The value of the expression is 32.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
50% of 88 - 33(1/3)% of 36
This can be written as,
= 50/100 x 88 - (100/3)/100 x 36
= 44 - 12
= 32
Thus,
The value is 32.
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What are the rectangular coordinates for (4. 5, -30 degrees)?
A. (-2. 3, 3. 9)
B. (3. 9, -2. 3)
C. (3. 9, 2. 3)
D. (2. 3, -3. 9)
The rectangular coordinates for (4.5, -30 degrees) are (3.9, -2.3), which is option B.
What is rectangle ?
A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle.
To find the rectangular coordinates for a point in a plane given its polar coordinates, use the following formula:
x = r * cos(θ)
y = r * sin(θ)
Where (r, θ) are the polar coordinates and (x, y) are the rectangular coordinates.
For the point (4.5, -30 degrees), have:
r = 4.5
θ = -30 degrees = -30 * (π / 180) radians
x = r * cos(θ) = 4.5 * cos(-30 * (π / 180)) = 3.9
y = r * sin(θ) = 4.5 * sin(-30 * (π / 180)) = -2.3
So, the rectangular coordinates for (4.5, -30 degrees) are (3.9, -2.3), which is option B.
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The rectangular coordinates for (4. 5, -30 degrees) are (3.9, -2.3).
The rectangular coordinates for (4.5, -30 degrees) can be found using the following formula:
x = r * cos(θ)
y = r * sin(θ)
where r is the magnitude (or distance from the origin) and θ is the angle in radians.
In this case, r = 4.5 and θ = -30 degrees = -30 * (π/180) radians.
So:
x = 4.5 * cos(-30 * (π/180)) = 4.5 * cos(-π/6) = 4.5 * sqrt(3)/2
y = 4.5 * sin(-30 * (π/180)) = 4.5 * sin(-π/6) = -4.5 / 2
Therefore, the rectangular coordinates are (x, y) = (4.5 * sqrt(3)/2, -4.5 / 2), which is approximately (3.9, -2.3).
Option B (3.9, -2.3) is the right response as a result.
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Which parallelograms have the same area? What is that area?
Answer:
Step-by-step explanation:25
Parallelogram II and IV have the same area.
A parallelogram with the same base and height has the same area, regardless of shape. The product of base and height is equal.
Characteristics of a ParallelogramThe following is a list of the characteristics of a parallelogram:
A parallelogram has opposite sides Opposite sides are parallel and congruent. Opposite angles are congruent. Successive angles are complementary. If one of the angles is a right angle, then all other angles will be right angles. The two diagonals bisect each other. Each diagonal bisects the parallelogram into two congruent triangles.Learn more about parallelogram at https://brainly.com/question/13795683
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[tex]4 3/8 + 2 5/12 -3 1/6[/tex]
55/24 will be the simplified form of the expression 43/8 + 25/12 -31/6.
What is Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.
given an expression 43/8 + 25/12 -31/6
Simplify given data
=> 43/8 + 25/12 -31/6
=> 5 + 3/8 + 2 + 1/12 - 5 - 1/6
=> 2 + 3/8 + 1/12 - 2/12
=> 2 + 3/8 -1/12
=> 2 + 9/24 -2/24
=> 2 + 7/24
=> 55/24
therefore, The simplified form of the given equation will be 55/24.
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The 7th grade Tigers went on a trip to Canobie. Admission was $15 per person and the bus fee was $270. The total cost for the trip was $1440. How many Tigers went on the trip?
Answer:
78 Tigers
Step-by-step explanation:
1440=270+15x
1170=15x
78=x
What is the multiplicative inverse of 3 − 7 a 3 − 7 b 3 7 c 1 3 7 d 7 − 3?.
The multiplicative inverse of 3/7 will be 7/3. Thus, correct option is B).
The word "inverse" refers to something that has an opposite impact. A number's multiplicative inverse is a number that, when multiplied by the inputted number, produces the result 1, or 1. It is the reciprocal of an integer, as defined by the multiplicative inverse.
1/N or N-1 is used to denote a number's multiplicative inverse, such as the number N. From the Latin word "reciprocus," it is also known as reciprocal. Inverse refers to something that is the opposite. The acquired reciprocal of a number is such that its value equals identity 1 when multiplied by the original number. To put it another way, it is a technique for dividing a number by itself to produce identity 1.
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Note that the correct question is:
What is the multiplicative inverse of 3/7 ?
A) - 3/7
B) 7/3
C) - 7/3
D) 1
Can we say that if lim x tends to a ( f(x)) exists, then limit x tends to b (f(x)) also exists, if b is close to a?
No, the existence of a limit at one point does not necessarily imply the existence of a limit at a nearby point.
How to ascertain Existence of limits at points?The limit of a function at a certain point is determined by the behavior of the function in a neighborhood of that point, not just the behavior at that point. Two points that are close to each other can have different limits.
Therefore, the statement in the solution cannot be founded. The existence of the limit as x approaches a (f(x)) does not guarantee the existence of the limit as x approaches b (f(x))
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The square root parent function is translated so that the endpoint is located at (-7,7). Write an equation that represents this new function
The square root function is translated so that the endpoint is located at (-7,7), [tex]g(x)= \sqrt{x+7} +7[/tex] and this can be determined by using the transformation.
The square root parent function is translated so that the endpoint is located at (-7,1).
The following steps can be used to determine the equation that represents this new function:
Write the square root parent function.[tex]f(x) =\sqrt{x}[/tex]
The graph of the above function is translated by a factor of 7 in the negative x-axis that is in the left direction.Then the graph obtained in the above step is translated by a factor of 7 in the positive y-axis in the upward direction.Write the equation of the function that obtains in step 3.[tex]g(x)= \sqrt{x+7} +7[/tex]
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Is 66 a real number?.
Yes. 66 is a real number. Every real number is either a rational number or a irrational number.
The Real numbers are defined as the numbers which have values that can be expressed as an infinite decimal expansion. It include integers, natural numbers. Real numbers can be positive and can be negative numbers. Real numbers can be a rational number or a irrational numbers. These two are the main groups of real numbers. Rational numbers can be written as the ratio of two integers. Irrational numbers cannot be written as the ratio of two integers. Irrational numbers are also the type of real numbers. The real numbers has the closure property, commutative property, the associative property and the distributive property.
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In 2014, the U. S. House of Representatives approved a new farm bill establishing the Margin Protection Program (MPP) for dairy producers. Assume that the program has effectively created a price floor for milk at $0. 18 per pound. Use the following additional information to answer the following questions: Without the price floor, the equilibrium price of milk is $0. 15 per pound, and the equilibrium quantity is 200 billion pounds of milk. The supply curve intersects the price axis at $0. 05 and the demand curve intersects the price axis at $0. 25. At the price floor of $0. 18, the quantity supplied is 260 billion, and the quantity demanded is 140 billion. To support the price floor, the USDA buys up the 120 billion pounds of excess milk. In the absence of a price floor, how much consumer surplus is created? How much producer surplus? What is the total surplus (producer surplus plus consumer surplus)?
Without the price floor, the equilibrium price is $0.15, and the equilibrium quantity is 200 billion pounds of milk.
Consumer surplus is calculated as the difference between the maximum price a consumer is willing to pay for a good and the price they actually pay. With an equilibrium price of $0.15, the consumer surplus can be calculated by calculating the area between the demand curve and the price line at $0.15.
The producer surplus can be calculated using an equilibrium price of $0.15 by calculating the area between the supply curve and the price line at $0.15. The producer surplus is the triangular area between the two prices and the supply curve, which intersects the price axis at $0.05.
The sum of the consumer and producer surpluses is the total surplus. Without the price floor, the consumer and producer surpluses would be different than they are now. The total surplus would also differ, reflecting changes in consumer and producer behavior.
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Sides of a triangle are (x^2-1), (x^2+1) and 10cm. If the area of the triangle is 120cm^2, find x
If the area of the triangle is 120 cm^2, the value of x is equal to 6.
How to calculate the area of a triangle?Mathematically, the area of a triangle can be calculated by using this mathematical expression:
Area of a triangle (A) = 1/2 × b × h
Where:
b represents the base area of a triangle.h represents the height of a triangle.According to Hero's Formula area of triangle by Heron of Alexandria, if a, b, c are the side lengths of a triangle, then, the area of a triangle can be calculated by using this mathematical expression:
Area of a triangle (A) = √[s(s − a)(s − b)(s − c)]
Where:
s = (a + b + c)/2
s = (x + x + 1 + 2x - 1)/2
s = 4x/2
s = 2x
Substituting the parameters into Hero's Formula formula, we have the following;
x√10 = √[2x(2x − x)(2x − x - 1)(2x − 2x + 1)]
x√10 = x√2(x − 1)
√10 = √2(x − 1)
Taking the square of both sides, we have:
10 = 2(x - 1)
10 = 2x - 2
2x = 12
x = 12/2
x = 6.
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Given m∥n, find the value of x.
The value of x is 16.2degrees
What are supplementary angles?Two angels whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
Given;
(x+14), (9x-4)
Now,
According to supplementary angles;
(x+14)+ (9x-4)=180
10x+18=180
10x= 180-18
10x= 162
x= 16.2
Therefore, in these angles the value of x will be 16.2degree
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What will be the result of substituting 2 for x in both expressions below?
One-half x + 4
x + 6 minus one-half x minus 2
A.Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.
B.Both expressions equal 6 when substituting 2 for x because the expressions are equivalent.
C.One expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent.
D.One expression equals 6 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent.
Both expressions equal 5 when substituting 2 for x because the expressions are equivalent. Option A is correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
= 1/2x + 4
put x = 2
= 1/2 × 2 + 4
= 5
Now, another expression
= x + 6 - 1/2x - 2
Put x = 2
= 2 + 6 - 1/2 × 2 -2
= 5
Thus, both expressions equal 5 when substituting 2 for x because the expressions are equivalent. Option A is correct.
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Would you expect one mole of solid sodium, Na, to have the same volume as one mole of liquid bromine, Br2? Explain.
The value for 1 mol Na is 23 gm/mol and 1 mol Br_2 is 160 gm/mol, so the volume will be different.
What is mole?
The mole idea is a useful way to indicate how much of a substance there is. Any measurement can be divided into two components: the magnitude in numbers and the units in which the magnitude is expressed.
Even one gram of a pure element is known to have an enormous number of atoms when working with particles at the atomic (or molecular) level. The mole idea is frequently applied in this situation. The unit of measurement that receives the most attention is the "mole," which is a count of a sizable number of particles.
The molar mass for 1 mole of solid sodium (Na) = 23 gm/mol
The molar mass for 1 mole of liquid bromine (Br) = 79.90 gm/mol
The molar mass for 1 mole of liquid bromine (Br_2) = 160 gm/mol
The molar mass of both the substances in 1 mol quantity is different.
The volume of both the elements will be different.
The molar mass of any element does not corresponds with the mole value.
Therefore, there is different in volumes.
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−3x(4x−2),2x(6x 2 +4x−3) multiply
(2x−3)(5x+6),multipy the polynomial by the box method
2x(6x2 + 4x − 3) × (2x − 3)(5x + 6)
= (2x)2(6x2 + 4x − 3)(5x + 6)
= 12x3(5x + 6) + 8x2(5x + 6) − 6x(5x + 6)
= 60x4 + 48x3 − 45x2 − 36x
The number of people etimated to vote in an election wa 7,000. The actual number of people who voted wa 5,600. By what percent did the etimate vary from the actual amount?
75%
1400%
14%
25%
The estimate of the no. of people to vote varies by 25% from the actual no. of voters turned out.
Finding the per cent variation of estimated votes from the actual turnout
The no. of people estimated to vote in the election = 7000
The actual no. of people who voted = 5600
A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
∴ The per cent by which the estimate vary from the actual turnout is given by,
= [{7000 – 5600}/ {5600}]×100
= [1400/5600]×100
= 0.25×100
= 25%
Therefore, the 25% of the estimate vary from the actual amount.
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what do we know about data points that are plotted below our y=x? (line of best fit)
Data points plotted below the line y=x (also known as the line of best fit) indicate that the observed value is less than the predicted value.
What exactly is a math graph?
A math graph is a visual representation of mathematical data or concepts. It typically uses Cartesian coordinates (x, y) to plot points, lines, and shapes that help to illustrate mathematical relationships. Graphs can be used to represent many types of mathematical information, including functions, equations, data sets, and geometric shapes. They are commonly used in fields such as science, engineering, economics, and statistics to analyze and understand complex information. Graphs are also an important tool for conveying mathematical ideas and results in a clear and understandable way.
This could be due to measurement errors, outliers, or other factors that are not accounted for in the model used to generate the line of best fit. It's important to note that the location of data points relative to the line of best fit can provide insight into the underlying pattern or relationship between the variables being studied, but further investigation is needed to determine the specific cause of the discrepancy.
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What is the area of this triangle in the coordinate plane?
25. 0 units²
27. 5 units²
50. 0 units²
55. 0 units²
Previous
Next
The area of this triangle in the coordinate plane with coordinates A( 4,5) , B(1,2) and C( 6,2) is equals to the 15 unit². So, option (d) is correct.
The basic formula for the area of a triangle is (1/2) × base × altitude. But we have to calculate the area of a triangle in coordinate geometry. Coordinate geometry is defined as the study of geometry using coordinate points. If coordinates of the triangle are(x₁, y₁), (x₂, y₂), and (x₃, y₃) then the area of the triangle is defined as Area = 1/2[ x₁(y₂ - y₃) + x₂( y₃ - y₁) + x₃(y₁ - y₂) ]
We have a triangle ABC in coordinate plane in above figure. The coordinates of triangle are A( 4,5) , B(1,2) and C( 6,2). Here, x₁ = 4 , y₁ = 5 , x₂ = 1 , y₂ = 2 ,x₃ = 6 , y₃ = 2. So, Area of ∆ABC
= 1/2[ 4( 2 - 2)+ 1( 2 - 5) + 6(5 - 2)
= 0 + (-3) + 18 = 15
Hence, the required area is 15 unit².
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Complete question:
What is the area of this triangle in the coordinate plane? See the above figure.
a)25. 0 units²
b) 27. 5 units²
c) 50. 0 units²
d) 15. 0 units²
thirty subtract from four times a number is greater than twenty-five
Answer: 4x -30 > 25 would be your answer
Step-by-step explanation: I hope this helps!
Find the length of a rectangle whose breadth is 1.8m and area is 6.12m
a)2. 2.6 m
b)3.2 m
c)3.4 m
d)3.6 m
Answer:
C
Step-by-step explanation:
Rectangle Area = Length x Breadth
6.12 = Length x 1.8
Therefore, Length = 3.4m
3. Let R be the region in the first quadrant bounded by the graph of y = x2, the x-axis, and the line x = 3. Part A: Find the area of the region R. Part B: Find the value of h such that the vertical line x = h divides the region R into two regions of equal area.Previous question
The dimensions of the region bounded by the curve, y² = x, the lines, x = 1 and x = 4, and the x-axis exists the dimensions ABCD
What is meant by angle?Two straight lines or rays intersect at a same terminus to make an angle. The vertex of an angle is the point at which all points meet. The word "angle" is derived from the Latin word "angulus," which means "corner," and there are numerous types of angles depending on measurement. Acute, obtuse, right, straight, reflex, and full rotation are the names of basic angles. Two rays can be joined at their termini to form the geometric shape known as an angle.Everyone has an angle, according to cynical belief, is wisdom. Having an angle refers to operating in a way that prioritises your own needs over those of others. No one can be impartial or selfless if everyone has a point of view.Thus area of ABCD = [tex]\int_1^4 \mathrm{ydx} \\[/tex]
[tex]& =\int_1^4 \sqrt{\mathrm{x}} \mathrm{dx} \\[/tex]
[tex]$& =\left[\frac{\mathrm{x}^{\frac{3}{2}}}{\frac{3}{2}}\right]_1^4 \\[/tex]
[tex]$& =\frac{2}{3}\left[(4)^{\frac{3}{2}}-(1)^{\frac{3}{2}}\right][/tex]
simplifying,
[tex]$& =\frac{2}{3}[8-1] \\[/tex]
Then we get,
[tex]$& =\frac{14}{3} \text { units }[/tex]
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6) Cream comes in two sizes. The smaller size is 3/5 of a cup, the larger size is 5/6 of a cup. The smaller one costs £0.60 and the larger one costs 90p. Which is better value for money?
We are aware that x+y=15 (the total number of mugs he buys).The man then purchased 5 large cups and 10 mini mugs .
Find the value ?Let x represent how many little cups he buys.
Let y represent how many large mugs he purchases.
We are aware that x+y=15 (the total number of mugs he buys)
We are also aware of the mugs' costs.
The total price (69) can therefore be deduced to equal 3.50x + 6.80y.
To find x, use the first equation.
x = 15 - y
You can now enter that x-value into the other equation.
69 = 3.50(15 - y ) + 6.80y
Solve for y now.
69 = 52.5 -3.50y + 6.80y
69= 52.5 + 3.3y
16.5 = 3.3y\sy = 5
So, we are aware that the man purchased 5 huge cups.
You can re-insert the y value into x+y=15.
x+5=15\sx+10
The man then purchased 5 large cups and 10 mini mugs!
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Paul received a $15 tip on a meal that cost $120. What percent of the meal cost was the tip?.
Answer:
12.5%
Step-by-step explanation:
12.5% of 120 is 15 so if you take 15 divided by 120 you would get 0.125 and turned into a percentage is the 12.5%
Find a number that is 33 less than twice its opposite. Translate this sentence
into an algebraic equation and solve to find the unknown number.
-2x-33=x
simplify by adding 2x on both sides
-33=3x
divide by 3 on both sides
x=-11
50 points!!!
7. Write and solve an inequality for the value of x.
The value of x must be between -18 and -6. The solution has been obtained using Triangle inequality theorem.
What is Triangle inequality theorem?
The triangle inequality theorem explains how a triangle's three sides interact with one another. This theorem states that the sum of the lengths of any triangle's two sides is always greater than the length of the triangle's third side. In other words, the shortest distance between any two different points is always a straight line, according to this theorem.
We are given three sides of a triangle as 8, 6 and x+20
Using Triangle inequality theorem,
⇒8+6 > x+20
⇒14 > x+20
⇒-6 > x
Also,
⇒x+20+6 > 8
⇒x+26 > 8
⇒x > -18
Also,
⇒x+20+8 > 6
⇒x+28 > 6
⇒x > -22
From the above explanation it can be concluded that x is less than -6 but greater than -22 and -18.
This means that x must lie between -18 and -6.
Hence, the value of x must be between -18 and -6.
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How do you graph an absolute value piecewise function?.
The process to graph an absolute value piecewise function is explained below .
Let us consider the Absolute value function as :
y = | x -2 | ;
this absolute function can be written in piecewise wise form as :
⇒ [tex]y =\begin{array}{cc} \{ & \begin{array}{cc} -x+2 & x < 2 \\ x-2 & x\geq 2 \end{array}\end{array}[/tex] ;
this piecewise function means that the main function divides into two pieces ,
for any input value that is less than 2 , the function"-x+2" will be used , and
for any input value greater than or equal to 2, the function "x-2" , will be used ;
for example : if x = 3 , then ⇒ y = 3 - 2 = 1 ;
and is x = 1 , then ⇒ y = -1 +2 = 1 ;
the points to be plotted are (3,1) and (1,1) .
The graph of this absolute value piecewise function is shown below .
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If point A is located at (-9, 3) on a coordinate plane, and point B is located at (-9, 10), what is the distance between the two points?
Answer: 7
Step-by-step explanation:
the -9 coordinate is the same, so to get the distance you do 10 - 3 which is 7
The distance between points A and B is 7units if point A is located at (-9,3) on a coordinate plane, and point B is located at (-9,10).
A point A is located at (-9,3) on a coordinate plane, and point B is located at (-9, 10)
The coordinate of point A is (-9, 3)
The coordinate of point B is (-9, 10)
The distance formula can be given as:
d=[tex]\sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]
d=[tex]\sqrt{((-9)+9)^2 + (10-3)^2}[/tex]
d=[tex]\sqrt{7^2}[/tex]
d=7
The distance is 8 units.
Therefore, the distance between points A and B is 7 units if point A is located at (-9,3) on a coordinate plane, and point B is located at (-9, 10).
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Why is a circle not 100 degrees?.
A circle not 100 degrees because 360 is a highly composite number, when a circle is drawn it completes a whole loop making it a 360 degrees.
As you surely well know, we modern people like to divide a circle into 360 wedges that resemble pies. We define the angle at the vertex of each of these wedges as being one degree in size. As you presumably well know, we can measure angles in other ways other in degrees. Angles are also measured in radians and, on a very rare occasion, in the enigmatic gradians used by the military (thus the presence of "deg rad grad" buttons on many calculators).
While the reason the 360 degree convention was chosen is unknown to us, we do know roughly when and where it all began (more on that in a moment). We at least know that it originated a very, very long time ago—around 4,000–5,000 years ago with the Babylonians, the Greeks, and possibly other much older peoples.
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Where are exponential functions used?.
In the biological sciences, exponential functions are frequently employed to simulate the evolution of a certain quantity over time, such as population number. Experimental data graphs are often created with the quantity on the y-axis and the time on the x-axis.
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth. You will find the formulas, rules, characteristics, charts, deviations, exponentially series, and examples of exponential functions in this article.
Depending on the exponential function, an exponential curve might increase or decrease. A quantity should have either exponential growth or exponential decay if it regularly increases or decreases by a predetermined percentage.
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Solve (2x – 1)2 = 8 using the quadratic formula.
A) x = 1∕2 B) x = –1∕2 + , x = –1∕2 – C) x = –1∕2 D) x = 1∕2 + , x = 1∕2 –
The solutions of the quadratic equation are:
[tex]x = 1/2 \pm \sqrt{2}[/tex]
How to solve the quadratic equation?Here we want to solve the quadratic equation:
(2x - 1)^2 = 8
To use the quadratic formula, we need to expand this.
(4x^2 - 4x + 1) = 8
4x^2 - 4x + 1 - 8 = 0
4x^2 - 4x - 7 = 0
Remember that for a quadratic equation:
a*x^2 + b*x + c = 0
The quadratic formula is:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
Then in this case the solutions are:
[tex]x = \frac{4 \pm \sqrt{(-4)^2 - 4*4*(-7)} }{2*4} \\\\x = \frac{4 \pm \sqrt{128} }{8}\\\\x = 1/2 \pm \sqrt{128/64} \\\\x = 1/2 \pm \sqrt{2}[/tex]
These are the solutions.
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in birr 24000is invested at interested rate of 4% compounded you fairly then the amount of money after 10 years in birr?
Answer:
To find the amount of money after 10 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt)
Where:
A = the amount of money after 10 years
P = the initial investment (24000 birr)
r = the interest rate (4%)
n = the number of times the interest is compounded per year
t = the number of years
In this case, since the interest is compounded annually, n = 1.
So,
A = 24000(1 + 0.04)^(1*10)
A = 24000(1.04)^10
A = 24000(1.46) = 24000*1.46 =35,040 birr
So, after 10 years the total amount of money will be 35,040 birr.
