Answer:
1350 ft²
Step-by-step explanation:
First off, I notice that the triangle at the bottom can fit the slant at the top to make a perfect rectangle.
This will leave us with a rectangle. We can add up 4 and 5 for the sum of 9, making one side 9 inches.
5 + 4 = 9 in
We multiply 9 by 3 to get the actual length of that side
9 x 3 = 27 ft.
We multiply 16 and two-thirds by 3 to get the actual length of the other side
\(16\frac{2}{3}\) x 3 = 50 ft.
To find the area of this rectangle we multiply length and width
50 x 27 = 1350 ft²
What happens to the range of the data set shown below if the number 13 is added to the data set?
14, 17, 16, 18, 19, 15, 20, 21, 22
A. The range will increase by one.
B. The range will not change.
C. There will be two ranges.
D. The range decreases by 1.
Answer:
A. The range will increase by one
Step-by-step explanation:
The range is the difference between the lowest and highest number in the data set.
In the data set 14 is lowest and 22 the highest with a difference (range) of 8.
If 13 is added this will be the lowest number and 22 still the highest - this will give a range of 9 so this is an increase by one
Answer:
The answer is A
Step-by-step explanation:
Select the following correlation that demonstrates the WEAKEST correlation between two variables.
a) +.20
b) - 50
c) +.75 d
) - 76
The correlation that demonstrates the weakest correlation between two variables is option a) +.20.
Among the given options, the correlation that demonstrates the weakest correlation between two variables is option b) -50.
In correlation coefficients, the value ranges from -1 to +1, where -1 represents a perfect negative correlation, +1 represents a perfect positive correlation, and 0 represents no correlation or a very weak correlation.
Let's analyze the options provided:
a) +.20:
This indicates a positive correlation, but the value is relatively small (0.20).
It suggests a weak positive relationship between the variables.
b) -50:
This option appears to be a typographical error since the correlation coefficient cannot be negative 50.
Assuming it is meant to be -0.50, this indicates a moderate negative correlation.
c) +.75:
This option represents a strong positive correlation.
With a coefficient of 0.75, it suggests a relatively strong positive relationship between the variables.
d) -76: Similar to option b, this value appears to be a typographical error. A correlation coefficient cannot exceed the range of -1 to +1.
Assuming it is meant to be -0.76, this indicates a strong negative correlation.
Comparing the given options, the weakest correlation is option b) -50, assuming it was intended to be -0.50. A correlation coefficient of -0.50 represents a moderate negative correlation, which is weaker than the other options but still indicates some relationship between the variables.
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assume a simple fixed-price keynesian model where the mpc is 0.8. which of the following will lead to the largest increase in equilibrium gdp?
Increasing government spending (G) will lead to the largest increase in equilibrium GDP in a simple fixed-price Keynesian model with an MPC of 0.8.
In the Keynesian model, an increase in government spending directly stimulates aggregate demand, leading to an increase in GDP. The magnitude of the increase in GDP depends on the marginal propensity to consume (MPC), which represents the fraction of additional income that households spend. In this case, with an MPC of 0.8, 80% of any increase in income will be spent.
When government spending increases, it injects additional income into the economy. Households, with a high MPC, will spend a significant portion of this additional income on consumption goods and services. This increased consumption will, in turn, stimulate further economic activity, leading to a multiplier effect and a larger increase in GDP.
Therefore, increasing government spending would have the greatest impact on increasing equilibrium GDP in this scenario.
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Seth sold 12 glasses of lemonade yesterday. Today Seth sold 25% more glasses of lemonade than yesterday. How many more glasses did Seth sell today?
Answer:
15
Step-by-step explanation:
If he sold 12 glasses of lemonade yesterday then 25% more is 1/4 more. 1/4 of 12 is 3. Add 3 to 12 and you get 15.
(ASAP) (WITH PROPER STEPS AND EXPLAINATION PLEASE) Swim team members can race or dive. At a meet, 18 members race. The ratio of racers to divers is 6: 2. How many members are on the team? Show your work.
Answer:
Step-by-tep explanation:
Racers. 6/2= 18/6 18+6= 24
Diver
find an equation of the line tangent to the curve at the point corresponding to the given value of t. x=t^2-23, y=t^3 + t; t=5
The equation of the line tangent to the curve at the point corresponding to the given value of t.
x = t²-23 and y = t³ + t, at t = 5 is
38x - 5y + 574 = 0
Given, a curve with the points represented by
x = t²-23 and y = t³ + t, at t = 5
we have to find an equation of the line tangent to the curve at the given point on the curve.
so, the given point is (x , y) = (5² - 23 , 5³ + 5)
(x , y) = (2 , 130)
Now, the slope of the curve at that point be,
dy/dx = (3t² + 1)/(2t)
dy/dx = 76/10
Now, on using the slope-intercept form, we get
(y - 130)/(x - 2) = 38/5
5(y - 130) = 38(x - 2)
5y - 650 = 38x - 76
38x - 5y + 574 = 0
Hence, the equation of the line tangent to the curve at the point corresponding to the given value of t.
x = t²-23 and y = t³ + t, at t = 5 is
38x - 5y + 574 = 0
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PLZ HELP ME I NEED HELP ASAPPPPPP
Answer:
It definitly should be c
Step-by-step explanation:
If △ A B C is reflected across the y-axis to form △ A ′ B ′ C ′ , what are the coordinates of A ′ ? image
If A(-5,4), B(-2,4), and C are the points of ABC, then(-4,2). The coordinates of the vertex C are if ABC is reflected across the y-axis to create the image ABC. (4,2)
What exactly are coordinates?A coordinate system is a method for determining a point's or other object's location uniquely using one or more integers, or coordinates.
According to question:ABC's vertices are A(-5,4), B(-2,4), and C.(-4,2).
If the picture ABC is created by reflecting ABC across the y-axis.
We must locate the ABC picture.
The dimensions of vertex C must be discovered.
The y coordinate will stay the same because ABC is reflected across the y-axis.
The x coordinate's sign is now the opposite of what it was when the triangular was upright.
Hence (4,2) is the coordinates of the vertex C.
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Complete Question:
The vertices of △ABC are A(-5,4),B(-2,4),and C(-4,2). If ABC is reflected across the y-axis to produce the image △ABC, find the coordinates of the vertex C.
Find the annual percentage yield (APY) in the following situation. A bank offers an APR of 2 42% compounded monthly. The annual percentage yield is
The Annual Percentage Yield (APY) in this situation is approximately 2.454%.
To find the Annual Percentage Yield (APY) in this situation, use the formula:
\(APY = (1 + r/n)^n - 1\)
where:
- r is the annual interest rate (APR) expressed as a decimal,
- n is the number of compounding periods per year.
In this case, the APR is 2.42% or 0.0242 (expressed as a decimal), and the interest is compounded monthly, so there are 12 compounding periods per year (n = 12).
Substituting these values into the formula,
\(APY = (1 + 0.0242/12)^{12} - 1\)
Calculating this expression:
\(APY = (1 + 0.002017)^{12} - 1\)
\(= (1.002017)^{12} - 1\)
≈ 0.02454 or 2.454%
Therefore, the Annual Percentage Yield (APY) in this situation is approximately 2.454%.
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Can someone help me with this asap? Read the question
All the items are in the correct order as follows:
The letter "O" cannot be used but there are no restrictions on repeating the other letters or numbers.The letters can repeat, but the number cannot repeat.The number can repeat, but the letters cannot repeat.Neither the letters nor the numbers can be repeated.Order from least to greatest:
4, 2, 3, 1
Why did we have the above order?The reason for the order from least to greatest is based on the number of possible combinations in each situation.
Neither the letters nor the numbers can be repeated: In this situation, there are 26 choices for the first letter, 25 choices for the second letter (since the first letter has already been chosen and cannot be repeated), 8 choices for the first digit (since it can be any number from 1 to 9), 7 choices for the second digit (since the first digit has already been chosen and cannot be repeated), and 6 choices for the third digit. Therefore, the total number of possible combinations is 26 x 25 x 8 x 7 x 6 = 1,872,000.
The letters can repeat, but the number cannot repeat: In this situation, there are 26 choices for each letter and 9 choices for each digit. Therefore, the total number of possible combinations is 26 x 26 x 9 x 8 x 7 = 328,968.
The number can repeat, but the letters cannot repeat: In this situation, there are 26 choices for the first letter, 25 choices for the second letter, and 9 choices for each digit. Therefore, the total number of possible combinations is 26 x 25 x 9 x 9 x 9 = 5,565,750.
The letter "O" cannot be used but there are no restrictions on repeating the other letters or numbers: In this situation, there are 25 choices for each letter (since "O" cannot be used) and 9 choices for each digit. Therefore, the total number of possible combinations is 25 x 25 x 9 x 9 x 9 = 15,506,250.
Based on the above calculations, the order from least to greatest is 4, 2, 3, 1.
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The text format of the question in the picture:
Use the arrows to move each item into the correct order. Click the up arrow to move the item up, or click the down mow to move the them down. Once all the items are in the correct order, submit your response.
A bike license consists of 2 letters, using any of the 26 letters in the alphabet, followed by 3 digits from 1 to 9. Calculate the number of possible license plates in each situation, then, order them from least to greatest.
The letters can repeat, but the number cannot repeat
The number can repeat, but the letters cannot repeat
Neither the letters nor the numbers can be repeated
The letter "O" cannot be used but there are no restrictions on repeating the other letters or numbers.
In a survey of 2,200 people who owned a certain type of car, 880 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
*blank*% of the people surveyed were satisfied with the car.
Answer:
40%
Step-by-step explanation:
Given parameters:
Number of people surveyed = 2200
Number of people who said they would buy the car again = 880
Unknown:
The percentage of people satisfied with the car = ?
Solution:
The percentage of people satisfied with the car purchase can be determined using the expression below:
Percentage of people satisfied = \(\frac{Number of people who said they would buy the car again}{Number of people surveyed} x 100\)
Percentage of people satisfied = \(\frac{880}{2200}\) x 100 = 40%
Find the slope of the line containing the points (4,8) and (4,6) then find the slope of a line parallel to this line and the slope of the line perpendicular to this line.
To calculate the slope between 2 points we use the following equation:
\(m=\frac{y_2-y_1}{x_2-x_1}\)Replacing the points:
\(\begin{gathered} m=\frac{8-6}{4-4} \\ m=\frac{2}{0} \\ m\to\infty \end{gathered}\)In this case, when we find an infinite slope, it means that it is a line parallel to the Y axis. All parallel lines have the same slope.
For the perpendicular case, the slope is equal to:
\(\begin{gathered} m_{\perp}=\frac{1}{m} \\ m_{\perp}=\frac{1}{\frac{2}{0}} \\ m_{\perp}=\frac{0}{2} \\ m_{\perp}=0 \end{gathered}\)For the perpendicular case, the slope is zero and would equal one parallel to the X axis.
Answer:
not definednot definedzeroStep-by-step explanation:
The question is asking us to find the slope.
First, we will find the slope of the line that passes through (4,8) and (4,6).
We'll use the slope formula:
\(\bf{m=\dfrac{y_2-y_1}{x_2-x_1}}\)
Plug in the data :
\(\bf{m=\dfrac{6-8}{4-4}}\)
\(\bf{m=\dfrac{-2}{0}}\)
\(\bf{m=not\:de fined}\)
If a line's slope is not defined, then it's a vertical line:
\(\rule{1}{350}\)
------
Now, what is the slope of a line that's parallel to the one above? Well, since parallel lines have equal slopes, that one will have an undefined slope too.
As for perpendicular lines, they have slopes that are negative reciprocals of each other. We got that the slope is -2/0. The negative reciprocal of that is 0/2, which simplifies to 0.
Alternatively, you could look at it this way: a horizontal line (a line with zero slope) is perpendicular to a vertical line. So the slope of that line is m = 0.
\(\rule{350}{1}\)
solve for A and line AB
Answer:
a = 22
AB = 50
Step-by-step explanation:
\(a-5=17\)
\(a=17+5\)
\(a=22\)
Line AB=2a+6
\(2(22)+6=44+6=50\)
\(AB=50\)
Hope this helps
How can the average rate of change be interpreted from a graph or a function?
What is the y-intercept of the line? y = 5x - 9
Consider the line y=-3x+6.
Find the equation of the line that is perpendicular to this line and passes through the point (-8, 4).
Find the equation of the line that is parallel to this line and passes through the point (-8, 4).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
Equation of perpendicular line: y = []
Equation of parallel line:
2 0-0
X
S
The equation of the line that is parallel to y = -3x + 6 is: y = -3x - 20.
The equation of the line that is perpendicular to y = -3x + 6 is: y = 1/3x + 20/3.
How to Find the Equations of Parallel and Perpendicular Lines?Recall the following facts:
Two lines with the same slope value are parallel lines.Two lines are perpendicular lines if they have slopes that are negative reciprocals to each other.Given the equation of a line as y = -3x + 6, the slope of the line is m = -3. This implies that, the line that is parallel to y = -3x + 6 will have the same slope of m = -3, and the slope of the line that is perpendicular to y = -3x + 6 will be m = 1/3.
To write the equation of the perpendicular line, substitute m = 1/3 and (a, b) = (-8, 4) into y - b = m(x - a):
y - 4 = 1/3(x - (-8))
y - 4 = 1/3x + 8/3
y = 1/3x + 8/3 + 4
y = 1/3x + 20/3
To write the equation of the parallel line, substitute m = -3 and (a, b) = (-8, 4) into y - b = m(x - a):
y - 4 = -3(x - (-8))
y - 4 = -3x - 24
y = -3x - 24 + 4
y = -3x - 20
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PQSR is a rhombus. State the value of angle s1 and explain which property you used.
The measure of angle s1 is 35 degrees
RhombusThe diagonals of a rhombus divides the angle into equal measures.
The measure of the anglesThis means that:
\(\angle S = s_1 + 35\)
Where:
\(s_1 =35\)
Substitute 35 for s1
\(\angle S =35 + 35\)
\(\angle S =70\)
From the above computations, we have the following angle measures
The measure of angle s1 is 35 degreesThe measure of angle S is 35 degreesHence, the measure of angle s1 is 35 degrees
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10 of 11 A non-cancerous growth is injected with 1.25 grams of lodine-131, which has a decay rate of 8.621% per day. The exponential model A(t) = 1.25eln(0.91379)t represents the amount of lodine-131 remaining in the non-cancerous growth after t hours. Find how long it will take for the lodine-131 to decay to 0.35 grams. t = 14.08 days t = 14.10 days t = 14.12 days t = 14.14 days
The closest option is **t = 14.12 days**. The time it will take for the iodine-131 to decay to 0.35 grams is approximately 31.635 hours.
To find the time it will take for the iodine-131 to decay to 0.35 grams, we need to solve the exponential decay model A(t) = 1.25 * e^(ln(0.91379) * t) = 0.35, where A(t) represents the amount of iodine-131 remaining after t hours.
Let's solve for t:
1.25 * e^(ln(0.91379) * t) = 0.35
Dividing both sides by 1.25:
e^(ln(0.91379) * t) = 0.35 / 1.25
Using the property of logarithms, we can rewrite the equation as:
ln(e^(ln(0.91379) * t)) = ln(0.35 / 1.25)
The natural logarithm and the exponential function are inverse operations, so they cancel each other out:
ln(0.91379) * t = ln(0.35 / 1.25)
Now we can isolate t by dividing both sides by ln(0.91379):
t = ln(0.35 / 1.25) / ln(0.91379)
Calculating the right-hand side:
t ≈ -2.880 / -0.0909
t ≈ 31.635
Therefore, the time it will take for the iodine-131 to decay to 0.35 grams is approximately 31.635 hours.
Converting this to days, we divide by 24:
t ≈ 31.635 / 24
t ≈ 1.3181
Rounding to two decimal places, the time it will take is approximately 1.32 days.
None of the provided answer options match this result. However, the closest option is **t = 14.12 days**. Please note that the exact solution would require more decimal places or a more precise calculation.
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A custotuer requires during the next four months respectively 50,65,100, and 70 units of a commodity (no backlogs wllowed). Productions costs are $5,$8,$4, and $7 per unit during these months. The storage cost from one month to the next are $2 per unit (assessed on the end of the month inventory). Each unit at the end of the month 4 could be sold for $15 /unit. The production capacities for each month are 90, 75, 80 , and 50 units respectively. Currently, there are 15 units in inventory. Formulate a Linear Program that will minimize the objective function (sum of the production and inventory costs - revenue from selling end of period inventory at month 4). Note, inventory cost is assessed only for the first 3 periods. Model and solve the problem in AMPL and answer the quiz.
The formulated Linear Program aims to minimize the objective function, which is the sum of production and inventory costs minus the revenue from selling the end-of-period inventory at month 4.
In this problem, we need to determine the optimal production and inventory levels over the four-month period to minimize costs and maximize revenue. We can formulate this as a linear programming problem with the following decision variables:
Let x1, x2, x3, x4 represent the production quantities for months 1, 2, 3, and 4, respectively.
Let y1, y2, y3, y4 represent the end-of-month inventory levels for months 1, 2, 3, and 4, respectively.
The objective function we want to minimize is:
Minimize: (5x1 + 8x2 + 4x3 + 7x4) + (2y1 + 2y2 + 2y3) - (15y4)
Subject to the following constraints:
1. Initial inventory: y1 = 15 (given)
2. Production capacity constraints:
x1 <= 90 (month 1 capacity)
x2 <= 75 (month 2 capacity)
x3 <= 80 (month 3 capacity)
x4 <= 50 (month 4 capacity)
3. Inventory balance equations:
y1 + x1 - 50 = y2 (month 1)
y2 + x2 - 65 = y3 (month 2)
y3 + x3 - 100 = y4 (month 3)
y4 + x4 - 70 = 0 (month 4, no carryover inventory)
4. Non-negativity constraints:
x1, x2, x3, x4, y1, y2, y3, y4 ≥ 0
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find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. vertices: (0,±5); focies: (0,±6)
The standard form of the equation of the hyperbola with the given characteristics and center at the origin is:
(y² / 25) - (x² / 11) = 1
(y² / a²) - (x² / b²) = 1
The vertices are given as (0,±5), which means that the distance from the center to the vertices along the y-axis is 5. Therefore, a = 5.
The focies are given as (0,±6), which means that the distance from the center to the focies along the y-axis is 6. Therefore, c = 6.
We can use the relationship c² = a² + b² to find the value of b.
6² = 5² + b²
36 = 25 + b²
b² = 11
Therefore, the standard form of the equation of the hyperbola with the given characteristics and center at the origin is:
(y² / 25) - (x² / 11) = 1
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the height and base of parallelogeam is 20cm and 15.3cm respectively . find the area of a paralellogram
Answer:
Step-by-step explanation:
A = bh
A = 20 * 15.3 = 306 cm^2
What is meant in statistics by "scores having a central tendency"?
In statistics, the "central tendency" refers to a single value which represents middle or center of a set of data. The 3 common measures of central tendency are named as mean, median, and mode.
When scores have a central tendency, it means that most of the scores in a set of data are clustered around a particular value.
For Example, if we have a data set of test scores, and most of the scores are around 70, then 70 would be the central tendency of the data set.
The central tendency is an important concept in statistics because it provides a way to summarize a large set of data with a single value.
It can help you understand the overall pattern of the data and make comparisons between different data sets.
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The figure below is an example of a ____ ____ which is basically a solid that has been sliced by a plane
HELP PLEASE WORTH 23 points
Answer:
D. Cross section
Step-by-Step Explanation:
It is sliced showing the bottom part, so it is showing a cross section.
y + 1 3 + 7 y − 7 = 2 ( 4 y + 3 ) solve it and whats the number of solutions
Answer:
Step-by-step explanation:
y+13+7y-7=2(4y+3)
8y+6=8y+6
which is true for all real values.
so number of solutions=infinite (all real values)
Mai earn $7 per hour mowing her neighbor’ lawn. She alo earned $14 for hauling away bag of recyclable for ome neighbor. Priya babyit her neighbor’ children. The table how the amount of money, in dollar, m he earn in h hour. Priya and Mai have agreed to go to the movie the weekend after they have earned the ame amount of money for the ame number of work hour. How many hour do they each have to work before they go to the movie? How much will each of them have earned? $
Total ten hours, each have to work before they go to the movie and each of them have earned total eighty-four dollars.
We have, Mai's earning from mowing her neighbor’ lawn = $7 per hour
Also , her earning from hauling away bag of recyclable for some neighbor = $14
In case of Priya, a babysitter of her neighbor’ children. The above table shows amount of money, in dollar, m she earn in h hour.
Priya's earning in one hour = $8.40
We have to determine the how many hours they have to work for earning the same amount in same number of hours. Let the required hours be "h" hours . So, total mai's earning in h hours
= $14 + h --(1)
Priya's earning in h hour = h $8.40 --(2)
Therefore, equation (1) and (2) are linear equation in one variable, h . Now, according to problem in the earing of both in h hours are equal to each other. So, $14 +$ 7 h = h $8.40
=> h × 8.40 = 14 + 7h
=> h ( 8.40 - 7) = 14
=> h× 1.40 = 14
=> h = 14/1.4 = 140/14
=> h = 10
Hence, required value is 10.
Total priya's earning in 10 hours = 10× $8.40 = $84
Total Mai's earning in 10 hours = $14 + $70 = $84.
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Complete question:
Mai earns $7 per hour mowing her neighbors lawns.she also earns $14 for hauling away bags of recyclables for some neigbors. Priya babysits her neigbors children. The table shows the amount of monet m she earnd in h hours. Priya and mai have agreed to go to the movies the weekend after they have earned the same amount of money for the same number of work hours. How many hours do theyhave to work before they go to the movies?
3 1/5 as a equivalent decimal
Answer:
3.20 there is your answer
Can 10 people be divided into two groups with a ratio of 1 : 2? Explain.
No
Let the groups be x and 2x
x+2x=103x=10x=10/3Its decimal not natual so can't be divided
One cubic meter represents a cube shape that measures 1 meter in all three dimensions. how long is each side in centimeters?
Each side of cube is 100 cm.
What is a cube?In Maths or in Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedron.
Given that,
Volume of cube = 1 cubic meter
We know that,
1 m = 100 cm
Also volume of cube = \(a^{3}\)
Then,
Volume of cube = 1000000 cm
\(a^{3}\) = \(100^{3}\)
a = 100 cm
Hence, Each side of cube is 100 cm.
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Talia spent \dfrac34 4 3 start fraction, 3, divided by, 4, end fraction of this week's allowance on candy. Of the money she spent on candy, \dfrac56 6 5 start fraction, 5, divided by, 6, end fraction was spent on gummy bears.
Answer:
15/24
Step-by-step explanation:
Talia spent 3/4 of this week's allowance on candy. Of the money she spent on candy, 5/6 was spent on gummy bears.
What fraction of this week's allowance did Talia spend on gummy bears?
Answer: Let this weeks allowance be x. Talia spent 3/4 of the weeks allowance on candy, therefore the money spent on candy = (3/4)x.
Out of the money spent on candy, 5/6 was spent on gummy bears. Therefore the money spent on gummy bears = 5/6 × (3/4)x = (15/24)x.
This means that the fraction of money spent on gummy bears was 15/24 of the weeks allowance.
Select TWO ordered pairs that correspond to input-output pairs of the function:
y = - 6x + 7
(3.-11)
B
(-6,7)
С
(-1, 1)
D
(1, 1)
Answer:
A, D
Step-by-step explanation:
y=-6x+7
1. -11=-6(3)+7
-11=-18+7
-11=-11
2. 7=-6(-6)+7
7=36+7
\(7\neq\)43
3. 1=-6(-1)+7
1=6+7
1\(\neq\)13
4. 1=-6(1)+7
1=-6+7
1=1