By reduction to the absurd, the two lines do not intercept each other because of the following absurd: 5 = - 4.
How to find the point of intersection between two lines in space
From statement we have two lines in space, whose vector forms are described below:
(x, y, z) = (1, - 9, 1) + t · (4, 1, 2) (1)
(x, y, z) = (1, 0, - 9) + s · (5, - 1, 5) (2)
The point of intersection satisfies the following condition:
(1, - 9, 1) + t · (4, 1, 2) = (1, 0, - 9) + s · (5, - 1, 5)
(1, - 9, 1) - (1, 0, - 9) = s · (5, - 1, 5) + t · (- 4, - 1, - 2)
s · (5, - 1, 5) + t · (- 4, - 1, - 2) = (0, - 9, - 8)
There is a point of intersection if the resulting system of linear equations has at least a solution:
5 · s - 4 · t = 0 (2)
- s - t = - 9 (3)
5 · s - 2 · t = - 8 (4)
By (2):
s = 4 · t/5
(2) in (3):
- 4 · t/5 - t = - 9
- 9 · t/5 = - 9
t/5 = 1
t = 5
(2) in (4):
5 · (4 · t/5) - 2 · t = - 8
4 · t - 2 · t = - 8
2 · t = - 8
t = - 4
By reduction to the absurd, the two lines do not intercept each other because of the following absurd: 5 = - 4.
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Please help ASAP!
What is the measure of arcXY shown in the diagram below?
Applying the angles of intersecting secants theorem, the measure of arc XY is: 32°.
How to Apply the Angles of Intersecting Secants Theorem?According to the angles of intersecting secants theorem, m∠XZY = 1/2(arc VW - arc XY).
Plug in the values:
39 = 1/2(110 - arc XY)
2(39) = 110 - arc XY
78 = 110 - arc XY
78 - 110 = - arc XY
-32 = - arc XY
Arc XY = 32°
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Which expression is equivalent to √2+4?
OA. (2+4)²
OB. (2+4)²
OC. 6
D. 62
When Billy's asked how old he is, he replies, "In two years I will be twice as old as I was five years ago." How old is he?
brainliest to whoever answers
Answer:
12 years old
Step-by-step explanation:
Set up the following equation:
x + 2 = 2(x - 5) (distribute the 2)
x + 2 = 2x - 10 (subtract 2 from both sides)
x = 2x - 12 (subtract 2x from both sides)
-x = -12 (multiply both sides by negative 1)
x = 12
Brainliest, please :)
Answer: 12
Step-by-step explanation:
Let's algebraically represent this situation. Say his current age is x. We can rephrase the sentence to say that in two years, his age is the same as twice his age 5 years ago.
The phrase "in two years" means when his age is 2 more than his current age, or x + 2.
The phrase "same as" represents equality. The expressions on both sides have the same value.
The phrase "twice his age 5 years ago" is his age minus 5, multiplied by 2. We can write this as 2*(x-5).
Now that we have "translated" the equation from words to numbers, let's put it all in one equation and solve:
[tex]x+2=2(x-5)[/tex]
[tex]x+2=2x-10[/tex] [Distributive Property]
[tex]x+2-2x-2=2x-10-2x-2[/tex] [Adding -2x-2 to both sides]
[tex]-x=-12[/tex] [Combining like terms and simplifying]
[tex]x=12[/tex] [Multiplying both sides by -1 to remove the negative]
Hence, Billy's age is 12.
5.5(x+6 1/2)-(x+9 1/3) - (19-x)
The simplest form of the expression given in the task content is; 5.5x +7.42.
What is the simplest form of the expression?The expression given in the task content is;
5.5(x+6 1/2)-(x+9 1/3) - (19-x)
Hence, the expression can be written in its simplest form as follows;
5.5x + 35.75 -x -9.33 -19 +x
= 5.5x +7.42.
Remarks: The complete task requires that the expression be written in its simplest form.
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I need help with my work
The area of the interior above the polar axis is -0.858 square units
The area bounded by a polar curveThe area bounded by a polar curve between θ = θ₁ and θ = θ₂ is given by
[tex]A = \int\limits^{\theta_{2} }_{\theta_{1} } {\frac{1}{2}r^{2} } \, d\theta[/tex]
Now, since we have the curve r = 1 - sinθ and we want to find the area of the interior above the polar axis, we integrate from θ = 0 to θ = π, since this is the region above the polar axis.
So, [tex]A = \int\limits^{\theta_{2} }_{\theta_{1} } {\frac{1}{2}r^{2} } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}(1 - sin\theta)^{2} } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}[1 - 2sin\theta + (sin\theta)^{2}] } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}\, d\theta - \int\limits^{\pi}_{0} 2sin\theta \, d\theta+ \int\limits^{\pi}_{0} (sin\theta)^{2} } \, d\theta\\[/tex]
[tex]A = \int\limits^{\pi}_{0} {\frac{1}{2}\, d\theta - 2\int\limits^{\pi}_{0} sin\theta \, d\theta+ \int\limits^{\pi}_{0} \frac{(1 - cos2\theta)}{2} } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}\, d\theta - 2\int\limits^{\pi}_{0} sin\theta \, d\theta+ \int\limits^{\pi}_{0} \frac{1}{2} } \, d\theta -\int\limits^{\pi}_{0} \frac{cos2\theta}{2} } \, d\theta\\[/tex]
[tex]A = \int\limits^{\pi}_{0} \, d\theta - 2\int\limits^{\pi}_{0} sin\theta \, d\theta -\int\limits^{\pi}_{0} \frac{cos2\theta}{2} } \, d\theta\\= [\theta]_{0}^{\pi} - 2[-cos\theta]^{\pi} _{0} - [\frac{sin2\theta}{4}]_{0}^{\pi} \\= [\theta]_{0}^{\pi} + 2[cos\theta]^{\pi} _{0} - [\frac{sin2\theta}{4}]_{0}^{\pi}\\= [\pi - 0] + 2[cos\pi - cos0] - \frac{ [sin2\pi - sin0]}{4}\\= \pi + 2[-1 - 1] - \frac{ [0 - 0]}{4}\\= \pi + 2[-2] - \frac{ [0]}{4}\\= \pi - 4 - 0\\= \pi - 4\\= 3.142 - 4\\= -0.858[/tex]
So, the area of the interior above the polar axis is -0.858 square units
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The x-intercept of a line is 2 and the y-intercept is 4. Explain how to use this information to write the equation of the line.
Answer:
y = -2x + 4
Step-by-step explanation:
The x-intercept would be the point (2,0) and the y intercept would have the point (0,4). Once we know two points we can write the equation in the line intercept for of y = mx + b.
We need to find the slope and the y intercept. The slope is the steepness of the line and it is the change in y over the change in x.
The ordered pairs are written in the form of (x, y). From our two points, we will subtract the y's to find the top number of our fraction.
0 - 4 = -4 that is the numerator (top number) of our slope. We do the same with the two x numbers that we have been given.
2 - 0 = 2 This is our numerator (or bottom number of our slope)
Our slope is -4 /2 to simplify, we divide the top and bottom number by 2 to get -2 / or just -2
Now that we have the slope we need to find the y-intercept. We can use either of our original two points and our slope to determine the y-intercept. It does not matter if you use the point (2,0) or (0,4). I will use (2,0) and the slope of -2
y = mx + b
0 = -2(2) + b
0 = -4 + b add 4 to both sides of the equation
4 = b
Now that we have the slope and the y-intercept, we can write the equation
y = mx + b
y = -2x + 4
How do you solve for m?
m= −(4+m)+2
Answer:
[tex]\bf m = - 1[/tex]
Step-by-step explanation:
[tex]\bf m= −(4+m)+2[/tex]
First of all, let's Rearrange the given terms :-
[tex]\bf m = - ( m +4) + 2[/tex]
Now, let's distribute:-
[tex]\bf m = - m - 4 + 2[/tex]
Add numbers -4 + 2 = -2
[tex]\bf m = - m - 2[/tex]
Add m to both sides, and combine like terms :-
[tex]\bf 2m = - 2[/tex]
Divide both sides by 2 :-
[tex]\bf m = - 1[/tex]
Lamonte has 50 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 288 square meters. List each set of possible dimensions (length and width) of the field.
The dimensions of the length and width are 25 meters and 12. 5 meters respectively.
How to determine the valuesArea of a rectangle
area of rectangle = l × w
where
l = length
w = width
Note that,
Perimeter = 2w+ l
50 = 2w + l
l = 50 - 2w
Hence,
area = w(50 - 2w)
288 = 50w - 2w²
-2w² + 50w - 288 = 0
-w² + 25w - 144 = 0
The dimension w can be found as follows;
w = - b / 2a
where
a = -1
b = 25
w = - 25 / 2 × -1
w = 12.5 meters
Then, we have that
l = 50 - 2w
Substitute the value of w
l = 50 - 2(12.5)
l = 50 - 25
I = 25 meters
Thus, the dimensions of the length and width are 25 meters and 12. 5 meters respectively.
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18. Which TWO linear inequalities are shown in the
graph below?
y
A.
B.
C.
D.
E.
F.
G.
H.
y> -2
y < -2
x<-2
X > -2
x+y<1
x-y<-1
x+y>1
x-y> -1
Answer: A and H
Step-by-step explanation:
y=x+1 is shaded below and dotted, so [tex]y < x+1 \implies x-y > -1[/tex].
Also, y=-2 is dotted and shaded above, so it represents [tex]y > -2[/tex]
I need help ASAP please
Answer:
8.1
Step-by-step explanation:
[tex]\sqrt{(-1-0)^2 + (5-(-3))^2}=\sqrt{65} \approx 8.1[/tex]
3.5.3 Test (CST): Functions
Does this graph show a function? Explain how you know.
-5
5-
OA. No; there are y-values that have more than one x-value.
B. No; the graph fails the vertical line test.
OC. Yes; there are no y-values that have more than one x-value.
D. Yes; the graph passes the vertical line test.
Jhy
Answer:
D
Step-by-step explanation:
It pass the vertical line test.
Hope this helps <3
As per the given graph, the graph fails the vertical line test. The correct option is B.
What is graph?A graph is a visual representation of data that uses lines, bars, or other symbols to show how different values are related to each other.
Graphs are often used to display information in a way that is easy to understand and interpret.
The vertical line test is a way to determine whether a given graph represents a function.
According to this test, if any vertical line intersects the graph at more than one point, then the graph does not represent a function.
In the given graph, we can see that there are some vertical lines that intersect the graph at more than one point, such as the vertical line passing through x = 2.
Therefore, the graph does not pass the vertical line test and does not represent a function.
Thus, the correct answer is B.
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Janet Lopez is establishing an investment portfolio that will include stock and bond funds. She has $720,000 to invest, and she does not want the portfolio to include more than 65% stocks. The average annual return for the stock fund she plans to invest in is 18%, whereas the average annual return for the bond fund is 6%. She further estimates that the most she could lose in the next year in the stock fund is 22%, whereas the most she could lose in the bond fund is 5%. To reduce her risk, she wants to limit her potential maximum losses to $100,000.
a. Formulate a linear programming model for this problem.
Based on the amounts that Janet Lopez has to invest in stocks and bonds, the linear programming model would be:
0.18x + 0.06y = maximized returns 0.22x + 0.05y ≤ 100,000x + y ≤ 720,000x/ y + y ≤0.65What is the linear programming model?The return on stocks (x) is 18% and the return on bonds (y) is 6%, The objective function:
= 0.18x + 0.06y
There are constraints to watch out for:
Maximum to lose on stocks is 22% and on bonds is 5% but these are to be less than the total amount of $100,000.
0.22x + 0.05y ≤ 100,000
The total amount to invest is $72,000 which means that both bonds and stocks need to be less than this amount:
x + y ≤ 720,000
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What is the value of x
83
58
50
70.5
Answer:
58
Step-by-step explanation:
[tex]x = \frac{141 - 25}{2} = 58[/tex]
Simplify the following
Answer is 6
Firstly changing mixed fraction.
[tex] \frac{3}{2} - \frac{5}{4} + \frac{23}{4} [/tex]
By taking the LCM
[tex] \frac{6 - 5 + 23}{4} [/tex]
-5 + 23 (-) (+) = (-)
[tex] \frac{6 + 18}{4} [/tex]
[tex] \frac{24}{4} [/tex]
[tex]6[/tex]
Hope it helps you, any confusions you may ask!
Answer:
6 (work below)
Step-by-step explanation:
1 1/2 = 3/2
1 1/4 = 5/4
5 3/4 = 23/4
The least common multiple of the denominators is 4, so 3/2 will become 6/4.
6/4 - 5/4 = 1/4 + 23/4 = 24/4 = 6
Brainliest, please :)
anybody answer me please with step by step explanation need complete detailed answer
Answer:
A = 55
Step-by-step explanation:
take the two identical triangles and join them so that you get a rectangle wih sides 5 and 11. now multiply them togeter to get the are of the polynom
The area of triangle is 55 square centimeters.
What is area?Area is the amount of space occupied by a two-dimensional figure.
What is the formula for the area of triangle?The formula for the area of triangle is
[tex]Area = \frac{1}{2} \times base\times height[/tex]
According to the given question.
We have a figure of a quadrilateral which is made up of four right angled tringles.
Now,
The area of a triangle with base 5cm and height 7 cm
= [tex]\frac{1}{2} \times 5\times 7[/tex]
[tex]=\frac{35}{2}[/tex]
[tex]= 17.5[/tex] square centimeters
And, the area of triangle with base 4cm and height 5cm
= [tex]\frac{1}{2} \times 4\times 5[/tex]
[tex]= 10[/tex] square centimeters
Since, the quadrilateral is made up of 2 right angled triangle with base 5cm and height 7cm and 2 right angled triangle with base 4cm and height 5cm.
Therefore, the area of quadrilateral or the given fiure
= 2( area of triangle with height 7cm and base 5cm + area of triangle with base 4cm and height 5cm )
= 2(17.5 + 10) square centimeter
= 2 × 27.5
= 55 square centimeters
Hence, the area of triangle is 55 square centimeters.
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PLEASE HELP PLEASE I DONT KNOW THIS QUESTION AND IVE BEEN STUCK ON THIS FOR A DAY
Answer:
A = -5
B = 1
Step-by-step explanation:
Hello!
You simply plug in the given x-value into the equation to find the missing y-value.
Solve for APlug in -1 for x into y = 2x - 3.
y = 2x - 3y = 2(-1) - 3y = -2 - 3y = -5Solve for BPlug in 2 for x into y = 2x - 3.
y = 2x - 3y = 2(2) - 3y = 4 - 3y = 1Calculate the geometric center of the graph the function
The geometric center of the graph under the function is 5/3
How to determine the geometric center of the graph under the function?The equation of the function is given as:
f(x) = 3 - |x - 2|
The interval is given as:
x ∈ [0, 3]
The geometric center (gc) of the graph under the function is calculated using
gc = ∫x f(x) dx/∫f(x) dx
Substitute the known values in the above equation
gc = ∫x * (3 - |x - 2|) dx/∫3 - |x - 2| dx
Integrate the numerator and the denominator of the above equation
gc = [-1/6(x - 2)((2|x -2| - 9)x + 2|x - 2| - 18)]/[3x - 1/2[|x - 2|(x - 2)]]
Recall that the interval is given as x ∈ [0, 3]
Substitute the interval values in the above equation.
The equation is then simplified using a graphing calculator.
So, we have
gc = (65/6)/(13/2)
Express the quotient expression as a product
gc = (65/6) * (2/13)
Divide 65 by 13
gc = 5/6 * 2
Divide 2 by 6
gc = 5/3
Hence, the geometric center of the graph under the function is 5/3
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Find the missing coordinate.
x = cos t
y = sin t
(-1, [?])
Answer:
0
Step-by-step explanation:
sin²t + cos²t = 1, so since cos²t = 1, sin²t = 0, and thus sint = y = 0.
Suppose that 37% of college students own cats. If you were to ask random college students if they own a cat what would the probability that:
a) a single student doesn’t own a cat?
b) 3 students own cats?
c) 2 students own cats while 2 students don't own cats?
Using the binomial distribution, the probabilities are given as follows:
a) 0.37 = 37%.
b) 0.5065 = 50.65%.
c) 0.3260 = 32.60%.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the fixed parameter is:
p = 0.37.
Item a:
The probability is P(X = 1) when n = 1, hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{1,1}.(0.37)^{1}.(0.63)^{0} = 0.37[/tex]
Item b:
The probability is P(X = 3) when n = 3, hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.37)^{3}.(0.63)^{0} = 0.5065[/tex]
Item c:
The probability is P(X = 2) when n = 4, hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{4,2}.(0.37)^{2}.(0.63)^{2} = 0.3260[/tex]
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The soil samples for the next field indicate that fertilizer
In order to have a greater fertilizer coverage, you need to increase flow rate and: A. increase speed to approximately 7.1 mph so that you cover the field more quickly.
What is a flow rate?A flow rate is an average rate and it can be defined as the number of flow units that are created per unit time such as fertilizer coverage on a farm.
In this context, we can infer and logically deduce that you have to increase flow rate and your increase speed to approximately 7.1 mph, so that you can cover the field more quickly and have a greater fertilizer coverage.
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Complete Question:
The soil samples for the next field indicate that fertilizer coverage needs to be greater. To achieve this, you need to increase flow rate. How would you achieve this?
A. Increase speed to approximately 7.1 mph so that you cover the field more quickly
B. Increase the engine speed to approximately 2,000 rpm
C. Decrease speed to approximately 6.0 mph so that you cover the field more slowly
D. Shift to second gear so that the engine speed slows
The graph of the function f(x) = (x - 3)(x + 1) is shown.
Ty
-10-8-6
10
8
6
-6
8
-10-
6
10
X
Which describes all of the values for which the graph is
positive and decreasing?
O all real values of x where x < -1
O all real values of x where x < 1
O all real values of x where 1
O all real values of x where x > 3
Answer:
all real values of x where x < -1
The correct statement is all real values of x where x < -1.
Option A is the correct answer.
We have,
To determine the values for which the graph of the function
f(x) = (x - 3)(x + 1) is positive and decreasing, we need to analyze the behavior of the function.
Let's consider the factors individually:
(x - 3): This factor is positive for x > 3 and negative for x < 3.
(x + 1): This factor is positive for x > -1 and negative for x < -1.
To determine the overall sign of the function, we need to consider the signs of both factors together.
When both factors are positive or both factors are negative, the function is positive.
When the factors have opposite signs, the function is negative.
From the above analysis, we can conclude the following:
When x > 3, both factors are positive, so the function is positive.
When -1 < x < 3, the factor (x - 3) is negative, while the factor (x + 1) is positive. Therefore, the function is negative.
When x < -1, both factors are negative, so the function is positive again.
Since we are looking for values where the function is positive and decreasing, we can eliminate the options that include positive and increasing regions (such as x > 3).
Thus,
The correct statement is all real values of x where x < -1.
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Please help ASAP! Clear explanations are greatly appreciated!
Using a system of equations, it is found that her normal week is of €285.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: Her normal hours.Variable y: Her time and a half hours.The first equation, considering the first sentence, is given by:
x + 8y = 375.
The second equation, considering the second sentence, is given by:
x + 4y = 330.
Then the system is:
x + 8y = 375.x + 4y = 330.Multiplying the second equation by -2, the system is:
x + 8y = 375.-2x - 8y = -660.Adding the equations, we have that her normal week is given by:
x = 660 - 375 = €285.
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1. Based on the circular
angle below. What is the
best measurement
the angle?
for
a. less than 90°
b. more than 90°
C. more than 180°
d. less than 60°
Answer:
B. More than 90
Step-by-step explanation:
Hope this helps!
The measure of the second angle of a triangle is three times the measure of the first. The measure of the third angle in the triangle is 12 degrees less than twice the measure of the first angle. Find the measures of each angle in the triangle.
Answer:
First angle:
x =32
Second angle:
3x
3(32) = 96
Third angle:
2x - 12
2(32) -12 =52
Step-by-step explanation:
x + 3x + 2x - 12 = 180 The sum of the interior angles of a triangle is 180
6x -12 = 180 Combine the x terms
6x = 192 add 12 to both sides
x = 32
Check: 52 + 96 + 32 = 180
Can anyone help me find all the calculations to these cups?
The volume of the glasses is as follows;
glass 1 = 170 cm³glass 2 = 141 cm³glass 3 = 60 cm³How to find volume ?The volume of cylinder glass 1 = πr²h
The volume of cylinder glass 1 = 3.14 × 3² × 6
The volume of cylinder glass 1 = 3.14 × 9 × 6
The volume of cylinder glass 1 = 169.56 cm³ = 170 cm³
The volume of the glass 2 = 2 / 3 π r³ + πr²h
The volume of the glass 2 = 2 / 3 × 3.14 × 3³ + 3.14 × 3² × 3
The volume of the glass 2 = 56.52 + 84.78
The volume of the glass 2 = 141.3 cm³ = 141 cm³
The volume of conical glass 3 = 1 / 3 πr²h
The volume of conical glass 3 = 1 / 3 × 3.14 × 3² × (√7² - 3² = √40)
The volume of conical glass 3 = 9.42 × √40
The volume of conical glass 3 = 59.5773111176
The volume of conical glass 3 = 60 cm³
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will give brainliest
The equation of a hyperbola is [tex]x^{2}[/tex]/9 - [tex]y^{2}[/tex]/4 = 1
What are the steps to Hyperbola equation ?
To find the equation of hyperbola, the following steps must be taken. You need to identify;
The coordinate of the centerThe coordinate of the verticesThe coordinate of the fociThe general equation of a hyperbola can be expressed as
[tex]x^{2}[/tex]/[tex]a^{2}[/tex] - [tex]y^{2}[/tex]/[tex]b^{2}[/tex] = 1
From the graph, we have the following parameters
a = 3
[tex]a^{2}[/tex] = [tex]3^{2}[/tex] = 9
b = 2
[tex]b^{2}[/tex] = [tex]2^{2}[/tex] = 4
The equation of a hyperbola can be expressed as
[tex]x^{2}[/tex]/9 - [tex]y^{2}[/tex]/4 = 1
The vertices = V(+/-a,0) = (+/-3,0)
The center = C(0,0)
The focus = F(+/-C, 0)
Where [tex]C^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex]
C = [tex]\sqrt{9 + 4}[/tex]
C = [tex]\sqrt{13}[/tex]
Focus = F(+/- [tex]\sqrt{13}[/tex], 0)
The general equation for asymptote = +/- b/a X
= +/-2/3X
Therefore, the equation of a hyperbola can be expressed as
[tex]x^{2}[/tex]/9 - [tex]y^{2}[/tex]/4 = 1
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Divide the polynomials.
Answer:
x^4-3x+2
Step-by-step explanation:
There are several different ways to divide algebraic expressions. Here the most simple way to do it (and good idea to try first) is to FACTOR and CANCEL.
see image.
Factor an x from the top. Cancel that x with the bottom x. See image.
(***Also, note: never "cancel" anything connected by a + or a - )
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\frac{x^{5}+(3\times x^{2}) +(2\times x) }{x}} \end{gathered}$}[/tex]
Takes into account expressions that have not yet been taken into account.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\frac{\red{\not{x}}(x-1)(x^{3}+x^{2} +x-2) }{\red{\not{x}} } } \end{gathered}$}[/tex]
Cancel x in both the numerator and the denominator.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{(x-1)(x^{3}+x^{2} +x-2) } \end{gathered}$}[/tex]
The expression expands
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{x^{4}-3x+2 } \end{gathered}$} }[/tex]
Alec starts up a monthly subscription potato box. It costs 18.20 dollars per month,
and comes with 16 potatoes in each box. Each subscriber may order any amount of
”luxury potatoes”, that are separate from the 16 that normally come in the box, for
an additional 5 dollars each.
(a) Write a formula for the monthly revenue, R in dollars, earned by Alec as a function
of s, the number of monthly subscribers, and n, the total number of luxury potatoes that his clients order. R(s, n) =
(b) Using your formula from above, find R(10, 3)
A. The formula (mathematical function) for the monthly revenue, R, earned by Alec, R(s, n) = $18.20s + $5n.
B. Using the formula above, the value of R(10, 3) is $197.
What is a function?A function is an expression, rule, or law defining the relationship between an independent variable and a dependent variable.
Functions are used to define physical relationships between variables.
Data and Calculations:Cost monthly subscription = $28.20 per box
Number of normal potatoes in each box = 16
Cost of additional luxury potatoes = $5 per potato
If the monthly revenue function, R, is given as R(s, n) where:
s = number of monthly subscribers
n = total number of luxury potatoes ordered
The monthly revenue, R, earned by Alec, R(s, n) = $18.20s + $5n.
The value of R(10, 3) is $197 ($18.20 x 10 + $5 x 3)
Thus, using the formula above, the value of R(10, 3) is $197.
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Express the following
The sum of the exponential expression is e^8x + e^2x
Simplifying exponential functionExponential functions are inverse of logarithmic function
Given the exponential function below;
(e^4x)² + e^2x
Expand
e^8x + e^2x
Hence the sum of the exponential expression is e^8x + e^2x
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At full price, Melvin would pay 1.679 dollars per liter of gasoline. Using his loyalty card, Melvin only pays 1.439 dollars per liter
He pays $0.24 less when using his loyalty card.
How much less does Melvin pay per liter when using his credit card?
We know that, without the card, he would pay $1.679 dollars per liter of gasoline.
With his card, he would pay $1.439
To find the relation between the two prices, we just need to take the difference between the two values (a difference is a subtraction).
d = $1.679 - $1.439 = $0.24
He pays $0.24 less when using his loyalty card.
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