The given expression x² + 2x + 3 is a polynomial.
In the math term expression is defined as an expression that is made up of variables and constants, along with algebraic operations
Here we have given the expression that can be written as x² + 2x + 3 and here we need to identify the given expression is polynomial or not.
AS we all know that the term polynomial means an expression that consists of variables (or indeterminate), terms, exponents and constants
And we have also know that the polynomials can be identified by noting which expressions contain only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
And the non-polynomial expressions will be the expressions which contain other operations.
Based on these rule we have identified that the given expression is an polynomial.
Complete Question:
Is the expression x² + 2x + 3 is polynomial or not?
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The price of gas today is 200% of the price last year.
Does that mean the price has doubled?
Answer: Yes, it does.
Step-by-step explanation: Let x represent the price of gas today. 200% of x=200/100*x, which can be written as 2x because 200/100=2. 2x is x doubled, and therefore, it does mean the price has doubled.
Answer:
yes, the price has doubled
PLS HELP!!!
SNOWBOARDING Manuel wants to go snowboarding with his friends. The closest ski and snowboard resort is approximately 20 miles west and 50 miles north of his house. Manuel picks up his friend who lives 15 miles south and 10 miles east of Manuel's house. How far away are the two boys from the resort?
The two boys are far away from the resort and distance measured about 35.81m.
The Pythagoras Theorem's fundamental formula is what?The Pythagoras theorem equation is written as c² = a² + b², with c denoting the hypotenuse of the right triangle and a and b denoting the other two legs. So, any triangle that has a 90° angle creates a Pythagoras triangle, which can then be solved using the Pythagoras equation.
We must first use the Pythagoras theorem to determine how far the resort is from Manuel's home.
S₁ = √50²+20²
S₁ = √2500+400
S₁ = √2900
S₁ = 53.85m.
The distance between Manuel's house and his friend's house must then be calculated.
S₂ = √15²+10²
S₂ = √225+100
S₂ = √325
S₂ = 18.03m.
The displacement of the two boys will be,
∆S = S₁-S₂
∆S = 53.84-18.03
∆S = 35.81m.
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The two boys are far away from the resort and the distance measured about 35.81 m.
The Pythagoras Theorem's fundamental formula is what?The Pythagoras theorem equation is written as c² = a² + b², with c denoting the hypotenuse of the right triangle and a and b denoting the other two legs. So, any triangle that has a 90° angle creates a Pythagoras triangle, which can then be solved using the Pythagoras equation.
We must first use the Pythagoras theorem to determine how far the resort is from Manuel's home.
S₁ = √50²+20²
S₁ = √2500+400
S₁ = √2900
S₁ = 53.85m.
The distance between Manuel's house and his friend's house must then be calculated.
S₂ = √15²+10²
S₂ = √225+100
S₂ = √325
S₂ = 18.03m.
The displacement of the two boys will be,
∆S = S₁-S₂
∆S = 53.84-18.03
∆S = 35.81m.
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find the volume of a cube with the side length of 1/5cm
How many solutions does the following pair of linear equations have 3x 5y 20 6x 10y 40?.
The pair of linear equations 3x + 5y = 20 and 6x + 10y = 40 have infinitely many solutions.
The given pair of linear equations can be represented in the form of Ax + By = C and Dx + Ey = F, where A = 3, B = 5, C = 20, D = 6, E = 10, and F = 40.
To find the number of solutions for the given pair of linear equations, we can use the following method:
Form the determinant of the coefficients of the variables (x and y) by taking the product of A and E and subtracting the product of B and D.Calculate the value of the determinant, in this case (3 * 10) - (5 * 6) = 30 - 30 = 0. If the determinant is zero, the system has either no solution or infinitely many solutions. In this case, the system of equations has infinitely many solutions, since the determinant is zero.So, the pair of linear equations 3x + 5y = 20 and 6x + 10y = 40 have infinitely many solutions.
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What transformation has changed the parent function f(x) = (0.5)x to its new appearance shown in the graph? exponential graph passing through point negative 3, 2 and negative 2, 1 a f(x) − 2 b f(x + 2) c f(x) + 1 d −1 • f(x)
Correct option is A, f(x) -2 has changed the parent function f(x) = (0.5)x to its new appearance.
What modification has caused the parent function to change?The parent function f(x) = log5x has been modified by reflecting it over the x-axis, extending it vertically by a factor of three, and moving it down by three units.
In the picture below you can see the blue line is the graph of the function
f(x) = log(5x) and the green line is the graph of the function
g(x) = log[5(x + 4)] - 2
Since the function f passes at point (2, 1), we must reduce it by 2 units to ensure that it also passes at position (-2, -1). To do this, we add 2 to the function f.
We only need to add 4 to the variable x to have the function go left when we obtain log(5x) - 2.
The function shifts to the left when you add a number to x;
The function moves to the right when you remove a number from x;
The function increases when you add a number to it;
The function decreases when you take a number away from it.
Then we get a function g(x) = log[5 (x + 4)] - 2.
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What are the coordinates of the vertex of the graph of the function y 3x² 12x 3?.
The coordinates of the vertex of the function y = -3x² -12x + 3 is (-2,15) and the graph of the function is attached below.
Vertex in math is known as a point on a polygon where the sides or edges of the object meet or where two rays or line segments meet.
Here we have given that the function y = -3x² - 12x + 3 and we have to find the coordinates of the vertex.
As we all know that for any equation of the type y = ax² + bx + c the vertex is given by (h, k)
And the value of the vertex is calculated by using the formula h = -b/2a and k = (4ac - b2)/4a.
From the given question we have identified the value of a = -3, b = -12 and c = 3
Then the value of h is calculated as,
=> h = -(-12)/2(-3)
When we simplify this one then we get the value of h as -2
Similarly the value of k is calculated as,
=> 4ac = 4(-3)(3) = -36
Then the equation is written as,
=> k = [-36 - (-12)2]/4(-3)
When we simplify this one then we get
=> k = -180/-12
Therefore, the value of k is 15
Hence the coordinates of the vertex is (h, k) = (-2, 15).
Complete Question:
What are the coordinates of the vertex of the graph of the function y = -3x² -12x + 3?
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HELP PLEASE!
At the beginning of a storm, a pond was 8 cm deep. During the storm, the depth increased by 1.5 cm every hour for 8 hours.
Click "Show your work" to graph the function in the whiteboard.
What is the difference between the largest 5 digit number and smallest 6 digit number?.
The difference between the largest 5-digit number and the smallest 6-digit number is 1.
The aim is to find the largest 5-digit and the smallest 6-digit numbers, and then we need to identify the difference between these two values.
Let's start by finding the smallest 6-digit number.
We know that 0 is the smallest digit that can not be used in the highest place value, so we will consider the next smallest digit; that is, 1 and 1 can be used in the highest place value.
Thus, we can create the required 6-digit smallest number with 0 and 1.
Hence, the smallest 6-digit number is 100000.
Now, we will discover the largest 5-digit number.
As we know, the largest digit is 9, which can be used anywhere. So, we will form the largest 5-digit number with the digit 9.
Thus, the largest 5-digit number is 99999.
Next, we need to find the difference between these two values.
So, we can determine the difference between the smallest 6-digit number and the largest 5-digit number by subtracting the smallest from the largest.
Thus, we get,
⇒100000 - 999999
⇒1
Hence, 1 is the difference between the smallest 6-digit and the largest 5-digit numbers.
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31.002 in expanded form
Answer: 30+1+.002
Step-by-step explanation:
Just break it up into number groups. Like tens, ones, or hundreds
Write an algebraic expreion that repecent the um of y to the fifth power and eleven
The given expression is expressed in an algebraic expression as: y^5 + 11
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
In mathematics, when we express “sum” we mean an addition. So the expression "the sum of y... and eleven" is represented by:
y + 11
When we refer "fifth power" we mean an exponent equal to five. So the expression “y to the fifth power” is represented by:
y^5
The complete expression "the sum of y to the fifth power and eleven" in an algebraic expression represented by: y^5 + 11
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Correctly written question:
Write an algebraic expression that represent the sum of y to the fifth power and eleven
If AB = 12, then A’B’ =
The solution is, A’B’ = 12 units, when AB = 12.
What is transformation?A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.
here, we have,
Given
Line segment AB = 12 units
Translation of AB → A'B' by the rule T(x +0, y+5)
This translation won't change the length of A'B' as the difference in (x2-x1) and (y2-y1) stays same
because x-coordinate stays as is and y-coordinate's change cancelled when subtracting.
So, A'B' = 12 units.
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Solve each equation and please answer like (x,y) x=smaller number y=larger number:
1: x(x-32)=0
2: (y-3) (y+2) =0
3: (2y+5)(y-4)=0
4: 2z^2+20z=0
5: 9x^2 =27x
Quadratic equations' solutions are x=0, x=32 , y=3, y=-2 , [tex]y=-\frac{5}{2}, y=4$$[/tex] , z=0, z=-10 , and x=0, x=3
What is the quadratic equation ?[tex]$$x(x-32)=0 \quad: \quad x=0, x=32$$[/tex]
Steps
x(x-32)=0
If a b=0, then either a=0 or b=0, according to the Zero Factor Principle.x=0 or x-32=0
Solve x-32=0: x=32
The following are the quadratic equation's solutions:
x=0, x=32
2 . [tex]$$(y-3)(y+2)=0 \quad: \quad y=3, y=-2$$[/tex]
Steps
(y-3)(y+2)=0
If a b=0, then either a=0 or b=0, according to the Zero Factor Principle. y-3=0 or y+2=0
Solve y-3=0 : y=3
Solve y+2=0 : y=-2
The following are the quadratic equation's solutions:
y=3, y=-2
3. [tex](2 y+5)(y-4)=0 \quad: \quad y=-\frac{5}{2}, y=4$$[/tex]
Steps
(2 y+5)(y-4)=0
If a b=0, then either a=0 or b=0, according to the Zero Factor Principle. 2 y+5=0 or y-4=0
Solve 2 y+5=0: y=-[tex]\frac{5}{2}[/tex]
Solve y-4=0 : y=4
The following are the quadratic equation's solutions:
[tex]y=-\frac{5}{2}, y=4$$[/tex]
4.[tex]$$2 z^2+20 z=0 \quad: \quad z=0, z=-10$$[/tex]
steps
[tex]$$2 z^2+20 z=0$$[/tex]
The following are the quadratic equation's solutions:
[tex]$$z_{1,2}=\frac{-20 \pm \sqrt{20^2-4 \cdot 2 \cdot 0}}{2 \cdot 2}$$$$\sqrt{20^2-4 \cdot 2 \cdot 0}=20$$$$z_{1,2}=\frac{-20 \pm 20}{2 \cdot 2}$$[/tex]
Distinguish the answers
[tex]$$\begin{aligned}& z_1=\frac{-20+20}{2 \cdot 2}, z_2=\frac{-20-20}{2 \cdot 2} \\& z=\frac{-20+20}{2 \cdot 2}: 0 \\& z=\frac{-20-20}{2 \cdot 2}:-10\end{aligned}$$[/tex]
The following are the quadratic equation's solutions:
z=0, z=-10
5 .
[tex]$$\begin{aligned}& 9 x^2=27 x: x=0, x=3 \\& \text { Steps } \\& 9 x^2=27 x\end{aligned}$$[/tex]
Move 27 x to the left side
[tex]$$9 x^2-27 x=0$$[/tex]
[tex]$$\begin{aligned}& \text { Factor } 9 x^2-27 x: \quad 9 x(x-3) \\& 9 x(x-3)=0\end{aligned}$$[/tex]
If a b=0, then either a=0 or b=0, according to the Zero Factor Principle. x=0 or x-3=0
Solve x-3=0: x=3
The following are the quadratic equation's solutions
x=0, x=3
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What is the sum rule in integration?.
∫(f(x) + g(x)) dx = ∫f(x) dx + ∫g(x) dx is the sum rule in integration.
The sum rule in integration states that if f(x) and g(x) are two functions that are both integrable over a given interval, then the integral of the sum of these functions over that interval is equal to the sum of the integrals of the individual functions over that interval. Mathematically, this can be expressed as:
∫(f(x) + g(x)) dx = ∫f(x) dx + ∫g(x) dx
The sum rule of integration is: Integral of the sum of two functions is equal to the sum of integration of individual functions.
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Determine the degree of the following polynomial: -7xy^3z^2
Answer:
The given expression is -7xy^3z^2
The degree of x is 1
The degree of -7 is 0
The degree of y^3 is 3
The degree of z^2 is 2
The degree of a polynomial is the highest exponent of its variables. In the case of the polynomial -7xy^3z^2, the degree is the highest exponent among x, y, and z.
The highest exponent is 3, which is the exponent of y. So the degree of the polynomial -7xy^3z^2 is 3.
It's worth noting that the coefficient -7 has no effect on the degree of the polynomial. The degree of a polynomial is determined by the exponents of its variables, not its coefficients.
Samuel has 1 cup of rubbing alcohol and will use the entire amount. He plans to store the cleaning solution in containers that each hold a maximum of 6 cups. How many containers does he need.
Samuel needs a total of 6 containers for his plan
How to determine the number of container he needs?The complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
1 cup of rubbing alcohol = 1/(1/2) = 2 shares
Also, we have
1 cup of rubbing alcohol contains = 1 + 1/2 + 16 = 17.5
For the 2 shares calculated above, we have
2 shares = 17.5 * 2
Evaluate
2 shares = 35
Given that each can hold a maximum of 6 cups, the number of containers needed is
Container = 35/6
This gives
Container = 5.83
Round up
Container = 6
Hence, he needs 6 containers
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There are 4 boxe of apple there are 10 apple in each box how many apple are there in all
By using the multiplication formula, the number of apples in all 4 boxes are 40.
Aside from addition, subtraction, and division, multiplication is also considered to be one of the four fundamental mathematical operations. Multiplying in mathematics refers to the process of repeatedly adding together groups of the same size.
The multiplication formula is expressed as:
Multiplicand × Multiplier = Product
Where:
Multiplicand: The first number (factor)
Multiplier: The second number (factor)
Product: The final result after multiplying the multiplicand and multiplier
In this case, we are given that:
Multiplicand = 4 boxes
Multiplier = 10 apples
Thus, the number of apples in 4 boxes are:
Product = 4 x 10
Product = 40
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An automated car wah can wah 30 car in 5 hour. How long would it take to wah 120 car?
Repone
A 15 h B 20 h
C 25 h D 30 h
pleae help
It would take the automated car wash 20 hours to wash 120 cars.
What is rate ?
In general, a rate is a measure of how much of something happens within a certain period of time. It can be thought of as a ratio that compares two different units of measurement.
In the context of the problem, the rate at which the automated car wash can wash cars is the number of cars that it can wash per unit of time.
The rate at which the automated car wash can wash cars is 30 cars per 5 hours. To find out how long it would take to wash 120 cars, we can use the formula:
Time = (Number of cars / Rate)
Time = (120 cars / 30 cars per 5 hours)
Time = (120/30) * 5 hours
Time = 20 hours
So it would take the automated car wash 20 hours to wash 120 cars.
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The rate at which the automated car wash can wash cars is 30 cars per 5 hours. To find out how long it would take to wash 120 cars, we can use the formula:
Time = (Number of cars / Rate)
Time = (120 cars / 30 cars per 5 hours)
Time = (120/30) * 5 hours
Time = 20 hours
So it would take the automated car wash 20 hours to wash 120 cars.
Pleae anwer any number if you can, anwer will be reported if it i nonene. 1. (-8-6-5)-(-25-4-9)=
2. (-2614-26)-(-88-12)=
3. (14-23-12)-(15-15-12)=
4. (-16-813)-(-2119-12)=
5. (-1316-15)-(-16-1123)=
6. (19-29-39)-(21-2223)=
7. (-20-2131)-(331232)=
8. (-5022-34)-(32-16-24)=
9. (14-25-19)-(-483541)=
10. (-2934-67)-(634651)=
All questions are solved using BODMAS rule.
BODMAS stands for Brackets, Orders (of operations), Division, Multiplication, Addition, and Subtraction. It is a commonly used acronym in mathematics to remember the order in which mathematical operations should be performed. When solving mathematical expressions, operations within brackets should be done first, followed by any exponents or roots.
Next, perform any divisions or multiplications from left to right, followed by any additions or subtractions from left to right. This order ensures that the expression is evaluated correctly and avoids confusion or errors.
(-8-6-5)-(-25-4-9) = -24 - -38 = 14(-2614-26)-(-88-12) = -2640 - -100 = -2540(14-23-12)-(15-15-12) = -11 - -12 = 1(-16-813)-(-2119-12) = -829 - -2131 = -298(-1316-15)-(-16-1123) = -1331 - -1139 = -192(19-29-39)-(21-2223) = -50 - -2202 = -2152(-20-2131)-(331232) = -2151 - 331232 = -332383(-5022-34)-(32-16-24) = -5056 - -8 = -5048(14-25-19)-(-483541) = -30 - -483541 = -483571(-2934-67)-(634651) = -3001 - 634651 = -637652Lear more about bodmas:
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A patio has an area of 214
2
1
4
square yards. 34
3
4
of the patio is carpeted. What is the area of the carpeted part of the patio?
The area of the carpeted part of the patio is 1 [tex]\frac{11}{16}[/tex] square yards.
What are Mixed Fractions?Mixed fractions are type of fractions which consist of a whole number part and a fractional part.
Mixed fractions are of the form a b/c where a is the whole number part and b/c is the fractional part.
Given that,
Area of the patio = 2 1/4 square yards
= (2 × 4 + 1) / 4 square yards
= 9/4 square yards
Also given that, 3/4 of the patio is carpeted.
Area of the carpeted part of the patio = 3/4 (9/4)
= 27/16 square yards
= 1 11/16 square yards
Hence the area of the carpeted part is 1 [tex]\frac{11}{16}[/tex] square yards.
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The complete question is as follows :
A patio has an area of 2 1/4 square yards. 3/4 of the patio is carpeted. What is the area of the carpeted part of the patio?
Quadrilateral DEFG is similar to quadrilateral HIJK. Find the measure of side IJ.
Figures are not drawn to scale.
D
E
6
F
H
23.6
I
J
Answer:
23.6 units.
Step-by-step explanation:
Since quadrilateral DEFG is similar to quadrilateral HIJK, the ratios of corresponding sides are equal. We can use this information to find the measure of IJ.
We know that:
DF/HJ = EF/IJ = 6/23.6 = 2/8 = 1/4
So we can set up the proportion:
IJ/EF = HJ/DF
IJ/6 = 23.6/6
IJ = 23.6/6 * 6 = 23.6
A scoop from a bin of assorted jelly beans contained a mix of flavors. root beer 5 licorice 22 cinnamon 6 What is the experimental probability that the next jelly bean scooped from the bin will be a cinnamon jelly bean? Write your answer as a fraction or whole number.
The experimental probability of getting a cinnamon jelly bean is P = 2/11
How to get the experimental probability?Suppose that we have an experiment with some given number of outputs, and we perform that experiment N times.
The experimental probability of a given outcome is equal to the quotient between the number of times that we got that outcome and the total number of times we performed the experiment.
Here we have the data:
root beer = 5
licorice = 22
cinnamon = 6
For a total of 5 + 22 + 6 = 33 tries.
Then the probability of getting a cinnamon jelly bean is:
P = 6/33 = 2/11
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What is the graph of the function? y=2x2^x
Answer:
use symbolab it will give you the answer
Step-by-step explanation:
What is the ratio of tan θ?.
The tan function is referred to as the ratio of a right-angled triangle's opposite side to its neighbouring side.
The length of the neighbouring side to the angle and the opposite side to the angle are compared using the Tan formula. If we know the angle and either side of the triangle.
The six inverse trigonometric ratios are as follows: sin-1 (opposite)/(hypotenuse) = cos-1 (base)/(hypotenuse) = tan-1 (opposite)/(hypotenuse)=θ
we can also use the tan formula to determine the lengths of the triangle's sides. Tan Formula is formally defined as
tanФ = Opposite SideAdjacent Side
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The port lavca fihing pier i 3200 feet long. There i one peron fihing for each ten feet of length. Write and olve an equation to find how many people are fihing from the peir
320 peoples are fishing for their peir.
What is equation?A statement that demonstrates the link between various variables using mathematical processes is called an equation. It is applied to problem-solving and forecasting. The same relationship can be expressed in an equation in a number of ways, and it can be used to obtain the value of an unknown variable by setting it to a known value.
length of fishing pier 3200 feet
Requirement of one person = 10 feet
so the let x person can accomodate in the given length
so 10 * x =3200
so , x = 3200/10
=> x =320
so 320 are fishing for their pier.
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The volume of this cylinder is 2880π cm3.
Find the length of the radius, r.
Give your answer as a surd in its simplest form.
Step-by-step explanation:
[tex]volume \: of \: cyinder = \pi{r}^{2}h \\ \pi {r}^{2} \times 120cm = 2880\pi {cm}^{3} \\ {r}^{2} = 24 \: {cm}^{2} \\ r = \sqrt{24} \: = 4.899 \: cm[/tex]
A toy american eskimo dog has a mean weight of 8 pounds with a standard deviation of 1 pound. Assuming the weights of toy eskimo dogs are normally distributed, what range of weights would 95% of the dogs have?.
95% of toy eskimo dogs have weight between 6.04 and 9.96 pounds assuming normal distribution.
What is weight ?
Weight is a measure of the force exerted on an object due to gravity. It is typically measured in units of mass such as kilograms (kg) or pounds (lbs). The weight of an object can be determined by multiplying its mass by the acceleration due to gravity.
Assuming the weights of toy eskimo dogs are normally distributed, we can use the standard normal distribution table to find the range of weights that would include 95% of the dogs.
The standard normal distribution table gives the proportion of data within a given number of standard deviations from the mean. Since the standard deviation of the toy eskimo dog's weight is 1 pound, we can use this table to find the range of weights that are within 1.96 standard deviations from the mean.
Using this method, we can find that 95% of the toy eskimo dogs will have a weight that is between 6.04 pounds (8 - 1.96) and 9.96 pounds (8 + 1.96).
95% of toy eskimo dogs have weight between 6.04 and 9.96 pounds assuming normal distribution.
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How do you find the sine of an angle in a right triangle?.
To find the sine of an angle in a right triangle, we can use the following relationship:
[tex]sin(angle) = opposite side / hypotenuse\\[/tex]
What is right triangle?
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (also known as a right angle). This angle is formed by the intersection of two legs of the triangle, which are not the hypotenuse of the triangle. The side opposite the right angle is called the hypotenuse and it is always the longest side of the triangle.
To find the sine of an angle in a right triangle, you can use the following relationship:
[tex]sin(angle) = opposite side / hypotenuse\\[/tex]
This relationship holds true for any angle in a right triangle, not just the acute angles.
For example, if you have a right triangle with an angle of 30 degrees and the opposite side is 5 units and the hypotenuse is 12 units, you can find the sine of the angle by dividing the opposite side by the hypotenuse:
[tex]sin(30) = 5/12 = 0.4166\\[/tex]
It's also important to note that the sine of an angle is always between -1 and 1, and the sine of an acute angle is always positive.
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To find the sine of an angle in a right triangle, we can use the following relationship:
sine = opposite side / hypotenuse side
What is right triangle?
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (also known as a right angle). This angle is formed by the intersection of two legs of the triangle, which are not the hypotenuse of the triangle. The side opposite the right angle is called the hypotenuse and it is always the longest side of the triangle.
To find the sine of an angle in a right triangle, you can use the following relationship:
sine = opposite side / hypotenuse side
This relationship holds true for any angle in a right triangle, not just the acute angles.
For example, if you have a right triangle with an angle of 30 degrees and the opposite side is 5 units and the hypotenuse is 12 units, you can find the sine of the angle by dividing the opposite side by the hypotenuse:
sin(30) = 5/12 = 0.4166
It's also important to note that the sine of an angle is always between -1 and 1, and the sine of an acute angle is always positive.
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When you solve an equation for one variable and then substitute the resulting expression in for that variable in the other equation This is known as the?.
When you solve an equation for one variable and then substitute the resulting expression in for that variable in the other equation its is known as Substitution method.
I will demonstrate how the substitution method works. Suppose we have the following systems of linear equations with two variables:
Equation 1: 3x + 2y = 11
Equation 2: -x + y = 3
By solving these two equations we get x=1 and y=4.
Equation 2: -x + y = 3
-x + x + y = x + 3
y = x + 3
Next, substitute the value of y in Equation 2 (from the previous step), and substitute its value into Equation 1 to solve for x:
Equation 1: 3x + 2y = 11
Substitute y = x + 3 into Equation 1:
3x + 2(x + 3) = 11
3x + 2x + 6 = 11
Combine like terms:
5x + 6 = 11
5x + 6 - 6 = 11 - 6
5x = 5
Divide both sides by 5 to solve for x:
[tex]\frac{5x}{5} = \frac{5}{5}[/tex]
x = 1
Substitute the value of x into Equation 2 to solve for y:
Equation 2: -x + y = 3
-1 + y = 3
y = 3 + 1
y = 4
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What are the 2 real solutions?.
The 2 real solutions are rational and irrational solutions.
Quadratic Formula is the simplest method to find the roots of a quadratic equation. There are particular quadratic equations that cannot be easily factorized, and here we use this quadratic formula to find the roots in the quickest possible way.
Quadratic Formula: The roots of a quadratic equation ax² + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.
The value b² - 4ac is called the discriminant of a quadratic equation and is represented as 'D'. The nature of the roots of the quadratic equation can be predicted based on the discriminant value.
If D > 0, the roots are real and distinct (two real solutions).
If D = 0, the roots are real and equal (one real solution).
If D < 0, the roots do not exist, or they are imaginary (two imaginary solutions).
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A number has exactly 8 factors, two of which are 4 and 20. List all the factors of the number.
The number in question is 4*20 = 80.
The factors of 80 are:
1, 2, 4, 5, 8, 10, 16, 20, 40 and 80
A factor of a number is an integer that divides the number completely without leaving a remainder. To find the factors of 80, we can start with 1 and divide 80 by each number up to 80. Any number that divides 80 without leaving a remainder is a factor of 80.
1, 2, 4, 5, 8, 10, 16, 20, 40 and 80 are the factors of 80.