The equation of line / is y=3x/a +5, where a is a positive constant. If the value of a in this equation is doubled, then the resulting equation will represent a line whose slope is how many times the slope of line / ?
The resulting equation will represent a line whose slope is 1/2 times the slope of the line
How to determine the slope of the new line?The equation of the line is given as:
y = 3x/a + 5
The constant a is a positive constant.
So, when the value of a in the equation is doubled, we have:
y = 3x/2a + 5
A linear equation is represented as
y = mx + b
Where m represents the slope.
So, we have:
m1 = 3/a
m2 = 3/2a
Substitute m1 = 3/a in m2 = 3/2a
m2 = 1/2 * m1
Hence, the resulting equation will represent a line whose slope is 1/2 times the slope of the line
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The difference of four times a number and seven is 21
Answer: 4n - 7 = 21, n = 7
Step-by-step explanation:
A difference indicates subtraction of two terms. Four times a number indicates that a number of any value has to be multiplied by 4.
Hence, the equation that is represented by the question is
[tex]4x - 7 = 21[/tex]
We can also solve this equation (i.e., find the value of x that makes this equation true).
Adding 7 to both sides, we get
[tex]4x - 7 + 7 = 21 + 7[/tex]
Since the -7 and 7 add to 0, the equation becomes
[tex]4x = 28[/tex]
To get x by itself, we can divide both sides by 4, making the equation
[tex]x=7[/tex]
Hence, x must be 7 to make the equation true, or 7 is a solution to the equation.
the sum of a number increased by three and the number decreased by seven
Answer is (n + 3) + (n - 7)
Simplified to 2n - 4
Using “n” for number
25 POINTS, QUICKLY PLEASE!
1. Which system is represented in the graph?
A. y > x2 + 4x – 5, y > x + 5
B. y < x2 + 4x – 5, y < x + 5
C. y ≥ x2 + 4x – 5, y ≤ x + 5
D. y > x2 + 4x – 5, y < x + 5
2. Which type of function describes f(x)?
A. Exponential
B. Logarithmic
C. Rational
D. Polynomial
Answer:
1) y > x² + 4x - 5, y > x + 5
2) Rational
Step-by-step explanation:
For a parabola, if the shade is inside the curve then the value of y will be greater or equal to:
For a line, if the shade is above it then the value of y will be greater or equal to:
Therefore, since parabola doesn't have solid curve (--- graph) then the inequality is ">"
Therefore, the inequality for parabola is y > x² + 4x - 5
For a line, it does not have solid graph so the inequality is ">"
Therefore, the inequality for line is y > x + 5
-----------
The graph of function describes the shape of rational function. It cannot be exponential as exponential only has one curve. It cannot be logarithm for same reason as exponential. It cannot be polynomial as polynomial is continuous function but the graph is discontinuous at specific point x = 0.
That being said, all choices except rational are all continuous function by default but rational function isn't and since the graph is discontinuous then we can say that it's rational function.
What is the ratio between 40,000 and 200?
The ratio between 40,000 and 200 is 200 : 1
How to determine the ratio?The numbers are given as:
40,000 and 200
Express as ratio
Ratio = 40000 : 200
Divide each number by 200
Ratio = 200 : 1
Hence, the ratio between 40,000 and 200 is 200 : 1
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Borrwed 25000 at ir10.5%
for ten years accured interest
60 POINTS IF CORRECT AND BRAINLIEST ANSWER FOR COMPLETE ANSWER
1. The solution to the first percent puzzle is as follows:
75% 66²/₃ 11¹/₉
33¹/₃% 25% 22¹/₅% 3⁷/₁₀%
50% 37¹/₂% 33¹/₃% 5¹/₂%
50% 37¹/₂% 33¹/₃% 5¹/₂%
2. The solution to the second percent puzzle is as follows:
10% 90%
50% 5% 45%
50% 5% 45%
What is a percent puzzle?A percent puzzle is a puzzle that engages students to practice working with percentages.
The percent puzzle involves a matrix format, in which students multiply the column percent by the row percent to find the percent they must put in the missing boxes to complete the puzzle.
The multiplication results for the missing boxes can be either stated in decimals, fractions, or a combination.
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What is lcm of 3,6,9
Answer:
lcm of 3,6,9 is 18
One month Kevin rented 2 movies and 5 video games for a total of $30. The next month he rented 8 movies and 3 video games for a total of $35. Find the rental cost for each movie and each video game. Rental cost for each movie: s Rental cost for each video game
Answer:
M = $2.5; V = $5
Step-by-step explanation:
We need to set up a system of equations to find the price for both movies (M) and video games (V).
We can use 2M + 5V = 30 and 8M + 3V = 35
We can use elimination:
[tex]-4(2m+5v=30)\\8m+3v=35\\\\-8m - 20v = -120\\8m+3v=35\\-17v=-85\\v=5\\\\2m+5(5)=30\\2m+25=30\\2m=5\\m=5/2 ;m=2.5[/tex]
A design consists of the capital letter E. What kind of symmetry would be shown in the design? Explain.
The kind of symmetry that would be shown in the design is an axial symmetry.
What is an axial symmetry?It should be noted that an axial symmetry simply means a symmetry around an axis.
In this case, the capital letter E has an acid of symmetry. Therefore, an axial symmetry is appropriate.
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The graph of f(x) = x3 + x2 – 9x – 9 is shown.
Based on the graph, what are the solutions of x3 + x2 – 9x – 9 = 0?
x = –1, 3
x = –3, –1
x = –3, –1, 3
x = –9, –3, –1, 3
Answer:
the third option, x = –3, –1, 3
Step-by-step explanation:
Find the measure of MON
Answer: 77 degrees
mLON is the total angle. mLOM is part of the angle, and is 55 degrees. To find the missing degree, subtract the part we know from the part the whole. In this case, subtract 55 from 132. mMON is 77 degrees.
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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A ______ function is a specific type of function that represents the relationship between two variables, usually x and y. The graph of this function is a line.
the answer choices are
dependent
independent
parallel
slope
perpendicular
rate
scale
y
change
linear
Instructions: Identify the vertices of the feasible region for the given linear programming constraints.
Optimization Equation: z=−3x+5y
Constraints:
x+y≥−2
3x−y≤2
x−y≥−4
Fill in the vertices of the feasible region:
(0, )
(-3, )
(3, )
The vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)
How to identify the vertices of the feasible region for the given linear programming constraints?The optimization equation is given as
z=−3x+5y
The constraints are given as:
x+y≥−2
3x−y≤2
x−y≥−4
Next, we plot the constraints on a graph and determine the points of intersections
See attachment for the graph
From the attached graph, the points of intersections are
(-3, 1), (3, 7) and (0, -2)
So, we have:
(0, -2)
(-3, 1)
(3, 7)
Hence, the vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)
So, the complete parameters are:
Optimization Equation:
z=−3x+5y
Constraints:
x+y≥−2
3x−y≤2
x−y≥−4
Vertices of the feasible region
(0, -2)
(-3, 1)
(3, 7)
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In a game of chance, two fair dice are thrown. If the sum of the two dice is seven, you get paid out $90. If the sum of two dice is a six or an eight, you must pay $90(No money is exchanged for all other sums). How much money would you expect to win or lose, on average, per game?
You are expected to lose $ 10 on an average per game
How to determine the amount of money you would winTotal outcome = 36Event of sum of 7 = 6Amount per sum of 7 = $ 90Amount won per game =?Probability of sum of 7 = 6 / 36
Probability of sum of 7 = 1 / 6
Amount won per game = (1 / 6) × 90
Amount won per game = $ 15
How to determine the amount of money you would loseTotal outcome = 36Event of sum of 6 = 5Event of sum of 8 = 5Event of sum of 6 or 8 = 5 + 5 = 10Amount per sum 6 or 8 = $ 90Amount lose per game =?Probability of sum 6 or 8 = 10 / 36
Probability of sum 6 or 8 = 5 / 18
Amount lose per game = (5 / 18) × 90
Amount lose per game = $ 25
How to determine your expect earning on an avarge per gameAmount won per game = $ 15Amount lose per game = $ 25Expected earnings =?Expected earnings = Amount won per game - Amount lose per game
Expected earnings = 15 - 25
Expected earnings = -$ 10
Thus, you are expected to lose $ 10 on an average per game
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please help im failing what is the answer
The general-form equation of the circle is:
A. [tex]x^2 + y^2 - 8x - 8y + 23 = 0[/tex]
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
This circle has center at (4,4), hence:
[tex]x_0 = 4, y_0 = 4[/tex]
The radius is of 3 units(distance of A and B from the center), hence the equation is:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
[tex](x - 4)^2 + (y - 4)^2 = 3^2[/tex]
We expand the equation to find the general form, hence:
[tex]x^2 - 8x + 16 + y^2 - 8y + 16 = 9[/tex]
[tex]x^2 + y^2 - 8x - 8y + 23 = 0[/tex]
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The average amount of electricty consumed by a household in a day is strongly correlated to the average daily temperature for that day. This relationship is given by y=0.503x+3.31 where x is the temperature in F and y is the amount of electricity consumed in kilowatt-hours (kWh).
What does the y-intercept of this function represent?
A. the average amount of electricity consumed for each degree Fahrenheit
B. the average electricity consumption for a daily average temperature of 0 F
C. the minimum amount of electricity consumed
D. the change in temperature for each increase in electricity consumption
The y-intercept of this function represents C. the minimum amount of electricity consumed
How to interpret the y-intercept?The function is given as:
y = 0.503x + 3.31
The y-intercept of a function represents the minimum or the initial value of the function
This means that the y-intercept of this function represents C. the minimum amount of electricity consumed
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Estimate the difference of the decimals below by rounding to the nearest
whole number.
61.621
7.173
Answer:
55
Step-by-step explanation:
61.621 rounded to the nearest whole number is 62. We know this by looking at the whole number "61" and rounding its last digit by the digit to the right of it, depending if its <5 or >5. In this case, the right ones digit is "6", being greater than 5 means we can round 61.621 to 62.
The same applies to 7.173, given that "1" is less than 5, we don't round down (because we are rounding up), instead we replace remaining digits with 0, leaving us with 7.
To find the difference means to subtract;
62-7 = 55.
8 cm
Find h.
9 cm
h = √[?] cn
Answer:
[tex]\sqrt{65}[/tex], so [?] = [65]
Step-by-step explanation:
This is a classic Pythagorean Theorem problem :)
We are given a right triangle with 2 sides, so all we have to do is plug it into the formula a² + b² = c², or in simple terms: the square of one side plus the square of the other equals the square of the hypotenuse.
line h is going to bisect the diameter of the circle (8) so one side will be 4. We're given 9 as our hypotenuse, so:
(4)² + (h)² = (9)².
16 + h² = 81
h² = 81 - 16, h² = 65, h = [tex]\sqrt{65}[/tex].
Indicate the equation of the given line in standard form. Show all of your work for full credit.
The line containing the diagonal, BD, of a square whose vertices are A(-3, 3), B(3, 3), C(3, -3), and D(-3, -3). Find two equations, one for each diagonal.
The linear equations are given as follows:
For diagonal AC: [tex]x + y = 0, -3 \leq x \leq 3[/tex].For diagonal BD: [tex]x - y = 0, -3 \leq x \leq 3[/tex].What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For diagonal AC, the line contains points (-3,3) and (3,-3), hence the line is:
y = -x.
In standard form:
[tex]x + y = 0, -3 \leq x \leq 3[/tex].
For diagonal BD, the line contains points (3,3) and (-3,-3), hence the line is:
y = x.
In standard form:
[tex]x - y = 0, -3 \leq x \leq 3[/tex].
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What is the classification of each system?
Answer:
inconsistentconsistent independentconsistent dependentStep-by-step explanation:
Consistent Independent = exactly ONE solution
Consistent Dependent = INFINITELY many solutions
Inconsistent = NO solution
what is the inverse of the function f(x)=x/5-2
Answer:
[tex]\huge\boxed{\sf f^{-1}(x)=5x+10}[/tex]
Step-by-step explanation:
Given function:[tex]\displaystyle f(x)=\frac{x}{5} -2[/tex]
Put f(x) = y
[tex]\displaystyle y=\frac{x}{5} -2[/tex]
Swap x and y
[tex]\displaystyle x = \frac{y}{5} -2[/tex]
Now, solve for y
[tex]\displaystyle x = \frac{y}{5} -2[/tex]
Add 2 to both sides
[tex]\displaystyle x + 2 =\frac{y}{5}[/tex]
Multiply 5 to both sides
[tex]5(x+2)=y[/tex]
Distribute
[tex]5x + 10 =y[/tex]
Put y = f⁻¹(x)
[tex]\boxed{f^{-1}(x)=5x+10}[/tex]
[tex]\rule[225]{225}{2}[/tex]
there are 60 minutes in one hour and 60 seconds in one minute. Using this information, explain how you could convert 20 miles per hour to feet per second
The conversion is given as 1, 760 feet per second
How to convert the valueWe need to convert 20miles per hour to feet per second
First, we should convert miles to feet
1 mile = 5280 feet
Then,
20 miles = x
Cross multiply
20 × 5280 = x
x = 105, 600
Per hour = I hour = 60 seconds
To find the conversion, we divided the conversion to feet by that of the time
= 105, 600/60
= 1, 760 feet per second
Thus, the conversion is given as 1, 760 feet per second
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IfX+9=11,
then the value of 7 X = ......
The answer is 14.
First, we need to find X using the first statement.
X + 9 = 11X = 11 - 9X = 2Now, we have to substitute this in the required expression.
7X7(2)14Determine whether AB and CD are parallel, perpendicular, or neither. A(-3, 2), B(5, 1), C(2, 7), D(1, -1)
Answer:
perpendicular
Step-by-step explanation:
We'll find the slope of both lines and see what it tells us.
If the slopes are the same, the lines are parallel. If the slopes are opposite sign and flipped (negative reciprocals) then they are perpendicular.
The slope is y-Y on top of a fraction and x-X on the bottom.
Slope of AB:
m = 2-1 / -3 -5
= 1/-8 = -1/8
Slope of CD:
m = 7- -1 / 2-1
= 8/1 = 8
Since the slopes are -1/8 and 8, the lines are perpendicular, because they are opposite sign and flipped (negative reciprocals)
A rental car company charges $20 per day to rent a car and $0.10 for every mile driven. Addison wants to rent a car, knowing that:
She plans to drive 100 miles.
She has at most $80 to spend.
Considering the definition of an inequality, the inequality that can be used to determine x is 20x + 10≤ 80
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
This caseA rental car company charges $20 per day to rent a car and $0.10 for every mile driven.
Addison wants to rent a car, knowing that:
She plans to drive 100 miles.She has at most $80 to spend.On the other hand, x represents the maximum number of days Alyssa can afford to rent for while staying within her budget.
Then, the inequality that can be used to determine x is:
20x + 0.1×100≤ 80
So:
20x + 10≤ 80
In summary, the inequality that can be used to determine x is 20x + 10≤ 80
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A music store sells music equipment at a 35%
markup. It a piece of equipment costs $150.00
what will the selling price be? I
The selling price of an equipment costing $150.00 with 35% markup is $202.50
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Given that the mark up is 35%, hence:
Markup = [(selling price - cost price)/cost price] * 100%
Substituting:
$202.50
Selling price = $202.50
The selling price of an equipment costing $150.00 with 35% markup is $202.50
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9
What is the price of a two year bond with a 9% annual coupon and a yield to maturity of 8%?
97.51
102.53
101.78
105.25
The price of a two-year bond is 101.78 and the correct option is C.
Given that a 9% annual coupon and a yield to maturity of 8%.
Simple yield is the amount of interest received by a bond issuer divided by the current market price of the associated bond.
Implicit Face value, FV=$100
Time, N=2 years
Coupon, C=(9/100)×$100=9
The yield of maturity, r=8%=0.08
Now, we will find the bond price using the formula
Price of bond = C× [1-{1/ (1+r)ⁿ}/r] +M/ (1+r)ⁿ
Substitute the values in this formula, we get
Price of bond=9×[1-{1/(1+0.08)²}/0.08]+100/(1+0.08)²
Price of bond=9×[1-{1/(1.08)²}/0.08]+100/(1.08)²
Price of bond=9×[1-{1/1.1664}/0.08]+100/1.1664
Price of bond=9×[(1-0.857)/0.08]+85.73
Price of bond=9×[0.143/0.08]+85.73
Price of bond=9×1.7875+85.73
Price of bond=16.0875+85.73
Price of bond=101.78
Hence, the price of a two-year bond with a 9% annual coupon and a yield to maturity of 8% is 101.78.
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1. There are 50 contestants signed up for a TV show. There are 36 more female contestants than male contestants. How many female contestants have signed up to compete? Show your solution and explain how you plan to explain this to your students.
Considering the definition of an equation and the way to solve it, 43 female contestants have signed up to compete.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.
The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.
To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Amount of females contestantsBeing "m" the number of male contestants, and knowing that:
There are 50 contestants signed up for a TV show.There are 36 more female contestants than male contestants.the equation in this case is:
m + (m+36) = 50
Solving:
m + m = 50 - 36
2m= 14
m= 14 ÷ 2
m= 7
Since there are 36 more female contestants than male contestants, then m +36= 7 + 36= 43
Finally, 43 female contestants have signed up to compete.
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