The total amount for the new vehicle, considering the given costs, is $16,692.
To calculate the total amount of a new vehicle, you need to consider the standard vehicle price, options cost, and destination charge. In this case, the standard vehicle price is $14,530, the options cost is $1,717, and the destination charge is $445.
To find the total amount, simply add these three amounts together:
$14,530 (standard vehicle price) + $1,717 (options cost) + $445 (destination charge) = $16,692
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Gym City charges a $30 sign-up fee, plus a monthly fee of $25. FitnessExpress charges a $20 sign-up fee, plus a monthly fee of $30. How muchmoney would Leslie save in a 6-month period by joining Gym City insteadof Fitness Express? PLSSSS
Answer:
$20
Step-by-step explanation:
Gym city fees are:
Sign up = 30
6 monthly sub = 6 x 25 = 150
Total fees = 30 + 150
FitnessExpress fees are:
Sign up = 20
6 monthly sub = 6 x 30 = 180
Total fees = 20 + 180 = 200
Therefore, the difference between the two is $20
Tan ø =15/8 and sec Ø =17/8, which of the following can be proven using a Pythagorean identity
Since the equation is true, we can conclude that the following can be proven using a Pythagorean identity:
(15/8)² + 1 = (17/8)²
To determine which of the following can be proven using a Pythagorean identity, we need to use the given trigonometric values of tan Ø and sec Ø.
Given:
tan Ø = 15/8
sec Ø = 17/8
Using the Pythagorean identity for tangent and secant:
tan² Ø + 1 = sec² Ø
Substituting the given values:
(15/8)² + 1 = (17/8)²
Simplifying:
(225/64) + 1 = (289/64)
Combining fractions:
(225 + 64) / 64 = 289 / 64
Both sides have the same denominator, so we can compare the numerators:
289 = 289
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100 Points. Algebra question. Photo attached. Find the amplitude, if it exists, and period of the function, phase shift, and vertical shift. Then graph the function. Please show as much work as possible. Thank you!
The amplitude and the period of the function are 3 and π
The Phase shift is 90 and the vertical shift is 2
How to determine the amplitude and period of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 3sin[2(θ - 90)] + 2
A sinusoidal function is represented as
f(x) = Asin(B(x + C)) + D
Where
Amplitude = APeriod = 2π/BPhase shift = Cvertical shift = DUsing the above as a guide, we have the following:
Amplitude = 3
Period = 2π/2 = π
Next, we have
Phase shift = 90
vertical shift = 2
Hence, the amplitude is 3 and the period is π
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What are the explanation sentences of this question
The ratio of the original length of the longer candle to the shorter candle was 27/23.
Let us assume that,
the original lengths of the longer and shorter candles L and S, respectively.
Hence, We can set up two equations based on the information given:
L - 7x = S - 11x
where x is the length remaining after 3 hours
L = S + 4x
We can solve for x by substituting equation 2 into equation 1:
S + 4x - 7x = S - 11x
-3x = -6x
x = 2
Now we can use equation 2 to solve for L in terms of S:
L = S + 4x = S + 8
We know that after 3 hours, both candles had the same length remaining, so we can set up an equation based on this:
L - 3(7) = S - 3(11)
S + 8 - 21 = S - 33
S = 46
Therefore, the original length of the shorter candle was 46, and the original length of the longer candle was
L = S + 8 = 54.
The ratio of the original length of the longer candle to the shorter candle is:
L/S = 54/46 = 27/23
So, the ratio of the original length of the longer candle to the shorter candle was 27/23.
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The daily discharge of a particular river in April and June is modeled by the following functions where the discharge is measured in millions of cubic feet per day.
I need help with finding the percentage this part of the question:
It should be noted that 78.03% of the lake's volume flows through the river in April and June.
How to calculate the percentageFirst, we need to convert the volume of the lake from cubic miles to cubic feet. There are 5280 feet in a mile, so 0.67 mi³ is equal to 35,616,000 cubic feet.
Next, we need to divide the volume of water that flows through the river in April and June by the volume of the lake. This gives us a percentage.
(39,498.97 + 37,458.14) million cubic feet / 35,616,000 cubic feet
= 0.7803
Therefore, 78.03% of the lake's volume flows through the river in April and June.
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Solid of revolution (hyperbola) — related rates Calculus
The rate at which the depth of the liquid is increasing when it reaches one-third of the height of the bowl is (7/3)π cm³/s.
What is the rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl?To ascertain the rate at which the liquid's depth rises, let's find the derivative of the depth function with respect to time.
Let;
h(t) = depth of the liquidt = timeThe rate of change of the volume of the liquid with respect to time is constant and equal to 7π cm³/s.
To determine the height of the bowl, we can evaluate the curve y = [-4 / (8 - x)] - 1 when x = 4 and y = 7.6 and then find the absolute difference between the values.
h = |[-4 / (8 - 4)] - 1 - [-4 / (8 - 7.6)] - 1|
Let's calculate the rate at which the depth rises when it reaches one-third of the bowl's height.
D = depth of bowl
Using this relationship from the question given;
D = (1/3) * h
In order to determine the rate at which D will change with respect to time, let's differentiate both sides of the equation.
dD/dt = (1/3) * dh/dt
Since dh/dt is the rate at which the depth of the liquid is changing, which is constant and equal to 7π cm³/s, we can substitute it into the equation:
dD/dt = (1/3) * (7π)
Simplifying, we have:
dD/dt = (7/3)π cm³/s
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Choose two numbers that the variable for the height (in inches) of a bookcase can represent from the following lists; -80, 10208, 80, 65
From the given list, we can choose the numbers 80 and 65 as potential values for the variable representing the height (in inches) of a bookcase.
Let's go through each number and reason why it could represent the height of a bookcase:
-80: It is highly unlikely for a bookcase to have a negative height as it implies being below ground or submerged. Negative heights do not make sense in this context, so we can eliminate -80 as a viable option.
10208: This number seems unreasonably high for the height of a bookcase. Most bookcases are not taller than a few feet or a couple of meters. A height of 10208 inches would be more than 850 feet, which is much larger than any standard bookcase. Therefore, we can eliminate 10208 as a realistic option.
80: This is a plausible height for a bookcase. Many bookcases range in height from a few feet to around six or seven feet, and 80 inches falls within this typical range.
65: Similarly, a height of 65 inches is also plausible for a bookcase. Smaller bookcases or shelves designed for specific purposes, such as children's bookcases or shorter units, often have heights around this range.
Based on these considerations, we can conclude that the numbers 80 and 65 are reasonable options for representing the height of a bookcase.
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What is an approximate solution to this equation?
An approximate solution for the system of equations in this problem is given as follows:
C. x ≈ 5.81.
How to obtain the solutions?When we want to solve a system of equations graphically, we must obtain the point of intersection of the equations that compose the system.
The equations for this problem are given as follows:
y = 4/(x - 5).[tex]y = \sqrt{x + 3} + 2[/tex]From the graph, the x-coordinate of the point of intersection is given as follows:
x = 5.805.
Which is rounded as follows:
C. x ≈ 5.81.
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The company also has plans to open a third obstacle course, The Gridiron, where the first three checkpoints will have coordinates A′′(0,−5), B′′(9,−5), and C′′(4,−5). What relationship could this location have to the previous locations? Select all answers that apply.
Answer: It is a reflection of Reflections of You (second location) in the x-axis.
Step-by-step explanation: Based on the given information, the relationship between the new location (The Gridiron) and the previous locations can be determined.
The correct answer is:
It is a reflection of Reflections of You (second location) in the x-axis.
The coordinates of the first three checkpoints of The Gridiron (A''(0,−5), B''(9,−5), and C''(4,−5)) indicate that they have the same y-coordinate (-5) as the corresponding checkpoints in the second location, Reflections of You. However, there is no indication of a reflection in the y-axis or any transformation related to the first location, Transformation Fitness Studios. Therefore, the correct answer is that The Gridiron is a reflection of Reflections of You in the x-axis.
f(x)
g(x)
=∣x∣
=∣x+9∣−5
We can think of
�
gg as a translated (shifted) version of
�
ff.
Complete the description of the transformation.
Use nonnegative numbers.
To get the function
�
gg, shift
�
ff
by
units and to the
by
units.
The function g( x ) is translated to the left by 9 units and down by 5 units.
Given data ,
Let the first function be represented as f ( x )
where the value of f ( x ) = | x |
Let the translated function be g ( x )
where the value of g ( x ) = | x + 9 | - 5
A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.
On translating to the left , f ( x + a )
So , the function f ( x ) is translated 9 units to the left by f ( x + 9 ) = | x + 9 |
Now , when the function is translated 5 units down , f ( x ) - 5
So , the translated function is g ( x ) = | x + 9 | - 5
Hence , the function is translated to the left by 9 and up by 5 units.
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The vertices of one of the diagonals of a square are located at (-34) and (2-1)
Enter values and select a phrase to describe the location of the other vertices of the square.
and
The other vertices of the square must be located at
because those points make the diagonals
The other vertices of the square must be located at (1.5, -3.5), (-2.5, 6.5), and (3.5, -8.5) because these points make up the diagonals of the square with the given endpoints.
The vertices of one of the diagonals of a square are located at (-3,4) and (2,-1). To find the other vertices of the square, we can use the fact that the diagonals of a square intersect at their midpoints.
The midpoint of the diagonal with endpoints (-3,4) and (2,-1) can be found by averaging the x-coordinates and the y-coordinates separately. The x-coordinate of the midpoint is (-3 + 2)/2 = -0.5, and the y-coordinate is (4 + (-1))/2 = 1.5.
Now, we have the coordinates of the midpoint of the diagonal as (-0.5, 1.5). To find the other vertices of the square, we can reflect this midpoint across the given diagonal.
Reflecting the midpoint across the diagonal, we get the coordinates for the other vertices of the square as follows:
Vertex 1: (-0.5, 1.5) (the midpoint)
Vertex 2: (-0.5 + 2, 1.5 - 5) = (1.5, -3.5)
Vertex 3: (-0.5 - 2, 1.5 + 5) = (-2.5, 6.5)
Vertex 4: (-0.5 + 4, 1.5 - 10) = (3.5, -8.5).
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Help pleaseee
I dont know how to do this
The rate of change for each linear function would be = increase 8 pt/gal. That is option B.
How to determine the rate of each linear function?To determine the rate of each linear function, the relationship between the ratio X and y should be calculated as follows. That is;
When X( gallons) is 1 : Y( pints) is 8
Also X( gallons) is 2 : Y( pints) is 16
When reduced;
X = 1 when Y = 8
Therefore, the rate of change for each linear function would be when there is increase in 8 pints is 1 gallon.
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Graph the solution to the equations below. y = 1 4 x + 2 and y = −2x −7
simplify: 2+3 •10 ÷ 5•3 -9
(a) -5
(b) 21
(c) -60
(d) 11
the answer is (D) 11
pls help will mark bainleist
Answer:
x=61°
Step-by-step explanation:
angles in triangle add up to 180°
180°-80°-39°=x
61°=x
Answer:
x = 61°Step-by-step explanation:
We know that,
Sum of three side of triangle is 180 °
So,
80°+ 39° + x = 180°
119°+ x = 180°
x = 180°-119°
x = 61°
Thus,
value of x =61°[tex] \underline{\rule{190pt}{4pt}}[/tex]
Martin and Gale play an exciting game of "toss the coin," where they toss a fair coin until the pattern HH occurs (two
consecutive Heads) or the pattern TH occurs (Tails followed immediately by Heads). Martin wins the game if and only
if the first appearance of the pattern HH occurs before the first appearance of the pattern TH. Note that this game is
scored with a 'moving window'; that is, in the event of TTHH on the first four flips, Gale wins, since TH appeared on
flips two and three before HH appeared on flips three and four.
Which of the following statements is correct?
a) Martin and Gale are equally likely to win, because their two patterns show up equally often when two coins are flipped
b) Martin is less likely to win because as soon as Tails is tossed, TH will definitely occur before HH
c) Martin is less likely to win because getting two heads in a row is less likely than getting tails and heads
The correct statement is :-c) Martin is less likely to win because getting two heads in a row is less likely than getting tails and heads.
To understand why this statement is correct, let's analyze the probabilities of the two patterns occurring.
The probability of getting two heads in a row (HH) in a single coin toss is (1/2) * (1/2) = 1/4, as each coin toss has a 1/2 probability of landing on heads.
The probability of getting tails and heads (TH) in a single coin toss is (1/2) * (1/2) = 1/4, as each coin toss has a 1/2 probability of landing on tails and a 1/2 probability of landing on heads.
However, in order for Martin to win the game, the first appearance of the pattern HH must occur before the first appearance of the pattern TH. This means that Martin needs to get two heads in a row (HH) before getting tails and heads (TH).
Since the probability of getting two heads in a row (HH) is 1/4, which is the same as the probability of getting tails and heads (TH), it is less likely for Martin to achieve the pattern HH before the pattern TH. Therefore, Martin is less likely to win the game compared to Gale.
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Find the area of right triangle. If necessary, round to the nearest tenth.
a. 8 yards squared
b. 24 yards squared
c. 48 yards squared
d. 64 yards squared
Answer:
b. 24 yd
Step-by-step explanation:
since we have a right triangle we have to apply the Pythagorean Theorem:, to find the missing side
c^2 = a^2 + b^2
Where c is the hypotenuse of the triangle (10 yd) and a and b are the other sides.
Replacing with the values given:
10^2 = 6^2 + b^2
100 = 36+b^2
100-36 = b^2
64 = b^2
√64 = b
b= 8
Now, we can calculate the area:
A =1/2x base x height = 1/2 x 8 x 6 = 24 yd
Feel free to ask for more if needed or if you did not understand something.
Among the men, what is the relative frequency of wearing a
watch? What is the relative frequency of not wearing a watch?
What is the relative frequency of the total? If necessary, round the
relative frequencies to two decimal places.
The relative frequencies for this problem are given as follows:
Wearing a watch: 0.7.Not wearing a watch: 0.3.Total: 1.How to calculate a relative frequency?A relative frequency is calculated as the number of desired outcomes divided by the number of total outcomes.
The total number of people is given as follows:
32 + 68 = 100.
Of those, 25 + 45 = 70 wear a watch, hence the relative frequency is given as follows:
70/100 = 0.7.
30 do not wear a watch, hence the relative frequency is given as follows:
30/100 = 0.3.
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What is the probability that both events will occur? Two dice are tossed. Event A: the first die is a 5 or 6. Event B: The second die is not a 1
Answer: The probability that both events A and B will occur is 5/18 or 0.28.
Step-by-step explanation:
To determine the probability that both events A and B will occur, we need to calculate the probabilities of each event separately and then multiply them together.
Event A: The probability of rolling a 5 or 6 on the first die is 2 out of 6 (since there are two favorable outcomes out of six possible outcomes on a fair six-sided die). Therefore, the probability of event A is 2/6 or 1/3.
Event B: The probability of not rolling a 1 on the second die is 5 out of 6 (since there are five favorable outcomes out of six possible outcomes). Therefore, the probability of event B is 5/6.
To find the probability that both events A and B occur, we multiply the probabilities:
Probability(A and B) = Probability(A) * Probability(B) = (1/3) * (5/6) = 5/18.
The heights of American men are normally distributed. If a random sample of American men is taken and the confidence interval is (66.2,74.6), what is the sample mean x¯? Give just a number for your answer. For example, if you found that the sample mean was 12, you would enter 12.
The sample mean x¯ is 70.4.
The sample mean, denoted as x¯, can be obtained directly from the midpoint of the confidence interval.
In this case, the confidence interval given is (66.2, 74.6).
To find the sample mean, we take the average of the lower and upper bounds of the confidence interval:
x¯ = (lower bound + upper bound) / 2
Substituting the given values, we have:
x¯ = (66.2 + 74.6) / 2
Calculating the expression, we find:
x¯ = 140.8 / 2
Simplifying, we get:
x¯ = 70.4
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Find the population (P) of a town growing at 15% each year after (n) years
Use formula P=6,000 x 1.5 to the power of (n)
Based on an exponential growth function, P = 6,000 (1.15)ⁿ, the population of the town with an initial population of 6,000 growing at 15% annually after n years is 15,960.
What is an exponential growth function?An exponential growth function is one of the two exponential functions, including an exponential decay function.
An exponential growth function is written in the form of y = abˣ, where y is the ending value after time x (the exponent), a is the initial value, and b is the growth factor based on a constant rate of growth.
The current population of the town = 6,000
The growth rate per year = 15% = 0.15
Growth factor = 1.15 (1 +1.15)
The number of years of growth, n = 7 years
Exponential Growth Function:P = 6,000(1.15)ⁿ
P = 6,000(1.15)⁷
P = 15,960
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PLEASE HELP
Given that AABE~ AACD, what is the value of x?
A.
B.
C.
D.
1
4
6
12
5
6 E
A
2
C
X+4
B
Answer:
6
Step-by-step explanation:
We can begin by finding EA, which is 1 unit.
Using similar triangles AEB and ADC, we can set up a ratio.
1:6=2:x+6.
if a:b=c:d, then ad=bc
x+6=12
x=6
Feel free to tell me if I did anything wrong! :)
Answer:
C
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{AB}{AC}[/tex] = [tex]\frac{AE}{AD}[/tex] ( substitute values )
[tex]\frac{2}{2+x+4}[/tex] = [tex]\frac{6-5}{6}[/tex]
[tex]\frac{2}{x+6}[/tex] = [tex]\frac{1}{6}[/tex] ( cross- multiply )
x + 6 = 12 ( subtract 6 from both sides )
x = 6
Please show working for #3 . Appreciate it
Based on the information, the critical value of F to 3 decimal places is 2.17.
How to calculate the valueHere are the steps on how to calculate the critical value of F:
Identify the significance level. In this case, the significance level is 10%, or 0.10.
Identify the degrees of freedom. The degrees of freedom for the numerator is 1, and the degrees of freedom for the denominator is 23.
Look up the critical value of F in the F-table. The F-table is a table that lists the critical values of F for different significance levels and degrees of freedom.
The F-table shows that the critical value of F for a significance level of 0.10 and degrees of freedom of 1 and 23 is 2.17.
Therefore, the critical value of F to 3 decimal places is 2.17.
Here is the solution in mathematical form:
F = (60.0 - 54)/(14.9 / ✓(24)) = 2.17
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A manufacturer produces three types of plastic fixtures. The time required for molding trimming, and packaging is given in the table below. (Times are given in hours per dozen .)
The table is presented with five columns. The first column is labeled "Process" and lists four categories: Molding, Trimming, Packaging, and Profit. The next three columns are labeled "Type A," "Type B," and "Type C," respectively. These columns provide the time required in hours per dozen fixtures for each process and each type of fixture.
Under the "Process" column:
- The first row is "Molding" and shows the time required for Type A fixtures as 1 hour, Type B fixtures as 2 hours, and Type C fixtures as 3/2 hours.
- The second row is "Trimming" and shows the time required for Type A fixtures as 2/3 hours, Type B fixtures as 2/3 hours, and Type C fixtures as 1 hour.
- The third row is "Packaging" and shows the time required for Type A fixtures as 1/2 hour, Type B fixtures as 1/3 hour, and Type C fixtures as 1/2 hour.
- The fourth row is "Profit" and displays the profit associated with each type of fixture ($11 for Type A, $16 for Type B, and $15 for Type C).
The last column is labeled "Total Time Available" and provides the total available time in hours for each process. It shows 12000 hours available for Molding, 4600 hours available for Trimming, and 2400 hours available for Packaging.
How many dozen of each type of fixture should be produced to obtain a maximum profit?
set up;
(i). Data presentation,
(ii). LP problem defining viriables, objective function and correctly name the set of constraints.
(i) Data is presented below.
(ii)The optimal solution for the LPP is
⇒ x = 7600, y = 0, and z = 2800.
Type A fixtures, 0 dozens of Type B fixtures, and 2800 dozens of Type C fixtures to maximize their profit while staying within the time constraints for each process.
According to the given information,
(I) The Linear Programming Problem can be formulated as follows:
Maximize 11x + 16y + 15z
Subject to: x + 2y + 3/2z ≤ 12000 (Molding time)
2/3x + 2/3y + z ≤ 4600 (Trimming time)
1/2x + 1/3y + 1/2z ≤ 2400 (Packaging time)
Where, x, y, z >= 0
where x, y, z represent the number of dozens of each type of fixture produced.
(ii) To convert the problem to standard form,
Introduce slack variables and express all constraints as equations.
The problem in standard form can be written as,
Maximize 11x + 16y + 15z + 0s1 + 0s2 + 0s3
Subject to: x + 2y + 3/2z + s1 = 12000 (Molding time)
2/3x + 2/3y + z + s2 = 4600 (Trimming time)
1/2x + 1/3y + 1/2z + s3 = 2400 (Packaging time)
Where x, y, z, s1, s2, s3 >= 0
(iii) Using the simplex tableau method, we can find the optimal solution to the LPP.
The initial tableau is,
Basis x y z s1 s2 s3 RHS
Basis x y z s1 s2 s3 RHS
s1 1 2 3/2 1 0 0 12000
s2 2/3 2/3 1 0 1 0 4600
s3 1/2 1/3 1/2 0 0 1 2400
------- --- --- --- ---- ---- ---- -----
z 11 16 15 0 0 0 0
We choose s1, s2, and s3 as the initial basis since they have a non-zero coefficient in the objective function.
The pivot element is 2/3 in row 2 and column x. We perform row operations to make the pivot element 1 and eliminate the other x-coefficients in column 1:
Basis x y z s1 s2 s3 RHS
s1 0 4/3 1/3 1 -2/3 0 9400
x 1 1 3/2 3/2 0 0 18000
s3 0 -1/3 1/3 -1/6 2/9 1 600
------- --- --------- --- ----------- ----------- ---- -------
z 0 5/3 7/6 -11/3 16 0 35200
The new pivot element is 5/3 in row 2 and column y. We perform row operations to make the pivot element 1 and eliminate the other y-coefficients in column 2,
Basis x y z s1 s2 s3 RHS
s1 0 0 1/5 13/15 -2/15 0 11600
x 1 0 2/15 -7/15 1/15 0 7600
s3 0 0 2/5 1/15 2/15 1 2000
------- --- --- --------- ----------- ----------- ---- -------
z 0 1 7/15 -11/9 16/9 0 21100
Hence,
The optimal solution for the Linear Programming Problem is
⇒ x = 7600, y = 0, and z = 2800.
This means that the manufacturer should produce 7600 dozens of Type A fixtures, 0 dozens of Type B fixtures, and 2800 dozens of Type C fixtures to maximize their profit while staying within the time constraints for each process.
The maximum profit achievable with this optimal solution is,
⇒ (11 x 7600) + (16 x 0) + (15 x 2800) = R 295,600.
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what are the 2 types of intergers
Answer:
1. positive integers
2. negative integers.
Explanation:
The two types of integers are positive integers and negative integers.
Positive integers are whole numbers greater than zero, such as 1, 2, 3, 4, and so on.
Negative integers are whole numbers less than zero, denoted by a negative sign (-) before the number. Examples of negative integers are -1, -2, -3, -4, and so on.
Together, positive and negative integers make up the set of integers, which includes all whole numbers both greater than and less than zero, including zero itself.
5z + 3y = 4
-2x -8y = 6
Answer:
To eliminate a variable, you need to choose a strategy that allows you to add or subtract the equations in such a way that one variable will be eliminated. Let's go through the given options to determine the correct strategy:
A. Multiply the first equation by 2. Then add the equations.
If you multiply the first equation by 2, you get 10x + 6y = 8. If you add this equation to the second equation, you will not be able to eliminate either variable, as the coefficients of x and y do not match.
B. Multiply the first equation by 5 and the second equation by 2. Then add the equations.
If you multiply the first equation by 5, you get 25x + 15y = 20. If you multiply the second equation by 2, you get -4x - 16y = 12. Adding these equations gives you 21x - y = 32. This strategy allows you to eliminate y.
C. Multiply the second equation by 5. Then add the equations.
If you multiply the second equation by 5, you get -10x - 40y = 30. If you add this equation to the first equation, you will not be able to eliminate either variable, as the coefficients of x and y do not match.
D. Multiply the first equation by 2 and the second equation by 5. Then add the equations.
If you multiply the first equation by 2, you get 10x + 6y = 8. If you multiply the second equation by 5, you get -10x - 40y = 30. Adding these equations gives you -34y = 38. This strategy allows you to eliminate x.
Based on the options given, the correct strategy to eliminate a variable in this system of equations is: B.) Multiply the first equation by 5 and the second equation by 2. Then add the equations.
help w geometry.. will give brainliest answer
1. Alternate interior angle.
2. Alternate Exterior Angle.
3. Vertical Angles.
4. 13x + 2= 15x - 2
5. x= 2
Since AB || CD
and, <BGF = 13x + 2, <EHC = 15x - 2
1. <BGF and <EHC are Alternate interior angle.
2. <FHD and <EGA are Alternate Exterior Angle.
3. <FHC and <EHD are Vertical Angles.
4. <BGF = <EHC
13x + 2= 15x - 2
5. Solving for x we get
-2x = -4
x= 2
6. <BGF = 26 +2 = 28
<EHC = 28
<FHD = 28
<EGB = 180 - 28 = 152
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Find the maximum value of
P = 9x + 8y
subject to the following constraints:
First, identify the y-intercept of the first inequality.
?
(8x + 6y≤ 48
7x + 7y ≤ 49
x ≥ 0
(y ≥ 0
Enter
The maximum value of the inequality is P = 72
Given data ,
8x + 6y ≤ 48 can be rewritten as y <= (-4/3)x + 8. Graphing this inequality, we have a line with a slope of -4/3 passing through the point (0, 8). Shade the region below this line.
7x + 7y ≤ 49 can be rewritten as y <= (-1)x + 7. Graphing this inequality, we have a line with a slope of -1 passing through the point (0, 7). Shade the region below this line.
x ≥ 0 represents the x-axis or the region to the right of the y-axis.
y ≥ 0 represents the y-axis or the region above the x-axis.
Now, we evaluate P = 9x + 8y at the corner points of the feasible region to find the maximum value.
The corner points of the feasible region are the intersections of the lines. In this case, the corner points are:
A: (0, 0)
B: (0, 7)
C: (8, 0)
D: (6, 2)
Now, substitute these points into P = 9x + 8y:
P(A) = 9(0) + 8(0) = 0
P(B) = 9(0) + 8(7) = 56
P(C) = 9(8) + 8(0) = 72
P(D) = 9(6) + 8(2) = 66
Hence , the maximum value of P = 9x + 8y is 72, which occurs at the corner point C: (8, 0)
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Which liner equation shows a proportional relationship
A linear equation which shows a proportional relationship include the following: B. y = -1/4(x).
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the x-variable.x represents the y-variable.k is the constant of proportionality.In this context, we can reasonably infer and logically deduce that the only linear equation that represents a proportional relationship is represented by the following;
y = kx
y = -1/4(x)
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Complete Question:
Which linear equation shows a proportional relationship?
y = 1/4(x) - 5
y = -1/4(x)
y = −4x+ 1
y = 4
Can someone answer this question?
The representation of given graphs are as following:
I. Identity
II. Reciprocal
III. Absolute value
IV. absolute function
According to the given graphs we have:
For graph 1:
This graph is represents a equation of line,
Which is of the form,
y = x
Then at x = 1 we get y = 1
at x = 2 we get y = 2
Hence,
This graph represents an identity function.
For graph 2:
This graph represents the graph of inverse functions ,
y = 1/x
Which represents a graph of reciprocal function.
For graph 3:
This graph is representation of mod function
y = |x|
Which is nothing but absolute function.
For graph 4:
This graph represents,
y = [x]
Which represents the graph of greatest integer function.
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