In mathematics, particularly in algebra, there are mainly two types of solutions for an equation: real and complex solutions.
Real solutions: These are type of solutions that are real numbers, which can be found by solving the equation algebraically. For example, if the equation is x² + 2x - 3 = 0, the real solutions are x = -1 and x = 3.
Complex solutions: These are solutions that are complex numbers, which can be found by solving the equation algebraically. Complex numbers are numbers that have both real and imaginary parts, represented by a + bi, where a and b are real numbers and i is the imaginary unit (i² = -1). For example, if the equation is x² + 1 = 0, the complex solutions are x = i and x = -i.
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I don’t know how to do this please explain
(a)1+2×3×4×5 is equal to 121 which shows it is square integer.
(b)1+3×4×5×6 is equal to 361 that shows it is square integer and 1+4×5×6×7 is equal to 841 that shows it is square integer.
(c)n(n+3) is equal to n²+3n and second expression would be a+2.
(d)The expression in the term of a is a²+2a+1
What is Integer?•Integers are any number, including positive, negative, and zero. The Latin root of the word "integer" means "whole" or "intact." Therefore, integers do not contain decimals or fractions.
•Consequently, both negative and positive whole numbers can be added to create a set of integers.
•An integer, which includes both positive and negative integers, including zero, is a number without a decimal or fractional component. Z stands for an assortment of integers that includes the following.
•If a number is smaller than zero, it is said to be negative. For instance, 1, 2, 3, etc. Zero is defined as not having a positive or negative value. The sum is a whole number.
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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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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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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
Jamila estimated that she would read 250 pages last week.
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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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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Juliet has a choice between receiving a monthly salary of $1920 from a company or a base salary of $1800 and a 4% commission on the amount of furniture she sells during the month. For what amount of sales will the two choices be equal?
Answer:
x=5000 I think
Step-by-step explanation:
1800-1600=200$ difference between choices
this difference equals a 4% commission on the amount of furniture she sells during the month
If the amount of sales is x$, then a 4% commission on the amount is 0.04x$
so 0.04x=200
x=200%2F0.04
x=5000$ amount of sales for that two choices will be equal
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!
Please answer this question with decent explanation. Ty
Answer:
2nd is the correct answer
The side that will be in palce of Questionmark by Similarity of Triangle is WZ.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Since Similar figures are described as items with the same shape but varying sizes, such as two or more figures.
Properties:
Similar equivalent side ratios exist.
Triangle WZX and WXY:
Angle WZX = angle WXY= 90 degrees
Angle WXY is a common angle .
So triangle WZX and WXY are similar (AAA similarity)
So, the ratio of sides are equal.
Therefore,
WY / WX = WX / WZ
The side that will be in place of WZ
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A varies jointly as b and c.if a=40,b-2,c=5.Find b when a=9 and c=3.
When a=9 and c=3, A varies as b and c together. If a=40, b-2, and c=5, B. [tex]40x^{2}[/tex] - 2 x + 5 = 0 and [tex]9x^{2} +3 = 0[/tex] are the quadratic equations.
What is the equation of a ,b and c ?When a=9 and c=3, A varies as b and c together. If a=40, b-2, and c=5, B. [tex]40x^{2}[/tex] - 2 x + 5 =0 and [tex]9x^{2} +3 =0[/tex] are the quadratic equations.
Domain of [tex]$40 x^2-2 x+5:\left[\begin{array}{cc}\text { Solution: } & -\infty < x < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$[/tex]
Range of [tex]$40 x^2-2 x+5:\left[\begin{array}{cc}\text { Solution: } & f(x) \geq \frac{199}{40} \\ \text { Interval Notation: } & {\left[\frac{199}{40}, \infty\right)}\end{array}\right]$[/tex]
Axis points of interception [tex]$40 x^2-2 x+5: \quad$[/tex] Y Intercepts: (0,5)
Vertex of [tex]$40 x^2-2 x+5: \quad$[/tex] minimum [tex]$\left(\frac{1}{40}, \frac{199}{40}\right)$[/tex]
Factor [tex]$9 x^2+3: \quad 3\left(3 x^2+1\right)$[/tex]
[tex]$$9 x^2+3$$[/tex]
Replace 9 with 3 - 3.
Put 3 in as 3 - 1.
[tex]$$=3 \cdot 3 x^2+3 \cdot 1$$[/tex]
Exclude common word 3
[tex]$$=3\left(3 x^2+1\right)$$[/tex]
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The formula M + 10 = 5.6p - 96 can be used to find the amount of
money, M, Kade will make if he sells p pounds of strawberries. Kade made $314 over the weekend. How many pounds of strawberries did
Kade sell?
Answer:
p = 73.21 pounds of strawberries
Step-by-step explanation:
M + 10 = 5.6p - 96
314 + 10 = 5.6p - 96
314 +96 = 410
410 = 5.6p
410/5.6 = p
73.2142857143 = p
p = 73.2142857143
Answer:
75 pounds
Step-by-step explanation:
Replace M in the equation with 314
314 + 10 = 5.6p - 96
324 = 5.6p - 96
5.6p = 324 + 96
5.6p = 420
Divide both sides by 5.6
p = 75
[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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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.
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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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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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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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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A triangle has two sides of length 2 and 10. What is the smallest possible whole-number length for the third side?
Answer:
11
Step-by-step explanation:
the answer is 11 because of therom
What is the complete factor of x² +5x +6?.
The complete factor of the polynomial x² + 5x +6 is (x + 3)(x + 2).
You can factor it by using the factorization methods such as
Factor by grouping
Factor by grouping and completing the square
Factoring by using difference of squares
Factoring by using sum and difference of cubes
For example, you can factor it by using the difference of squares method:
x² + 5x +6 = (x² + 6x + 9) - (x +3)
We know x² + 6x + 9 = (x + 3)², So
x² + 5x +6 = (x + 3)² - (x + 3)
Taking (x + 3) common
x² + 5x +6 = (x + 3)(x + 3 - 1)
x² + 5x +6 = (x + 3)(x + 2)
So (x + 3)(x + 2) is complete factor.
--The question is not readable, answering to the question below--
"What is the complete factor of x² + 5x + 6?"
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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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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%
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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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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The area of the triangle is 80 square millimeters
The measure of the base of the triangle is 10 millimetres
How to determine the base of the triangleFrom the question, we have the following parameters that can be used in our computation:
Area of the triangle = 80 square millimetres
Height of the triangle = 16 millimetres
Using the above as a guide, we have the following:
The base of the triangle = 2 * Area/Height
Substitute the known values in the above equation, so, we have the following representation
The base of the triangle = 2 * 80/16
Evaluate
The base of the triangle = 10
Hence, the base is 10 millimetres
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Complete question
The area of the triangle is 80 square millimeters and the height of the triangle is 16 millimetres.
Calculate the length of the base
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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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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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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Is an absolute value function increasing or decreasing?.
The absolute value function is increasing on [0,∞) and decreasing on (−∞,0].
There are a few ways to describe what is meant by the absolute value |x| of a real number x. You may have been taught that |x| is the distance from the real number x to the 0 on the number. So, for example, |5| = 5 and | − 5| = 5, since each is 5 units from 0 on the number line.
Another way to define absolute value is by the equation |x| = √x2. Using this definition, we have
|5| = √(5)² = √25 = 5 and | − 5| = √(−5)² = √25 = 5. The long and short of both of these procedures is that |x| takes negative real numbers and assigns them to their positive counterparts while it leaves positive numbers alone.
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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
