The solution to the inequality is x ≤ 1.
What is inequality?Inequality in mathematics is when two values are not equal. It can be expressed using symbols such as >, <, ≥ and ≤. This can be used to compare two values, express a range of values, or indicate that one value is greater or less than another. Inequality is a powerful tool for solving mathematical problems, as it can be used to deduce relationships between different variables.
To solve this inequality, we must first perform the operations on the left side of the equation to get an expression equal to 4. We can start by simplifying the fraction on the left side of the equation. We can multiply both the numerator and denominator by x, which will give us 5x - 3 = x + 2x. We can then add 3 to both sides to get 5x = 3 + 2x, which can then be simplified to 3x = 3. Finally, we can divide both sides by 3 to get x = 1. Therefore, the solution to the inequality is x ≤ 1.
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Cindy left Hillview Town at 4.20 pm, travelling towards Beach Town which was 600 km away at an average speed of 108 km/h. Claudia left Hillview Town at 5 pm, travelling at an average speed of 124 km/h.
(a) How long did Claudia take to catch up with Cindy?
(b) How far away were they from Beach Town when Claudia caught up with Cindy?
Answer:
(a) To find out how long it takes for Claudia to catch up with Cindy, we can first calculate the head start that Cindy had before Claudia started. Cindy had a head start of:
d = rt = 108 km/h x 1 h 40 min = 180 km
where d is the distance that Cindy traveled during the 1 hour 40 minutes (1.67 hours) between her departure and Claudia's departure, r is Cindy's speed, and t is the time she traveled.
When Claudia started, both Cindy and Claudia were 180 km away from Beach Town. The distance between them decreases at a rate equal to the difference in their speeds, which is:
124 km/h - 108 km/h = 16 km/h
So Claudia catches up at a rate of 16 km/h. The time it takes for Claudia to catch up is then:
t = d / r = 180 km / 16 km/h = 11.25 hours
However, we need to subtract the 1 hour 40 minutes (1.67 hours) that Cindy traveled before Claudia started to find the actual time Claudia took to catch up with Cindy:
t = 11.25 hours - 1.67 hours = 9.58 hours
Therefore, Claudia took about 9 hours and 35 minutes (0.58 x 60 minutes) to catch up with Cindy.
(b) When Claudia catches up with Cindy, they are both the same distance away from Beach Town. Cindy has already traveled 180 km when Claudia catches up, so the distance they are from Beach Town is:
600 km - 180 km = 420 km
Therefore, they were 420 km away from Beach Town when Claudia caught up with Cindy.
Solve the inequality
[tex]x { \\ }^{2} < 16[/tex]
The solution of the inequality is x < -4 or x < 4
How to solve inequality?An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4
An inequality can be expressed using one of several symbols, including < (less than), > (greater than), <= (less than or equal to), >= (greater than or equal to), and != (not equal to).
x² < 16
Take the square root of both sides:
x < ±√16
x < ±4
x < -4 or x < 4
Therefore, the solution is x < -4 or x < 4
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lee makes $64 an hour. if he wants to make no less than $400 each day to save for a trip, at least how many hours must he work each day? brainly
Answer:
PAYMENT = 64
AMOUNT WANTED = 64
SO: 400 / 64 = 6.25
SO LEE NEEDS TO WORK FOR 6.25 HOURS IN EACH DAY.
If triangle XYZ is dilated from center C by a scale factor of 0.5 to form triangle X’Y’Z’, where is the center of the dilation, point c, located?
The center of the dilation, point C, is located at the same point as it was before the dilation. This is because the center of dilation is the point from which the dilation occurs, and it does not change during the dilation process.
To find the coordinates of point C, we can use the properties of dilations. The coordinates of the vertices of the dilated triangle are found by multiplying the coordinates of the original triangle by the scale factor.
So, if the coordinates of point X are (x1, y1), the coordinates of point X' will be (0.5x1, 0.5y1). Similarly, the coordinates of point Y' will be (0.5x2, 0.5y2) and the coordinates of point Z' will be (0.5x3, 0.5y3), where (x2, y2) and (x3, y3) are the coordinates of points Y and Z, respectively.
Since point C is the center of dilation, the coordinates of point C will be the same as the coordinates of the midpoint of the line segment connecting points X and X', points Y and Y', and points Z and Z'. The midpoint of a line segment is found by averaging the coordinates of the endpoints. So, the coordinates of point C will be:
C = ((x1 + 0.5x1)/2, (y1 + 0.5y1)/2) = (0.75x1, 0.75y1)
Therefore, the center of the dilation, point C, is located at (0.75x1, 0.75y1).
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Help! 50 points, Sorry not the best picture…
The completed table in the question used to prove the proportional BD/AB = BC/(AB + AC), when AD is an angle bisector can be presented as follows;
Statement [tex]{}[/tex] Reason
1. EB ║ AD, AD bisects ∠ABC [tex]{}[/tex] 1. Given
2. ∠BEC = ∠DAC [tex]{}[/tex] 2. Corresponding angles theorem
3. ∠C = ∠C [tex]{}[/tex] 3. Reflexive property of congruence
4. ΔBEC = ΔDAC [tex]{}[/tex] 4. AAA similarity postulate
5. DC/AC = BC/EC [tex]{}[/tex] 5. Similar triangles have equivalent ratios
6. EC = EA + AC [tex]{}[/tex] 6. Segment addition postulate
7. DC/AC = BC/(EA + AC)[tex]{}[/tex] [tex]{}[/tex] 7. Similar triangles have equivalent ratios
8. AD/AB = DC/AC [tex]{}[/tex] 8. Triangle angle bisector theorem
9. BD/AB = DC/AC [tex]{}[/tex] 9. Substitution property
10. ∠EBA = ∠DAB [tex]{}[/tex] 10. Alt int. angles theorem
11. ∠DAB = ∠DAC [tex]{}[/tex] 11. Definition of a bisector
12. ∠EBA = ∠BEC [tex]{}[/tex] 12. Alt int. angles theorem
13. ΔEBA is isosceles [tex]{}[/tex] 13. Definition of isosceles triangles
14. CA = AB [tex]{}[/tex] 14. Side length of isosceles
15. BD/AB = BC/EC [tex]{}[/tex] 15. Similar triangles have equal ratios
16. BD/AB = BC/(EA + AC) [tex]{}[/tex] 16. Substitution property
17. EA = AB [tex]{}[/tex] 17. Definition of isosceles triangle ΔEBA
18. BD/AB = BC/(AB + AC) [tex]{}[/tex] 18. Substitution property
What is an angle bisector?An angle bisector is an line that divides an angle into two angles of the same measure.
The details of the some of the reasons useds to prove the specified proportion are presented as follows;
Corresponding angles theorem
The corresponding angles theorem states that the corresponding angles formed between parallel lines and a transversal are congruent
Reflexive property of congruence
The reflexive property of congruence states that a geometric figure, such as an angle is congruent to itself
AA similarity postulate
The AA similarity postulate states that triangles are similar two angles in one triangle are congruent to two angles in the other triangles.
Similar triangles have equivalent ratios
Segment addition postulate
The segment addition postulate states that the point B is located between the points A and C on a segment, only if AC = AB + BC.
Ratios of corresponding sides ar
Triangle angle bisector theorem
The triangle angle bisector theorem states that an angle bisector of a triangle divides the side facing the bisected angle in the ratio of the lengths of the other two sides.
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(Worth 20 points and will give brainliest if you're right.) Question 2 options: Factor a^3+2a+2a^2+4. Fill in the blanks using the correct sign: (a^2+ ) (a+ )
(please help as soon as you can.)
Answer:
(a^2+2)(a+2)
Step-by-step explanation:
Factor a^3+2a+2a^2+4.
Using Factoring by grouping
a^3+2a + 2a^2+4
Factor out a from the first two terms and 2 from the last two terms.
a( a^2 +2) + 2 ( a^2+2)
Factoring out a^2+2.
(a^2+2)(a+2)
A number increased by five percent result is then increased by five percent what is the percent of increase
Answer:
Step-by-step explanation:
The radius of a circle is 7 in. what is the nearest whole number.
Answer:
153.94 -> 154
Step-by-step explanation:
Have a good day
The proportion of American adults who own a motorcycle is 2%. Samip believes the proportion of adults who own a motorcycle in his hometown is even lower. He randomly surveys 50 adults from his hometown and finds that 3 of them own a motorcycle. Identify why the sample in this situation does not meet all three conditions to perform a significance test using a z-statistic
The sample is not approximately normal because (50) (0.02) is not equal to or greater than 10.
The conditions for performing a significance test using a z-statistic require a sample size large enough to satisfy the Central Limit Theorem, which means that the sample should be approximately normal. In this case, the expected number of adults who own a motorcycle in the sample is only 1, which is less than the threshold of 10 needed for approximate normality. Therefore, the sample distribution is not normal, and a z-statistic cannot be used for hypothesis testing. The other conditions, such as random sampling and independence, are not relevant to this particular issue.
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Complete question:
The proportion of American adults who own a motorcycle is 2%. Samip believes the proportion of adults who own a motorcycle in his hometown is even lower. He randomly surveys 50 adults from his hometown and finds that 3 of them own a motorcycle. Identify why the sample in this situation does not meet all three conditions to perform a significance test using a z-statistic
The sample is not large enough because (50) (1-0.02) is not equal to or greater than 10.
The sample was not randomly selected.
The sample does not have independence.
The sample is not approximately normal because (50) (0.02) is not equal to or greater than 10.
a line has a slope of -1/5 and passes through point (-5,7). Write it's equation in slope-intercept form
Answer: The slope-intercept form of the equation of a line is y = mx + b, where m is the slope of the line and b is the y-intercept. We are given the slope m = -1/5, and a point (-5,7) through which the line passes.
To find the y-intercept b, we can substitute the point (-5,7) and the slope m = -1/5 into the slope-intercept form of the equation and solve for b:
y = mx + b
7 = (-1/5)(-5) + b
7 = 1 + b
b = 6
So the y-intercept is b = 6, and the equation of the line in slope-intercept form is:
y = (-1/5)x + 6
Therefore, the equation of the line is y = (-1/5)x + 6.
Step-by-step explanation:
The slope-intercept form of the equation of a line that has a slope of -1/5 and passes through point (-5,7) is:
y = -x/5 + 6
What is meant by the slope-intercept form of a line?
The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.
Given,
the slope of line m = -1/5
The point on the line = (-5,7)
Then the equation of a straight line is:
y -y1 = m (x-x1)
y1 = 7
x1 = -5
Then the equation becomes:
y - 7 = -1/5 ( x - (-5))
y-7 = -1/5 ( x+5)
y-7 = -x/5 -1
y = -x/5 + 6
Therefore the slope-intercept form of the equation of a line that has a slope of -1/5 and passes through point (-5,7) is:
y = -x/5 + 6
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How much is $100 US in euro?
Because the exchange rate between the US dollar (USD) and the euro (EUR) changes over time, the exact conversion from $100 US to euros will be determined by the current exchange rate.
As of the 21 Feb 2023 cutoff date, the exchange rate was around 1 USD = 0.94 EUR.
Using this exchange rate, we can calculate the value of $100 US in euros:
$100 US x 0.94 EUR/USD = 94 EUR
Therefore, as of 21 Feb 2023, $100 US was equivalent to approximately 94 euros.
However, it's important to note that exchange rates are subject to change, and the exact conversion may differ depending on the current rate.
The price at which one currency can be exchanged for another is referred to as the currency exchange rate. Exchange rates fluctuate constantly and are determined by the global foreign exchange market's supply and demand for currencies.
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what is an acre in feet
An acre is a unit of measurement used to quantify land area, and it is commonly used in the United States to measure the size of plots of land, farms, and estates. One acre is equal to 43,560 square feet.
To visualize an acre, imagine a rectangle that is approximately 208 feet by 209 feet, or a square that is approximately 209 feet on each side.
To convert acres to square feet, you can use the following formula:
1 acre = 43,560 square feet
Therefore, to convert acres to feet, you can simply multiply the acre value by 43,560. For example, if you want to convert 5 acres to square feet, you can use the following formula:
5 acres x 43,560 square feet per acre = 217,800 square feet
So 5 acres is equal to 217,800 square feet.
It's worth noting that the acre is a unit of measurement used primarily in the United States, and other countries may use different units of measurement to quantify land area. For example, in the metric system, the hectare is commonly used to measure land area, with 1 hectare equal to 10,000 square meters (about 2.47 acres).
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please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A cone with height h and radius r has volume V = 1/3πr^2h. If a certain cone with a height of 9 inches has volume V = 3πx^2 + 42πx + 147π, what is the cone’s radius r in terms of x?
The cone’s radius r in terms of x is x + 7
How to determine tthe cone’s radius r in terms of x?From the question, we have the following parameters that can be used in our computation:
Volume, V = 3πx^2 + 42πx + 147π
Height, h = 9
The volume of a cone is
V = 1/3πr^2h
Substitute the known values in the above equation, so, we have the following representation
1/3πr^2 * 9 = 3πx^2 + 42πx + 147π
So, we have
3πr^2 = 3πx^2 + 42πx + 147π
Divide by 3π
r^2 = x^2 + 14x + 49
So, we have
r = √(x² + 14x + 49)
Take the square roots of both sides
r = x + 7
Hence, the value of r is x + 7
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Kayla is moving and must rent a truck. There is an initial charge for the rental plus a fee per mile driven. The total cost of renting the truck can be modeled by the equation C = 30 +2.50m, where m is the number of miles driven. What is the slope of the equation and what is its interpretation in the context of the problem? The slope of the function is which represents
The interpretation of the slope is that it represents the additional cost per mile driven, beyond the initial charge of $30.
What is the Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
The equation for the total cost of renting the truck is:
C = 30 + 2.50m
where C is the total cost
m is the number of miles driven.
The slope of the equation is the coefficient of "m", which is 2.50. The slope represents the rate of change of the total cost with respect to the number of miles driven.
In this case, the slope of 2.50 means that for each mile driven, the total cost of renting the truck increases by $2.50.
So, the interpretation of the slope is that it represents the additional cost per mile driven, beyond the initial charge of $30.
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A circle has a diameter of 28 m what is the circumference? Are used 3.14 for pie and do not round your answer. Be sure to include the correct unit in your answer
Somebody please help :Write an equation that is perpendicular to x - 3y = 3 and passes through the point (5, -9) in
in with test.
Oy = 3x - 6
Oy=-3x + 6
O y = 1/3 x + 1
Oy=1/3x -1
Answer:
y = - 3x + 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
x - 3y = 3 ( subtract x from both sides )
- 3y = - x + 3 ( divide through by - 3 )
y = [tex]\frac{1}{3}[/tex] x - 1 ← in slope- intercept form
with slope m = [tex]\frac{1}{3}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3 , then
y = - 3x + c ← is the partial equation
to find c substitute (5, - 9 ) into the partial equation
- 9 = - 3(5) + c = - 15 + c ( add 15 to both sides )
6 = c
y = - 3x + 6 ← equation of perpendicular line
Your uncle has $1,375,000 and wants to retire. He expects to live for another 25 years and to earn 7.5% on his invested funds. How much could he withdraw at the end of each of the next 25 years and end up with zero in the account? a. 592,514.13 b.5127,052.74 OC $97,448.22 d. 5124,585.70 6.5123,352.17
He can withdraw $114746.17 (approx.) at the end of each of the next 25 years and end up with zero in the account. The solution has been obtained by using the concept of present value of annuity.
What is present value of annuity?
With a specific rate of return, or discount rate, an annuity's present value is the current worth of its expected future payments. The present value of the annuity decreases with increasing discount rates.
We are given that uncle has $1,375,000 and wants to retire. He expects to live for another 25 years and to earn 7.5% on his invested funds.
Using present value of annuity,
Present value of annuity due = P + P [(1 - (1 + r)⁻⁽ⁿ⁻¹⁾) / r]
1375000 = P + P [(1 - (1+0.075)⁻⁽²⁵⁻¹⁾)/0.075]
1375000 = P [1 + 10.98297]
P = 1375000/11.98297
P = $114746.17 (approx.)
Hence, uncle can withdraw $114746.17 (approx.) at the end of each of the next 25 years.
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y=40(1-0.4)^x growth or decay
The given function,[tex]Y=40(1-0.4)^x[/tex] is an exponential decay
What is an exponential function?
An exponential function is a mathematical function of the form [tex]f(x) = a^x[/tex], where "a" is a constant and "x" is the input variable. These functions are commonly used to model situations that involve continuous growth or decay.
In the given example you provided,[tex]Y=40(1-0.4)^x[/tex] represents an exponential decay function where the initial value is 40 and the common ratio is (1-0.4), which is 0.6. As x increases, the value of the function approaches zero, but never reaches it.
Hence, the given function,[tex]Y=40(1-0.4)^x[/tex] is an exponential decay.
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why did the congruent triangles get caught cheating
Which binomial is a factor of x4 − 4x2 − 4x 8?
Answer: The binomial factor is (x+2) . This was determined by factoring the given expression x4−4x2−4x+8 x 4 − 4 x 2 − 4 x + 8 by grouping then factoring one of the binomial terms
Step-by-step explanation:
4/5=3/a what is a (solve for the variable using cross products)
Answer:
15/4 is a prime number so that's the answer to this question
Step-by-step explanation:
4/5 = 3/a
4•a = 5•3
4a = 15
4a/4 = 15/4
a = 15/4
(1 point) Let A = | | 1-1-1-1 | . Find a non-zero vector x in the null space of A.
The null space of A is spanned by the vector x = (t, -t, -t, -t), where t is a real number
Vectors are an important mathematical tool for representing data, equations, and other mathematical objects. In this problem, we are given a matrix A and asked to find a non-zero vector x in the null space of A.
The matrix A = | | 1-1-1-1 | can be reduced to row-echelon form using row operations. The resulting matrix is A = | | 1 0 0 0 | , which has a single non-zero row, indicating that the null space of A is one-dimensional.
Therefore, the non-zero vector x in the null space of A can be written as x = (t, -t, -t, -t), where t is a real number.
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30c^8d^3 - 3bc^6 d^2 + 6c^8 d divided by 12c^2 d (polynomials divided by monomials written in standard form)
To divide polynomials by a monomial written in standard form, you can divide each term of the polynomial by the monomial separately. Applying this to the given expression, we get:
(30c^8d^3 - 3bc^6d^2 + 6c^8d) / (12c^2d)
= 30c^8d^3/(12c^2d) - 3bc^6d^2/(12c^2d) + 6c^8d/(12c^2d)
= 2.5c^(8-2)d^(3-1) - 0.25bc^(6-2)d^(2-1) + 0.5c^(8-2)d^(1-1)
= 2.5c^6d^2 - 0.25bc^4d + 0.5c^6
= 5c^6d^2 - 0.5bc^4d + c^6/2
Therefore, the simplified expression is 5c^6d^2 - 0.5bc^4d + c^6/2.
please help ASAP!!
(the question above is the previous question)
need help answering #6!!
For each point, their position with respect to its location on the circle are as follows;
(4, 0) will be located inside the circle.
(-3, 3) will be located outside the circle.
(-2, -2) will be located on the circle.
What is the equation of a circle?In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.In this exercise, we would use an online graphing calculator to plot the equation of this circle as shown in the image attached below.
(x - 2)² + (y - 1)² = 25
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How much would $10,000 due in 50 years be worth today if the discount rate were 7.5%? a $285.02 b. $266.20 c. S204.36 d. $217.80 e $268.89
The amount would $10,000 due in 50 years be worth today if the discount rate were 7.5% is,
P = $7,042
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We know that;
The formula is,
⇒ Amount = P (1 + r)ⁿ
Hence, We get;
10,000 = P (1 + 0.75)⁵⁰
10,000 = P (1.75)⁵⁰
10,000 = P × 1.42
P = 10,000 / 1.42
P = $7,042
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. Molly travels 90km to get home after work. She leaves at 6pm and arrives home at 7:30pm.
Calculate her average speed in km per hour
Answer:
60 Kilometers per hour
Step-by-step explanation:
To solve for how long it took Molly to get home, we can use this equation:
7:30 - 6 = 1:30So, Molly took an hour and 30 minutes, or 90 minutes to travel 90km.
To get the number of km she traveled every hour, we can use this equation:
90 × [tex]\frac{2}{3}[/tex] = 60Why do we multiply by 2/3?
We multiply by [tex]\frac{2}{3}[/tex] because if we need to figure out the average speed for every hour (60) we need to convert 90 to 60, and to do that we multiply the 90 by [tex]\frac{2}{3}[/tex].
Therefore, Molly travels 60km every hour.
When can a correlation coefficient based on an observational study be used to support a claim of cause and​ effect?
A. When the correlation coefficient is close to −1 or +1.
B. When the scatterplot of the data has little vertical variation.
C. When the correlation coefficient is equal to −1 or +1.
D. Never
A correlation coefficient based on an observational study can only measure the strength of the relationship between two variables, and it cannot be used to prove a cause-and-effect relationship.
Even if the correlation is close to -1 or +1, this does not necessarily mean there is a cause-and-effect relationship between the two variables—it could be due to chance. Similarly, if the scatterplot of the data has little vertical variation, this does not necessarily mean there is a cause-and-effect relationship. The only way to prove a cause-and-effect relationship is through a controlled experiment. Therefore, the correlation coefficient based on an observational study can never be used to support a claim of cause and effect.
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Admission to Overjoy Amusement Park is $20 $ 20 per visit. However, with a season pass, which costs $40 $ 40 , each admission is $12 $ 12 . Complete the table and write a system of equations to represent the admission costs, where a is the number of admissions and c is the total cost. CLEAR CHECK Complete the table. Cost of Admission($ $ ) Number of Admissions Amount Spent on Season Pass($ $ ) Total Cost With season pass a c Without season pass a c Write a system of equations to represent this problem. With a season pass: Without a season pass:
Total cost with pass = $20a
Total cost without pass = $12a + 40
According to the information
We can write a system of equations for this problem,
Equation 1:
Cost with season pass = 12a + 40
Equation 2:
Cost without season pass = 20a
Therefore,
The system of equations that represents this problem is:
12a + 40 = c ...(i)
20a = c ...(ii)
Now making table for it:
Cost Number Amount Spent Total Cost With Total Cost Without
Ad. Ad. Pass ($) Season Pass Season Pass
20 a 0 20a + 0 20a
12 a 40 12a + 40 12a + 40
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Divide 15a6b4 by 5a2b.
Answer:
Step-by-step explanation:
15a6b4/5a2b
you can scrap the a and b
15*6*4/ 5*2=
now you keep simplifying the fraction
3*6*4/2=
3*6*2=
36
a car dealership pays $8,350 for a car. ther mask up the price by 17.4% to get the retail price. what is the retail price of the car at this dealership?
The retail price of the car at the dealership is $9,803.90. This means that the dealership is adding a markup of $1,453.90, or 17.4% of the cost, to sell the car to customers.
To find the retail price of the car at the dealership, we need to add 17.4% to the dealership's cost of $8,350. Here are the steps to do this calculation:
Multiply the cost of the car by the percentage markup as a decimal. To convert a percentage to a decimal, divide it by 100. So 17.4% as a decimal is 0.174.
Markup = $8,350 x 0.174 = $1,453.90
Add the markup to the cost of the car to get the retail price.
Retail Price = $8,350 + $1,453.90 = $9,803.90
It's important to note that the final selling price of the car may be negotiable, and that other fees and taxes may also be added to the retail price.
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