\(\boxed{y=4x+19}\)
Verizon Wireless charges
$0.09 for every 5 text
messages sent. How much
is your bill if you send 75
texts?
Make this into a equation
Solve: -6n + 5 < 11
Which graph shows the solutions?
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-6-5-4-3 -2 -1 0 1 2 3 4 5 6
-6-5 -4 -3 -2 -1 0 1 2 3 4 5 6
Answer:
graph should show an open circle on -2 with shading to the right
Step-by-step explanation:
-6n + 5 < 11
-6n < 6
n > -1
solutions consist of all number greater than -1
thirty-six students at a local middle school were randomly selected to participate in a taste test to select a new menu item for a cafeteria. each student was given a choice between the macaroni and cheese and the cajun potato barrels. from the sample, 20 students selected macaroni and cheese and 16 students chose the cajun potato barrels. each student was asked to rate the item they chose on a scale from 1 (extremely dislike) to 9 (extremely like). which of the following prevents this study from being a well-designed experiment?
The treatments (new menu item) were not randomly assigned to the students when 36 local middle school kids were chosen at random to take part.
Given that,
36 local middle school kids were chosen at random to take part in a taste test to choose a new menu item for a cafeteria. The Cajun potato barrels or the macaroni and cheese were the options offered to each pupil. 20 pupils chose the macaroni and cheese from the sampling, while 16 selected the Cajun potato barrels. On a scale from 1 (very dislike) to 9 (very much like), each student was asked to rank the object they selected (extremely like).
We have to find which of the following keeps this study from being an experiment with a sound design.
Each student was given the option of choosing either the macaroni and cheese or the Cajun potato barrels. Because the students' treatments were not distributed at random, those who preferred their cuisine chose it and gave it high marks. As a result, the study has selection bias.
Therefore, The treatments (new menu item) were not randomly assigned to the students when 36 local middle school kids were chosen at random to take part.
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Select the system of linear inequalities whose solution is graphed. O y < 3x-2, x + 2y > 4 O y ≤ 3x-2, x + 2y 2 4 O y> 3x-2, x + 2y < 4 O y2 3x-2, x + 2y ≤ 4
Option D is the correct answer.
From the graph, we can conclude that,
1. The two lines are continuous lines and not broken lines. So, the inequality sign should be either ≤ or ≥.
2. The points on the lines of the shaded region are also included in the solution.
The only option that matches with the above conditions is option D. So, option D is the correct answer.
Let us verify it.
Now, let us consider a point that is inside the shaded region and also on any one line.
Let us take (0, 2).
Plug in 0 for x and 2 for y in each of the options and check which inequality holds true.
Considering the inequalities,
y ≥ 3x - 2
x + 2y ≤ 4
Solving we get,
2 ≥ 3(0) - 2
2 ≥ -2
x + 2y ≤ 4
0 + 2(2) ≤ 4
4 ≤ 4
Here, both inequalities are correct.
So, option D is the correct answer.
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The complete question is =
Which system of linear inequalities is graphed?
A. y < 3x-2
x + 2y ≥ 4
B. y < 3x - 2
x + 2y > 4
C. y > 3x - 2
x + 2y < 4
D. y ≥ 3x - 2
x + 2y ≤ 4