They both represent the same information - for every 96 action/ adventure movies, there are 38 sci-fi movies to stream. 96:38 and 38:96 are both equivalent ratios because they are inverse proportions of each other.
What is the inverse ?Inverse is the opposite of something. It can be used to describe the opposite of a mathematical operation, such as taking the reciprocal of a number, or the opposite of a logical statement, such as negating the statement. It can also be used to describe the opposite of an action, such as reversing a direction or undoing an action. Inverse can also be used to describe the opposite of an effect, such as the opposite of a physical reaction or the opposite of an emotional response. Inverse relationships can often be seen in nature, such as how a decrease in temperature results in an increase in pressure, or how an increase in the amount of light results in a decrease in the number of insects in a certain area.
a:
1. 96:38
2. 38:96
3. (96/38):1
b: 96:38 and 38:96 are both equivalent ratios because they are inverse proportions of each other. They both represent the same information - for every 96 action/adventure movies, there are 38 sci-fi movies to stream. The only difference is the order of the numbers, but the ratio remains the same.
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from a group of 8 men and 7 women, 5 persons are to be selected to form a committee so that at least 3 men are there on the committee. in how many ways can it be done?
5 persons are to be selected to form a committee so that at least 3 men are there on the committee, in 3192 ways the committee can be formed.
Combinations are decisions that are made by choosing some or all of a group of objects, regardless of how they are arranged. the variety of n distinct combinations, each taken r at a time,
We may have four males and one lady or three men and two women (5 men only).
∴ Required number of ways = (⁸C₃ x ⁷C₂) + (⁸C₄ x ⁷C₁) + ⁸C₅
= [tex]\frac{8*7*6}{3*2*1} *\frac{7*6}{2*1} + \frac{8*7*6*5*4}{4*3*2} *\frac{7}{1} + \frac{8*7*6}{3*2}[/tex]
= 1176 + 1960 + 56
= 3192
Therefore, at least 3 men are there on the committee can be formed 3192 times.
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How do you multiply fractions with a common denominator?
When multiplying fractions, multiply the numerator (top number), then the denominator (bottom number), and finally reduce to the lowest term if necessary.
Fractions are subsets of wholes. They are made up of a numerator (the number on top) and a denominator (the number on the bottom). The numerator represents the number of parts, while the denominator represents the total number of available parts.
To multiply two fractions, follow these three simple steps:
Step 1: Multiply the numerators of each fraction by themselves (the numbers on top). The answer's numerator is the result.
Step 2: Add the denominators of each fraction together (the numbers on the bottom). The answer's denominator is the result.
Step 3: Simplify or reduce your response.
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A store employee creates a display of gymnastics mats priced at $73 apiece. The store paid $50 for each gymnastics mat. What percentage is the mark-up?
Rephrasing a question I had because people keep misunderstanding it
write the equation 8-2x= 3(y+1)^2 in x-h=a(y-k)^2 form
Step-by-step explanation:
[tex](8 - 2x) = 3(y + 1) {}^{2} [/tex]
If we factor out -2
[tex] - 2( - 4 + x) = 3(y + 1) {}^{2} [/tex]
[tex](x - 4) = - 1.5(y + 1) {}^{2} [/tex]
Disclaimer: this is a weird question because they would usually have you isolate the quadratic(the term being squared) but this is the answer is you're form you asked about
The vertex of this parabola is (4,-1)
Convert to the unit in brackets 1497 ml
(cm³)
After conversion, 1497 milliliters (ml) is equal to 1497 cubic centimeters (cm³) because 1 milliliter (ml) is equal to 1 cubic centimeter (cm³).
The units of volume, such as milliliters (ml) and cubic centimeters (cm³), measure the amount of space occupied by a substance. A milliliter (ml) is a unit of volume that is commonly used to measure small quantities of liquids. A cubic centimeter (cm³) is a unit of volume that is used to measure the volume of solid objects or substances.
One milliliter (ml) is equal to one cubic centimeter (cm³). This means that one milliliter of a substance takes up the same amount of space as one cubic centimeter of the same substance.
So, to convert 1497 milliliters (ml) to cubic centimeters (cm³), we simply use the conversion factor of 1 ml = 1 cm³:
1497 ml = 1497 * 1 cm³ = 1497 cm³
Therefore, 1497 milliliters (ml) is equal to 1497 cubic centimeters (cm³).
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The width of a rectangle is 4.25y-7.5 feet and its length is 7.5y+8 feet. Find the perimeter of the rectangle.
The perimeter of the rectangle is (23.5y + 1) feet.
The perimeter of the rectangle formula:
The perimeter = the width + the length + the width + the length
The perimeter = 2 × (the width + the length)
The perimeter = 2 × ((4.25y - 7.5) + (7.5y + 8))
The perimeter = 2 × ((4.25y + 7.5y) + (- 7.5 + 8)
The perimeter = 2 × (11.75y + 0.5)
The perimeter = 23.5y + 1
So, the perimeter of the rectangle is (23.5y + 1) feet.
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hassan built a fence around a square yard. it took 48 m 2 48 m 2 48, start text, space, m, end text, squared of lumber to build the fence. the fence is 1.5 1.51, point, 5 meters tall. what is the area of the yard inside the fence?
The fence surrounds a square yard with an area of 64 square meters. We first have to find length of fence and then multiply it by itself.
Given that it took 48 square meters of lumber to build the fence, and the fence is 1.5 meters tall, we can calculate the area of the yard inside the fence. To do this, we need to determine the total length of the fence. If we assume that the fence is built around a square yard, then the length of each side of the yard will be equal to the total length of the fence divided by 4.
Let's call the length of each side of the yard x. Then, the area of the yard inside the fence is x * x, or x^2. The total length of the fence is 4 * x. Since the fence is 1.5 meters tall, the total area of the lumber used to build the fence is 4 * x * 1.5, or 6x. This is equal to 48 square meters, so we have the equation:
6x = 48.
Solving for x,
x = 8.
Therefore, each side of the yard is 8 meters long.
Area of the yard inside the fence = 8 * 8 = 64 square meters.
This means that the fence surrounds a square yard with an area of 64 square meters.
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Jack want to buy a coat that 74.95. the sales tax rate in the city is 6 1/2% what is the total cost
Answer:
$79.82 (to 2 d.p.)
Step-by-step explanation:
100%=$74.95
1%=$74.95÷100
=$0.7495
100%+6.5%=106.5%
106.5%=$0.7495×106.5
=$79.82 (to 2 d.p.)
given that the augmented matrix in row-reduced form below is equivalent to the augmented matrix of a system of linear equations. determine whether the system has a solution and find the solution(s) to the system, if they exist.
We have solution as:
z =z and y -8-z
The solution set is
x=9, y = -8-z, w = 1, z = z
Matrix:Matrix is an arrangement of numbers into rows and columns. Make your first introduction with matrices and learn about their dimensions and elements. A matrix is a rectangular arrangement of numbers into rows and columns. For example, matrix A has two rows and three columns.
The augmented matrix in row-reduced form below is equivalent to the augmented matrix of a system of linear equations.
[ 1 0 0 0 | -9 ]
[ 0 1 1 0 | -8 ]
[ 0 0 0 1 | 1 ]
We find that this is a rectangular matrix 3 rows and 4 columns
i.e. the variables are four but independent equations are only 3.
So only parametric equations can be found out
First row gives x = -9
Last row gives w = 1
II row gives y + z =-8 and we do not have any other equation in y or z
Hence we have solution as:
z =z and y -8-z
The solution set is
x=9, y =-8-z, w =1, z=z
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The given question is incomplete, complete question is :
Given that the augmented matrix in row-reduced form below is equivalent to the augmented matrix of a system of linear equations. Determine whether the system has a solution and find the solution(s) to the system, if they exist.
[ 1 0 0 0 | -9 ]
[ 0 1 1 0 | -8 ]
[ 0 0 0 1 | 1 ]
A) x=-9, y=-8, z=-8, w=1
B) No solution.
C) x=-9, y=-8, z=1
D) x=-9, y=-8+z, w=1, z=any real number
E) z=-9, y=-8-z, w=1, z=any real number
F) None of the above.
a committee of congressmen will be selected from a group of democrats and republicans. find the number of ways of obtaining exactly one .
The number of ways of obtaining exactly one Democrat is 504
We are choosing 6 committee members, and exactly 1 of them must be a Democrat, which leaves 5 members to be selected from the Republicans. The number of ways to select 5 Republicans from 9 Republicans is 9 choose 5, which is 9! / (5! * (9-5)!).
Therefore, the total number of ways to form a committee with exactly 1 Democrat and 5 Republicans is 4 * (9 choose 5) = 4 * 126 = 504. or
There are a total of 13 members (4 Democrats and 9 Republicans), so the number of combinations that can be chosen is 13C6, or 1716. Since we are looking for a committee with exactly one Democrat, we need to subtract the total number of combinations with no Democrats (9C6, or 84) from the total number of combinations, giving us 1716-84 = 504 ways of obtaining exactly one Democrat.
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Your question is incomplete but probably the full question was:
A committee of six Congressmen will be selected from a group of four Democrats and nine Republicans. What is the number of ways of obtaining exactly one Democrat?
write the weight of caribou cows in kilograms as a prime factorization
Answer: Female caribou have a wide range of weight. They can average anywhere from 51 (3 x 17) to 156 (2 x 2 x 3 x 13) kg.
Step-by-step explanation:
what information do you need to be given to be able to use trig function to solve for a missing side length of a right triangle?
Here is a point on a circle centered (0,0) at .
Which equation defines the circle?
The equation of circle is,
⇒ x² + y² = 100
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
Here is a point (6, 8) on a circle centered (0,0) at.
Now, Distance between the point (6, 8) and (0, 0) is,
⇒ D = √(6 - 0)² + (8 - 0)²
⇒ D = √36 + 64
⇒ D = √100
⇒ D = 10
We know that;
Distance between the point (6, 8) and (0, 0) is the radius of circle.
And, The equation of circle is,
⇒ (x - a)² + (y - b)² = r²
Where, (a, b) is center of circle and r is radius of circle.
Here, Center of circle = (0, 0)
And, Radius of circle = 10
So, We get;
The equation of circle is,
⇒ (x - a)² + (y - b)² = r²
⇒ (x - 0)² + (y - 0)² = 10²
⇒ x² + y² = 100
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Matthew signed up for a streaming music service that costs $14 per moilth. The service allows Matthew to listen to unlimited music, but if he wants to download songs for offline listening, the service charges $1.50 per song. How much total money would Matthew have to pay in a month in which he downloaded 15 songs? How much would he have to pay if he downloaded s songs?
Answer:p-by-step explanation:
15 x$1.50 is $22.50 then add that to the monthly fee of $14.00 for a total of $36.50
3. Zachary earned $4, 236 in August as a salesman at the racetrack. His earnings include his monthly salary of $700 and commission. If Zachary's sales totaled $10, 654, what is his rate of commission?
-approximately 30.6%
-approximately 28.4%
-approximately 29.8%
-approximately 33.2%
Answer:
approximately 33.2%
Step-by-step explanation:
Find Zachary's commission by subtracting his basic salary from total monthly earnings.
Commission = 4236 - 700
= $ 3536
[tex]\sf rate \ of \ commission = \dfrac{commission}{total \ sales}*100[/tex]
[tex]\sf = \dfrac{3536}{10654}*100\\\\ = 33.19 \%\\ = 33.2 \%[/tex]
what is the value of x if 10 % of x is equal to x-405
Answer:
-4050
Step-by-step explanation:
you have to do inverse operation
so divide by 10 and times by 100
you can test it out by taking 10 percent of -4050
by dividing it by 100 and times by 10.
the answer comes out as -405
What is the equation of the line that passes through thé point (-1, 3) and has a
slope of -3?
The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the equation of the line that passes through the point (-1, 3) and has a slope of -3, we can use the point-slope form of a line: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.
Substituting the given values, we get: y - 3 = -3(x - (-1))
Expanding the right side, we get: y - 3 = -3x + 3
Adding 3 to both sides, we get: y = -3x + 6
So the equation of the line that passes through the point (-1, 3) and has a slope of -3 is y = -3x + 6.
Hope this helps,
- Jeron :- )
Answer: y=-3x+6
Step-by-step explanation:
The equation for slope intercept form is y=mx+b, and since you are given your y and x values from the point (-1, 3), you can plug those values into it. You are also given your slope of -3, and since m is your slope value, you would plug the -3 in as your m.
After you plug in your given values from the problem, you should should get 3 = -1 (3) + b.
Then, you isolate the b. Multiply the -1 and 3 to get -3.
3 = -1 (3) + b
3 = -3 + b
Next, add the 3 to both sides of the equation, and you should be left with b=6.
3 = -3 + b
+3 +3
--------------
6 = 0 + b
6 = b
Finally, you re-write the slope intercept equation with the y-intercept (b value) you just found along with the slope of -3 given by the problem to get y=-3+6.
Simplify
Sin A(cos A + sin A tan A)
The equation be Sin A(cos A + sin A tan A) then the trigonometric identities be tan (A).
What is meant by trigonometric identities?Trigonometric Identities are equality conditions that apply to all values of the equation's variables and which require trigonometry functions. There are numerous unique trigonometric identities that involve both the side length and angle of a triangle.
Trigonometry equations known as trig identities are used frequently to solve trigonometry and geometry problems and comprehend a variety of mathematical facts. Understanding and remembering fundamental mathematical concepts and resolving a variety of math issues are made easier by having a solid understanding of key trig identities.
Let the equation be Sin A(cos A + sin A tan A)
Express with sin, cos
[tex]$=\frac{\left(\cos ^2(A)+\sin ^2(A)\right) \sin (A)}{\cos (A)}$$[/tex]
Rewrite using trig identities
= tan (A)
Therefore, the equation be Sin A(cos A + sin A tan A) then the trigonometric identities be tan (A).
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suppose a researcher describes the age, race, and gender distributions for people who are charged with shoplifting. the unit of analysis is
The unit of analysis that supposed to use when researcher describes the age, race, and gender distributions for people who are charged with shoplifting is called individuals.
The entity that frames what is being investigated in a study, or the entity being studied as a whole is known as the unit of analysis. At the macro level of social science study, the state is the most frequently used analytical unit that is regarded as a society. Groups, organizations, and institutions are frequent observational units at the meso level, while individuals are the unit of observation at the micro level.
The individual unit of analysis could be either a human or an animal. A group might be made up of a single person or a number of people who communicate with one another. For instance, if we are interested in examining people's shopping behaviors, their learning outcomes, or their views about new technology, then the individual is the unit of analysis that we should use.
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Off track biking charges an hourly rate for mountain bike lessons and adds a charge of $100 for insurance. The overvalued cost (C) is represented by the formula, C=40h + 100 where h is the number of hours of lessons. Ben has 7 hours of lessons with off track biking.
How much does he pay?
Answer:
Step-by-step explanation:
If Ben has 7 hours of lessons with Off Track Biking, we can find the total cost (C) using the formula:
C = 40h + 100
where h is the number of hours of lessons. Substituting h = 7, we get:
C = 40(7) + 100
C = 280 + 100
C = 380
Therefore, Ben pays $380 in total for his 7 hours of lessons with Off Track Biking.
for the figures below assume they are made of semicircle quarter circles and squares for each shape find the area and the perimeter. Give your answers as a completely simplified exact value in terms of pie (no approximations)
Thank you
The area of the combined figure is 98.64 sq cm and the perimeter of the combined figure is 91.88 cm.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
What are the area and perimeter of a rectangle?
We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know, The area of a triangle is (1/2)×base ×height and the area of the semicircle is (1/2)πr².
Also, the perimeter of a triangle is the sum of the lengths of all the sides and the perimeter of a semicircle is πr.
From the given figure The right angle triangle is an isosceles therefore, The length of the side BC is also 12 units.
Hence the area is = (1/2)×12×12 = 72 sq cm.
And The area of the semicircle is,
(1/2)×π×(√12² + 12²) sq cm.
= (1/2)×3.14×√(288) sq cm.
= 26.64 sq cm.
Therefore, The total area is (72 + 26.64) sq cm.
= 98.64 sq cm.
And the perimeter is,
= (12 + 12 + 16.97) + (3.14×16.97) cm.
= 91.88 cm.
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Given the equation 3x + y = 6, write a second equation that, together with the first,
will create a system of equations that
(a) has one solution;
(b) has an infinite number of solutions;
(c) has no solution;
(d) has the ordered pair (4, -6) as its only solution.
This system of equations has the ordered pair (4, -6) as its only solution, as the two lines intersect only at that point.
What is the system of equations?
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
To create a system of equations that has one solution, we can write a second equation that intersects with the first equation in exactly one point.
One way to do this is to solve the first equation for y, then substitute the expression for y into a second equation. For example:
3x + y = 6
y = -3x + 6
This system of equations has one solution, as the two lines intersect at exactly one point.
To create a system of equations that has an infinite number of solutions, we can write a second equation that is identical to the first equation:=
3x + y = 6
3x + y = 6
This system of equations has an infinite number of solutions, as the two lines are coincident and overlap exactly.
To create a system of equations that has no solution, we can write a second equation that is parallel to the first equation:
3x + y = 6
3x + y = 8
This system of equations has no solution, as the two lines are parallel and do not intersect.
To create a system of equations that has (4, -6) as its only solution, we can write a second equation that passes through the point (4, -6):
3x + y = 6
y = -3x - 6 + 12
y = -3x + 6
Hence, This system of equations has the ordered pair (4, -6) as its only solution, as the two lines intersect only at that point.
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tyler can type twice as many words wpm as kyla
define variable=
Expression to represent problem=
if kyla can type 3 wpm how many wpm can Tyler type
Answer:
Your answer is: 6 wpm
Step-by-step explanation:
If Tyler types twice as fast as Kyla, you multiply the amount of wpm Kyla writes by 2. 3 multiplied by 2 equals 6. Therefore, Tyler writes 6 wpm.
Element X is a radioactive isotope such that its mass decreases by 8% every year. If an experiment starts out with 600 grams of Element X, write a function to represent the mass of the sample after t years, where the monthly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per month, to the nearest hundredth of a percent.
On solving the provided question we cans ay that the half life of the given exponential growth radioactive isotope will be 3.2894067399 years.
What is exponential growth?The process of quantity growth over time is called exponential growth. occurs when the rate at which a quantity changes instantaneously with time is proportionate to the quantity itself. A data pattern that shows bigger increases with time is known as exponential growth. Compound interest yields exponential rewards in the world of finance. Savings accounts with compound interest sometimes see exponential growth. characterized by an extremely fast exponential growth rate rise (in size or extent). exponentially. The exponential function has the formula f(x)=abx where a and b are positive real values. Sketch exponential functions using the app below for different values of a and b. Describe verbally how modifying a and b changes the graph's form.
Here, Element X starts with 490 grams
After 1 year we have (490 X 0.81 grams) or 396.9 grams
Now, We can solve for half-life by this equation:
Half life = (time X log 2) / log (beginning amount / ending amount)
Half-life = (1 year X 0.30102999566) / log (490 / 396.9)
Half life = (1 year X 0.30102999566) / log (1.2345679012 )
Half life = (0.30102999566) / 0.091514981109
Half-Life = 3.2894067399 years
Thus, the half life of the given exponential growth radioactive isotope will be 3.2894067399 years.
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To get the echo of a positive integer, we write it twice in a row without a space. For example,
the echo of 2023 is 20232023. Is there a positive integer whose echo is a perfect square? If
so, how many such positive integers can you find? If not, explain why not.
Answer: Yes, but it's extremely hard to find
Step-by-step explanation:
The echo number 20222022202220222022 is the perfect square of 4496890281.
What echo number is a perfect square
An echo number has a perfect square if its square root is also a natural number. After some iterations we found that echo number 20222022202220222022 is a perfect square:
The echo number 20222022202220222022 is the perfect square of 4496890281.
Match the exponent expression with it's correct solution.
The correct order for the exponent expression is,
A-3, B-1, C-4, and D-2.
What is Exponential Function?The formula for an exponential function is f (x) = aˣ, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
Given functions to match,
for the functions using property,
aⁿ.aᵇ = aⁿ⁺ᵇ
A; x¹⁸.x¹⁴
x¹⁸.x¹⁴ = x¹⁸⁺¹⁴ = x³²
B: x⁸.x⁵ = x⁸⁺⁵
x⁸.x⁵ = x¹³
C: x³⁵.x⁴⁰ = x³⁵⁺⁴⁰
x³⁵.x⁴⁰ = x⁷⁵
D: x⁴⁵.x² = x⁴⁵⁺²
x⁴⁵.x² = x⁴⁷
Hence correct order is, A-3, B-1, C-4, and D-2.
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Rebecca, Meg, and Kristin drive together for their home to visit their grandparents. Kristen drives 65 miles. Rebecca drives two times as far as Kristin. Then Meg drives twice as far as Kristin and Rebecca combined, which gets them to their grandparents house. How far did Meg drive?
Meg has drive 390 miles to visit Grandma.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are Given Number of miles Kristen drive = 65 miles
Rebecca drives two times as far as Kristin. Then Meg drives twice as far as Kristin and Rebecca combined
This means Number of miles Meg drive is equal to twice the number of miles driven Kristin .
Then equation we get;
Number of miles Meg drive = 2 × Number of miles Kristin drive =
Number of Miles Driven by Rebecca is equal to twice the sum of Number of miles Kristin drive and Number of miles Meg drive.
Then equation we get;
Number of miles Meg drive = 2 × (Number of miles Susie drive + Number of miles Meg drive) =
Hence Meg has drive 390 miles to visit Grandma.
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Greenlings are a group of fish that share common features.
The function
G(×) = -10×€2 +100× +44
What does the variable x represent? Include the units.
The variable x shows fish with common features.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range.
Given:
G(x) = -10x² + 100x +44
Now solving the Quadratic Equation we have
D = √(100)² - 4(-10)(44)
D = √10000 + 1760
D = √11760
D= 108.44
Now, x= -b ± D/2a
x= -100 ± 108.44 /2(-10)
x= -100 ± 108.44 / (-20)
x = -100 + 108.44 / (-20) or x= -100- 108.44 / (-20)
x= -0.422 or x= 10.422
Here x represents the fish with common features.
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I'm looking at data that show the number of new college programs in green studies, and a linear function appears to be a better choice than an exponential function for modeling the number of new college programs from 2005 through 2009.
The table represents the exponential function as f(x) = a(b)^3
What are exponential functions?When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.
Here we have the table:
Year number of new college programs
2005 3
2006 22
2007 27
2008 66
2009 100
Few things that are useful to identify this as an exponential equation are:
f(x) = a(b)^3
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HELPPPPPPPPPPPPPPPPPPPP
Answer:
i wish i knew but try just posting the pictures on the math page and boom
Answer: it should just be (x, -y)
Step-by-step explanation: