Study this table.
X
-3
-2
0
4
y
-2
0
4
12
Which best describes the function represented by the data in the table?
O linear with a common ratio of 2
Olinear with a common first difference of 2
O quadratic with a common ratio of 2
O quadratic with a common first difference of 2
Answers
The Function is linear with a common first difference of 2.
We have,
x y
-3 -2
-2 0
0 4
4 12
For the first set of points
m=(0-(-2))/(-2--3)
m = (0+2)/(-2+3)
m= 2/1 = 2
For the second set of points
m = (4-0)/(0-(-2))
m = 4/(0+2)
m = 4/2 = 2
For the third set of points
m = (12-4)/(4-0)
m = 8/4
m = 2
Thus, the function is linear with a common first difference of 2.
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Related Questions
a certain forest covers an area of 1700km^(2). Suppose that each year this area descreases by 7.5%. What will the area be after 11 years?
round your answer to the nearest square kilometer.
Answers
The area of the forest after 11 years will be 298 km².
To calculate the area of the forest after 11 years, we need to decrease the initial area of 1700 km² by 7.5% each year for 11 years.
First, let's calculate the decrease in area for one year:
Decrease in area for one year = 7.5% of 1700 km²
7.5% of 1700 km² = (7.5/100) × 1700 km²
= 127.5 km²
Now, we can calculate the total decrease in area over 11 years:
Total decrease in area over 11 years = 11 × 127.5 km² = 1402.5 km²
Finally, we can subtract the total decrease in area from the initial area to get the area of the forest after 11 years;
Area of the forest after 11 years = Initial area - Total decrease in area
= 1700 km² - 1402.5 km²
= 297.5 km²
Therefore, Rounding to the nearest square kilometer, the area of the forest after 11 years will be approximately 298 km².
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Find the interquartile range using the following.
Minimum: 1
Q1: 3
Median: 5
Q3: 7
Maximum: 9
A. 8
B. 4
C. 5
D. 10
Answers
Answer: B. 4
Step-by-step explanation: The interquartile range is just the distance in between the upper and lower quartiles. Therefore, to find the interquartile range, the equation in this case is 7 - 3, which equals 4.
y is less than or equal to two-thirds times x plus 1 y is greater than negative one-fourth times x plus 2 Which ordered pair is included in the solution to this system? (6, −2) (6, 0.5) (6, 5) (6, 8)
Answers
Answer:(6, −2), (6, 0.5) I’m pretty sure
A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}. Find the probability of getting two numbers whose sum is greater than 9. Group of answer choices
Answers
The probability of getting two numbers whose sum is greater than 9 = 5/36
We know that the probability is nothing but the number of favourable outcomes divided by the total number of outcomes.
Here, a single die is rolled twice.
and we get the set of 36 equally likely outcomes.
so, the total number of outcomes n(S) = 36
Let us assume that event A: getting two numbers whose sum is greater than 9
A = {(4, 6), (5,5), (5, 6), (6, 4), (6, 5)}
n(A) = 5
Using above formula of probability,
P(A) = n(A)/n(S)
P(A) = 5/36
Thus the required probability = 5/36
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answer quick i need done
Answers
The new vertices of the triangle after moving the triangle 5 units down, are A(1,-7), B(9,-7), and C(5,-3). So, correct option is B.
To determine the coordinates of the triangle after it is translated 5 units down, we need to subtract 5 from the y-coordinates of each vertex.
Let's start with vertex A(1,-2). If we subtract 5 from -2, we get -7. Therefore, the new coordinates of vertex A are (1,-7).
Next, let's look at vertex B(9,-2). Again, if we subtract 5 from -2, we get -7. So the new coordinates of vertex B are (9,-7).
Finally, let's consider vertex C(5,2). If we subtract 5 from 2, we get -3. So the new coordinates of vertex C are (5,-3).
In this case, we are moving the triangle 5 units down, which means that we are subtracting 5 from the y-coordinates of each vertex. This is a common transformation in geometry, and it's important to be familiar with it when working with shapes and figures in the Cartesian plane.
So, correct option is B.
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use your knowledge of transformations to find matching graph f (x) = ½ √x - 1
Answers
1. Shift the graph one unit to the right by adding 1 to the x-coordinate: y = √(x - 1)
2. Stretch the graph vertically by a factor of 1/2: y = ½√(x - 1)
Therefore, the graph of f(x) = ½ √x - 1 is a vertically stretched and horizontally shifted version of the graph of y = √x.
Answer:
Step-by-step explanation:
down 1
compress 1/2
107/103 X 101/100 =
What is 107 over 103 times 101 over 100
Answers
107 over 103 times 101 over 100 would result in 10807/10300.
Mathematical operationsIn order to multiply the fractions 107/103 and 101/100, we can simply multiply their numerators together and their denominators together:
(107/103) x (101/100) = (107 x 101) / (103 x 100)
Now we can simplify this fraction by finding the greatest common factor of the numerator and denominator and dividing both by it:
(107 x 101) / (103 x 100) = 10807 / 10300
Therefore, 107/103 times 101/100 simplifies to 10807/10300.
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Please please help me with my work thank you
Answers
The match to A line that has a slope of 5/3 and a y-intercept of 4 is 2y - x = -4.
We are given that;
The four equations to match from
Now,
Using the slope-intercept form, we can plug in m = 3/2 and b = -8:
y = (3/2)x - 8
This equation matches with y = 3/2x - 5 if we multiply both sides by 2:
2y = 3x - 16
Therefore, the correct equation is 2y - x = -16.
A line that contains the points (0,-2) and (4,0)
m = (0 - (-2)) / (4 - 0) m = 2 / 4 m = 1/2
Then we can plug in m = 1/2 and any of the given points to find b. For example, using (0, -2), we have:
-2 = (1/2)(0) + b -2 = b
Therefore, the equation is:
y = (1/2)x - 2
This equation matches with -5x - 3y = -12 if we multiply both sides by -6:
6y = -3x + 12
Therefore, the correct equation is -5x - 3y = -12.
A line that contains the y-intercept (0-2) and the slope of -3/4
Using the slope-intercept form, we can plug in m = -3/4 and b = -2:
y = (-3/4)x - 2
This equation matches with y = -3/4x - 2.
A line that has a slope of 5/3 and a y-intercept of 4
Using the slope-intercept form, we can plug in m = 5/3 and b = 4:
y = (5/3)x + 4
This equation matches with 2y - x = -4 if we multiply both sides by 3:
3y = (5/3)x + 12
Therefore, the correct equation is 2y - x = -4.
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how much cardboard is needed to make the single slice pizza box shown
Answers
that would be 5 pieces of cardboard needed
What is the slope of the line that passes through
the points (2,-4) and (2, 4)?
A. -3 B.0. C.8. D. Undefined
Answers
The line is a vertical line, then the correct option is D, the slope is undefined.
How to find the slope of the line?A general linear equation can be written as:
y = a*x + b
Where a is the slope, b is the y-intercept, and x is the variable.
If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of that line is given by the formula:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know that the two points are (2, -4) and (2, 4)
Replacing that we would have a problem, that is because we have the same x-value in both points.
Then we have a vertical line at x = 2.
That line has no defined slope, thus, the correct option is D.
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Please help me PLEASE ANYEONE?!!!?!!
Answers
Step-by-step explanation:
1/3 ÷ 3
= 1/3 ÷ 3/1
= 1/3 X 1/3 = 1/9
Similarly
1/4 ÷ 5 = 1/4 X 1/5 = 1/20
Answer: 1/9
Picture a pie and and having 1 slice out of the total 3 pieces, which would be 1/3 of the pie. Now, we want to divide the the pie into 3 more equal-piece groups. This means every original piece of the pie would now have 3 slices in each piece, so the pie would have a total of 9 pieces now. We want to keep our original 1 slice of pie, but now we have taken 1/9 of the pie, a much smaller slice.
What we have done is simply multiplied the denominator (bottom number of the fraction) by 3. In other words, the number of total pieces of pie is tripled from 3 to 9, meaning more slices would have to be cut, but the amount of pie stays the same. We are just taking a smaller slice. This is why the rule for dividing fractions is Keep Change Flip, because we really just want to the denominator to multiply.
Question 10: 1/4÷5
Answer: 1/20
The same logic applies.
geometry pls helpppppp
Answers
A graph of triangle TOW is shown below.
A graph of triangle T'O'W, the image of ΔTOW after a reflection in the y-axis is shown below.
The coordinates of ΔT'O'W are: T' (5, 6), O' (-1, 8), and W' (4, -2).
What is a reflection over the y-axis?In Mathematics and Geometry, a reflection over or across the y-axis is represented by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over or across the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
Next, we would apply a reflection over or across the x-axis;
(x, y) → (-x, y)
T (-5, 6) → (-(-5), 6) = T' (5, 6)
O (1, 8) → (-(-1), 8) = O' (-1, 8)
W (-4, -2) → (-(-4), -2) = W' (4, -2)
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Which choices are equivalent to the expression below? Check all that apply.
4√3
A. 48
B. 12.4
C. √24√2
D. 3 16
E. 4.3
F. 48
Answers
The choices that are equivalent to the expression 4√3 will be ✓48 and ✓24.✓2.
How to explain the expressionIt is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
4✓3 will be:
= ✓4² × ✓3
= ✓48
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The change in water level of a pond is shown in the table.
Week
1
2
3
4
5
Water level (inches)
-1 1/4
1 3/8
2 1/2
-1 5/8
-1 3/4
Between which two weeks did the water level change the most? Calculate the change.
Answers
Between Weeks 3 and 4, the water level varied the greatest.
To determine which two weeks had the greatest change in water level, we need to find the difference between each pair of consecutive weeks and identify the largest difference.
Here are the differences between consecutive weeks:
Week 1 to Week 2: (1 3/8) - (-1 1/4) = 2 5/8
Week 2 to Week 3: 2 1/2 - 1 3/8 = 1 1/8
Week 3 to Week 4: (-1 5/8) - 2 1/2 = -4 1/8
Week 4 to Week 5: (-1 3/4) - (-1 5/8) = -1/8
The largest difference is between Week 3 and Week 4, with a difference of 4 1/8 inches.
Therefore, the water level changed the most between Week 3 and Week 4.
Note that the differences are calculated by subtracting the water level of the earlier week from the water level of the later week.
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quadratic equations. A positive real number is 4 less than another. When 8 times the larger is added to the square of the smaller, the result is 48.
Answers
Substituting y = x + 4 into the second equation, we get:
8(x + 4) + x^2 = 48
Expanding and rearranging, we get:
x^2 + 8x - 16 = 0
Using the quadratic formula, we can solve for x:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = 8, and c = -16. Plugging in these values, we get:
x = (-8 ± sqrt(8^2 - 4(1)(-16))) / 2(1)
Simplifying, we get:
x = (-8 ± sqrt(96)) / 2
x = (-8 ± 4sqrt(6)) / 2
x = -4 ± 2sqrt(6)
Since x is a positive real number, we take the positive root:
x = -4 + 2sqrt(6)
Now that we have found x, we can use y = x + 4 to find y:
y = -4 + 2sqrt(6) + 4
y = 2 + 2sqrt(6)
Therefore, the two real numbers are approximately -4 + 2sqrt(6) and 2 + 2sqrt(6).
math hw for tonight
help solve this problem! Thank you!
ap cal bc
Answers
Answer:
3t^2i + 2tj is the correct answer.
Circle the students error in the problem below and rewrite what correct step should be
Answers
The students error is in step 3 and the correct solution is g(x) = 2x² + 4x - 4
Circling the students errorFrom the question, we have the following parameters that can be used in our computation:
The steps to solve the expression
From step 2 to step 3, we have
g(x) = 2(x + 1)(x + 1) - 6
g(x) = 2(x² + 1x + 1) - 6
The step 3 is incorrect
Because when the expression is expanded, we have
g(x) = 2(x² + 2x + 1) - 6
This gives a solution of
g(x) = 2x² + 4x - 4
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What is the initial value of Y=2x+3
Answers
Answer:3
Step-by-step explanation: Initial value = y-intercept
PLEASE HELP ME !!! I NEED THIS TO GRADUATE
Answers
Plot the coordinates on the number line provided and then find the coordinate of the indicated point
on a number line that partitions the segment into the given ratio.
A is at 1, and B is at 10. Find the point, T, so that T is two-thirds of the distance from A to B.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3
4 5 6 7 89
+
10
Answers
Answer:
t = 6.8
Explanation:
We know that A is at 1, B is at 10, so that is where we place those two.
First, we need to know what 2/3 of 10 is because the distance between A and B is 10.
Solving 2/3 of 10:
_____________________
- Divide 10 by the denominator, 3
10 ÷ 3 = 3.3333......
- Multiply 3.3333..... by 2
3.3333..... x 2 = 6.6666666666667
or about 6.8 if we round up, which is prefered in these scenarios
Now that we know what 2/3 of 10 is, we can use that number as where to put it on the number line.
So t = 6.8
Hope this helps :)
2. Solve 4.3(n + 6) > 47.3. Then graph the solution.
Answers
Answer: n>5
Step-by-step explanation:
Find the total cost for the month in dollars. The federal tax is 3%. Use the figure below.
Monthly phone service plan is $52.00. Four lines and 3,487 minutes are used.
Answers
Answer:
The total cost per month is $190.76 to the nearest cent.
Step-by-step explanation:
From the given table, the monthly service plan costing $52.00 is:
Monthly Service Plan = $52.00Number of included minutes per month = 2,000 minutesCost per additional line per month = $21.99Overage per minute rate = $0.06The base calling plan includes two lines.
Therefore, for 4 lines, we will need to pay for 2 additional lines per month:
⇒ $21.99 × 2 = $43.98 per month
If 3,487 minutes are used per month, then the overage of minutes is:
⇒ 3487 - 2000 = 1487 minutes per month
As the overage rate is $0.06 per minute, then the cost of the additional minutes is:
⇒ 1487 × $0.06 = $89.22 per month
Therefore, the total cost per month before tax is:
⇒ $52.00 + $43.98 + $89.22 = $185.20
To apply the federal tax of 3%, multiply the total cost by 1.03:
⇒ $185.20 × 1.03 = $190.756 = $190.76 (nearest cent)
Therefore, the total cost per month is $190.76 to the nearest cent.
A painter needs 3/8 gallon of green paint to finish a job. He has 5/8 gallon of red paint. He has 1/2 gallon more red paint than green paint. Can he finish the job?
Answers
Answer: 17/24 for both jobs
Step-by-step explanation:
An online television company is sending out surveys to rank 10 TV-show genres watched. What is the probability that you guess the top 3 genres correctly and in the correct order?
Write your answer as an exact fraction which is reduced as much as possible.
Answers
Answer:
The probability of guessing the first genre correctly is 1/10. After guessing the first genre, the probability of guessing the second genre correctly is 1/9. Similarly, the probability of guessing the third genre correctly is 1/8. Therefore, the probability of guessing the top 3 genres correctly and in the correct order is:
1/10 * 1/9 * 1/8 = 1/720
So the exact probability is 1/720, which is already reduced to its simplest form.
If the price of a particular chocolate bar is increased by 20%, and it used to be $2, what is the new price after the increase?
Answers
To find this, you can multiply the original price ($2) by 1.20, which represents the 20% increase.
$2 x 1.20 = $2.40
So the chocolate bar now costs $2.40 after the 20% increase.
please help me i relly need help
Answers
Answer:
h(x) = 3·2^x
Step-by-step explanation:
You want the equation of the exponential curve h(x) = a·b^x when it goes through the points (0, 3) and (1, 6).
PointsWhen x=0, the equation is ...
h(0) = a·b^0 = a
We know that h(0) = 3, so a = 3.
When x=1, the equation is ...
h(1) = 3·b^1 = 3b
We know that h(1) = 6, so 3b = 6, or b = 2.
The equation is h(x) = 3·2^x.
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∠A and ∠ � ∠B are vertical angles. If m ∠ � = ( 2 � − 2 ) ∘ ∠A=(2x−2) ∘ and m ∠ � = ( 3 � − 15 ) ∘ ∠B=(3x−15) ∘ , then find the value of x.
Answers
The calculated value of x if ∠A and ∠B are vertical angles is 13 degrees
How to find the value of x.From the question, we have the following parameters that can be used in our computation:
∠A = (2x − 2)
∠B = (3x − 15)
Since the ∠A and ∠B are vertical angles, then they are congruent angles
So, we have
3x - 15 = 2x - 2
Evaluate the like terms
So, we have
x = 13
Hence, the solution is x = 13
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Circle A has a circumference of 8π/x+2 units and Circle B has a circumference of 4π/x+2 units. What is a simplified expression for the difference in the areas of Circle A and B
Answers
The simplified expression for the difference in the area of circle A and B is 12π/(x+2)²
What is area of a circle?A circle is simply a round shape that has no corners or line segments. The area of a circle is expressed as;
A = πr²
The circumference of a circle = 2πr
for circle A;
8π/x+2 = 2πr
r = 8π/x+2 × 1/2π
r = 4/x+2
area = πr² = (4/x+2)²π
for circle B
4π/x+2 = 2πr
r = 4π/x+2 × 1/2π
r = 2/2x+2
area =( 2/2x+2)²π
difference = (4/x+2)²π - ( 2/x+2)²π
= π/(x+2)²( 4²-2²)
= π/(x+2)²(16-4)
= 12π/(x+2)²
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F(x) = 2^x
Elija todas las siguientes afirmaciones que describen el gráfico.
A. Cuando x tiende a infinito negativo, f(x) tiende a 0.
B. Cuando x tiende a infinito negativo, f(x) tiende a infinito.
OC. Cuando x tiende a infinito, f(x) tiende a 0.
OD. Cuando x tiende a infinito, f(x) tiende a infinito.
Answers
By analyzing the end behavior of the function we can see that the correct options are A and D.
Which statements are true for the given function?Here we have the exponential function:
[tex]F(x) = 2^x[/tex]
This is an exponential growth, this means that as x increases also does the function, then the end behavior of the function is:
as x → ∞, f(x) → ∞
And when x is a really large negative number, the function tends to zero, then we have:
as x →-∞, f(x) → 0
Then the correct options are A and D.
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Molly has four t-shirts in her closet that she plans to wear over the next four days without wearing the same one twice. She has a blue, green, yellow, and black shirt. What are the chances that she will wear the black shirt the first day?
Write your answer as an exact fraction which is reduced as much as possible.
Answers
Answer:
Molly has four choices for which shirt to wear on the first day, and one of those choices is the black shirt. So the probability that she will wear the black shirt on the first day is 1/4. Therefore, the answer is 1/4.
Step-by-step explanation: