Answers
Related Questions
How do you write quadratic equations in standard form give at least 3 examples?
Answers
The quadratic equations are
a) x² + 5x - 6 = 0 ( the roots are x = -6 , x = 1 )
b) x² - 5x + 6 = 0 ( the roots are x = 2 , x = 3 )
c) x² + 2x - 3 = 0 ( the roots are x = -3 , x = 1 )
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation in the standard form is ax² + bx + c = 0
Now , the value of A is
a)
Let the quadratic equation be x² + 5x - 6 = 0
Now , on simplifying the equation , we get
x² + 5x - 6 = 0
x² - x + 6x - 6 = 0
Taking the common factors in the equation , we get
x ( x - 1 ) + 6 ( x - 1 ) = 0
On factorizing the equation , we get
( x + 6 ) ( x - 1 ) = 0
So , ( x + 6 ) = 0 or ( x - 1 ) = 0
And , x = -6 or x = 1
So , the roots of the quadratic equations are x = -6 or x = 1
b)
Let the quadratic equation be x² - 5x + 6 = 0
Now , on simplifying the equation , we get
x² + 5x + 6 = 0
x² + 2x + 3x - 6 = 0
Taking the common factors in the equation , we get
x ( x + 2 ) + 3 ( x + 2 ) = 0
On factorizing the equation , we get
( x + 3 ) ( x + 2 ) = 0
So , ( x + 3 ) = 0 or ( x + 2 ) = 0
And , x = -3 or x = -2
So , the roots of the quadratic equations are x = -2 or x = -3
c)
Let the quadratic equation be x² + 2x - 3 = 0
Now , on simplifying the equation , we get
x² + 2x - 3 = 0
x² - x + 3x - 3 = 0
Taking the common factors in the equation , we get
x ( x - 1 ) + 3 ( x - 1 ) = 0
On factorizing the equation , we get
( x + 3 ) ( x - 1 ) = 0
So , ( x + 3 ) = 0 or ( x - 1 ) = 0
And , x = -3 or x = 1
So , the roots of the quadratic equations are x = 1 or x = -3
Hence , the quadratic equations are solved
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How many solutions does a pair of equations y =- 3 and y 0 has?
Answers
The pair of equations y = -3 and y = 0 have No Solution .
The pair of equations is given as y = 0 and y = -3 .
In order to find number of solutions of the equations ,
we use the graphical method ,
the graph of the equation y = 0 is x axis .
and the graph of the equation y = -3 is a straight line that is parallel to the x axis , as shown in the figure below .
From the graph drawn below , we can see that the two lines are parallel and
We know that , when two lines are parallel they have No Solution .
Therefore , given pair equations have No Solution .
The given question is incomplete , the complete question is
How many solutions does a pair of equations y = -3 and y = 0 has ?
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What is the easiest way to find the domain?
Answers
We simply solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain.
What is the domain?The collection of all potential inputs for a function is its domain.
For instance, the domain of f(x)=x² and g(x)=1/x are all real integers with the exception of x=0.
The set of numbers x for which a function has a valid definition is known as its domain.
A closed interval is referred to as a function's domain if it is specified over the interval a ≤ x ≤ b.
In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x).
Simply put, x=g(y) will calculate the function's range after we identify g(y).
Therefore, we simply solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain.
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Determine the Domain & Range.
Answers
Answer:
64, 2
Step-by-step explanation:
Range: [0, 64]
the two lines graphed below are not parallel. how many solutions are there to the system of equations
Answers
The number of solutions that are to the system of equations is (a) one
How to determine the number of solutions on the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (3, 1)
Hence, the solution is (3, 1) ie. one solution
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What is the graph of a quadratic equation and inequality called?
Answers
The graph of quadratic inequality when plotted represents the parabola.
The quadratic inequality will have a range of solutions, unlike the quadratic equation.
The quadratic inequality could be solved using factorization method for example
The quadratic inequality x²+6x+5 ≤0 can be solved by factorizing but instead of two solutions, there are a range of solutions.
For given equation we need to calculate value of x such that the graph is less than zero.
Hence solution to this inequality can be written as
−5≤x≤−1.
And the graph of given quadratic inequality represents the parabola.
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What is the slope-intercept form of a line that passes through points (2, 11) and (4, 17)?y = negative 3 x minus 5y = 3 x minus 5y = negative 3 x + 5y = 3 x + 5.
Answers
Answer:
y = 3x + 5
Step-by-step explanation:
The slope-intercept form of a line is [tex]y = mx + b[/tex], where m is the slope, and b is the y-intercept.
To solve for m (the slope), use the formula: [tex]m = \frac{y__{2} - y__{1}}{x__{2} - x__{1}}[/tex], where [tex](x_{1} , y_{1} )[/tex] and [tex](x_{2}, y_{2})[/tex] are the points you are given.
. . . . . . . . m = (17 - 11) / (4-2)
. . . . . . . . m = 6/2
. . . . . . . ∴ m = 3
Substitute the slope, m, into the slope-intercept equation.
y = 3x + b
Now we have to solve for b, the y-intercept. To do so, substitute a point that was given to you into the equation.
I chose the point (4,17), but you can also do (2,11).
. . . . . . . . 17 = 3(4) + b
. . . . . . . . . . remember that the x-variable is being multiplied to the m
. . . . . . . . -12 + 17 = 12 + b - 12
. . . . . . . . ∴ 5 = b
Substitute the y-intercept, b, into the slope-intercept equation, and you're done!
[tex]y = 3x + 5[/tex]
What are the 4 steps in constructing a line segment?
Answers
Line Segment has 2 end points.
How to construct a line segment?Building a line segment of a specified length involves the following stages.
First, draw a line.
Step 2: Pick any point on the line where point A is.
Step 3: Keep one end of the compass on the 0 cm mark at the specified length of the rule to extend it.
Step 4: Draw an arc on the line while maintaining the compass' pointed end on point A.
Make B the arc point.
In this way we can construct any line segment of given length using compass and scale.
Line Segment has 2 end points.
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What is the formula in solving rectangular prism?
Answers
The formula used to calculate the solving the volume of the rectangular prism is equal to ( length × width × height ).
As given in the question,
Given base of the prism is rectangular in shape ,
Area of the base with rectangular base is given by :
area of the rectangle = length × width
Volume of the rectangular prism = base area × height
⇒Volume of the rectangular prism = ( length × width ) × height
Therefore, the formula required to calculate the volume of the rectangular prism is given by ( length × width × height ).
The above question is incomplete , the complete question is:
What is the formula in solving volume of the rectangular prism?
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How much more than 23 is 9 * 9?
Answers
58 is the number which would be much more than 23 is 9*9.
Here,
It is asked that how much more we need to add in 23 to get the value 9*9.
Here, 9*9 means we simply have to multiply 9 with 9 and we will get 81.
so, we know that
9*9 = 81
Now, we have to find how much we need to substract in 81 to get the value as 23
81-23 =58
when we deduct 23 from 81 then we get 58.
hence, 58 is the answer.
In this situation we just replace the much more word with subtraction to get the answer.
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find (g o f)(3) f(x)=3x-2 g(x)=x^2. A.1 b.-8 c49 d. 52
Answers
Answer:
To find (g o f)(3), we need to first apply f to 3, which gives us f(3) = 3 * 3 - 2 = 7. Then we need to apply g to the result of f(3), which gives us g(7) = 7^2 = 49. Therefore, (g o f)(3) = 49, so the answer is c.
Step-by-step explanation:
Which of the following is equivalent to −2(5p − 2q)?
−10p + 4q
−10p − 2q
−7p + 4q
−7p − 4q
Answers
−10p + 4q is equivalent to −2(5p − 2q).
What is meant by equivalent expression?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).Using the equality (=) symbol, equivalent phrases are represented. Because both expressions have the same value for any value of x, 3(x + 2) and 3x + 6 are identical expressions. 3x + 6 = 3 × 4 + 6 = 18.When two expressions can be expressed similarly or when they can be combined into a single, simpler expression, they are said to be comparable. Furthermore, if values are replaced for the variable in two expressions and they both provide the same result, you can tell if the expressions are similar.Given data :
−2(5p − 2q)
= -2 x 5p -(-2p) x 2q)
= = 10p + 4q
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`-6+g=11 solve the equation
Answers
G=11+6
G=17
step by step instructions:
-6+g=11
+6 on both sides
g=17
Find the solution of the system of equations.
-5x - 5у = -30
10x+3y = -3
Answers
pls answer need help.
Answers
Answer:
No
Step-by-step explanation:
5+10<17
The volume of a box, a rectangular prism, is represented by the function f(x) = x3 5x2 – 8x – 12. the length of the box is (x 6), and the width is (x – 2). find the expression representing the height of the box. x – 1 x – 5 x 1 x – 12
Answers
The expression representing the height of the box is the difference between the length and width of the box, which is equal to x subtracting two, or x – 1.
The expression representing the height of the box can be determined by subtracting the width of the box from the length. The length of the box is x 6, and the width is x – 2. To calculate the height, we subtract the width from the length: x – (x – 2) = x – x + 2 = 2. Therefore, the expression representing the height of the box is x – 1. This indicates that the height of the box is equal to the length of the box minus one. This calculation can be applied to any rectangular prism to calculate the height.The volume of the box is represented by the function f(x) = x3 5x2 – 8x – 12. To calculate the volume, we can substitute the length and width into the function:
f(x) = (x – 6)(x – 2)(x – 1) = x3 – 8x2 + 11x – 12.
Therefore, the volume of the box is x3 – 8x2 + 11x – 12.
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How do you know if a curve is positive or negative?
Answers
Positive curve graphs will be upward-sloping.
Negative curve graphs will be downward-sloping.
Both graphs in the first image attached below, show curves sloping upward from left to right. As with upward-sloping straight lines, we can say that generally the slope of the curve is positive. While the slope will differ at each point on the curve, it will always be positive.
In the graphs in the second image attached, both of the curves are downward sloping. Straight lines that are downward sloping have negative slopes; curves that are downward sloping also have negative slopes. The slopes change from point to point on a curve, but all of the slopes along these two curves will be negative.
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Straight lines that are downward sloping have negative slopes; curves that are downward sloping also have negative slopes. The slopes change from point to point on a curve, but all of the slopes along these two curves will be negative.
What are the example of exponential equation?
Answers
Exponential equation has tow major types
exponential decay
f(x) = a(1.16)^xexponential growth
f(x) = a(0.84)^xWhat are exponential equation?Exponent-based equations in which the exponent or a portion of the exponent is a variable are known as exponential equations.
This is a type of function that are of 3 main parts
the starting or initial value
base function
the exponents
Atypical example includes: f(x) = 300(1.16)^x
the starting = 300
the base = 1.16
the exponents = x
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so forth.
The base is what determines exponential growth or decay
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What is the graph for y = 3x - 1?
Answers
Answer: i think c or d
Step-by-step explanation:
Answer:
the answer would be D
Step-by-step explanation:
Exercice 1
Sarah, who is twenty years old, runs regularly. During her workouts, she monitors her heart rate.It thus determined its maximum recommended heart rate and obtained 193 beats per minute. When she is forty years old, her maximum heart rate will be 178 beats per minute.Is it true that over this twenty-year period his maximum heart rate will have decreased by about 8%?
Answers
It is true that Sarah's maximum heart rate over this twenty-year period will have decreased by approximately 8%.
How is the percentage decrease computed?The percentage decrease is determined by ascertaining the reduction or difference in heart rate at the beginning and at forty.
This difference becomes the numerator of the division operation by the heart rate at the beginning and then multiplied by 100.
Sarah's heart rate at twenty years = 193 beats per minute
Sarah's heart rate at forty years = 178 beats per minute
Difference (Decrease) in heart rate = 15 beats per minute (193 - 178)
Percentage decrease = 7.77% (15/193 x 100)
= 8%
Thus, we can conclude that Sarah's heart rate has decreased by about 8%.
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two numbers which differ by 3 have a product of 88. Find the two numbers.
Answers
Answer:
Step-by-step explanation:
Let's call the two numbers x and y, where x is the smaller number and y is the larger number. We are given that x and y differ by 3, which means y - x = 3. We are also given that the product of x and y is 88, which means x * y = 88. We can solve this system of equations by substituting the second equation into the first equation:
y - x = 3
y = x + 3
Substituting this expression for y into the second equation, we get:
x * (x + 3) = 88
x^2 + 3x - 88 = 0
This is a quadratic equation that we can solve using the quadratic formula:
x = (-3 +/- sqrt(3^2 - 41(-88))) / (2*1)
= (-3 +/- sqrt(9 + 352)) / 2
= (-3 +/- sqrt(361)) / 2
= (-3 +/- 19) / 2
= -11/2 or 8/2
Therefore, the two numbers are x = -11/2 and y = 8/2, or x = -5.5 and y = 4. These are the solutions to the original system of equations.
let x, x 3 be two figures
also,
x( x 3) = 88
x2 3x- 88 = 0-88 = 11 ×(- 8)
= x2 11x- 8x- 88 = 0 3 = 11- 8
= x( x 11)-8( x 11) = 0
= ( x 11)(x-8) = 0
x = -11 or x = 8
verification 8 ×( 8 3) = 8 × 11 = 88
- 11 ×(- 11 3) = - 11 ×- 8 = 88
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The function , (1,4) (2,5) (n,3n) has a domain 1
Answers
Considering the given data which include the domain and the range the possible value of n is
1 ≤ n ≤ 7How to find the possible value of nThe possible value of n will be n such a way that both the domain and the range are not altered
for a domain of 1, 2, 3, 4, 5, 6, 7, 8 using n, 3n will have a range of
1, 6, 9, 12, 15, 18, 21, 22, 24,
The number 24 is outside the range which is 3, 4, 5, 6, 7, 8,,,,,,,20, 22
n = 8 gave the value of 24 hence 8 cannot be the value of n
n is 1, 2, 3, 4, 5, 6, and 7
written in the form: 1 ≤ n ≤ 7
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Why does the square root of 16 have two answers?
Answers
When we multiply 4 with 4 we get 16 again
when we multiply (-4) with (-4) we get 16. so 16 has 2 square root.
What are Square and Square root ?There are always two solutions to the square root of a number: a positive response and a negative answer. Because the square of a negative and positive integer is the same, there are two possible solutions.
Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root is a value that, when multiplied by itself, returns the original value.
The values that result from multiplying an integer by itself are known as square numbers. Among the attributes are:
The square of one is one.Positive squares have positive characteristics.The square of a negative integer has a positive aspect as well.Square of 0 equals 0The value under the root is equal to a number's square root.Only even numbers will be present in every even number's unit location of square.A number's square ends in 1 if either 1 or 9 were substituted for the unit.If a number has a 4 or 6 in the place of the unit, then the square it forms ends in 6.When we multiply 4 with 4 we get 16 again
when we multiply (-4) with (-4) we get 16. so 16 has 2 square root.
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What are the properties of equilateral triangles?
Answers
Properties of equilateral triangles are:
All three sides of an equilateral triangles are equal and let be a units.All three angles are equal to 60 degreesEquilateral triangles is a regular polygon of 3 side.Equilateral triangles have the same point as its ortho-centre as well as its centroid . The median, angle bisector, and altitude of an equilateral triangle are all equal and the same straight line.An equilateral triangle's area is = [tex]\frac{\sqrt{3} }{4} *a^2[/tex].perimeter of an equilateral triangle is 3a.The length of perpendicular form a vertex to the side opposite to that vetex measure[tex]\frac{\sqrt{3} }{2} *a[/tex].To know more about equilateral triangles click on below link:
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A boat traveled on a river 10 km upstream and then comes back to its starting point. Given that the trip takes 2 hours and the river has a current of 4 km an hour, write a quadratic equation that gives the boat's speed for the trip.
Responses
A 2x2 − 20x − 32 =0
B 2x2 − 8x − 32 =0
C 2x2 − 8x − 16 =0
D 2x2 − 16x − 32 =0
Answers
Answer:
2x² - 20x - 32 = 0
Step-by-step explanation:
Trip upstream:
distance = 10 km
time = t
current = 4 km/h
speed of boat in still water = x
speed upstream: x - 4
speed = distance/time
distance = speed × time
10 = (x - 4) × t
10 = tx - 4t
t(x - 4) = 10
t = 10/(x - 4)
Trip downstream:
Distance = 10 km
time = 2 - t
current = 4 km/h
speed downstream = x + 4
speed = distance/time
distance = speed × time
10 = (x + 4) × (2 - t)
10 = 2x - tx + 8 - 4t
10 = 2x - 10x/(x - 4) + 8 - 40/(x - 4)
10(x - 4) = 2x(x - 4) - 10x + 8(x - 4) - 40
10x - 40 = 2x² - 8x - 10x + 8x - 32 - 40
2x² - 20x - 32 = 0
Simplify completely. …..
Answers
By simplifying [tex]\sqrt{75a^{8}b^{5} }[/tex], we get 5[tex]a^{4} b^{2}[/tex][tex]\sqrt{3b}[/tex].
What is square root?
A number can be obtained by multiplying the square root of that integer by itself. The word "square root" is represented by the symbol "sqrt"—square root of, end square root. The opposite of squaring an integer is finding its square root.
How to find square root?
Factoring by squares: Find the factorsSeparate the factors into their own square rootsSolve for the individual squaresFinish solving the equationLong-form factoring:Find the factorsPull duplicate factors outSolve the remaining equationLong division method:Separate your square root base into pairsFind the largest square that divides into the first number or pairSubtract the square from the first number or pairDrop down the next pairMultiply the first digit of the square by twoSet up the next factor equationFind the number that fills the blanksPut the number next to the first digit[tex]\sqrt{75a^{8}b^{5} } =\sqrt{25*3*a^{4}*a^{4}* b^{2} *b^{2}*b }[/tex]
=[tex]\sqrt{5*5*3*a^{2}*a^{2}*a^{2}*a^{2}*b^{2}*b^{2}*b }[/tex]
=5×a×a×a×a×b×b[tex]\sqrt{3*b}[/tex]
=5[tex]a^{4}b^{2}[/tex][tex]\sqrt{3b}[/tex]
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The table shows the favourite type of film of 20 people.
Action
Horror
Comedy
Answers
The complete table for the pie chart is;
Type of Film Frequency Angle in °
Action 4 72°
Horror 11 198
Comedy 5 90
How to interpret Pie chart?
From the given table used to form the pie chart, we see that;
Type of Film Frequency Angle in °
Action 4 72°
Horror 11
Comedy 5
We know that the angles in a circle is equal to 360 degrees. Thus;
Angle composed of horror and comedy = 360 - 72 = 288°
Thus;
Angle for horror film = (11/(4 + 11 + 5)) * 360°
= (11/20) * 360°
= 198°
Thus;
Angle for comedy = 288° - 198° = 90°
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Use proportional reasoning skills to figure out the unit rate of bananas if it costs $1.50 for 2/3 pound of bananas.
Answers
The unit rate of bananas is $2.25 per pound.
What is the meaning of unit rate?
Unit Rate = Ratio between two separate quantities with different units. = a:b. = a/b. This formula can be used to determine the rate of any two given quantities, such as a and b.
Given that the cost of 2/3 pound of bananas is $1.50.
If the number of pound of bananas increase then the cost of bananas will be increase.
So the relation between amount of banana is directly proportion with the cost.
Therefore,
Amount of bananas/ cost of bananas = Amount of bananas/ cost of bananas
(2/3)/1.50 = 1/x
2/4.50 = 1/x
x = 4.50/2
x = 2.25
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90pts!! please help meh iwill mark brainliest!! please have a good day/night :)
What is the product of 1.2y and 3y?
4.2y
3.6y
3.6y2
4.2y2
Answers
Answer: 3.6y^2
Step-by-step explanation:
To calculate this, you simply multiply the two numbers together: 1.2y * 3y = 3.6y^2.
Answer:
[tex] \sf \: c) \: 3.6 {y}^{2} [/tex]
Step-by-step explanation:
Now we have to,
→ find the product of 1.2y and 3y.
Forming the problem,
→ 1.2y × 3y
Then the product will be,
→ 1.2y × 3y
→ (1.2 × 3)(y × y)
→ (1.2 × 3)y²
→ (3.6)y²
→ 3.6y²
Hence, the answer is 3.6y².
Is y² X² 16 a function?
Answers
Since in [tex]y^{2} x^{2} 16[/tex] , there is no "=" sign in the given expression so we can conclude that given expression is not a function.
What is a function?A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
What are mathematical expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You may think of expressions as being comparable to phrases.
Expression=[tex]y^{2} x^{2} 16[/tex]
Since there was not "=" sign in the given expression so output can't be achieved for any given inputs so we can conclude that the given expression is not a function.
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