Answers
The linear function that passes through the two points (-6, -2) and (-9, -1) is defined by the rule:
y = -(1/3)*x - 4
How to find the linear function with the given points?The general linear function in the slope-intercept form:
y = m*x + k
Where m is the slope (also called rate of change) and k is the intercept of the y-axis.
If we know that the line passes through two points (a, b) and (c, d) then the slope of the function is:
m = (d - b)/(c - a)
So with only two points, we can find the slope.
In this case, the line passes through the points (-6, -2) and (-9, -1) , then the slope is:
m = (-1 +2)/(-9 + 6) = 1/-3 = -1/3
Then the slope is m = -1/3
So the linear function is something like:
y = (-1/3)*x + k
To find the value of k i will use the pint (-9, -1), replacing these values we get:
-1 = -(1/3)*-9 + k
-1 = 3 + k
-1 - 3 = k
-4 = k
So the linear function that passes through these points is:
y = -(1/3)*x - 4
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Related Questions
At gym A is 76.50 for 8.5 hours. At gym B cost is 10.50 for 3/4 hours which plan of offers the best deal
Answers
Tell me if you want step by step explanation!
Hope this helped. :)
The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 34 minutes of calls is $14.69 and the monthly cost for 57 minutes is $17.68 . What is the monthly cost for 39 minutes of calls?
Answers
The monthly cost for 39 minutes of calls is $15.34.
According to given conditions :We can use the two given data points to form two equations and then solve for the unknown coefficients of the linear function.
Let the monthly cost (in dollars) be denoted by C, and let the total calling time (in minutes) be denoted by T. Then we can write:
C = aT + b
where a is the slope of the line (representing the rate of change of cost per minute of calling time), and b is the y-intercept of the line (representing the fixed monthly cost).
Using the given data points (34, 14.69) and (57, 17.68), we can form the following two equations:
14.69 = 34a + b (equation 1)
17.68 = 57a + b (equation 2)
Subtracting equation 1 from equation 2, we get:
17.68 - 14.69 = 57a - 34a + b - b
2.99 = 23a
a = 2.99/23
a = 0.13 (rounded to two decimal places)
Substituting the value of a into equation 1 (or 2), we get:
14.69 = 34(0.13) + b
b = 14.69 - 4.42
b = 10.27
Therefore, the linear function that represents the monthly cost in terms of total calling time is:
C = 0.13T + 10.27
To find the monthly cost for 39 minutes of calls, we can substitute T = 39 into this function:
C = 0.13(39) + 10.27
C = 5.07 + 10.27
C = $15.34 (rounded to two decimal places)
Therefore, the monthly cost for 39 minutes of calls is $15.34.
What is cost price ?The cost price (CP) is the original price paid to purchase a product or asset. It is the total cost incurred to acquire or produce the item, including all direct and indirect costs such as the cost of raw materials, labor, overhead expenses, transportation, taxes, etc.
The cost price is an important factor in determining the profitability of a business or investment, as it directly affects the profit margin. The profit margin is the difference between the selling price (SP) and the cost price (CP), expressed as a percentage of the cost price.
Profit Margin = (SP - CP) / CP * 100%
For example, if a product is sold for $100 and the cost price is $70, then the profit margin is:
Profit Margin = ($100 - $70) / $70 * 100%
Profit Margin = 30%
This means that for every $1 of cost, the business makes a profit of $0.30. The profit margin can be used to evaluate the efficiency and competitiveness of a business, and to compare the profitability of different products or investments.
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Find the intervals where the function is increasing and decreasing for the following functions. Using the first derivative test, state which critical value will give you your relative maximum/minimum. You DO NOT have to solve for relative max/min, just the value of c that would give me the min/max based off of the first derivative test.
Answers
f(x) = x^3 - 6x^2 + 12x the function is increasing for x < -2, increasing for x > 4 and decreasing for -2 < x < 4. The critical value that will give you a relative maximum is x = 4. The critical value that will give you a relative minimum is x = -2.
The derivative of the given function is f'(x) = 3x^2 - 12x + 12. Setting this equal to 0 gives us x = 0 and x = 4. By the first derivative test, we can determine that the function is increasing for x < -2, increasing for x > 4 and decreasing for -2 < x < 4. Therefore, the critical value that will give us a relative maximum is x = 4 and the critical value that will give us a relative minimum is x = -2. This can be verified by finding the second derivative of the function, which is f''(x) = 6x -12. Setting this equal to 0 gives us x = 2, which is between the two critical values. Since the second derivative is negative for x < 2, the critical value at x = -2 will give us a relative minimum and since it is positive for x > 2, the critical value at x = 4 will give us a relative maximum.
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In Lesson 5.2, you explored the concept of limits. Select the strongest description of what the following limit tells you. lim f(x) = 3 200 As x approaches 3 from both sides, the y-values approach different numbers. As x approaches infinity, the y-values of the function approach 3, indicating a horizontal asymptote. As x approaches 3, the y-values of the function approach infinity, indicating a vertical asymptote.
Answers
The given limit states that as x approaches 3, the corresponding y-values of the function f(x) approach 3.
This means that as x gets closer and closer to 3, the function f(x) gets arbitrarily close to 3. This also implies that there is no "gap" or "jump" in the values of f(x) around x=3, as the y-values approach the same limit from both sides of x=3.
Furthermore, the limit does not provide any information about the behavior of the function as x approaches infinity or negative infinity. It only tells us about the behavior of the function near x=3. Therefore, the option "As x approaches infinity, the y-values of the function approach 3, indicating a horizontal asymptote" is incorrect. Similarly, the option "As x approaches 3, the y-values of the function approach infinity, indicating a vertical asymptote" is also incorrect, as it suggests that the function has a vertical asymptote at x=3, which is not necessarily true.
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Taeghan spent $4428 at Old Navy. She bought eighteen new shirts at the same price. What was the price of each shirt?
Answers
Answer:
$246
Step-by-step explanation:
Find the perimeter of 2cm, 4cm, 2cm, 5cm, 4cm, 1cm
Answers
Answer:
Step-by-step explanation:
The perimeter is the distance around the edge of the shape.
\(P=2+4+2+1+4+5=18cm\)
What is the distance between the points (-2,1) and (5,-4)
Answers
Considering the definition of distance between two points, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.
Distance between two pointsThe distance between two points is equal to the length of the segment that joins them. Therefore, to determine the distance between two different points, you must calculate the squares of the differences between their coordinates and then find the root of the sum of said squares.
In other words, the distance between two points in space is the magnitude of the vector formed by said points.
So, given the coordinates of two distinct points (x1, y1) and (x2, y2), the distance between two points is the square root of the sum of the squares of the difference of the coordinates of the points:
distance= \(\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)
Distance between the points (-2,1) and (5,-4)In this case, you know:
(x1, y1): (-2,1)(x2, y2): (5,-4)Replacing in the definition of distance:
distance= \(\sqrt{(5-(-2))^{2} +(-4-1)^{2} }\)
distance= \(\sqrt{(5+2)^{2} +(-5)^{2} }\)
distance= \(\sqrt{7^{2} +(-5)^{2} }\)
distance= \(\sqrt{49+25 }\)
distance= √74= 8.6023
Finally, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.
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Determine g(x + a) – g(x) for the following function.
g(x) = 5x2 + 2x
Answers
Answer:
\(g(x + a) - g(x) = 10ax + 5a^2 + 2a\)
Step-by-step explanation:
We are given the function:
\(g(x) = 5x^2 + 2x\)
And we want to determine:
\(\displaystyle g(x+a) - g(x)\)
Substitute:
\(\displaystyle \begin{aligned}g(x + a) - g(x) &=\left[5(x+a)^2 + 2(x+a)\right] -\left[5x^2+2x\right] \end{aligned}\)
And simplify:
\(\displaystyle \begin{aligned}g(x + a) - g(x) &=\left[5(x+a)^2 + 2(x+a)\right] -\left[5x^2+2x\right] \\ \\ &= \left(5(x^2 + 2ax + a^2) + (2x + 2a) \right) + \left(-5x^2 - 2x\right) \\ \\ &= \left((5x^2 + 10ax + 5a^2) + (2x + 2a)\right) + \left(-5x^2 - 2x\right) \\ \\ &= (5x^2-5x^2) + (10ax + 2x - 2x) + (5a^2+2a) \\ \\ &= 10ax + 5a^2 + 2a \end{aligned}\)
In conclusion:
\(g(x + a) - g(x) = 10ax + 5a^2 + 2a\)
The population of a country has been increasing for several decades. In 1990, the population was about 263 million people In 2014, the population was about 307 million people Determine the percent in + The country's population increased by about % during this time period
Answers
Answer:
The country's population increased by about 16.73% during this time period.
Step-by-step explanation:
Percent increase:
The percent increase is given by the change multiplied by 100 and divided by the initial value.
In 1990, the population was about 263 million people In 2014, the population was about 307 million people.
Change: 307 - 263 = 44
Initial population: 263
Percentage increase:
44*100/263 = 16.73%
The country's population increased by about 16.73% during this time period.
10. Find measure of arc JK
pls help ASAP for points
Answers
The value of measure of arc JK is,
⇒ (arc KJ) = 28 degree
Since, The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
Measure of arc KL = 152°
Now, We know that;
⇒ m (arc LK) + m (arc KJ) = 180°
Substitute given values, we get;
⇒ 152° + m (arc KJ) = 180
⇒ m (arc KJ) = 180 - 152
⇒ (arc KJ) = 28 degree
Thus, The value of measure of arc JK is,
⇒ (arc KJ) = 28 degree
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Help I need the answer
Fast
Answers
Answer: 4
Step-by-step explanation: because he needs to divided by 2
5 · (4 · x) = ? help
Answers
Please help me in this math problem
Answers
Answer:
Step-by-step explanation: well, you will more than likely get it at least 60%-80% of the time! If this doesn't help i can try to explain in a lot more detail unless someone does for me!
By using graphical method, find optimal solution of the problem max z = 3x + y s.t 2x - y ≤ 5 -x + 3y ≤ 6 x ≥ 0, y ≥ 0
Answers
By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.
To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.
Let's start by graphing the constraints:
1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.
2. Plot the line -x + 3y = 6 using a similar process.
3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.
Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.
Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.
Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.
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Solve the equation for Y
3y=-6x+1
Answers
y is -2 is the answer for the question
Answer:
6x + 3y = 1
I hope this helps!
Lance’s team made 16 out of the 25 free-throws they attempted. What percent of the free-throws did the team make?
Answers
Answer:
64%
Step-by-step explanation:
16/25
Answer:
64%
Step-by-step explanation:
if they made 16/25 free-throws, you would multiply each side by 4 in order to get 100% on the right side, and if you multiply 16 by 4 it is 64
What is the domain of the square root function graphed below?
On a coordinate plane, a curve open up to the right in quadrant 4. It starts at (0, negative 1) and goes through (1, negative 2) and (4, negative 3).
x less-than-or-equal-to negative 1
x greater-than-or-equal-to negative 1
x less-than-or-equal-to 0
x greater-than-or-equal-to 0
Mark this and return
Answers
The domain of the square root function is x greater-than-or-equal-to 0, since the function is defined for all non-negative x-values or x-values greater than or equal to zero.
The domain of the square root function graphed below can be determined by looking at the x-values of the points on the graph.
From the given information, we can see that the curve starts at (0, -1) and goes through (1, -2) and (4, -3).
The x-values of these points are 0, 1, and 4.
Since the square root function is defined for any non-negative x-values or x-values more than or equal to zero, its domain is x greater-than-or-equal-to 0.
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A mixture of purple paint contains 6 teaspoons of red paint and 15 teaspoons of blue paint. To make the same shade of purple paint using 1 teaspoon of red paint, how much blue paint would you need?
Answers
Answer:
djekodoxlsksdiosoxx
Answer:
14 grrr pow pow pow zip
Step-by-step explanation:
answer asap................
Answers
Answer:
\( \sqrt{30} \)
can not be simplified further.
Decimal = 5.477225575
What the meaning of "a sequence of length n"?
Answers
In mathematics, a sequence is an ordered list of elements, often denoted by brackets or parentheses.
What the meaning of "a sequence of length n"?The term "a sequence of length n" refers to a sequence that contains a specific number of elements, where the number of elements is denoted by "n."
When the domain of a function is the set of natural numbers (N), it is called an infinite sequence. An infinite sequence can be thought of as an ordered list that continues indefinitely.
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4.
The distance around the school track is 0.25 mile. It takes Maribeth 5.1 minutes to run 2 laps around the school track. At that pace, how long does it take Marib
A 2.55 minutes
B 7.65 minutes
C 10.2 minutes
20.4 minutes
Answers
Answer:
the distance around the school track would be x
Step-by-step explanation:
you would have to divide 0.25 by 5.1 is 20.4
What's the sum of ⅖ and ¾? О A. % • в. ⅐ • C. % O D. 1%0
Answers
f(x)+x^2-3x-2x is shifted 4 units left. The result is g(x). What is g(x)
Answers
Answer:
g(x) = x² + 5x + 2
Step-by-step explanation:
If a function is f(x) = x²
And this function is shifted 4 units left then the rule to be followed is,
g(x) = f(x + 4)
Following the same rule,
For a function f(x) = x² - 3x - 2 when shifted 4 units to the left,
g(x) = f(x + 4)
g(x) = (x + 4)² - 3(x + 4) - 2
= x² + 8x + 16 - 3x - 12 - 2
= x² + 5x + 2
Therefore, g(x) = x² + 5x + 2 will be the transformed function.
Sayid wants to buy 3 sweaters for $37 each and 2 scarves for $11 each.
How much will Sayid
spend on these pieces of
clothing?
Answers
PLSSS HELPPP!!ฅ^•ﻌ•^ฅ
Answers
He spent $201.6 on the club altogether
Exercise
find the truth set of the
1.5(3x-5)-2(x-7)=11
Answers
Which expression is equivalent to 5^6
- 36 x 6 x 6 x 6
- 125 x 125
- 6 x 5
-25 x 5 x 5 x 5
Answers
Answer:
Option BStep-by-step explanation:
A. 36 × 6 × 6 × 6 = 6²⁺¹⁺¹⁺¹ = 6⁵ incorrect B. 125 × 125 = 5³ × 5³ = 5³⁺³= 5⁶ correct C. 6 × 5 incorrect D. 25 × 5 × 5 × 5 = 5² × 5 × 5 × 5 = 5²⁺¹⁺¹⁺¹ = 5⁵ incorrectAnswer:
the answer is 125.125
Step-by-step explanation:
Find the Discriminant and describe the solutions for given quadratic 3² – 2x +3=0
Answers
Answer:
Discriminant is 6.
Step-by-step explanation:
9-2x+3=0
-2x+9+3=0
-2x+12=0
-2x+12-12=0-12
-2x=-12
-2x/-2 = -12/-2
x=6
Probem
While racing around the track last week, Marco was able to get to 120 mph. This week Marco tried again and was
able to reach 135 mph. What was the percentage increase from last week to this week?
Answers
Answer:
Mark me as brainliest
Step-by-step explanation:
I don't know sorry bro
Multiplication Or Subtraction?
Mandy divided the sum of 12 and
24 by 6. Then, she found the sum of
the quotient and 4.
What number did she get?
Answers
Answer:
35
Step-by-step explanation:
I hope this helps you.
12+24=38
38÷6=31
31+4=35
Answer:
10
Step-by-step explanation:
12 + 24 = 36
36 divided by 6 = 6
6+4= 10