Answers
Answer:
1st page:
To determine if Jason and Arianna made a mistake in their solution, we can examine the slopes and y-intercepts of the two equations.
The first equation, 5x - 3y = -1, can be written in slope-intercept form as y = (5/3)x + 1/3, where the slope is 5/3 and the y-intercept is 1/3.
The second equation, 3x + 2y = 7, can be written in slope-intercept form as y = (-3/2)x + 7/2, where the slope is -3/2 and the y-intercept is 7/2.
To solve the system of equations, we need to find the point of intersection of the two lines. We can see from the slopes that the lines are not parallel, so they must intersect at some point. However, the slopes are not perpendicular either, so they do not intersect at a right angle.
By graphing the two equations on the same coordinate plane, we can see that the point of intersection is (2, 2), not (4.04, 7.31) as Jason and Arianna calculated. Therefore, they must have made a mistake in their solution.
In summary, we can tell that Jason and Arianna made a mistake in their solution by examining the slopes and y-intercepts of the two equations and graphing them to find the actual point of intersection.
2nd page:
To determine if Jason and Arianna made a mistake in their solution, we can graph the two linear equations on the same coordinate plane and look for the point of intersection.
We can begin by rearranging the equations into slope-intercept form:
5x - 3y = -1 → y = (5/3)x + 1/3
3x + 2y = 7 → y = (-3/2)x + 7/2
Now we can graph the two lines. We can plot two points for each line and connect them with a straight line to obtain the graphs.
For the first equation, when x = 0, we get y = 1/3. When x = 3, we get y = 6/3 = 2. Plotting these two points and connecting them, we get:
Graph of the first equation
For the second equation, when x = 0, we get y = 7/2. When x = 2, we get y = 1/2. Plotting these two points and connecting them, we get:
Graph of the second equation
We can see from the graphs that the lines intersect at the point (2, 2), not at (4.04, 7.31) as Jason and Arianna found. Therefore, they must have made a mistake in their solution.
In summary, we can tell from the graphs of the equations that Jason and Arianna must have made a mistake because the lines do not intersect at the point they found.
3rd page:
We can determine if there is a unique solution to the system of linear equations by examining the slopes of the two equations.
The slope of the first equation, 5x - 3y = -1, can be found by rearranging the equation into slope-intercept form y = (5/3)x + 1/3. We can see that the slope of the line is positive and not equal to the slope of the second equation, which is -3/2.
Similarly, the slope of the second equation, 3x + 2y = 7, can be found by rearranging the equation into slope-intercept form y = (-3/2)x + 7/2. Again, we can see that the slope of the line is negative and not equal to the slope of the first equation, which is 5/3.
Since the slopes of the two lines are not equal, they will intersect at a unique point. In other words, there is only one solution to the system of equations.
Therefore, we can conclude that there is a unique solution to the system of linear equations given by 5x - 3y = -1 and 3x + 2y = 7, based on the slopes of the graphs of the equations in the system.
Step-by-step explanation:
Related Questions
Use inspection to describe the inequality's solution set. Do not solve the ineque (x-8)^(6)<=0
Answers
The inequality's solution set can be described by inspection as x <= 8.
What is inequality?Inequality is the unequal treatment of people based on factors such as race, gender, class, or other social characteristics. It is often seen as unfair and can lead to social and economic disparities.
This is because the inequality (x-8)^(6)<=0 is asking when the quantity (x-8) raised to the 6th power is less than or equal to zero.
Since any number raised to an even power will always be positive or zero, the only way for this inequality to be true is when (x-8) is equal to zero. This occurs when x = 8. Therefore, the solution set is x <= 8.
To summarize, the inequality's solution set is:
x <= 8
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In the diagram, PQ is parallel to RS.
Find the measure of
Write your answer and your work or explanation in the space below.
Answers
The measure of <TAV is [tex]92^{o}[/tex].
What are supplementary angles?A set of given angles is said to be supplementary if on addition of the measure of the angles, it gives [tex]180^{o}[/tex].
In the given diagram, given that PQ is parallel to RS, it can be observed that;
<SCU ≅ <ACB (definition of vertically opposite angles)
Thus, <ACB = [tex]18^{o}[/tex]
<QAC = <BCA (alternate angle property)
So that,
<QAC = [tex]18^{o}[/tex]
But,
<TAP ≅ <QAC (definition of vertically opposite angles)
So that;
<BAP + <PAT + <TAV = [tex]180^{o}[/tex] (sum of angles on a straight line)
Then,
70 + 18 + <TAV = 180
<TAV = 180 - 88
= 92
<TAV = [tex]92^{o}[/tex]
The measure of <TAV = [tex]92^{o}[/tex].
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The graph of function g in terms of x is made by starting with the graph f(x)= square root of x reflecting across the x asis, and then translating to the right 7 units. Write an equation for g (x)
Answers
The equation of the graph of the function g(x) is -√(x-7).
What distinguishes a reflection from a translation?Turns are frequently used to refer to reflection, which is when an object is flipped over a line without affecting its size or shape. The preimage is flipped over a line in a rigorous transition known as a reflection, but its size and shape are left unchanged. Flips is another name for reflections.
A figure can be translated if it is moved in any direction without altering its size, form, or orientation. A hard transformation called a translation alters the preimage's position but not its size, shape, or orientation. Slides are another name for translations.
Given that, f(x)= square root of x, that is:
f(x) = √x
Reflect the graph over x-axis we have:
Reflecting f(x) across the x-axis gives us -f(x) = -√x.
Translating -f(x) = -√x 7 units to the right gives us -f(x-7) = -√(x-7).
Hence, the equation of the graph of the function g(x) is -√(x-7).
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Add: (x^(2)-4x+9)/(x^(2)+9x+20)+(x-37)/(x^(2)+9x+20) Solution These two fractions have the same denominator, s
Answers
The polynomial is (x - 4)(x - 7)/(x + 4)(x + 5).
The question asks to add the two fractions (x^(2)-4x+9)/(x^(2)+9x+20) and (x-37)/(x^(2)+9x+20). To solve this problem, we can first simplify the denominator by factoring the polynomial:
Denominator: (x^(2)+9x+20) = (x + 4)(x + 5)
Now, we can rewrite the two fractions with this new denominator:
(x^(2)-4x+9)/(x + 4)(x + 5) + (x-37)/(x + 4)(x + 5)
Then, we can use the distributive property to expand the fractions and combine like terms:
(x^(2)-4x+9 + x-37)/(x + 4)(x + 5)
= (x^(2) - 3x - 28)/(x + 4)(x + 5)
Finally, we can simplify the numerator by combining like terms:
= (x^(2) - 3x - 28)/(x + 4)(x + 5)
= (x - 4)(x - 7)/(x + 4)(x + 5)
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Find the standard matrix for the stated composition of linear
operators on R2.
A rotation of 270∘ (counterclockwise), followed by a
reflection about the line y = x.
Answers
The standard matrix for the stated composition of linear operators on R2 is:
| 0 -1 |
The standard matrix for the stated composition of linear operators on R2 can be found by multiplying the matrices for each individual operation.
First, let's find the matrix for a rotation of 270° counterclockwise:
| 1 0 |
Next, let's find the matrix for a reflection about the line y = x:
| 0 1 |
| 1 0 |
Now, let's multiply these two matrices to find the standard matrix for the composition of these two operations:
| 0 -1 | | 0 1 | | -1 0 |
| 1 0 | * | 1 0 | = | 0 -1 |
Therefore, the standard matrix for the stated composition of linear operators on R2 is:
| -1 0 |
| 0 -1 |
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14x + 2 is equivalent to 16x True or False
Answers
Answer:
false
Step-by-step explanation:
the pothagirum therum say that theres many reason its false
Answer: True
Step-by-step explanation:
True because we do not know the letters value, so in this case you only add the numbers 14 and 2. You will end up with the answer 16x after adding the letter/valuable.
Please help me with this math problem!! Will give brainliest!! :)
Answers
Answer:
area=66
perimeter=42
Step-by-step explanation:
area = (12 x 3) + (5 x 6)
=36 + 30
=66
perimeter = 12 +9 +5 +6 +7 +5
=42
Find all solutions of the equation: 2 cos x-1-0
I NEED HELP ASAP!
Answers
The solutions to the cosine functions are x = π/3 + 2nπ or x = 5π/3 + 2nπ, where n is an integer and x = 3π/4 + 2nπ or x = 5π/4 + 2nπ, where n is an integer.
What are the solutions of the equation1. 2 cos x - 1 = 0
Adding 1 to both sides and dividing by 2, we get:
cos x = 1/2
This equation has solutions for x of π/3 and 5π/3 (plus any integer multiple of 2π, since the cosine function is periodic with period 2π).
Therefore, the solutions are:
x = π/3 + 2nπ or x = 5π/3 + 2nπ, where n is an integer.
2. 5 cos x + 3√2 = 3 cos x + 2√2
Subtracting 3 cos x and 2√2 from both sides, we get:
2 cos x = -√2
Dividing by 2, we get:
cos x = -√2/2
This equation has solutions for x of 3π/4 and 5π/4 (plus any integer multiple of 2π).
Therefore, the solutions are:
x = 3π/4 + 2nπ or x = 5π/4 + 2nπ, where n is an integer.
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If u1,u2,u3 are linearly independent, show that v1,v2,v3 are also linearly independent if v1=u1+u2,v2=u1+u3,v3=u2+u3
Answers
Yes, if u1, u2, and u3 are linearly independent, then v1, v2, and v3 will also be linearly independent.
To show this, assume that v1, v2, and v3 are linearly dependent. This means that there are scalars a,b, and c, such that:
a*v1 + b*v2 + c*v3 = 0
Since v1 = u1 + u2, v2 = u1 + u3, and v3 = u2 + u3, the equation above can be rewritten as:
a*(u1 + u2) + b*(u1 + u3) + c*(u2 + u3) = 0
Simplifying, this gives us:
(a + b + c)*u1 + (a + c)*u2 + (b + c)*u3 = 0
But since u1, u2, and u3 are linearly independent, the coefficients (a + b + c), (a + c), and (b + c) must all be equal to 0. This implies that a = b = c = 0, meaning that the original equation must be equal to 0. This means that v1, v2, and v3 are linearly independent.
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How many milliliters of a 100:1000 solution would you need to obtain 40g of active ingredient? Select one: a. 0.4mL b. 4mL c. 400mL d. 40mL
Answers
To obtain 40g of active ingredient from a 100:1000 solution, you would need 400mL of the solution. The correct answer is option c. 400mL. A 100:1000 solution means that there are 100g of active ingredient in 1000mL of the solution. To find out how many milliliters of the solution you need to obtain 40g of active ingredient, you can use the following proportion:
100g/1000mL = 40g/x mL
Cross-multiplying gives:
100g * x mL = 40g * 1000mL
Simplifying and solving for x gives:
x = (40g * 1000mL)/100g
x = 400mL
Therefore, you would need 400mL of the 100:1000 solution to obtain 40g of active ingredient.
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PLSS PICK A ANSWER CHOICE PLEASE AND THXXSSSS
XOXOXOXO HURRY
Answers
Answer: I believe its A.
Step-by-step explanation:
Question 4 1 pts Use the following functions to evaluate each expression
f (x) = x² + 1 g(x) = 1 / (2 - X )
a.) (f + g)(0) = ____
b.) (f . g)(0) = ____
Answers
[tex](f+g)(x)= f(x) .g(x)[/tex][tex](f+g)(0) = f(0)+g(0) = 1+\frac{1}{2} = \frac{3}{2}[/tex][tex]g(0) = \frac{1}{2-0} =\frac{1}{2}[/tex]Answer:
Step-by-step explanation:
We are given:
[tex]f(x) = x^{2} +1\ ;g(x) = \frac{1}{2-x}[/tex]
We need to find:
a) [tex](f+g)(0)[/tex]
b) [tex](f.g)(0)[/tex]
[tex]f(0) = 0^{2} +1 = 1[/tex]
[tex]g(0) = \frac{1}{2-0} =\frac{1}{2}[/tex]
a) we know that
[tex](f+g)(x)= f(x) +g(x)[/tex]
[tex](f+g)(0) = f(0)+g(0)[/tex]
Using the value of f(0) and g(0)
we get
b) we know that
[tex](f+g)(x)= f(x) .g(x)[/tex]
[tex](f+g)(x)= f(x) .g(x) = (1)(\frac{1}{2}) =\frac{1}{2}[/tex]
So we have answer for a) 3/2 and for b) 1/2
Using the expressions to evaluate each function we are left with the following:
(f + g)(0) = 1.5(f · g)(0) = 0.5
To evaluate the expressions, we simply need to substitute the value of x with 0 in the given functions and then perform the indicated operations. For part a, we need to add the functions f and g, and for part b, we need to multiply them:
(f + g)(0) = f(0) + g(0) = (0² + 1) + (1 / (2 - 0)) = 1 + (1 / 2) = 1.5
(f · g)(0) = f(0) * g(0) = (0² + 1) * (1 / (2 - 0)) = 1 * (1 / 2) = 0.5
In conclusion, we have that (f + g)(0) = 1.5 and (f · g)(0) = 0.5.
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In order for Ms. Sartain's wonderful, arnazing car to have optimal gas mileage, her tire pressure should be at 32 psi. The manufacturer indicates the tire pressure should remain within 2 psi at all times. Write an absolute value inequality that models this situation. |x+32|<=2 |x-32|<=2 |x+2|<=32 |x-2|<=32 Previous
Answers
This |x - 32| <= 2 means that the tire pressure can be anywhere between 30 psi and 34 psi.
In order for Ms. Sartain's car to have optimal gas mileage, the tire pressure should remain within 2 psi of 32 psi at all times. This can be modeled with an absolute value inequality.
The absolute value inequality that models this situation is |x - 32| <= 2. This inequality states that the difference between the tire pressure, x, and the optimal pressure, 32, should be less than or equal to 2.
In other words, the tire pressure can be 2 psi above or below the optimal pressure of 32 psi and still be within the acceptable range. This means that the tire pressure can be anywhere between 30 psi and 34 psi.
So the correct answer is |x - 32| <= 2.
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A circle with center C and a radius of 10 inches (in) is shown above. Rounded to the nearest tenth of an inch, what is the length of arc XYZ
Answers
The length of the arc XYZ is 59.3 inches .
How to find the length of an arc?The radius of the circle is 10 inches. The central angle that subtend the arc is 340 degrees.
Therefore, the length of the arc xyz can be found as follows:
length of an arc = ∅/ 360 × 2πr
where
∅= central angler = radius of the circlelength of an arc(xyz) = 340 / 360 × 2 × 3.14 × 10
length of an arc(xyz) = 21352 / 360
length of an arc(xyz) = 59.3111111111
length of an arc(xyz) = 59.3inches
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Alexis is traveling to Egypt this summer and needs to exchange 750 US Dollars to Egyptian pounds.
How many Egyptian pounds will Alexis receive with the following exchange rate?
1 USD = 18.48 Egyptian pounds
Enter the correct answer in the box.
( ) Egyptian pounds
Answers
Answer:
13,860 egyptian pounds
Answer:
Step-by-step explanation:
1 USD = 18.48 Egyptian pounds
∴ 750 USD = 750 × 18.48 Egyptian pounds
= 13860 Egyptian pounds
Use the properties of kites to answer the questions.
a. If AB = 8x-2, and AD = 6x+4, solve for AD.
b. If mPlease show your work.
Answers
The values of the length and angle are;
AD = 22 units
m < ADC = 106 degrees
How to determine the valuesThe properties of a kite are given as;
It has one pair of opposite angles that are equalThe shorter diagonal forms two equal isosceles trianglesThe longer diagonal forms two equal or congruent trianglesThe diagonals are perpendicular to each otherIt has two adjacent and equal sidesFrom the information given, we have that;
AB = 8x - 2
AD = 6x + 4
Equate the sides
8x - 2 = 6x + 4
collect like terms
2x = 6
x = 3
AD = 22 units
Also,
m < ABC = m < ADC
Substitute the values
12x + 10 = 15x - 14
collect like terms
-3x = -24x
x = 8
m < ADC = 106 degrees
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Answer: AD = 22 units
Step-by-step explanation:
m < ADC = 106 degrees
AB = 8x - 2
AD = 6x + 4
Equate any sides
8x - 2 = 6x + 4
Collect terms
2x = 6
x = 3
AD = 22 units
m < ABC = m < ADC
Substitute the values
12x + 10 = 15x - 14
Collect terms
-3x = -24x
x = 8
m < ADC = 106 degrees
The common tangent of a certain compound curve is parallel to its long chord. Its 546m long chord makes an angle of 18° and 12° with the shorter and longer tangents, respectively. Determine the length (m) of the common tangent.
Answers
The common tangent of the compound curve is parallel to its long chord. This means that the angle between the common tangent and the long chord is 0°. The long chord makes an angle of 18° with the shorter tangent and 12° with the longer tangent. We can use the law of sines to determine the length of the common tangent.
Let's call the length of the common tangent x, the length of the long chord L, the angle between the common tangent and the long chord θ, the angle between the long chord and the shorter tangent α, and the angle between the long chord and the longer tangent β.
Using the law of sines, we have:
x/sin(θ) = L/sin(α+β)
Substituting the given values, we have:
x/sin(0°) = 546/sin(18°+12°)
Simplifying the equation, we get:
x = 546*sin(0°)/sin(30°)
Since sin(0°) = 0 and sin(30°) = 0.5, we have:
x = 546*0/0.5
x = 0
Therefore, the length of the common tangent is 0m.
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Salve the mquation. If there is more than one solution, separate them with a momm |9a+5|=68
Answers
The solution to the equation |9a+5|=68 is a = 7, -8.111. To solve the equation |9a+5|=68, we can use the property of absolute value that states that |x| = x or |x| = -x. This means that we can set up two equations to solve for a:
9a+5 = 68 or 9a+5 = -68
Now we can solve each equation separately:
9a+5 = 68
9a = 63
a = 7
9a+5 = -68
9a = -73
a = -8.111
So the solutions are a = 7 and a = -8.111. We can write these solutions separated by a comma as follows:
a = 7, -8.111
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a.) State the general exponential growth equation.
b.) State the general exponential decay equation.
Answers
a. The general exponential growth equation is given by: y = abˣ
b. The general exponential decay equation is given by: [tex]y = a (1 - r)^x[/tex]
Exponential growth:Exponential growth is a type of growth pattern in which a quantity grows at an increasing rate proportional to its current value. This means that the larger the quantity, the faster it grows.
a. The general exponential growth equation is given by:
y = abˣ
Where y is the final value, 'a' is the initial value, b is the growth factor or base, and x is the time or number of periods.
Exponential decay:Exponential decay is a type of decay pattern in which a quantity decreases at a decreasing rate proportional to its current value. This means that the larger the quantity, the slower it decays.
b. The general exponential decay equation is given by:
[tex]y = a (1 - r)^x[/tex]
Where y is the final value, a is the initial value, r is the decay rate, and x is the time or number of periods
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How would you modify the statement of the limit of a rational function?
Answers
This would give us a modified statement of the limit, which would be "the limit of the rational function as x approaches 4".
What is rational function?A rational function is a type of mathematical function that can be expressed as the ratio of two polynomials. It can be written in the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomials with q(x) not equal to zero. Rational functions are used to model many real-world phenomena, such as the rate of change of a quantity with respect to another. They can also be used to solve complex equations and to analyze the behavior of a system.
The statement of the limit of a rational function can be modified by substituting different values for the variable and determining the resulting limit. For example, if the limit of the rational function is as x approaches 3, then we can substitute x = 4 and determine the resulting limit. This would give us a modified statement of the limit, which would be "the limit of the rational function as x approaches 4".
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es, if possible, determine AB. Identify the dimensions of the resulting matrix and fill out the matrix, if it exis A=[[-1],[-6],[7]],B=[[-9,-7,-1]]
Answers
The product of these two matrices is a 3x3 matrix, AB.
AB = [[-9, -7, -1]
[-9, -42, -7]
[63, -42, 7]]
To determine AB, we need to multiply matrix A and matrix B. The dimensions of matrix A are 3x1 and the dimensions of matrix B are 1x3. Since the number of columns in matrix A is equal to the number of rows in matrix B, we can multiply these matrices. The resulting matrix will have the dimensions of the number of rows in matrix A and the number of columns in matrix B, which is 3x3.
To multiply the matrices, we take the dot product of each row in matrix A with each column in matrix B. The dot product is the sum of the products of the corresponding entries in the row and column.
AB = [[(-1)(-9) + (-6)(-7) + (7)(-1)], [(-1)(-9) + (-6)(-7) + (7)(-1)], [(-1)(-9) + (-6)(-7) + (7)(-1)]]
AB = [[-9, -7, -1]
[-9, -42, -7]
[63, -42, 7]]
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What is the weighted mean, if each unit has the following weightings? (4 pts) Trigonometry counts for 25% Algebra counts for 15% Statistics counts for 10% Financial Math counts for 12% Linear Functions counts for 20 % Quadratic Functions counts for 18% Use the chart provided to organize your work for this question.
Answers
The weighted mean is a type of average that takes into account the relative importance of each data point. In this case, each unit has a different weighting, so we need to take that into account when calculating the weighted mean. Here is how to calculate the weighted mean:
1. Multiply each unit's weighting by its corresponding value.
2. Add up all of the products from step 1.
3. Divide the sum from step 2 by the sum of all the weightings.
Using the chart provided, here is how to calculate the weighted mean for this question:
Unit Weighting Value Product
Trigonometry 25% x 0.25x
Algebra 15% y 0.15y
Statistics 10% z 0.1z
Financial Math 12% a 0.12a
Linear Functions 20% b 0.2b
Quadratic Functions 18% c 0.18c
Weighted mean = (0.25x + 0.15y + 0.1z + 0.12a + 0.2b + 0.18c) / (0.25 + 0.15 + 0.1 + 0.12 + 0.2 + 0.18)
Weighted mean = (0.25x + 0.15y + 0.1z + 0.12a + 0.2b + 0.18c) / 1
Weighted mean = 0.25x + 0.15y + 0.1z + 0.12a + 0.2b + 0.18c
So the weighted mean is a combination of the values of each unit, weighted by their relative importance.
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One type of fertilizer has 30% nitrogen and
a second type has 15% nitrogen. If a farmer
needs 600 kg of fertilizer that is 20%
nitrogen, how much of each type should the
farmer mix together?
Answers
[tex]x=\textit{kgs of solution at 30\%}\\\\ ~~~~~~ 30\%~of~x\implies \cfrac{30}{100}(x)\implies 0.3 (x) \\\\\\ y=\textit{kgs of solution at 15\%}\\\\ ~~~~~~ 15\%~of~y\implies \cfrac{15}{100}(y)\implies 0.15 (y) \\\\\\ \textit{60 kgs of solution at 20\%}\\\\ ~~~~~~ 20\%~of~60\implies \cfrac{20}{100}(60)\implies 0.2 (60)\implies 12 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{lcccl} &\stackrel{kgs}{quantity}&\stackrel{\textit{\% of kgs that is}}{\textit{nitrogen only}}&\stackrel{\textit{kgs of}}{\textit{nitrogen only}}\\ \cline{2-4}&\\ \textit{1st Fert.}&x&0.3&0.3x\\ \textit{2nd Fert.}&y&0.15&0.15y\\ \cline{2-4}&\\ mixture&60&0.2&12 \end{array}~\hfill \begin{cases} x + y = 60\\\\ 0.3x+0.15y=12 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{x+y=60}\implies y=60-x \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 2nd equation}}{0.3x+0.15y=12}\implies \stackrel{\textit{substituting from above}}{0.3x+0.15(60-x)=12} \\\\\\ 0.3x+9-0.15x=12\implies 0.15x=3\implies x=\cfrac{3}{0.15} \\\\\\ \boxed{x=20}\hspace{5em}\stackrel{ 60~~ - ~~20 }{\boxed{y=40}}[/tex]
In a coordinate plane, shade the region that consists of all points that have positive x-and y-coordinates whose sum is less than 5. Write a system of three inequalities thatdescribes this region.
Answers
The system of three inequalities that describes this region is:x > 0y > 0x + y < 5
In a coordinate plane, the region that consists of all points that have positive x-and y-coordinates whose sum is less than 5 is the triangular region in the first quadrant bounded by the x-axis, y-axis, and the line x + y = 5. The system of three inequalities that describes this region is:x > 0y > 0x + y < 5Explanation:To find the region that consists of all points that have positive x-and y-coordinates whose sum is less than 5, we need to first graph the line x + y = 5 on a coordinate plane. This line has a slope of -1 and passes through the points (0,5) and (5,0). The region that we are looking for is the triangular region in the first quadrant bounded by the x-axis, y-axis, and this line.To write a system of three inequalities that describes this region, we need to consider the following facts:- All points in this region have positive x-coordinates, so x > 0.- All points in this region have positive y-coordinates, so y > 0.- All points in this region have x-and y-coordinates whose sum is less than 5, so x + y < 5.Therefore, the system of three inequalities that describes this region is:x > 0y > 0x + y < 5
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Multiply the binomials: (i) 2a-9 and 3a+4 (ii) x-2y and 2x-y (iii ) kl+lm and k-l (iv) m^(2)-n^(2) and m+n
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The multiplied the binomials of
2a-9 and 3a+4 is 6a²- 19a - 36. x-2y and 2x-y is 2x² - 5xy + 2y² kl+lm and k-l is k²l - l²m - kl² + lmk m²-n² and m+n is m³ + m²n - mn² - n³Multiplying binomials involves using the distributive property to multiply each term in one binomial by each term in the other binomial.
(i) 2a-9 and 3a+4
(2a-9)(3a+4) = 2a(3a) + 2a(4) - 9(3a) - 9(4) = 6a²+ 8a - 27a - 36 = 6a² - 19a - 36
(ii) x-2y and 2x-y
(x-2y)(2x-y) = x(2x) + x(-y) - 2y(2x) - 2y(-y) = 2x² - xy - 4xy + 2y² = 2x^(2) - 5xy + 2y²
(iii) kl+lm and k-l
(kl+lm)(k-l) = kl(k) + kl(-l) + lm(k) + lm(-l) = k^(2)l - kl²+ lmk - l²m = k²l - l²m - kl² + lmk
(iv) m²-n² and m+n
(m²-n²)(m+n) = m²(m) + m²(n) - n²(m) - n²(n) = m³ + m²n - mn² - n²
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Could someone help me with these problems?
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Answer:
too blurry
Step-by-step explanation:
Card Name (APR %) Existing Balance Credit Limit Mark2 (6.5%) $475.00 $3,000.00 Bee4 (10.1%) $1,311.48 $2,500.00 You have $450.00 each month to pay off these two credit cards. You decide to pay only the interest on the lower interest card and the remaining amount to the higher interest card. Complete the following two tables to help you. Lower Interst Card (Payoff Option) Month 1 2 3 4 5 6 7 8 9 10 Principal Interest Accrued Payment End-of-month balance Higher Interest Card Month 1 2 3 4 5 6 7 8 9 10 Principal Interest Accrued Payment End-of-month balance 1) How long does it take to pay off the higher interest card? 2) What is the amount of the last payment on the higher interest card? Why? 3) At the end of the month that you pay off the higher interest card, after you have started to pay down your debt on the lower interest card, what is the balance of the lower interest card? Why? 4) Rework the problem so that you pay off the lower interest card first. 5) How much money do you save by paying off the higher interest card first?
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I really need help on this one
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1. 9 months 2) $163.06, because it is the remaining balance after paying off the principal and interest accrued for that month. 3) $348.16, because it is the balance remaining on the lower interest card after paying off the higher interest card and making the monthly payment for that month. 4) 9 months 5) $168.79, because it is the difference between the total amount paid to each card when paying off the higher interest card first versus paying off the lower interest card first.
What is interest ?Interest is the fee paid for the use of borrowed money, usually expressed as a percentage of the borrowed amount.
According to given information :Based on the payment plan described, it will take 12 months to pay off the higher interest card.The amount of the last payment on the higher interest card will be $173.01. This is because the remaining balance after 11 months of payments will be $173.01, which is the amount needed to fully pay off the card.At the end of the month that you pay off the higher interest card, the balance of the lower interest card will be $404.17. This is because during the first 11 months, only the interest was being paid on the lower interest card, so the balance remained the same. However, in the month that the higher interest card is paid off, the full $450 payment will be applied to the lower interest card, reducing the balance by $45.83 to $404.17.If the lower interest card is paid off first, the payment plan and balances would be as follows: Lower Interst Card (Payoff Option) Month 1 2 3 4 5 6 7 8 9 10 Principal Interest Accrued Payment End-of-month balance $475.00 $6.46 $6.46 $6.46 $6.46 $6.46 $6.46 $6.46 $6.46 $6.46 $0.00 Higher Interest Card Month 1 2 3 4 5 6 7 8 9 10 Principal Interest Accrued Payment End-of-month balance $1,311.48 $10.69 $10.69 $10.69 $10.69 $10.69 $10.69 $10.69 $10.69 $10.69 $0.00. Under this payment plan, the lower interest card is paid off in 10 months, and then the remaining payments are applied to the higher interest card, which is paid off in an additional 2 months.By paying off the higher interest card first, you save a total of $141.27 in interest charges over the course of the payment plan.Therefore, 1. 9 months 2) $163.06, because it is the remaining balance after paying off the principal and interest accrued for that month. 3) $348.16, because it is the balance remaining on the lower interest card after paying off the higher interest card and making the monthly payment for that month. 4) 9 months 5) $168.79, because it is the difference between the total amount paid to each card when paying off the higher interest card first versus paying off the lower interest card first.
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difierence between 220 and the age of the person. The uppet limit is found by using 65% of the dilterence. Complete parts a throoph d. a. Find formulas for the upper and lower limits (U and L ) as finear equations involving the age x U= (Use integers or decimals for any tumbers in the equaton. Do nol factor.) L= (Use integers or decimals for any numbers in the equation. Do not factor.) b. What is the target heart rate zone for a 40 -year-old? For a 40-year-odd person, the lower limit is and the upper limit is beats per minule. c. What is the target hean nate zone for a 60 -year-eld? For a 60-year-old person, the lower limit is and the ueper linit is beatt per minute. d. Two wemen in an aerobics dass slop to take their pulse and find that they have the same pulse. One woman is 34 years older than the other and is working at the upper imit of har target heart rate zone. The younger woman is woking at the lower limit of her target hewrt rate zone. What are the ages of the two women, and what is their pulse? The age of the younger woman is approximately years and that of older woman is approximiely years. (Round to Een nearedt integers as needed) Their pulse is agproximately beats per minute. (Round to the nearest integor as neoded)
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a. The formula for the upper limit (U) is U = 220 - x, where x is the age of the person. The formula for the lower limit (L) is L = 0.65(220 - x).
b. For a 40-year-old person, the lower limit is L = 0.65(220 - 40) = 117 beats per minute and the upper limit is U = 220 - 40 = 180 beats per minute.
c. For a 60-year-old person, the lower limit is L = 0.65(220 - 60) = 104 beats per minute and the upper limit is U = 220 - 60 = 160 beats per minute.
d. Let x be the age of the younger woman and y be the age of the older woman. Since the older woman is 34 years older than the younger woman, we have y = x + 34. Since the older woman is working at the upper limit of her target heart rate zone and the younger woman is working at the lower limit of her target heart rate zone, we have U = L. Substituting the formulas for U and L, we get 220 - y = 0.65(220 - x). Substituting y = x + 34, we get 220 - (x + 34) = 0.65(220 - x). Simplifying and solving for x, we get x = 38. Therefore, the age of the younger woman is approximately 38 years and that of the older woman is approximately 72 years. Their pulse is approximately U = 220 - 72 = 148 beats per minute.
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A fair 20-sided die is rolled 60 times, and the value of chi-square is computed using expected counts of 3 for each face. If this process is repeated many times, the shape of the distribution of the values of chi-square should be...
A) uniform
B) bimodal
C) skewed left
D) skewed right
E) approximately normal
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The correct answer is E) approximately normal.
When the process of rolling a fair 20-sided die 60 times and computing the value of chi-square using expected counts of 3 for each face is repeated many times, the distribution of the values of chi-square should be approximately normal. This is because the chi-square distribution is a special case of the gamma distribution, and as the degrees of freedom increase, the chi-square distribution approaches a normal distribution. In this case, the degrees of freedom are 19 (20-1), which is a relatively large number, so the distribution should be approximately normal.
To summarize, the repeated process of rolling a fair 20-sided die 60 times and computing the value of chi-square using expected counts of 3 for each face will result in an approximately normal distribution of the values of chi-square.
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Problem-2: A matrix, M, is given. Obtain the inverse of this matrix using Matlab. Note that you are not allowed to use Matlab inv() command. M=[\begin{array}{ccc}6&8\\1&4\end{array}\right]
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Method of inverse of matrix is given:
To obtain the inverse of the given matrix, M, without using the Matlab inv() command, you can use the following steps:
1. Compute the determinant of M, which is equal to 2.
2. Create the matrix of cofactors by taking the transpose of the matrix formed by the cofactors of the elements of M.
3. Divide each element of the cofactor matrix by the determinant of M, in this case 2, to obtain the inverse of M.
Therefore, the inverse of M is given by the following matrix: M-1 = [\begin{array}{ccc}\frac{4}{2}&-\frac{8}{2}\\-\frac{1}{2}&\frac{6}{2}\end{array}\right]
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