The homeowner should go with option 1 for his budget of $40,200 to use complete budget.
What is Quadratic equation?Any equation that can be rearranged in the standard form as is referred to as a quadratic equation (from the Latin quadratus, "square").
ax² + bx + c = 0
where x is a value that is unknown, a, b, and c are numbers that are known, and a is a negative number. The numbers a, b, and c are the equation's coefficients; they are referred to as the constant or free term, the quadratic coefficient, and the linear coefficient, respectively.
Solutions of the equation and roots or zeros of the expression on its left-hand side are the values of x that satisfy the equation. There can only be two solutions to a quadratic equation. One suggests that there is only one solution, which is a double root.
Given a rectangular pool of 35-foot by 20-foot
area of pool = 35 x 20 = 700 sq. foot
and to built a patio around pool of equal width,
budget of patio of $40,200 all amount to be used,
Option 1: Surround the pool with a concrete band of equal width on all sides. The concrete costs $50 per square foot.
the area covered by amount is 40200/50 = 804
let width of patio be x
new length = 35 + x and new breadth = 20 + x
area covered by patio = new area including width - area of pool
new area including width = area covered by patio + area of pool
new area including width = 804 + 700 = 1504
1504 = (35 + x)(20 + x )
1504 = x² + 35x + 20x + 700
x² + 55x - 804 = 0
solving the equation by quadratic formula
x = (-b ± [tex]\sqrt{b^{2} - 4ac }[/tex])/ 2a
where a = 1, b = 55, and c = -804
x = (-55 ± [tex]\sqrt{(55)^{2} - 4*1*(-804) }[/tex])/2
x = (-55 ± √(3025 + 3216))/2
x = (-55 ± 79)/2
taking positive values
x = (-55 + 79)/2 = 12
new length = 35 + 12 = 47 foot
new breadth = 20 + 12 = 32 foot
area covered by patio = (47x32) - (35x20)
area covered by patio = 804 sq. foot
and cost will be 804 x 50 = $40,200
for option 2: Surround the pool with a tile band of equal width on all sides. The tile costs $80 for each square foot tile.
area for patio = 40200/80 = 502.5
since the area is in fraction the cost will come in approximation.
Hence the homeowner should go with option 1 for complete use of budget.
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What is it? I swear I have no idea
By using matrix, it can be calculated that:
[tex]\frac{1}{4}C = \begin{bmatrix}3 & 4 & -5 \\ 1 & -6 & 7\end{bmatrix}[/tex]
What is a matrix?The term "matrix" refers to any configuration of numbers in the form of rows and columns. a collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers.
In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. Solving linear equations is made easier by it. Matrices are incredibly priceless items that are used in a variety of contexts. In addition to mathematical applications, matrices are employed in a wide range of scientific disciplines. Nearly every element of our life uses engineering mathematics.
Here,
[tex]C = \begin{bmatrix} 12 & 16 & -20 \\ 4 & -24 & 28 \end{bmatrix}[/tex]
[tex]\frac{1}{4}C = \begin{bmatrix} 12\times \frac{1}{4} & 16 \times \frac{1}{4} & -20 \times \frac{1}{4} \\ 4 \times \frac{1}{4} & -24 \times \frac{1}{4}& 28 \times \frac{1}{4}\end{bmatrix}\\\\\frac{1}{4}C = \begin{bmatrix}3 & 4 & -5 \\ 1 & -6 & 7\end{bmatrix}[/tex]
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use the mean value theorem to verify that at some time during the first 3 seconds of fall the instataneous velocity equals the average velocity
Verified that during the first 3 seconds of fall the instantaneous velocity equals the average velocity, the time is 1.5 seconds
The height of an object t seconds after it is dropped from a height of 300 meters is
s(t) = -4.9t^2 + 300
The average velocity of object during first 3 seconds
= s(3) - s(0) / 3 - 0
s(3) = -4.9 × (3)^2 + 300
= -44.1 + 300
= 255.9 meters
s(0) = -4.9(0)^2 + 300
s(0) = 300
The average velocity = (255.9 - 300) / 3 - 0
= -44.1 / 3
= -14.7 meter per second
To find instantaneous velocity differentiate the function
= -9.8t
The instantaneous velocity = The average velocity
-9.8t = -14.7
t = -14.7/-9.8
t = 1.5 seconds
Therefore, time is 1.5 seconds
I have answered the question in general, as the given question is incomplete
The complete question is :
The height of an object t seconds after it is dropped from a height of 300 meters is s(t) = -4.9t^2 + 300.
(b) Use the Mean Value Theorem to verify that at some time during the first 3 seconds of fall, the instantaneous velocity equals the average velocity. Find that time.
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An aircraft is flying at altitude H when it begins its descent to an airport runway that is at a horizontal ground distance L from the airplane. Assume that the landing path is described by the cubic polynomial function y=ax3+bx2+cx+d where y(-L)= H and y(0)= 0.a. What is dy\dx at x= 0?b. What is dy\dx at x= -L?
a. [tex]\frac{dy}{dx} \ at \ x=0 \ is \ c.[/tex]
b. [tex]\frac{dy}{dx} \at x=-L \ is \ 3aL^2+2bL+c.[/tex]
a. The derivative of a cubic function
[tex]y=ax^3+bx^2+cx+d[/tex] is [tex]y'=3ax^2+2bx+c[/tex].
Plugging in x=0, we get y'=c. Thus, [tex]\frac{dy}{dx}[/tex] at x=0 is c.
b. Plugging in x=-L, we get [tex]y'=3a(-L)^2+2b(-L)+c[/tex].
Thus, [tex]\frac{dy}{dx}[/tex] at [tex]x=-L \ is\ 3a(-L)^2+2b(-L)+c.[/tex]
A derivative is a financial instrument that derives its value from an underlying asset. It is a contract between two or more parties that specifies conditions (such as the date, price, and quantity of the underlying asset) under which payments, or payoffs, are to be made between the parties. Derivatives can be used for a variety of purposes, such as hedging risk or speculating on the future price of an asset.
A function is a mathematical relation between two sets of numbers that assigns each element in one set to exactly one element in the other set. For example, the function f(x) = 2x+3 assigns each real number x to the real number 2x+3
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Given h(x)=-5x-4 find h(3)
The value of the equation h(x) = -5x-4 is - 19 when h = (3).
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
The three primary forms of linear equations are point-slope, standard, and slope-intercept.
So, the equation we have is:
h(x) = -5x-4
Now, solve the equation when h = (3)
h(x) = -5x-4
h(3) = -5(3) -4
h(3) = -15 - 4
h(3) = - 19
Therefore, the value of the equation h(x) = -5x-4 is - 19 when h = (3).
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NO LINKS!! Please help me with this problem. Part 8ff
Answer:
[tex]\dfrac{1}{36n^2+6n}[/tex]
Step-by-step explanation:
Given factorial expression:
[tex]\dfrac{(6n-1)!}{(6n+1)!}[/tex]
[tex]\boxed{\begin{minipage}{6cm}\underline{Factorial Rule}\\\\$n!=\:n\cdot \left(n-1\right) \cdot \left(n-2\right) \cdot ... \cdot 3 \cdot 2\cdot 1$\\ \end{minipage}}[/tex]
Apply the factorial rule to the numerator and denominator of the given rational factorial expression:
[tex](6n-1)!=\left(6n-1\right)\cdot \left(6n-2\right)\cdot \left(6n-3\right)\cdot... \cdot 3 \cdot 2\cdot 1[/tex]
[tex]\left(6n+1\right)!=\left(6n+1\right)\cdot \:6n \cdot (6n-1) \cdot...\cdot 3 \cdot 2\cdot 1[/tex]
Therefore:
[tex]\begin{aligned}\implies \dfrac{(6n-1)!}{(6n+1)!}&=\dfrac{\left(6n-1\right)\cdot \left(6n-2\right)\cdot \left(6n-3\right)\cdot... \cdot 3 \cdot 2\cdot 1}{\left(6n+1\right)\cdot \:6n \cdot (6n-1) \cdot...\cdot 3 \cdot 2\cdot 1}\\\\&=\dfrac{1}{(6n+1) \cdot 6n}\\\\&=\dfrac{1}{6n(6n+1)}\\\\&=\dfrac{1}{36n^2+6n}\end{aligned}[/tex]
Answer:
[tex]\cfrac{1}{6n(6n+1)}[/tex]--------------------------------
We know that:
n! = 1·2·3·4·...·nTherefore:
(6n + 1)! = (6n - 1)!·6n·(6n + 1)Therefore:
[tex]\cfrac{(6n-1)!}{(6n+1)!} =\cfrac{(6n-1)!}{(6n-1)!(6n)(6n+1)} =\cfrac{1}{6n(6n+1)}[/tex]Can anyone solve I need help urgent thank you
Answer:
Step-by-step explanation:
3.14 x 3=9.42
write an equation of a circle with a radius of 8 and a center of (3,-4)
Answer: [tex](x-3)^2+(y+4)^2=64[/tex]
Step-by-step explanation:
The equation of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex]. h and k are the points of the center corresponding with x and y respectively. r is radius. All we have to do is plug the values in.
[tex](x-3)^2+(y-(-4))^2=8^2[/tex]
With our values plugged in, we can now simplify.
[tex](x-3)^2+(y+4)^2=64[/tex]
Therefore, our final equation is [tex](x-3)^2+(y+4)^2=64[/tex].
and drop each item into the correct column. Order does not matter:
(1, 5); (4, 7) - corresponding, (3, 5) - Alternate Interior, (2, 7); (1, 8) - Exterior
(3, 6) are Consecutive Interior Angles.
Line of transversal:
Any line that crosses two straight lines at different locations is known as a transversal.
Corresponding Angles:
When two parallel lines cross the third one, the angles that are in the same relative position at each junction are referred to as corresponding angles to one another
Alternate Interior Angles:
The alternative interior angles are those that are on the inner side of the parallel lines but on the opposing sides of the transversal.
Alternate Exterior Angles:
Alternate external angles are positioned on the opposing sides of the transversal and are always outside the two lines where the transversal intersects.
Consecutive Interior Angles:
The pair of non-adjacent internal angles that are located on the same side of the transversal are referred to as consecutive interior angles.
Here we have
Two parallel lines intersected and formed the angles, ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8.
By the given information,
∠1 and ∠ 5 are corresponding angles
∠4 and ∠ 7 are corresponding angles
∠3 and ∠5 are Alternate Interior Angles
∠2, and ∠7 are Alternate Exterior angles
∠1 and ∠ 8 are Alternative Exterior angles
∠3 and ∠ 6 are Consecutive Interior Angles
Therefore,
(1, 5); (4, 7) - corresponding, (3, 5) - Alternate Interior, (2, 7); (1, 8) - Exterior
(3, 6) are Consecutive Interior Angles.
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Which system of linear inequalities is graphe
Answer:
B
Step-by-step explanation:
The vertical dashed line is x = -3. Since the shading is to the right, that is x > -3.
The solid line has slope -4/5 and y-intercept -2. It's shaded above, so it is y ≥ -x - 2.
Answer: B
use proof by contraposition to show that for intergers m and n that if mn is even then m is even and n is even
In order for m n to be even, m must be even or n must be an even number.
Let's understood what is integers.
In mathematics, a collection of both positive and negative integers is referred to as an integer. Like whole numbers, integers do not contain a fractional portion. The definition of an integer is that a number that can be either positive, negative, or zero but is not a fraction. On integers, we can carry out all arithmetic operations, including addition, subtraction, multiplication, and division. Examples of integers include 1, 2, 5, 8, -9, and -12. "Z" stands for an integer.
Proof by contraposition:
Suppose that the statement m“ is even or is even n” is not true. Consequently, m and n should both be odd. Let's check to determine if the sum of two odd numbers is even or odd: Let m and n be equal to 2a+1 and 2b+1 respectively, then their product is:
(2a+1) (2b+1) = 4ab+2a+2b+1 =2(2ab+a+b) +1
This shows that the expression 2(2ab+a+b) +1 is of the form 2n+1, thus the product is odd. If the product of odd numbers is odd, then m n is not true to be even. Therefore, in order for m n to be even, m must be even, or n must be an even number.
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let $f(x)$ be a polynomial with integer coefficients. suppose there are four distinct integers $p,q,r,s$ such that $$f(p)
The smallest possible value of f ( t ) = 9 based on the values of p , q , r , s.
Given :
Let f ( x ) be a polynomial with integer coefficients. Suppose there are four distinct integers p , q , r , s such that f ( p ) = f ( q ) = f ( r ) =f ( s ) = 5. If t is an integer and f ( t ) > 5,
Let g(x) = f(x) − 5.
g(x) = (x−p)(x−q)(x−r)(x−s)h(x)
The condition f(t) > 5 translates to g(t) > 0.
Since p,q,r,s,t are distinct integers, the smallest possible positive value of (t−p)(t−q)(t−r)(t−s) is 4 :
the four numbers in the parentheses are all distinct integers ≠ 0, so the smallest value we can get from the product (−2)⋅(−1)⋅1⋅2. }
The smallest possible positive value of h(t) is 1, since we must have g(t)≠0.
Thus the smallest possible value of g(t) is 4, and therefore the smallest possible value of f(t) is 9, and it is achieved for t=2 if we have
f(x)=x(x−1)(x−3)(x−4)+5
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Full question ;
Let f(x) be a polynomial with integer coefficients. Suppose there are four distinct integers p,q,r,s such that f(p)=f(q)=f(r)=f(s)=5. If t is an integer and f(t)>5, what is the smallest possible value of f(t)?
1 hour 15 minutes. is what in minutes
Answer:
75
Step-by-step explanation:
I hour and 15 minutes in minutes is 75 minutes
1 hour = 60 minutes
you add 15 and you get
60+15=75
The answer would be 75 Minutes.
1 Hour = 60 Minutes
[tex]60 + 15 = 75[/tex] Minutes.
If 24000 bricks of the same shape and size are required to build a wall of dimension 15m*6m*20m find the volume of each brick
The volume of each brick is 0.75m³
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object. It is measured in cubic units.
A brick has a cuboidal shape. This means the volume of a cuboid is given as:
V = l×b×h
This means volume = area × height
The volume of the whole wall is calculated as:
15× 6× 20 = 18000m³
Since there are 24000 bricks needed for the wall. The volume of each brick is therefore calculated as:
V =18000/24000
= 0.75m³
Therefore the volume of each brick is 0.75m³
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Helpp!! GIVING BRAINIEST
The value of the c in the function c = 19m - 15 when m=10 is 175.
What is a function?A relationship between a number of inputs and outputs is termed a function. In a function, which is an association of inputs, each input is associated to exactly one output. Each function has a domain, range, and co-domain.
Given the function;
c = 19m - 15,
where m represents the number of months and c represents the total number of car sent to New York.
To find the value of c:
when m = 10,
Substitute the value of m to the function;
c = 19 (10) - 15
c = 190 - 15
c = 175.
Therefore, the value of c is 175.
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Apply Math Models You have 20 quarters. You
find 40% more quarters in your room. Then you go
shopping and spend 50% of the total number of
quarters.
a. Write an expression that represents the
total number of quarters you take with
you when you go shopping.
b. How much money do you have left?
18. H
F
S
F
t
Answer:
a. Let Q be the total number of quarters you take with you when you go shopping. The total number of quarters you have is 20, and you find 40% more quarters in your room, which is an additional 0.4 * 20 = <<0.420=8>>8 quarters. Therefore, the total number of quarters you have after finding more quarters in your room is 20 + 8 = <<20+8=28>>28 quarters. When you go shopping, you spend 50% of the total number of quarters, which is 0.5 * 28 = <<0.528=14>>14 quarters. Therefore, the total number of quarters you take with you when you go shopping is 28 - 14 = <<28-14=14>>14 quarters. This can be represented by the expression Q = 28 - 0.5 * 28.
b. If you have 14 quarters with you when you go shopping, and you spend 50% of the total number of quarters, then you have 0.5 * 14 = <<0.514=7>>7 quarters left. Since each quarter is worth $0.25, you have 7 * 0.25 = $<<70.25=1.75>>1.75 left. Answer: \boxed{1.75}.
Karla is saving money to visit her relatives in Florida. It costs $1,000 for the plane ticket and $250 per night for the hotel. Using the function that represents the cost c based on the number of nights n Karla spends in Florida, how many nights can Karla stay in Florida if she saves $3,000?
Answer: 8 Nights
Step-by-step explanation:
Cost of a plane ticket to Florida(c) = $1000
cost at the hotel per night (n)
Amount left with Karla after spending on the flight ticket =
$3000-$1000= $2000
To find out how many nights she can stay we should divide the remaining amount she has with (n) = $2000/$250 = 8
Hence Karla can stay for 8 nights
maria is selling chips and candy bars. each box of chips has 20 bags for $13.80 and the candy bars is $6.60 for a box of 12 bars. if maria only has $100 to spend, write an inequality that represents the possible number of boxes of chips (x) and boxes of candy bars (y) maria could buy.
The inequality that represents the possible number of boxes of chips (x) and boxes of candy bars (y) Maria could buy is 13.80x + 6.60y ≤ 100.
How to represent inequality?Maria is selling chips and candy bars. each box of chips has 20 bags for $13.80 and the candy bars is $6.60 for a box of 12 bars.
Maria has only 100 dollars to spend. The inequality that represent the possible number of boxes of chips (x) and boxes of candy bars (y) Maria could buy can be calculated as follows:
Therefore,
x = number of boxes of chipsy = number of boxes of candy barsHence each box of chips is 13.80 dollars and each candy bars is 6.60 dollars.
Therefore, the inequality is 13.80x + 6.60y ≤ 100.
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(A TEST I NEED IT ASAP)
1. Use each digit from 1 to 5 once to make the following equation true. ■ − ■ ■/■ = 3 ■/6
2. The sum of three mixed numbers is 8 2/5. The difference between the first number and second number is 1. The difference between the first number and third number is 2. What is the least number?
3. Tori plays the tuba. She plays for 4 1/2 measures, rests for 8 3/8 measures, plays for another 16 measures, rests for 2 1/4 measures, and plays for the rest of a 36-measure song. How long was the last section that she played?
Answer:
2
Step-by-step explanation:
lucy buys a $68 pair of shoes. she receives a 15% employee discount. if the sales tax is 6 1/4 %, how much does she pay for the shoes?
The amount that Lucy pays for the shoes is $61.56.
How to calculate the amount paid?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this situation, Lucy buys a $68 pair of shoes. she receives a 15% employee discount and the sales tax is 6 1/4. The amount paid will be:
= $68 - (15% × $68)
= $57.80
Addition of the sale tax will be:
= $57.80 + (6.5% × $57.80)
= $57.80 + $3.76
= $61.56.
The price is $61.56.
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Which choice is equivalent to the quotient shown here when x > 0?
98x³+√72x²
O A. TV₂
OB. √26x
7x
O C. 7
6
OD. √98x3 - 72x²
Answer:
A.[tex] \frac{7}{6} \sqrt{x} [/tex]
Step-by-step explanation:
Solution Given:
[tex] \sqrt{98{x}^{3} } \div \sqrt{72 {x}^{2} } [/tex]
Bye using indices formula
[tex] \sqrt{x} \div \sqrt{y} = \sqrt{ \frac{x}{y} } [/tex]
we get
[tex] \sqrt{ \frac{98{x}^{3} }{72 {x}^{2} } } [/tex]
[tex] \sqrt{ \frac{49 {x}^{3} }{ 36 {x}^{2} } }[/tex]
[tex] \sqrt{ \frac{{7}^{2} {x}^{3 - 2} }{{6}^{2} } } [/tex]
[tex] \frac{7}{6} \sqrt{x} [/tex]
A side of the triangle below has been extended to form an exterior angle of
132°. Find the value of x
Answer:
x = 15°
Step-by-step explanation:
⭐the exterior angle of a triangle is equal to the sum of the angles that is opposite of said exterior angle
Thus, to solve for x, we have to make an equation in regards of the exterior angle.
132° = x° + 117°
∴ 15 = x° . . . . subtract 117 from LHS and RHS
⭐if this response helped you, please mark it the "brainliest"!⭐
Find the volume of a cone with a radius of 3 feet and a height of 7 feet. Enter
the answer in terms of pie
convert the following equation into standard form.
Y = -2x
2x − y = 0
The standard form of a linear equation is:
Ax + By= C
where, if at all possible, A, B, and C are integers, A is non-negative, and, A, B, and C have no common factors other than 1.
The equation in the problem can be converted into standard form by the following method:
−2x + y= −2x + 2x
−2x + y = 0
−1(−2x+y) = −1 × 0
2x − y = 0
2x − 1y = 0
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1. Using the stopping distance calculator and your internet browser complete the following table to compare stopping distances at various speeds.
2. You overhear your friend say “It is OK to go 10 mph over the speed limit.” Explain why your friend is wrong using your evidence from the table above to support your answer.
The stopping distance table and the analysis of the stopping distance are presented as follows;
1. The stopping distance calculator, an online tool, provides the stopping distance at a specified speed as presented in the table on the following sections.
2. Increasing the vehicle speed by 10 mph, increases the required stopping distance exponentially, which reduces the safety of driving
What is the stopping distance?The stopping distance is the distance traveled by a vehicle, which is the sum of the distance traveled during the reaction time and the distance traveled during braking (the braking distance)
The table in the question using a perception–reaction time of 2.5 seconds, and the online stopping distance calculator is completed as follows;
Speed (mph) [tex]{}[/tex] Speed (m/s) Stopping Distance (m)
60 mph [tex]{}[/tex] 26.82 m/s 119.55 m
50 mph [tex]{}[/tex] 22.35 m/s 92.34 m
40 mph [tex]{}[/tex] 17.88 m/s 68.05 m
30 mph [tex]{}[/tex] 13.41 m/s 46.665 m
20 mph [tex]{}[/tex] 8.94 m/s 28.197 m
10 mph [tex]{}[/tex] 4.47 m/s 12.642 m
2. The details from the above table indicates that as the speed increases, the stopping distance increases exponentially, such that increasing the speed by 10 mph increases the required stopping distance when the vehicle is moving at an already high speed, thereby reducing safety by increasing the speed by 10 mph.
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Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is given by
C(p) =
8100p
100 − p
(a) Is C(p) undefined at any p-value? If so, what value? (If an answer does not exist, enter DNE.)
p =
(b) What is the domain of C(p) as given by the equation? (Enter your answer using interval notation.)
(c) What is the domain of C(p) in the context of the application? (Enter your answer using interval notation.)
(d) What happens to the cost as the percent of pollution removed approaches 100%?
The cost increases (bounded by 8100) as p increases.
The cost decreases (bounded by 0) as p increases.
The cost decreases without bound as p increases.
The cost increases without bound as p increases.
The cost remains constant a
(a) C(p) is not defined since we can't divide by 0.
(b) The domain of C(p) as given by the equation is (-∞, 100) ∪ (100, ∞)
(c) The domain of C(p) in the context of the application is [0, 100)
(d) The percentage of particulate pollution removed from an industrial plant can't be negative or higher or equal than 100
Here we have given that Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is given by
C(p) = 8100p / (100 − p)
And we need to find the following.
(a) In general ma the we know that dividing by zero is not possible one.
Therefore, C(p) is undefined when we try to divide it by 0.
(b) The domain of C(p) is the function is not defined at p =100 the domain would be written as,
=> D = (-∞, 100) ∪ (100, ∞)
(c) The domain of C(p) in the context of the application is calculated as,
=> D = [0, 100)
Therefore, the percentage of particulate pollution removed from an industrial plant can't be negative or higher or equal than 100.
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A group consisting of 28 aggressive zombies triples in size every hour. Which
equation matches the number of zombies after 7 hours?
Answer:196
Step-by-step explanation:
-x+y≤-1
x + 2y ≥ 4
Graph the system of inequalities.
Answer:
Step-by-step explanation:
[tex]-x+y\leq -1\\x-y\geq 1\\x+2y\geq 4[/tex]
dark blue is the required region.
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=630(1.06)^x
percentage rate increase by 206%
What is exponential growth?
An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases with time.
Consider a population of mice that increases exponentially every year by a factor of two, starting with 2 in the first year and increasing to 4 in the second, 8 in the third, 16 in the fourth, and so on. The population is rising by a factor of 2 per year in this example. If mice gave birth to four pups instead, you would then have 4, 16, 64, and 256.
Linear growth, which is additive, and geometric growth can be contrasted with exponential growth, which is multiplicative (which is raised to a power).
This equation represents exponential growth because the base is greater than 1, the function represents growth and Whenever the base is less than 1, the function represents decay.
The base 1.06 is greater than 1, hence The equation represents exponential growth.
The formula for exponential growth:
[tex]y=a(1+r)^{x}[/tex]
where,
f(x) = exponential growth function
a = initial amount
r = growth rate
x = number of time intervals
In this case, [tex]r=1.06+1 = 2.06[/tex]
which represents percentage rate increase by 206%
To learn more about exponential growth checkout https://brainly.com/question/12490064
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8x + 2 = 26
can someone please help?..
Answer:
x = 3
Step-by-step explanation:
8x + 2 = 26
8x = 26 - 2
8x = 24
x = 24/8
x = 3
Check:
8*3 + 2 = 26
24 + 2 = 26
Solve the equation 6x² + 1 = 10x to the nearest tenth.
