The total cost c (in dollars) to participate in a triathlon series is given by the literal equation c= 90x + 35, where x is the number of triathlons in which you participate
Answers
Participating in approximately 5.17 triathlons would result in a total cost of $500, based on the given equation. We solve this equation to get the value of x.
The equation c = 90x + 35 represents the total cost (c) in dollars to participate in a triathlon series, where x is the number of triathlons in which you participate. To solve this equation for x, we can isolate x on one side of the equation.
First, let's start with the equation c = 90x + 35. To isolate x, we can begin by subtracting 35 from both sides of the equation:
c - 35 = 90x
Next, we can divide both sides of the equation by 90 to solve for x:
(c - 35) / 90 = x
This gives us the solution for x. By dividing the quantity (c - 35) by 90, we obtain the value of x that corresponds to the given total cost (c) of participating in the triathlon series. The expression (c - 35) / 90 represents the number of triathlons in which you participate.
For example, if the total cost is $500, we can substitute c = 500 into the equation and solve for x:
x = (500 - 35) / 90 = 465 / 90 ≈ 5.17
Therefore, participating in approximately 5.17 triathlons would result in a total cost of $500, based on the given equation. It's important to note that since x represents the number of triathlons, it is not required to be a whole number and can be a decimal value depending on the given total cost.
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Related Questions
how to identify the center, foci, vertices, co-vertices, and lengths of the semi-major and semi-minor axes of an ellipse given the equation of the ellipse.
Answers
To identify the center, foci, vertices, co-vertices, and lengths of the semi-major and semi-minor axes of an ellipse given its equation, convert the equation to standard form, determine the alignment, and apply the relevant formulas.
To identify the center, foci, vertices, co-vertices, and lengths of the semi-major and semi-minor axes of an ellipse given its equation, follow these steps:
Rewrite the equation of the ellipse in the standard form: ((x-h)^2/a^2) + ((y-k)^2/b^2) = 1 or ((x-h)^2/b^2) + ((y-k)^2/a^2) = 1, where (h, k) represents the center of the ellipse.
Compare the denominators of x and y terms in the standard form equation: if a^2 is the larger denominator, the ellipse is horizontally aligned; if b^2 is the larger denominator, the ellipse is vertically aligned.
The center of the ellipse is given by the coordinates (h, k) in the standard form equation.
The semi-major axis 'a' is the square root of the larger denominator in the standard form equation, and the semi-minor axis 'b' is the square root of the smaller denominator.
To find the vertices, add and subtract 'a' from the x-coordinate of the center for a horizontally aligned ellipse, or from the y-coordinate of the center for a vertically aligned ellipse. The resulting points will be the vertices of the ellipse.
To find the co-vertices, add and subtract 'b' from the y-coordinate of the center for a horizontally aligned ellipse, or from the x-coordinate of the center for a vertically aligned ellipse. The resulting points will be the co-vertices of the ellipse.
The distance from the center to each focus is given by 'c', where c^2 = a^2 - b^2. For a horizontally aligned ellipse, the foci lie at (h ± c, k), and for a vertically aligned ellipse, the foci lie at (h, k ± c).
The lengths of the semi-major axis and semi-minor axis are given by 2a and 2b, respectively.
By following these steps, you can identify the center, foci, vertices, co-vertices, and lengths of the semi-major and semi-minor axes of an ellipse given its equation.
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A rectangle has the following vertices: A(-1.9), B(0,9). C(0-8), D(-1,-8). What is the perimeter of rectangle ABCD?
18 units
34 units
36 units
17 units
Answers
Answer:
the answer of that question is 36 units
Rapunzel has a savings account with $880 in it that earns 9.4% simple interest per year. How much money will Rapunzel have in 10 years?
Answers
Answer:
$1707.2
Step-by-step explanation:
Given data
Principal= $880
Rate= 9.4%
Time= 10years
The simple interest formula is
A= P(1+rt)
substitute into the formula to solve for A
A= 880(1+0.094*10)
A=880(1+0.94)
A=880*1.94
A=$1707.2
Hence the Amount after 10 years is $1707.2
10.85 . ((1.7) =
answers:
1. 18.445
2. 12.55
3. 20.29
4. 1.845
Answers
Answer:
18.445
Step-by-step explanation:
Multiply
A wet bicycle tire leaves a trace of water on the floor. The tire has a radius of 30 \text{ cm}30 cm30, start text, space, c, m, end text, and the bicycle wheel makes 333 full rotations before stopping.
How long is the trace of water left on the floor?
Round your answer to the nearest \text{cm}cmstart text, c, m, end text
Answers
The trace of water left on the floor is the circumference of 565.2 cm.
Water traces are seen on the floor from a wet bicycle tire.
The bicycle wheel makes three complete rotations before coming to a stop, circumference and the tire has a radius of 30 cm.
The circle of the cycle is indicated by the water stain left on the floor.
Given the radius = 30 cm
So,
C = 2 × 3.14 × 30
C = 188.4
Given that a bicycle wheel turns three times before pausing to pick up a trace of water, the answer is,
3 x 188.4 = 565.2 cm
the floor has a 565.2 centimeter trace of water.
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13. Janine has job offers at two companies. One
company offers a starting salary of $23,000 with
a raise of $3000 each year. The other company
offers a starting salary of $36,000 with a raise of
$2000 each year.
a. After how many years would Janine's salary be
the same with both companies?
b. What would that salary be?
Answers
9514 1404 393
Answer:
13 years$62,000Step-by-step explanation:
a) The 36000 -23000 = 13000 difference in salary is being made up at the rate of 3000 -2000 = 1000 per year. It will take 13000/1000 = 13 years for the salaries to be the same.
__
b) After 13 years, the salary will be ...
23000 +13(3000) = 23000 +39000 = 62,000 . . . dollars
36000 +13(2000) = 36000 +26000 = 62,000 . . . dollars
Answer:
after the first company, her salary would be 48000 in 5 years
after the second company, her salary would be 48000 in 4 years
Step-by-step explanation:
Subject is power series, prove or disprove.
d,e,f please
(d) If R 0. Then the series 1 – + $ -+... is convergent if and i only if a = b. (f) If an is convergent, then (-1)"+la, is convergent. nal n=1
Answers
The series Σ(-1)^n*an converges because its sequence of partial sums Tn converges to a finite limit M. Hence, the statement is proven.
(d) The statement "If R < 1, then the series 1 – a + a^2 - a^3 + ... is convergent if and only if a = 1" is false.
Counterexample: Consider the series 1 - 2 + 2^2 - 2^3 + ..., where a = 2. This series is a geometric series with a common ratio of -2. Using the formula for the sum of an infinite geometric series, we find that the series converges to 1/(1+2) = 1/3. In this case, a = 2, but the series is convergent.
Therefore, the statement is disproven.
(f) The statement "If the series Σan is convergent, then the series Σ(-1)^n*an is convergent" is true.
Proof: Let Σan be a convergent series. This means that the sequence of partial sums, Sn = Σan, converges to a finite limit L as n approaches infinity.
Now consider the series Σ(-1)^nan. The sequence of partial sums for this series, Tn = Σ(-1)^nan, can be written as Tn = a1 - a2 + a3 - a4 + ... + (-1)^n*an.
If we take the limit of the sequence Tn as n approaches infinity, we can rewrite it as:
lim(n→∞) Tn = lim(n→∞) (a1 - a2 + a3 - a4 + ... + (-1)^n*an).
Since the series Σan is convergent, the sequence of partial sums Sn converges to L. As a result, the terms (-1)^n*an will also converge to a limit, which we can denote as M.
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An airport, a factory, and a shopping center are at the vertices of a right triangle formed by three highways. The airport and factory are 6.0 miles apart. Their distances from the shopping center are 3.6 miles and 4.8 miles, respectively. A service road will be constructed from the shopping center to the highway that connects the airport and factory. What is the shortest possible length for the service road? Round to the nearest hundredth.
The answer is(_______) miles
Answers
Step-by-step explanation:
the shortest possible length for the service road
= (3.6 × 4.8) / 6.0
= 2.88 miles
Find the size of the final unknown exterior angle in a polygon whose other exterior angles are: 37°, 84°, 49°, 38°, 35° and 68°.
Answers
Answer:
49°
Step-by-step explanation:
the sum of the exterior angles of a polygon = 360°
let x be the unknown exterior angle , then summing gives
37° + 84° + 49° + 38° + 35° + 68° + x = 360° , that is
311° + x = 360° ( subtract 311° from both sides )
x = 49°
HURRY IM TIMED!!
What is the area of the regular trapezoid below?
6 cm-
8 cm
10 cm-
O 64 cm²
O 80 cm²
O 240 cm²
O480 cm²
Answers
find the larger of two consecutive integers,x, if the sum of the smaller and larger is -9. write an equation and solve
Answers
Answer:
-4
Step-by-step explanation:
PLEASE HELP ASAP!!
Which relationship is always correct for the angles x, y, and z of triangle ABC?
x + z = y
y + z = x
x + y + z = 180 degrees
x + y + z = 90 degrees
Answers
y + z = x
Plz mark me as brainliest
The relationship between the angles of a triangle is y + z = x. Then the correct option is B.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The triangle ABC is shown. The sum of the interior angle of the triangle is 180°. Then the equation is given as,
∠BAC + y + z = 180° ...1
The sum of the interior angle and exterior angle is equal to 180°. Then the equation is given as,
∠BAC + x = 180° ...2
From equations 1 and 2, then we have
∠BAC + y + z = ∠BAC + x
y + z = x
The relationship between the angles of a triangle is y + z = x. Then the correct option is B.
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HELPP I WILL GIVE BRAINLEST TO YOU IF YOU ANSWER RIGHT !!!!!
Answers
Answer:
Leg a = 2.6 mi
Leg b = 3.2 mi
No, the biologist will not hike more than 5 mi.
Step-by-step explanation:
The legs of the figure are the two shorter sides. So, the legs on this triangle are 2.6 mi and 3.2 mi long.
To find the hypotenuse, we can use this formula, with c being the length of the route the biologist will take.
a² + b² = c²
We can already plug in the values for a and b.
2.6² + 3.2² = c²
This can simplify to-
6.76 + 10.24 = c²
17 = c²
Now, find the square root of 17 and c² to find the value of c.
\(\sqrt{17}\) = \(\sqrt{c^{2} }\)
4.1 = c
The hypotenuse is 4.1 mi long.
4.1 > 5, so the answer is no.
Good luck ^^
If a fraction is equal to 3/7 and the sum of the numerator and denominator is 100, what is the fraction?
Answers
The fraction is equal to 3/7
the sum of numerator and denominator is equal to 100
Let the numerator = x
Since, Numerator + Denominator = 100
x + Denominator = 100
Denominator = 100 - x
Thus, the fraction is in the form of;
\(\frac{Numerator}{Deno\min ator}=\frac{x}{100-x}\)Since it is given that the fraction is equal to 3/7
So,
\(\frac{x}{100-x}=\frac{3}{7}\)Simplify the expression for x;
\(\begin{gathered} \frac{x}{100-x}=\frac{3}{7} \\ \text{ Apply crossmultiplication;} \\ 7x=3(100-x) \\ 7x=300-3x \\ 7x+3x=300 \\ 10x=300 \\ x=\frac{300}{10} \\ x=30 \end{gathered}\)So, the numerator is 30
Since, Denominator = 100 - x
Substitute x = 30
Denominator = 100 - x
Denominator = 100 - 30
Denominator = 70
Thus, we have numerato = 30 denominator = 70
So, the resulting fraction is given as;
\(\frac{30}{70}\)Answer: 30/70
The width of a rectangle is 9 cm less than twice the length. the perimeter is 72 cm. What is the length and width
Answers
9 times 9=72
Step-by-step explanation:
if if the width is 9 then the length is 9 because 9 times 9 equals 72
Answer:
The length is 15
The width is 21
Step-by-step explanation:
Say the length of the rectangle is x.
Then, the width would be 2x-9.
You can use this to make the equation
x+x+2x-9+2x-9=72
6x-18=72
6x=90
x=15
2x-9=30-9=21
Therefore,
The length is 15
The width is 21
given 2x - 9y - 12 = 0, express 5x - 4y + 7 = 0 in terms of x only
Answers
Answer:
\(4 \frac{1}{9}x\) + \(12\frac{1}{3}\) = 0
Step-by-step explanation:
Based on 2x - 9y - 12 = 0
-9y = 12 - 2x
9y = -12 + 2x
y = \(-1\frac{1}{3} + \frac{2}{9} x\)
Therefore...
5x - 4y + 7 = 0
5x - 4(\(-1\frac{1}{3} + \frac{2}{9} x\)) + 7 = 0
5x + \(5\frac{1}{3}\) - \(\frac{8}{9} x\) + 7 = 0
\(4 \frac{1}{9}x\) + \(12\frac{1}{3}\) = 0
Which of the following statements is true? 642 is not divisible by 3 or 9 642 is divisible by 3 but not by 9 642 is divisible by 9 but not by 3 642 is divisible by 3 and 9
I NEED ANSWER NOW
Answers
Answer:
642 is divisible by 3 but not by 9
Step-by-step explanation:
642/3
= 214
642 / 9
= 71 remainder 3.
solve attachment EASY
Answers
Answer:
\(x=\frac{-3d-9}{k-d}\)
Step-by-step explanation:
Step 1: Write out equation
d(-3 + x) = kx + 9
Step 2: Distribute
-3d + dx = kx + 9
Step 3: Subtract dx on both sides
-3d = kx - dx + 9
Step 4: Subtract 9 on both sides
-3d - 9 = kx - dx
Step 5: Factor
-3d - 9 = x(k - d)
Step 6: Divide both sides by k - d
\(x=\frac{-3d-9}{k-d}\)
Answer:
Step-by-step explanation:
Step 1: Write out equation
d(-3 + x) = kx + 9
Step 2: Distribute
-3d + dx = kx + 9
Step 3: Subtract dx on both sides
-3d = kx - dx + 9
Step 4: Subtract 9 on both sides
-3d - 9 = kx - dx
Step 5: Factor
-3d - 9 = x(k - d)
Step 6: Divide both sides by k - d
Which of these shapes are rectangles? Choose ALL the correct answers
Answers
Answer:
Bottom two
Step-by-step explanation:
The shapes that are rectangles are the two blue shapes on the right-hand side in the image attached.
What are rectangles?A rectangle is a plane figure that comprises four side sides and it also has four right angles. The opposite sides of a rectangular shape are usually equal.
From the given image, the shapes that exhibit the rectangular shapes are the second and the fourth blue shapes which can be seen on the right-hand side in the image attached.
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Can you list all the properties of a parallelogram ?
Answers
Answer:
1. the interior angle measure of a parallelogram is 360 degrees
2. diagonal of a parallelogram bisect it into two congruent triangles
3. opposite angles of a parallelograms are congruent
4. a parallelogram has two pairs of parallel sides.
5. consecutive angles of a parallelogram are supplementary
Step-by-step explanation:
Gavin is analyzing the success of a newly launched game app. The game takes place on an island that's been overrun with zombies. When a player is on level one of the game, the population of zombies is 50,000. Each time the player advances to a new level, that population grows at a rate of 5%. Answer the questions that follow to continue Gavin’s analysis. Use the initial zombie population and growth rate per level to complete the table and estimate the population at level 5. Round to the nearest whole number, if necessary.
.
Game Level: 1 | 2 | 3 | 4 | 5
Population: 50,000 |
Answers
Answer:
Answer: Level 1 - 50,000
Level 2 - 52,500
Level 3 - 55,125
Level 4 - 57,881
Level 5 - 60,775
Step-by-step explanation:
Level 1 population will be 50,000
Level 2 population will be 52,500
Level 3 population will be 55,125
Level 4 population will be 57,881
Level 5 population will be 60,775
What is a product?
Merging objects and identifying them since one big bunch is done through addition. In arithmetic, addition is the technique of adding two or more integers together. Product can meet are the quantities that are included, and the outcome of the operation, or the final response.
The zombies would be 50,000 * 5% if Gavin were level 1, and 50,000 * (5% * 2) if Gavin were level 2, which would be equivalent to 50,000 * 10%. Gavin calculates the number of zombies by multiplying the player's stage by 5%, which equals 50,000 * 5%x Initial Density of Zombie.
The population of the 2 level is
50000 + (50000 * 5%)
50000 + 2500 = 52500
The population of 3 levels is
52500 + (52500 * 5%)
= 55,125
The population of 4 levels is
55,125 + (55,125 * 5% )
= 57,881
The population of 5 level is
57,881 + ( 57,881 + 5%)
= 60,775
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A map has a scale of 1 cm = 30 km . If two cities are 11 cm apart on the map, what is the actual distance between the two cities to the nearest tenth of a km !
Answers
Lale is mixing together some fertilizer. The instructions say to mix 20 liters of water with 5 liters of liquid fertilizer.
How many liters of water should Lale mix with 1 liter of liquid fertilizer?
O A 4 liters
B. 5 liters
C. 10 liters
D. 15 liters
Answers
Answer:
a. 4 liters of water......
Answer:
20/5 = 4
Step-by-step explanation:
the answer at the pic
In a certain lottery, five different numbers between 1 and 34 inclusive are drawn: These are the winning numbers. To win the lottery, a person must select the correct 5 numbers in any order in which they were drawn: What is the probability of winning? 1/278,256 1/34' 120/33,390,720 1/33,390,720
Answers
Answer:
it is 5/34
Step-by-step explanation:
the number that u list is not clear 4 me so I don't consider the numbers
Fill in the blank with the correct response.
What is the scale factor?
3
S
R
ARST - AMNO
5.5 T
6
N
M
X
O
Answers
The scale factor of the dilation of the triangles is 2
What is the scale factor of the dilation?From the question, we have the following parameters that can be used in our computation:
The similar triangles
The scale factor of the dilation is the division of the corresponding sides
So, we have
Scale factor = 6/3
When evaluated, we have
scale factor = 2
Hence the scale factor is 2
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PLS HELP 100 PTS
If u could help me with a that would be great TYSM
Answers
Answer:
a. 1.5
b 1.6 or 1.7
c. 90
Step-by-step explanation:
a. the initial height is 1.5 m (x=0)
b. the maximum height occurs at x = 20, probably 1.6 or 1.7 m
c. the arrows reaches 90 m when it lands (y=0)
hope this helps.
Work the problem using the three-step method. Show your work.
Aunt Mary is 6 times as old as Jane. If Aunt Mary is 72 years old, how old is Jane?
Answers
Answer:
12
Step-by-step explanation:
Im very sorry if it is wrong. I do not know any 3 step method.
Jane needs $150 for the hot air balloon ride. She already has $45 and she can earn the rest by working 12 hours at her job. If h represents her hourly earnings, which of the following equations can be solved to find
Jane's hourly earnings? Circle two correct equations.
150 = 12h
12 = 150 - h
150 = 45 + 12h
150 + 45 = 12h
150 = 12h + 45
Answers
Answer:
C and E
Step-by-step explanation:
C and E are the only ones that are the same and represent the excerpt
Hope this help s plz mark brainliest if correct :D
Answer:
the last answer and the 3rd one
Step-by-step explanation:
use the kkt
Use the method of steepest ascent to approximate the solution to max z = -(x₁ - 3)² - (x₂ - 2)² s. t. (x₁, x₂) E R²
Answers
To approximate the solution and maximize the given objective function we need to find the steepest ascent direction and iteratively update the values of x₁ and x₂ to approach the maximum value of z.
The method of steepest ascent involves finding the direction that leads to the maximum increase in the objective function and updating the values of the decision variables accordingly. In this case, we aim to maximize the objective function z = -(x₁ - 3)² - (x₂ - 2)².
To find the steepest ascent direction, we can take the gradient of the objective function with respect to x₁ and x₂. The gradient represents the direction of the steepest increase in the objective function. In this case, the gradient is given by (∂z/∂x₁, ∂z/∂x₂) = (-2(x₁ - 3), -2(x₂ - 2)).
Starting with initial values for x₁ and x₂, we can update their values iteratively by adding a fraction of the gradient to each variable. The fraction determines the step size or learning rate and should be chosen carefully to ensure convergence to the maximum value of z.
By repeatedly updating the values of x₁ and x₂ in the direction of steepest ascent, we can approach the solution that maximizes the objective function z. The process continues until convergence is achieved or a predefined stopping criterion is met.
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Sophie uses a scale to weight a large stone that she found. Then, she weights a handful of smaller rocks that are 2 pounds each. The equation y=2x+z describes the weight of the stone and rocks (in pounds). what does the variable z represent in this equation? A. the number of smaller rocks B. the weight of the smaller rocks C. the weight of the large stone D. the combined weight of the large stone and small rocks