a) Relationship between corresponding sides: the corresponding sides are parallel and have a ratio of k in length.
b) Relationship between corresponding sides' orientations: The corresponding sides will still be parallel to the original sides.
c) Relationship between corresponding angles:the corresponding angles are congruent.
What do you mean by congruent angles?
Congruent angles are angles that have the same measure or size. In other words, if two angles have the same number of degrees or radians, they are said to be congruent. When we say that two angles are congruent, it means that they are exactly the same shape and size, and they can be superimposed on each other without any rotation or scaling. Congruent angles play an important role in geometry, as they allow us to prove that two figures are similar or congruent.
To apply a dilation with scale factor k centered at the origin, we multiply the coordinates of each vertex by k. So, to find the coordinates of A', B', and C', we will multiply the coordinates of A, B, and C by the scale factor.
a) The relationship between corresponding sides in terms of their lengths:
Let's denote the scale factor by k. The distance between two points (x1, y1) and (x2, y2) is given by the distance formula, which is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
When we multiply each coordinate by k, the distance between the two points is multiplied by k as well. So, if AB has length dAB and A'B' has length dA'B', we have:
dA'B' = k * dAB
Similarly, we can find the relationship between the lengths of BC and B'C', as well as between the lengths of AC and A'C'.
b) The relationship between corresponding sides in terms of their orientations:
The orientation of a line is given by its slope. If two lines have the same slope, they are parallel or collinear. If they have slopes that are negative reciprocals of each other, they are perpendicular. When we multiply the coordinates of a point by k, the slope of any line passing through that point is multiplied by k as well. So, if the slope of AB is mAB and the slope of A'B' is mA'B', we have:
mA'B' = k * mAB
We can use this to find the relationship between the slopes of BC and B'C', as well as between the slopes of AC and A'C'.
c) The relationship between corresponding angles in terms of their measures:
The measure of an angle is determined by the slope of the line that contains the angle. When we multiply the coordinates of a point by k, the slope of any line passing through that point is multiplied by k as well. This means that the measure of any angle that includes the origin is unchanged by the dilation. However, the measure of any angle that does not include the origin is multiplied by a factor of k. So, if angle ABC has measure x and angle A'B'C' has measure y, we have:
y = k * x
We can use this to find the relationship between the measures of angles BAC and B'A'C', as well as between the measures of angles CBA and C'B'A'.
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Triangle abc is reflected over the line y = x to produce triangle a'b'c'. What will be the coordinates of a'?.
The coordinates of A' in triangle A'B'C' which was produced after reflection with condition y =x is equal to option d. ( 1, 2).
Graph is attached.
Triangle A'B'C' is produced after reflection of the triangle ABC over the line y = x.
From the graph we have ,
Coordinates of A is ( 2 , 1)
Coordinates of B is (-1, 4)
Coordinates of C is ( 0, -2)
Condition of reflection of triangle ABC over the line y = x.
x-coordinates replace by y and y replace by x.
Coordinates of triangle A'B'C' are
Coordinates of A' is ( 1, 2)
Coordinates of B' is (4, -1 )
Coordinates of C' is ( -2, 0 )
Therefore, if the coordinates of point A in triangle ABC are (2, 1), the coordinates of point A' in triangle A'B'C' would be option d. (1, 2).
The above question is not complete , the complete question is:
Triangle ABC is reflected over the line y = x to produce triangle A'B'C'. What will be the coordinates of A'? Graph is attached.
a. (2,−1) b. (−2,−1) c. (2,1) d. (1,2)
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What is the rate of change?
Answer:
Step-by-step explanation:
75%
A
65°
B
Reflex Angle B =
degrees.
The solution is, B = 245, is a Reflex Angle., when it is given that A=65.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
We know that, a ray is a line that continues on forever inn one direction with a point at it's start.
here, we have,
A = 65°
now, B is a Reflex Angle ,
so, we know that Reflex Angle means the angle with value >180 to <270.
now, we get,
B = 180 + 65
= 245
Hence, The solution is, B = 245, is a Reflex Angle.
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The measure of an angle is 119.4°. What is the measure of its supplementary angle?
Answer:
180 - 119.4 = 60.6
So the answer is 60.6
Answer:
60.6°
Step-by-step explanation:
Supplementary angles equal 180 degrees. So we can show this with the following equation:
119.4 + x = 180
where x is the measure of the other supplementary angle.
If we subtract 119.4 from both sides, we get the the value of x, which is 60.6.
The area of a rectangular pool is 6² − 11 + 3.
Part A
Factor 6² − 11 + 3 to determine the dimensions (length and width) of the rectangular pool.
Understand & Think: What are you being asked or told to do _________________
What information do you know? _________________
Do & Answer: Factor the trinomial to determine the expressions that give the dimensions (length and width) of the rectangular pool.
Show all work and use the algebra skills
What are your factors? What do your factors mean? __________________________________________________________
Show how you would check your factors are correct here:
The dimensions of the rectangular pool are (2x − 1) and (3x − 3). The length of the pool is 3x − 3 and the width of the pool is 2x − 1.
What is Area of Rectangle?The area of Rectangle is length times of width.
Area of rectangular pool = 6x² − 11x + 3
To factor the trinomial, we need to find two binomials that multiply together to give the trinomial 6x² − 11x + 3.
We use product-sum method of factoring to find the two binomials.
We need to find two numbers that multiply to 6 (the coefficient of the x² term) and add to -11 (the coefficient of the x term).
6x² − 11x + 3
6x² −2x-9x + 3
(2x − 1)(3x − 3)
Hence, the dimensions of the rectangular pool are (2x − 1) and (3x − 3). The length of the pool is 3x − 3 and the width of the pool is 2x − 1.
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is this relationship proportional 4/5 = 15/20
Answer:no
Step-by-step explanation:
if it was then it supposed to be like 4*20=5*15 which is not right equation
Acellus
40°
Find the value of x.
X
190°
x= [ ? ]
Enter
Resources
Help
The value of x for the given circle is 115°.
What is Geometry?Geometry is a branch of mathematics that deals with the study of shapes, sizes, positions, and properties of objects in space. It includes the study of points, lines, planes, angles, curves, surfaces, and solids.
Using the Angles of Intersecting Chords Theorem,
When two chords cross inside of a circle, the resulting angle's measure is equal to the product of the lengths of the arcs it intercepts and its vertical angle, divided by two.
So, angle x = (190° + 40°)/2 = 115°
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please help with this
Answer:
1. S = 20w + 100
2. M = -400w + 3,500
Step-by-step explanation:
1. Since Mateo is starting with a balance of $100, we can set this as our constant term (the 'b' in y = mx + b). Every week, he earns $20, so we can set this as the coefficient on the variable w (which represents how many weeks have passed).
2. Emily is spending money in this situation, so the coefficient on w is negative, as the amount of money she has left is getting smaller. The exact amount that she spends each week is $400, so the negative of that is going to be the coefficient of w in the equation. We can set the constant term in this equation to $3500, as Emily starts with that much money when no weeks have passed (when w = 0).
Oliver's Credit Card number has 16 digits. The sum of any three adjacent digits is 13. and the second digit is 2 and the tenth digit is 4.
What are the last three digits of the credit card number?
****IMPORTANT****
Please put steps of solving the question, Thanks!
The Credit Score is 4274274274274274.
What is Sequence?A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts.
A phrase is used to describe each number in the series.
Given:
The sum of any three adjacent digits is 13.
The second digit is 2 and the tenth digit is 4.
So, _2_ _ _ _ _ _ _ 4 _ _ _ _.
Now, the 2nd, 5th, 8th, 11th, 14th digits are equal and so are the 3rd, 6th, 9th, 12th, 15th.
So, the credit card number is 4274274274274274 and the last three digits are 274 which shows the sum is 13.
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Liz is buying a home for $426,000. She is making a 22% down payment and financing the rest with a 20-year loan at 5.25% interest.
What will her total payment for the home be? Round your answer to the nearest dollar.
Use a mortgage table to find the monthly mortgage payment per 1000 dollars borrowed.
$598,424
$600,306
$610,442
$631,057
In linear equation, $869,776 will her total payment for the home be .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
You have to use the number in the intersection of the row for 5.25% interest and the column for 20 years.
The number is $6.74.
That means that, for every $1,000 borrowed for 20 years at 5.25% interest you will pay $6.74 every month.
2. Amount borrowed
You will make a 22% down payment:
Thus the amount borrowed is $426,000 - $93,720 = $332,280
3. Monthly payment
Multiply the monthly payment per 1,000 by the amount borrowed divided by 1,000:
4. Total monthly payments:
Multiply the number of payments by the monthly payment.
Number of payments = 20 years × 12 payments /year = 240 payments.
5. Total payment for the home.
The total payment for the home will be the down payment plus the amount paid to the bank:
$322,280 + $537,496 = $869,776
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Rochelle is conducting an experiment on cells of Elodea, a kind of water plant. To induce plasmolysis at the correct rate, she needs to use an 8% saline solution, but she has only the solutions shown on hand.
A. If Rochelle mixes the two solutions to get 100 mL of an 8% saline solution, which will she use more of? Explain.
Enter your answer.
B. How can Rochelle determine the amount of each solution she needs to make the 8% saline solution?
Enter your answer.
C. Use Appropriate Tools Are there any methods for solving this problem other than the one you used in part B? Explain.
Enter your answer.
A pharmacist wants to mixture of 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution. He used 85 ml of 40% saline solution and 34 ml of 12% saline solution.
What is mixture?Mixture word problems require you to combine two or more separate items, and then calculate some quantity of the resulting mixture (such as a percentage, price, or number of liters, for example). There will always be some type of "rate," like miles per hour or price per pound. Mixtures are substances that contain two or more distinct substance categories. To separate them, utilize physical tools. Examples include air, different gases, a mixture of sugar and water, a solution of salt and water, and so on.
here, we have,
Given,
A pharmacist wants to mixture of 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution.
Equation:
X + y = 119
y = 119 - x
0.40x + 0.12y = 119 of 0.32
0.40x + 0.12y = 38.08
Using y = 119 -x
0.40x + 0.12(119 - x) = 38.08
0.40x + 14.28 - 0.12x = 3808 Eq(2)
0.28x = 23.8
x = 85
and,
y = 119 - 85
y = 119 - 85
y = 34
Equating values in equation (2),
=0.40(85) + 0.12(34)
=34 + 4.08
=38.08
A pharmacist wants to mix a 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution. He used 85 ml of 40% saline solution and 34 ml of 12% saline solution.
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you sell small candles for 14$ and large candles for 16$ at the warehouse. At the warehouse, you pay x dollars for small candles and y dollars for large candles after one month you sold 45 small candles and 68 large candles at a store. A write and simplify and expression. B if you buy the candles at the warehouse for 5$ for small candles and 7$ for large candles what is the profit after your month of selling at the store?. Thank you so much
The diameter of a circle is 24 cm. Find its area to the nearest whole number.
Answer:
Area = 452 cm²
Step-by-step explanation:
[tex] = \frac{\pi }{4} {d}^{2} [/tex]
[tex] = \frac{\pi}{4} {(24)}^{2} = 452.39 \: cm²[/tex]
Solve for x show proofs urgentttt
The value of the length, x is 5√3
How to determine the value of the length, xFrom the question, we have the following parameters that can be used in our computation:
Rise = 11
Length = x
Hypotenuse = 14
The value of the length , x is calculated as
x^2 = Hypotenuse^2 - Rise^2
Substitute the known values in the above equation, so, we have the following representation
x^2 = 14^2 - 11^2
So, we have
x^2 = 75
Take the square root of bpth sides and evaluate
x = 5√3
Hence, the value of x is 5√3
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What is 90 degree F in C?
90 degrees Fahrenheit is equal to approximately 32.2 degrees Celsius using conversion formula method.
To convert Fahrenheit to Celsius, the following formula can be used:
Celsius = (Fahrenheit - 32) x 5/9
Plugging in 90 degrees Fahrenheit, we get:
Celsius = (90 - 32) x 5/9
Celsius = 58 x 5/9
Celsius = 290/9
Celsius ≈ 32.2
Therefore, 90 degrees Fahrenheit is approximately 32.2 degrees Celsius.
Fahrenheit is a temperature measurement system developed by the German physicist Daniel Gabriel Fahrenheit in 1724.
The Celsius scale is widely used throughout the world for measuring temperature, and it is the standard unit of temperature used in most scientific research and international trade. In addition to measuring air temperature, Celsius is used to measure temperature in a variety of fields, including chemistry, biology, and engineering.
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help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The percentage of decrease is 20%
How to find the missing percentage?First, if we have an initial value A, and we increase it by x (a percentage in decimal form) then the new value will be:
A' = A*(1 + x)
Whle a decrease is written as:
A' = A*(1 - x)
In this case we have an increase of the 25%, it is written as:
A' = A*(1 + 0.25)
A' = A*1.25
IF we pass the factor to the other side, will get:
(1/1.25)*A' = A
(0.8)*A' = A
Now we want to write the coefficient on the left in the form (1 - x)
We will get:
0.8 = 1 - 0.2
0.2 is the percentage (in decimal form) decreased from A' to get A. Then the answer is 20%.
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Solve the system of equations below. Show work.
2x+y=10
3x-y=5
The solution to the simultaneous equation given is (3, 4)
Solving system of equationGiven the system of equation below
2x+y=10
3x-y=5
From equation 2, the value of y is expressed as:
y = 3x - 5
Substitute the result into equation to have:
2x + 3x - 5 = 10
5x - 5 = 10
5x = 15
x = 3
Since y = 3x - 5
y = 3(3) - 5
y = 4
Hence the solution to the system of equation is (3, 4)
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A function is shown below.
f(x) = 3x - 7
What is the value of f(-3)?
Answer:
Step-by-step explanation:
Put ' - 3' whre 'x' is and compute the answer
f(-3) = 3 (-3) - 7
= -9 - 7 = - 16
Find the weighted average of the numbers -3 and 5 with 3/5 lf the weight on the first number and 2/5 on the second number.
The weighted average of the numbers is 0.1.
What is the average?The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average.
Given that, average of the numbers -3 and 5 with 3/5
The weight of first number and 2/5 of second number.
Here, -3(3/5)+5(2/5)/2
= (-1.8+2)/2
= 0.2/2
= 0.1
Therefore, the weighted average of the numbers is 0.1.
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PLEASE HELP ME ASAP WHAT IS THE VALUE OF X IN THE QUADRILATERAL
From the sum of the interior angles, it is possible to find x=70°.
Quadrilaterals
There are different quadrilaterals, for example square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a square, all angles are 90° and all sides present the same value.
The sum of the interior angles of a quadrilateral is equal to 360°.
The question gives a trapezoid and its respective angles. Thus,
x+85+150+55= 360
x+140+150=360
x+290=360
x=360-290
x=70°
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Answer:
b) 70°
Step-by-step explanation:
We know that,
→ The sum of all interior angles in a quadrilateral is 360°.
Now we have to,
→ Find the required value of x.
Forming the equation,
→ 85° + 150° + 55° + x = 360°
Then the value of x will be,
→ 85° + 150° + 55° + x = 360°
→ 290° + x = 360°
→ x = 360° - 290°
→ [ x = 70° ]
Hence, the value of x is 70°.
If a least-squares regression line fits the data well, what characteristics should the residual plot exhibit? Sketch a well-labeled example
x' is the mean of all the x-values, y' is the mean of all the y-values, and n is the number of pairs in the data set.
[tex]y=b_1x+b_0[/tex]
There is always one straight line that fits the data more accurately than any other, in the sense of minimizing the total of the squared errors, given any set of integers in pairs (apart from the case when all the x-values are the same). The least squares regression line is what it is known as. Additionally, its slope and y-intercept have formulae.
Given a collection of pairs (x,y) of numbers, there is a line [tex]y=b_1x+b_0[/tex] that best fits the data in the sense of the least squares regression line, its slope is b1 and the y-intercept is b0.
[tex]b_1=\frac{SS_{xy}}{SS{_xx}}}\\\\and\\\\b_0=y-b_1x\\\\SS_{xx}=\sumx^2-1/n[\sum x]^2\\\\SS_{xy}=\sum{xy}-1/n(\sum x)(\sum y)[/tex]
x' is the mean of all the x-values, y' is the mean of all the y-values, and n is the number of pairs in the data set.
[tex]y=b_1x+b_0[/tex]
specifying the least squares regression line is called the least squares regression equation.
Example,
Find the least squares regression line for the five-point data set
x = 2 2 6 8 10
y= 0 1 2 3 3.
compute the table,
x y x2 xy
2 0 4 0
2 1 4 2
6 2 36 12
8 3 64 24
10 3 100 30
28 9 208 68 (sum)
[tex]S_{xx}=208-(1/5)(28)^2=51.2\\\\SS_{xy}=68-(1/5)(28)(9)=17.6\\\\x'=\frac{28}{5}=5.6\\\\y'=1.8\\\\b_1=17.6/51.2=0.34375\\\\b_0=y-b_1(x)=1.8-(0.34375)(5.6)= -0.125[/tex]
The regression line is y=0.34375x-0.125
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what is the answer to this
The value of x is 15√2
The value of the side y is 30
How to determine the length of the sidesThe sum of angles in a rectangle is 360 degrees
To determine the value of the variable, x
Let's use the trigonometric identity, cosine
cos = adjacent/hypotenuse
substitute the values
cos 45 = 15/x
Find the value
1/√2 = 15/x
cross multiply
x = 15√2
For y, we have;
sin 45 = y/15√2
1/√2 = y/15√2
Make y subject
y= 15√2 /√2
y = 60/2
y = 30
Hence, the values are 30 and 15√2
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what is the mass to the nearest tenth of a gram of 3.50 moles of sodium metal?
Answer:
The mass of 3.5 moles of Ca (Sodium) is 140 g to two significant figures.
Two sides of a triangle have lengths 16 and 17. Which expression describes the length of the third side?
Answer:
We can use the triangle inequality theorem to determine the possible lengths of the third side of the triangle. According to the theorem, the length of any side of a triangle must be less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.
So, for a triangle with sides of length 16 and 17, the length of the third side must satisfy the following inequality:
17 - 16 < third side < 17 + 16
1 < third side < 33
Therefore, the length of the third side must be described by the expression:
1 < third side < 33
Step-by-step explanation:
which go's to which.................................
the matches are
-2(2x+5) ≤ -7(x+4) x<=-6
4x-3x-1 x<=-1
5(x-3)9(x+1) x>=-6
3(x-4)+5 2x-9 x>=-2
What is inequality?Generally, Inequality is a mathematical statement that compares two values or expressions and indicates whether they are equal or not equal, or which one is greater or smaller. Inequalities are expressed using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).
For example, 5 < 8 is an inequality that indicates that 5 is less than 8, and x + 3 ≥ 7 is an inequality that indicates that the value of x plus 3 is greater than or equal to 7.
Inequalities are commonly used in algebra and other branches of mathematics to represent relationships between quantities.
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The correct matching of the inequalities can be shown from the calculations below
What is inequality?
Inequalities are an important tool in mathematical modeling and optimization problems, where they are used to express constraints and objective functions.
Using the principle of inequalities we have;
1) -2(2x + 5) ≤ - 7(x + 4)
-4x -10 ≤ -7x -28
-4x +7x ≤ -28 + 10
3x ≤ -18
x ≤ -6
2) 4x - 6/2 ≥ 3x - 1
4x - 6 ≥ 6x - 2
4x - 6x ≥ -2 + 6
-2x ≥ 4
x ≤ -2
3) 5(x - 3) ≤ 9(x + 1)
5x - 15 ≤ 9x + 9
5x - 9x ≤ 9 + 15
-4x ≤ 24
x ≥ -6
4) 3(x - 4) + 5 ≥ 2x - 9
3x - 12 + 5≥ 2x - 9
3x - 2x ≥ -9 + 12 -5
x ≥ -2
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Change 0.7 to fraction
Answer:
7/10
Step-by-step explanation:
Here ya go!
7 27. MODELING REAL LIFE Find the length of the slide.
(See Example 6.)
MTR
12 ft
53°
The length of the slide shown is 15 feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Let l represent the length of the slide, hence:
sin(53) = 12/l
l = 12/sin(53)
l = 15 feet
The length is 15 feet
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Two planes, which are 2235 miles apart, fly toward each other. Their speeds differ by 45 mph. If they pass each other in 3 hours, what is the speed of each?
In a case whereby two planes, which are 2235 miles apart, fly toward each other. Their speeds differ by 45 mph. If they pass each other in 3 hours, the speed of slower is 350mph and faster is 395mph.
How can the speed of each be calculated?
The concept here is simplification.
Let represent the speed of the slower plane using the( x),
Let us represent the speed of the faster to be ( x + 45)
The distance traveled that can be associated to the slower plane ( 3x).
then the distance that can be attributed toi that of the faster plane = 3(x + 45).
given that the total distance=(2235 miles).
[3x + 3(x + 45) ]= 2235
3x + 3x + 135= 2235
[6x ]= 2235-135
6x = 2100
x=350
hence, the speed of the slower plane is 350
the speed of the faster= x + 45 = 350+45= 395
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The speed of first plane is 350 miles/hour and the speed of second plane is 395 miles/hour .
Given, Distance between the planes = 2235 miles
Let, the speed of the first plane be 'x' miles/hour.
Let, the speed of the second plane be 'x+45' miles/hour.
Since, they are flying towards each other, their speed will get added.
The collective speed of both the planes = (2x + 45) m/h.
A/Q, they pass each other in 3 hours, i.e. they collectively covers the distance of 2235 miles in 3 hours.
We know Distance = Speed × Time
Given, Distance = 2235 miles , Time = 3 hours , Speed = (2x + 45) m/h
2235 = 3 × (2x + 45)
745 = 2x + 45
x = 350 miles/hour.
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What is 60 kph into miles?
60 kilometers per hour (kph) is equal to roughly 37.28 long hauls (miles) per hour( mph).
To convert kilometers per hour to long hauls per hour, you can use the following conversion formula:
long hauls per hour = kilometers per hour x0.621371.
Plugging in 60 kilometers per hour, we get,
long hauls per hour = 60 x0.621371
long hauls per hour ≈37.28.
Thus, 60 kilometers per hour is roughly 37.28 long hauls per hour.
A kilometer (km) is a unit of length or distance used in the metric system. It is roughly original to 0.621 long hauls.
Mile is a unit of length or distance used in the customary system of dimension, primarily in the United States and United Kingdom. One afar is original to 280 bases or 760 yards, which is roughly 1.609 kilometers in the metric system.
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Black diamond ski resort charges $25 for ski rental and 10$ an hour to ski bunny hill ski resort charges $50 for ski rental and $5 an hour to ski. Create an equation to determine at what point the cost of both ski slopes is the same
skiing for 5 hours will make the cost of skiing at both ski resorts equal.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Given, Bunny Hill Ski Resort charges $50 for ski rentals and $5 per hour of skiing, while Black Diamond Ski Resort charges $25 for rentals and $10 per hour of skiing.
Let's define:
x as the number of hours of skiing
C₁ as the total cost of skiing at Black Diamond ski resort
C₂ as the total cost of skiing at Bunny Hill ski resort
At Black Diamond ski resort, the total cost of skiing is the sum of the cost of rental and the cost of skiing per hour:
C1 = 25 + 10x
At Bunny Hill ski resort, the total cost of skiing is the sum of the cost of rental and the cost of skiing per hour:
C₂ = 50 + 5x
We want to find at what point C₁ = C₂, so we set the two equations equal to each other:
25 + 10x = 50 + 5x
Simplifying the equation, we get:
5x = 25
Dividing both sides by 5, we get:
x = 5
Therefore, skiing for 5 hours will make the cost of skiing at both ski resorts equal.
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