a. Solving the equation for x gives x = (C - 60)/85.
b. The number of ski trips that you would take if you spend a total of $315 is 3 ski trips.
The number of ski trips that you would take if you spend a total of $315 is 5 ski trips.
In Mathematics and Geometry, a linear equation is a type of function with a constant slope and whose equation is graphically represented by a straight line on the xy-plane or cartesian coordinate.
Part a.
By making x the subject of formula in the given equation, we have:
C = 85x + 60
85x = C - 60
x = (C - 60)/85
Part b.
When the value of C is 315, number of ski trips (x) is given by;
x = (315 - 60)/85
x = 3 ski trips.
When the value of C is 485, number of ski trips (x) is given by;
x = (485 - 60)/85
x = 5 ski trips.
Complete Question:
The total cost C (in dollars) to participate in a ski club is given by the literal equation C=85x+60, where x is the number of ski trips you take.
a. Solve the equation for x.
b. How many ski trips do you take if you spend a total of $315? $485?
An art student wants to make a model of the classroom. The length of the classroom is 2.4 times its width. The length of the student's model is 42 in. What should the width of the model be?
Answer:
Width of the model is:
17.5 in
Step-by-step explanation:
The length of the classroom is 2.4 times its width.
Length=2.4×width
The length of the student's model is 42 in.
Let w be the width of student's model.
By using the equation Length=2.4×width , we get
42=2.4×w
⇒ [tex]w=\dfrac{42}{2.4}[/tex]
⇒ w=17.5
Hence, width of the model is:
17.5 in
Answer:answer is actually 17.5 in
Step-by-step explanation:
You are going to order some of your favorite cookies. If you order two boxes it will cost you $14. If you place an order for eight boxes it will cost you $26. Write an equation that represents the cost of ordering your favorite cookies.
Step 1: Decide what information represents your two points.
Hint: The points are in the format (number of boxes of cookies, cost) as these are your two variables.
Point 1: Point 2:
Step 2: Use your two points to write an equation.
The lateral surface area of the wrapper for an ice cream cone is 47.1 cm squared.If the lateral height of the ice cream cone is 6cm,what would be the radius of the ice cream cone?
How to simplify 8x2+7x-3+4x-8
Need help! Please. It could be a integer or a decimal
Kaitlin drove 260 miles using 12 gallons of gas. at this rate, how many gallons of gas would she need to drive 286 miles?
if a 40-foot tree casts a 12-foot shadow,find the length of a shadow cast by a 23-foot tree
The length of the shadow cast by the 23 feet tree is 6.9 feet
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
Let the height of the tree A = 40 feet
The height of the shadow of the tree A = 12 feet
Now ,
The height of the tree B = 23 feet
Let the height of the shadow of the tree B = x
So , the proportion equation is
height of the shadow of the tree A / height of the tree A = height of the shadow of the tree B / height of the tree B
And the proportion will be ,
12 / 40 = x / 23
Multiply by 23 on both sides , we get
x = ( 12 × 23 ) / 40
x = ( 3 × 23 ) / 10
x = 69 / 10
x = 6.9 feet
Therefore , the value of x is 6.9 feet
Hence , The length of the shadow cast by the 23 feet tree is 6.9 feet
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The real number -16 belongs to which sets of numbers?
-16 is an integer and rational number.
What are natural numbers, rational numbers, integers and irrational numbers?Natural numbers are: 1, 2, 3, ....
Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )
Irrational numbers are those real numbers which are not rational numbers.
Know that all natural numbers are integers, all integers are rational numbers. That means natural numbers are not irrational.
The counting numbers or natural numbers are like 1,2,3,4,5,6, etc
Note that whole numbers include counting numbers, but with 0, so 0,1,2,3,4, 5, etc
Also rational numbers are numbers that can be written in form a/b where a and b are integers and b≠0
so -16 is an integer and rational number
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What is the answer for 7-2n=n-14
Defined by two lines or rays diverging from a common point.
A) arc
B) angle
C) parallel lines
D) perpendicular lines
Defined as bounded by two distinct end points that contain every point on the line between its end points.
A) circle
B) line segment
C) parallel lines
D) perpendicular lines
Answer:
1. Angle
2. Line Segment
Step-by-step explanation:
Two lines or rays diverging from a common point defines an 'angle', which is a figure forming from two rays starting from the same end-point.
Now, a figure bounded by two distinct end points which contain every point on the line between its end points defines a 'line segment'.
Hence, the answer are: Angle and Line Segment respectively.
the current value of a baseball card is 80 times its original value the baseball card is worth $36 write and solve an equation to find the original value of the baseball card
To find the original value of a baseball card that is now worth 80 times its original value, you divide the current value of $36 by 80, resulting in an original value of $0.45.
Explanation:The student wants to find the original value of a baseball card that is currently worth 80 times its original value and has a present worth of $36. We set up the equation: original value multiplied by 80 equals current value (80 × original value = $36). To find the original value, we divide the current value by 80.
Write the equation: 80 × original value = $36.Divide both sides of the equation by 80 to isolate the original value. So, original value = $36 ÷ 80.Calculate the result: original value = $0.45.The original value of the baseball card was $0.45.
juan drives to work. Due to traffic, he averages 22 miles per hour. He returns home averaging 32 per hour. The total time is 22.5 hours. Write and solve an equation to find the time juan spends driving to work.
Alan drove 756 miles in 12 hours. at the same rate, how many miles would he drive in 8 hours?
Alan would drive 504 miles in 8 hours.
Explanation:To find out how many miles Alan would drive in 8 hours, we can set up a proportion using the information given. Since Alan drove 756 miles in 12 hours, we can write the proportion as:
12 hours / 756 miles = 8 hours / x miles.
To solve for x, we can cross-multiply and then divide:
12 * x = 8 * 756
x = (8 * 756) / 12
x = 504
Therefore, Alan would drive 504 miles in 8 hours.
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How to find slope of any given line segment?
Which ordered pairs are solutions to the inequality 4x+y>−6?
Select each correct answer.
(2, 0)
(−3, 6)
(4, −20)
(0, −9)
(−1, −1)
Answer:
(2,0) , (4,-20) and (-1,-1)
Step-by-step explanation:
[tex]4x+y>-6[/tex]
WE need to select an ordered pair that is solution to our inequality
Lets check with each option
(2,0) , plug in 2 for x and 0 for y
[tex]4x+y>-6[/tex]
[tex]4(2)+0>-6[/tex]
[tex]8>-6[/tex] True
(−3, 6), plug in -3 for x and 6 for y
[tex]4x+y>-6[/tex]
[tex]4(-3)+6>-6[/tex]
[tex]-6>-6[/tex] False
(4, −20) , plug in 4 for x and -20 for y
[tex]4x+y>-6[/tex]
[tex]4(4)-20>-6[/tex]
[tex]-4>-6[/tex] True
(0, −9) , plug in 0 for x and -9 for y
[tex]4x+y>-6[/tex]
[tex]4(0)-9>-6[/tex]
[tex]-9>-6[/tex] False
(-1, −1) , plug in -1 for x and -1 for y
[tex]4x+y>-6[/tex]
[tex]4(-1)-1>-6[/tex]
[tex]-5>-6[/tex] True
Final answer:
The ordered pairs that are solutions to the inequality 4x+y>-6 are (2, 0), (4, -20), and (-1, -1) as they satisfy the condition when substituted into the inequality.
Explanation:
To determine which ordered pairs are solutions to the inequality 4x+y>-6, we need to plug the x and y values from each ordered pair into the inequality.
For the pair (2, 0), we substitute x = 2 and y = 0 into the inequality: 4(2) + 0 > -6, which simplifies to 8 > -6. This is true, so (2, 0) is a solution.For the pair (-3, 6), we substitute x = -3 and y = 6: 4(-3) + 6 > -6, which simplifies to -12 + 6 > -6. This gives -6 > -6, which is not true, so (-3, 6) is not a solution.For the pair (4, -20), we substitute x = 4 and y = -20: 4(4) - 20 > -6, which simplifies to 16 - 20 > -6. This gives -4 > -6, which is true, so (4, -20) is a solution.For the pair (0, -9), we substitute x = 0 and y = -9: 4(0) - 9 > -6, which simplifies to -9 > -6. This is not true, so (0, -9) is not a solution.For the pair (-1, -1), we substitute x = -1 and y = -1: 4(-1) - 1 > -6, which simplifies to -4 - 1 > -6. This gives -5 > -6, which is true, so (-1, -1) is a solution.The correct solutions to the inequality are the ordered pairs (2, 0), (4, -20), and (-1, -1).
The clean up hitter on a baseball tean batted 1/3 of the runs the team scored. The hitter batted in 3 runs. Select the equation that represents the number of n of runs the team scored. Then solve the equation:
A.1/3n=3
B.n/3=1/3
C.3n=1/3
D.3n=9
How do i solve for x 30x - 60 = 20x
I already know x equals 6, but i dont know how to get the answer
Give an example of an open equation
What can you infer about elements that are in the same group?
a. they will have the same atomic mass
b. they will display similar chemical and physical properties
c. they will contain the same number of protons
d. they will emit x rays of similar frequency
Answer:
b.They will display similar chemical and physical properties.
Step-by-step explanation:
We have to find about the elements that are in the same group.
In modern periodic table
Elements are arranged in group according to similar properties.
The elements which have same properties are placed in the same group and mass of different elements are different in the group.
The outer electronic configuration of every element in the same group are same.
Therefore, the physical and chemical properties of the elements are same in the group.
Hence, option B is true.
Answer:b.They will display similar chemical and physical properties.
Write an equation for the line through p that is parallel to l and perpendicular to l
Mr. rancher wants to build a pen for his horse. he wants the pen to be 40 yards long and 50 yards wide. if the fencing comes in 5 foot pieces, how many pieces does mr. rancher need to buy?
There are 36 pieces need to buy by Mr. rancher.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The length of pen for his horse = 40 yards
The width of pen for his horse = 50 yards
And, The fencing comes in 5 foot pieces,
Now,
The perimeter of the pen for his horse = 2 (50 + 40)
= 2 x 90
= 180 yards
Since, The fencing comes in 5 foot pieces,
Hence, Number of pieces to buy by Mr. rancher = 180 / 5
= 36
Thus, There are 36 pieces need to buy by Mr. rancher.
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Kim estimates that the faucet in her kitchen drips at a rate of 1 drop every 2 seconds. Erik wants to know how many times the faucet drios in a week
The sum of 5 consecutive even numbers is 505 What is the third number in this sequence?
you can't have 5 even numbers add to 505
even numbers can only add up to an even number.
Students received these scores: 70, 75, 80, 90, 95, 95, and 100. the score of 95 is what?
confused how do i create this?
Write the domain of the function given in the graph in set builder notation.
a. {x|x<=10}
b. {x|x<=0}
c. {x|x>10}
d. {x|x>0}
I can't get a picture of the graph so I'll try to explain. Y axis 0-5, going up by 1's, x axis 0-50, going up by 5's. Line starts at 10 on the x axis, goes up at an angle and stops at 40.
2 times as many as 8 is 16
Answer:
or 16 is the result of doubling 8
Step-by-step explanation:
I need math help. Look at the attachment. No multiple choice.
there are 4 quarters per year
if annual rate = 8%
quarterly rate would be 8%/4 = 2%
so the (1+r) beomes (1+0.02) = 1.02
The measure of an angle and the measure of its supplement are equal. find the measure of each of the supplementary angles
Answer:
Step-by-step explanation:
Sorry, here are the problems:
160: 20 degrees
90: 90 degrees
X: ____
Prove that a triangle with sides n^2 1, n^2 - 1 and 2n (for n > 1) is a right triangle