Answer:
x - 9y = -45
Step-by-step explanation:
y = 1/9 x + 5 Multiply all the way through by 9 to clear the fraction
9y = x + 45 -9y from both sides
0 = x - 9y + 45 Subtract 45 from both sides
-45 = x - 9y You can rewrite
x - 9y = --45
The curvature of a circle is inversely proportional to its radius. What is the exact circumference of a circle with one-third the curvature of a circle of radius 1?
The circumference of a circle with one-third the curvature of a circle of radius 1 is 18.85 units
What is circumference ?
The perimeter of a circle is known as its circumference. It is the length of the circle's whole perimeter. The diameter of a circle and the constant are multiplied to get the circumference of the circle. This measurement of a circle's circumference is necessary for someone to cross a circular park or for a circle-shaped table to have a border. The units of the circumference are the same as the units of length and it is a linear value.
If a circle has a radius of 1,
the curvature is inversely proportional to this
So, the curvature= 1
A circle with a curvature of 1/3 :
radius=3
Thus, the circumference of the circle = 2 *π * radius
= 2*π * 3
= 6π
≈ 18.85 units
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lmjnhnlknlkjnlijknlkm
Answer:
Step-by-step explanation:
A rental car agency charges $160 per week plus $0.25 per mile to
rent a car. How many miles can you travel in one week for $335?
The number of miles travelled by the family in one week is 700 miles
How to determine the number of miles travelledFrom the question, we have the following parameters that can be used in our computation:
Charges per week = $160
Charges per mile = $0.25
Total charges = $335
The above parameters mean that
Total charges = Charges per week + Charges per mile x Number of miles
Substitute the known values in the above equation, so, we have the following representation
160 + 0.25 * Number of miles = 335
This gives
0.25 * Number of miles = 175
Multiply both sides by 4
Number of miles = 700
Hence, the number of miles is 700
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The half-life of a drug in the bloodstream is 14 hours. What fraction of the original drug dose remains in 36 hours? in 72 hours?
What fraction of the original drug dose remains in 36 hours?
(Do not round until the final answer. Then round to the nearest hundredth as needed.)
16.82 % and 2.83% of the original drug dose remain in 36 hours and 72 hours respectively.
What is half-life?
Half-life is a characteristic unit for the exponential decay equation and is constant across the lifespan of an exponentially decaying quantity.
Given, the half-life of a drug(h) = 14 hours
The first condition, time duration (t) = 36 hours
Then, the half-life of the substance can be calculated by:
[tex]A = A_{0} * (1/2)^{\frac{t}{h} }[/tex]
or, [tex]A = A_{0} * (1/2)^{\frac{36}{14} }\\A = A_{0} * (0.1682)\\[/tex]
16.82 % of the original drug dose remains in 36 hours
Hence, 16.82 % of the original drug dose remains in 36 hours
The second condition, time duration (t) = 72 hours
Then, the half-life of the substance can be calculated by:
[tex]A = A_{0} * (1/2)^{\frac{t}{h} }[/tex]
[tex]A = A_{0} * (1/2)^{\frac{72}{14} }\\A = A_{0} * (0.0283)\\[/tex]
2.83 % of the original drug dose remains in 72 hours
Hence, 2.83 % of the original drug dose remains in 72 hours
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An adult harbor seal can eat food up to 6% of its body weight. If an adult harbor seal eats 18 pounds of food, how much does the adult harbor seal weigh? Use any strategy to solve.
The weight of the adult harbor seal is 300 pounds.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
An adult harbor seal can eat food up to 6% of its body weight.
An adult harbor seal eats 18 pounds of food
We need to find the adult harbor seal weigh
Let x be the weigh of food
6% of x= 18 pounds
Convert 6% to decimal
6/100=0.06
0.06x=18
Divide both sides by 0.06
x=300
Hence, the weight of the adult harbor seal is 300 pounds.
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what property is illustrated below
-5x + 2 =2 -5x
Answer:
distributive property
Can someone solve this please? Where to put the points
Answer:
(40, 100) (x,y) Also, In the image below
Step-by-step explanation:
I used this website to do this. It is a very accurate website I used it all the time in algebra. So it should be right
I hope this helps!!!
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5/6 over -2/3 minus 1.25 over 1/4 write your answer in simplest form.....please help
Answer: -1.5625
Step-by-step explanation:
5/6/-2/3 - 1.25/1/4 = -25/16 = -1 9/16 = -1.5625
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Answer:
17.3
Step-by-step explanation:
A bicyclist travels the first 800 m of a trip 1.4 minutes, the next 500 m in 1.6 minutes, and finishes up the final 1200 m in 2 minutes.
What is the total distance traveled on the bicycle?
______ meters
What is the total time the bike traveled?
_______ minutes
Find the average speed (in meters/min) of the bicyclist for this trip. _______ meters
The total distance traveled on the bicycle is 2500m
The total time the bike traveled is 19.4 minutes.
The average speed (in meters/min) of the bicyclist for this trip is 128.9 m/minutes.
What is speed?Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed.
The total distance traveled on the bicycle will be:
= 800 + 500 + 1200
= 2500m
The total time the bike traveled will be:
= 1.4 + 16 + 2
= 19.4 minutes
Speed = Distance / Time
= 2500 / 19.4
= 128.9 meters per minute
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.Ansel wants to borrow $10,000 from the Hampton County Bank. They offered him a 6-year loan with an APR of 6.35 %. How much will he pay in interest over the life of the loan ?
Ansel has to pay an interest of $167.4 per months for the the life of the loan to the Hampton County Bank.
Explain the term APR?That yearly interest amount you'll spend if you have a balance off your credit card is referred to as the annual percentage rate (APR). Some credit cards feature variable APRs, which means that over time, your rate may go up or down. Your annual percentage rate, which is determined by the particulars of your loan and includes the interest rate as well as additional costs like borrower and mortgages broker fees, is often greater than your interest rate.The formula for the monthly installments are-
M = P(r/12)(1 + r)∧12t / (1 + r)∧12t - 1
Put the values;
Principal P =$10,000.
Rate of interest r = 6.35%
Time t = 6 years 72 months
M = 10,000(0.0635/12)(1 + 0.0635)∧72 / (1 + 0.0635)∧72 - 1
M = $167.4
Thus, Ansel has to pay an interest of $167.4 per month for the the life of the loan to Hampton County Bank.
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What two ways could you describe the shape pattern below?
ΔΟΔΟΔΟ
Answer:
The pattern is a repeated triangle and circle.
So, the next shape would be a triangle and a circle.
Step-by-step explanation:
what is the value of x?
Options: 4, 3, 5, 2
Answer: X = 3
Step-by-step explanation:
3x + 6 = 15
6x - 3 = 15
5 times 3 = 15
selling price of car if rs 50,000 , profit is 10% and cost price of car will be ?
Answer:
Rs 45,000
Step-by-step explanation:
The profit is the difference between the selling price and the cost price of the car. In this case, the profit is 10% of the selling price, or 10% * Rs 50,000 = Rs 5,000.
Therefore, the cost price of the car is the selling price minus the profit, or Rs 50,000 - Rs 5,000 = Rs 45,000. This is the amount that the seller paid for the car, before adding the profit.
A town's population is 47,750 . About 100 people move out of the town each month. Each month,175 people on average move into town. A nearby town has a population of 50,500. It has no one moving in and an average of people moving away every month. In about how many months will the populations of the towns be equal? Write an equation to model the situation. Then solve the equation and answer the question.
Which equation models the situation?
The equation that models the given situation is; 175x - 100x + 47750 = 50500 - 200x
The number of months it will take the populations to be equal is 10 months
How to model the equation of the word problem?Let us suppose after x months the population of both town's will be equal.
From the given directions, we have;
The population of the first town after x months is given by;
175x - 100x + 47750
The population of the second town after x months is given by;
50500 - 200x
Now, In order to the population of the both town's to be equal, we have;
175x - 100x + 47750 = 50500 - 200x
275x = 50500 - 47750
x = 2750/275
x = 10
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Two ocean beaches are being affected by erosion. The table shows the width, in feet, of each beach at high tide measured where 1995 is represented by year 0.
Year number Western Beach width (in feet) Dunes Beach width (in feet)
0 100 20
5 90 45
10 80 70
11 78 75
12 76 80
15 70 95
Describe the patterns shown by the erosion data measurements shown for each of the beaches in the table.
Between which years will the beaches have approximately the same width?
Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width?
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If A is the center of dilation how can we find which point is the dilation of b?
Answer:
C is point of the dilation with a scale factor to 2
D is the point of the dilation with a scale factor of 1/3
Step-by-step explanation:
C is twice as far from A as B.
D is 1/3 the distance from A when compared to B
The radius of a circular play ground is 77 m. Calculate the distance covered by a runner in 5 complete rounds around the ground.
Answer:
Step-by-step explanation:
77*5=385
The table shows a proportional relationship. x 15 9 21 y 5 3 7 Describe what the graph of the proportional relationship would look like. A line passes through the point (0, 0) and continues through the point (15, 5). A line passes through the point (0, 0) and continues through the point (7, 21). A line passes through the point (0, 0) and continues through the point (5, 15). A line passes through the point (0, 0) and continues through the point (3, 9).
The option that describes the graph of the proportional relationship is the option;
A line passes through the point (0, 0) and continues through the point (15, 5).What is a proportional relationship?
A proportional relationship is one in which one variable in the relationship is a constant multiple of the other variable.
The table of values can be presented as follows;
x; 15 9 21
y; 5 3 7
The domain of the function is therefore; 15, 9, 21
The range of the function is therefore; 5, 3, 7
The coordinates of points on the graph of the function is therefore;
(15, 5), (9, 3), (21, 7)
The relationship between the xi and y-values of the function is therefore;
5/15 = 3/9 = 7/21 = 1/3
The constant of proportionality in the relationship is 1/3
The relationship is therefore a proportional relationship.
The characteristics of the graph of a proportional relationship includes;
The graph passes through the origin, (0, 0).
The correct option that therefore describes the graph is the option;
A line passes through the point (0, 0), and continues through the point (15, 5)
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Solve the equation without using a calculator
[tex]\bf\\x^{x^2-2x+1}=2x+1[/tex]
The value of the variable x in the equation xˣ²⁻²ˣ⁺¹ = 2x + 1 is 1 + √2
Exponential EquationsAn equation is a mathematical statement that shows that two mathematical expressions are equal.
An equation combines two expressions connected by an equal sign. These two expressions on either side of the equals sign are called the “left-hand side” and “right-hand side” of the equation. We generally assume the right-hand side of an equation is zero.
Basically, an equation is a statement that equate or says two expressions are equal to one another.
The problem given may be assumed as an exponential equation
xˣ²⁻²ˣ⁺¹ = 2x + 1
Solving for x by isolating the variable;
x = 1 + √2
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Answer:
x = 1 ±√2
Step-by-step explanation:
You want to solve the exponential equation ...
x^(x² -2x +1) = 2x +1
without using a calculator.
GuessThere are no algebraic methods for solving such an equation.
We can solve quadratic equations, so we can guess that the exponent of x is 2:
x² -2x +1 = 2
x² -2x -1 = 0
Using 2 as an exponent, the given equation becomes ...
x² = 2x +1 . . . . . . . exponent on the left is 2
x² -2x -1 = 0
That is, the exponent being 2 is consistent with the requirements on x.
QuadraticThe solution to the quadratic can be found using the quadratic formula:
x² -2x -1 = 0
x = (-(-2) ±√((-2)² -4(1)(-1))/(2(1)) = (2±2√2)/2
x = 1±√2
Either of these values will make the exponent of x be 2, so both are solutions to the equation. The negative solution is not found by the graphing calculator (attached).
simplify the expression -3(x + 9) by either combining like terms of distributive property
Answer:
-3x+-27
-3 multiplied by x=-3x
-3x9=-27
sorority has 35 members, 25 of whom are full members and 10 are pledges. Two persons are selected at random from the membership list of the sorority. Find the requested probabilities The second person selected is a pledge if the first person selected was a full member.
(a) The probability that the first person selected is a pledge is; 10/35
(b) The probability that the first person selected is not a pledge is; 25/35
(c) The probability that the second person selected is a pledge if the first person selected was also a pledge is; 9/34
How to find the probability of selection?We are given;
Total number of members in the Sorority = 35
Number of full members = 25
Number of members that are pledges = 10
Formula for probability is;
Probability = Number of Favorable Outcomes / Total Number of Outcomes.
1) Probability that the first person selected is a pledge = number of pledges/total number of members = 10/35
2) Probability that the first person selected is not a pledge = 1 - (Probability that the first person selected is a pledge)
= 1 - 10/35 = 25/35
3) If the first person selected was also a pledge, then for the second pledge, one pledge is out, so we have 9 pledges in 34 people.
P = number of pledges / total = 9/34
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Complete question is;
A sorority has 35 members, 25 of whom are full members and 10 are pledges. Two persons are selected at random from the membership list of the sorority. Find the requested probabilities. (Enter the probabilities as fractions.)
(a) The first person selected is a pledge.
(b) The first person selected is not a pledge.
(c) The second person selected is a pledge if the first person selected was also a pledge.
about how long is a real bed in real life
Answer:
All beds come in different shapes and sizes but for example a queen sized mattress is 60” x 80”
Step-by-step explanation:
John read the first 114 pages of a novella, this was 3 pages less than 1/3
Answer:
351 pages
Step-by-step explanation:
In order to figure this out, we need to know what 114 plus 3 is.
114 + 3 = 117
Now that we have 117, we know that this is equal to 1/3 of the book.
In order to find out the total pages in this book, we need to multiply 117 by 3.
117 × 3 = 351
There are 351 pages in Johns book.
y = 3x + 2
y = 2x + 2
One solution
No solution
Infinite solutions
Answer:
The answer would be One solution.
Step-by-step explanation:
Solving by substitution.y=3x+2;y=2x+2
Step: Solve y=3x+2 for y:
y=3x+2
Step: Substitute 3x+2 for y in y=2x+2:
y=2x+2
3x+2=2x+2
3x+2+−2x=2x+2+−2x(Add -2x to both sides)
x+2=2
x+2+−2=2+−2(Add -2 to both sides)
x=0
Step: Substitute 0 for x in y=3x+2:
y=3x+2
y=(3)(0)+2
y=2(Simplify both sides of the equation)
Answer:
x=0 and y=2
If it was no solution you would not be able to solve. If it was infinite then there would be infinite solutions, but there is not so One Solution is the answer.
The width of a rectangle is 4 more than the length. If the perimeter is 36 cm, ind the dimensions (length and width) of the rectangle.
Answer with step-by-step explanation:
Let the width of the rectangle be x.
Given that,
length ⇒ 4
width ⇒ x + 4 ( Because, the rectangle's width is 4 more than the length.)
Perimeter ⇒ 36cm
The formula to find the perimeter of rectangle is:
P = 2 ( l + w )
Now to find the value of x replace P, l & w with 36, 4 & (x + 4) with respectively.
P = 2 ( l + w )
36 = 2 ( 4 + x + 4 )
36 = 2 ( x + 8 )
Solve the brackets.
36 = 2x + 16
Substract 16 from both sides.
36 - 16 = 2x
20 = 2x
Divide both sides by 2.
10 = x
And now let us find the exact dimensions of the rectangle.
Length = 4 cm
Width = x + 4 = 10 + 4 = 14 cm
A diver starts out at 342 feet below the surface (or -342 feet). She then swims upward 224 feet. Use a signed number to represent the diver's current depth.
Answer:
-118 feet
Step-by-step explanation:
[tex]-342+224=-118[/tex]
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Given the inequality 4x ≤ 28, which of the following is a solution that makes the inequality true?
For the inequality 4x ≤ 28 the solution that makes the inequality true will be x≤7.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
It is given that the inequality is 4x ≤ 28.
Now that the equation has been simplified, we obtain both sides of the inequality equation, divide by 4, and we obtain
x ≤ 7
As a result, x must be less than or equal to 7.
The requirement for x is satisfied by any numbers that are less than or equal to 7.
Thus, for the inequality 4x ≤ 28 the solution that makes the inequality true will be x≤7.
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Answer:
a
Step-by-step explanation:
7
(LOTS OF POINTS)
4. (Multiple Choice) In the figure shown, which of the following is the greatest?
A. a
B. b
C. c
D. d
E: e
Answer:
The answer is e
Step-by-step explanation:
Solve the system of quadratic equations, explain each step if possible:
The solutions to the system of equations formed by the linear equation 9 · x + 9 · y - 79 = 0 and the quadratic equation x² + 5 · x - y - 4 = 0 are (x₁, y₁) = (5 / 3, 64 / 9) and (x₂, y₂) = (- 23 / 3, 148 / 9).
How to solve a system of equations
Herein we find a system of equations formed by a linear equation and a quadratic equation. This system must be resolved by means of algebra properties. First, write the system of equations:
9 · x + 9 · y - 79 = 0
x² + 5 · x - y - 4 = 0
Second, clear the variable y in the first equation:
9 · x + 9 · y - 79 = 0
9 · y = 79 - 9 · x
y = 79 / 9 - x
Third, substitute y on the second equation:
x² + 5 · x - (79 / 9 - x) - 4 = 0
x² + 6 · x - 115 / 9 = 0
Fourth, use the quadratic equation to find the solutions of x:
x₁ = 5 / 3, x₂ = - 23 / 3
Fifth, calculate the solutions of y:
y₁ = 79 / 9 - x₁
y₁ = 64 / 9
y₂ = 79 / 9 - x₂
y₂ = 148 / 9
The solutions are (x₁, y₁) = (5 / 3, 64 / 9) and (x₂, y₂) = (- 23 / 3, 148 / 9).
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