The quadratic equations 5x² + 20x + 20 = 0 and x² + 6x + 9 = 0 are the only correct equations having only one solution.
Solutions of a quadratic equationQuadratic equations has it highest power to the degree of two and they have two solutions that makes them true. The solutions could be different or similar ( which implies there is only one solution). From the question we shall concentrate on the equations which have similar solution or rather only one solution.
For the equation 5x² + 20x + 20 = 0;
we divide through by 5 to get;
x² + 4x + 4 = 0
x² + 2x + 2x + 4 = 0 {we group the terms}
x(x - 2) +2(x + 2) = 0 {factorize}
(x + 2)(x + 2) = 0
either; x + 2 = 0 or x + 2 = 0
x = -2 or x = -2 {which are the same solutions}
For the equation x² + 6x + 9 = 0;
x² + 3x + 3x + 9 = 0 {we group the terms}
x(x + 3) + 3(x + 3) = 0 {factorize}
(x + 3)(x + 3) = 0
either; x + 2 = 0 or x + 2 = 0
x = -2 or x = -2 {which are the same solutions}
Therefore, the quadratic equations 5x² + 20x + 20 = 0 and x² + 6x + 9 = 0 each have only one solution which are -2 and -3 respectively.
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y-5=1/2(x-4) what are the coordinates
Answer:
The ordered pair (3, 4) is found in the coordinate system when you move 3 steps to the right on the x-axis and 4 steps upwards on the y-axis.
Step-by-step explanation:
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The quotient of the given division problem is 2 remainder is 13.
What is a number system?The number system is a way to represent or express numbers.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.
As per the given division problem,
If we divide 77 by 32 then it goes to 2 times that is called the quotient.
The remainder is 77 - 32 x 2 = 13
Hence "The above division issue has a quotient of 2 and a remainder of 13.".
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HELP ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:i think its the second one
Step-by-step explanation:
QUESTION 2
Consider the hyperbolic function (y + 2)(x − 4) = 3.
2.1 Write down the domain and range of the function.
13. Mark and his brother signed up for the Catch Up
phone plan. They share the minutes every month
equally. How many minutes can Mark use each
day without going over his share of minutes?
Answer: 12 minutes
Let us suppose the number of minutes per month is 720. ( i have assumed this data from myself, you use any data you want, remember the procedure)
Now, Mark and his brother share the minutes every month equally.
So, clearly, Mark and his brother would get 360 minutes each every month.
Now, Mark has 360 minutes each month
therefore, Mark has 360/30 minutes per day
= 12 minutes each day.
Step-by-step explanation:
NO LINKS!! Please help me with the Domain and Range and Functions Part 3bb
Domain - the set of possible x-coordinates of a function.
Range - the set of possible y-coordinates of a function.
Question 30
Domain is:
x ∈ [- 6, 6], both ends included as part of graph.Range is:
y ∈ [-3, 7], both ends included as part of graph..This is not a function as it fails the vertical line test.
Question 31Domain is:
x ∈ [- 2, 2], one end is is part of the graph and the other is closed circle.Range is:
y ∈ [-6, 6], both ends included as closed circles.This is not a function as it fails the vertical line test.
Answer:
30.a) Domain: [-6, 6]
30.b) Range: [-3, 7]
30.c) Function: No
31.a) Domain: [-2, 2]
31.b) Range: [-6, 6]
31.c) Function: No
Step-by-step explanation:
Definitions
An open circle indicates the value is not included in the interval.A closed circle indicates the value is included in the interval.An arrow shows that the function continues indefinitely in that direction.Interval notation
( or ) : Use parentheses to indicate that the endpoint is excluded.[ or ] : Use square brackets to indicate that the endpoint is included.The domain is the set of all possible input values (x-values).
The range is the set of all possible output values (y-values).
Question 30The graph is a conic section (ellipse) and therefore it is not a function.
The smallest x-value is x = -6 and the greatest x-value is x = 6.
The smallest y-value is y = -3 and the greatest y-value is y = 7.
Therefore, the domain and range in interval notation are:
Domain: [-6, 6]Range: [-3, 7]The graph is a not a function as almost all the inputs (x-values) are related to more than one output (y-value).
Question 31From inspection of the graph, the endpoints of the continuous line are:
(-6, 0) and (2, 6)Both endpoints are closed circles, so the values are included in the domain and range.
The smallest x-value is x = -2 and the greatest x-value is x = 2.
Therefore, the domain in interval notation is:
Domain: [-2, 2]The smallest y-value is y = -6 and the greatest y-value is y = 6.
Therefore, the range in interval notation is:
Range: [-6, 6]The graph is a not a function as not all inputs (x-values) are related to one output (y-value).
Can someone pls help me with this I’ll mark brainliest
A study of college football games shows that the number of holding penalties assessed has a mean of 2.3 penalties per game and a standard deviation of 1.1 penalties per game.
What is the probability that, for a sample of 40 college games to be played next week, the mean number of holding penalties will be 2 penalties per game or more?
Carry your intermediate computations to at least four decimal places. Round your answer to at least 3 decimal places
The probability that, for a sample of 40 college games to be played next week, the mean number of holding penalties will be 2 penalties per game or more is of:
0.9582 = 95.82%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this distribution are given as follows:
[tex]\mu = 2.3, \sigma = 1.1, n = 40, s = \frac{1.1}{\sqrt{40}} = 0.1739[/tex]
The probability that the mean number of holding penalties will be 2 penalties per game or more is one subtracted by the p-value of Z when X = 2, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (2 - 2.3)/0.1739
Z = -1.73.
Z = -1.73 has a p-value of 0.0418.
Hence:
1 - 0.0418 = 0.9582 = 95.82%.
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a racing venue wants to make the charity race 5% longer. If the race was 25km, what is the new race length
The length of the racing venue after the increase of 5 % is 26.25 km
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the increased length of the racing venue be = A
Let the total length of the racing venue be = 25 km
The percentage increase in the length of the racing venue = 5 %
So , the equation will be
Increased length of the racing venue = total length of the racing venue + ( percentage increase in the length of the racing venue x total length )
Substituting the values in the equation , we get
Increased length of the racing venue = 25 + ( 5/100 ) x 25
Increased length of the racing venue = 25 + ( 5/4 )
Increased length of the racing venue = 25 + 1.25
Increased length of the racing venue = 26.25 km
Therefore , the value of A is 26.25 km
Hence ,
The length of the racing venue after the increase of 5 % is 26.25 km
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find x . geometry please help
The value of x in the circle is given as follows:
x = 23.
How to calculate the value of x?The value of x in the circle is calculated using the tangent-secant theorem, which states that when a secant and a tangent are drawn to a circle from the same external product, the product of the length of the secant and of it's external segment equals the square length of the tangent segment.
The parameters for this problem are given as follows:
Secant: 27 + 2x + 2 = 2x + 29.External segment: 2x + 2.Tangent: 3x - 9.Then, the value of x is obtained applying the product from the tangent-secant theorem as follows:
(2x + 29)(2x + 2) = (3x - 9)²
4x² + 62x + 58 = 9x² - 54x + 81
5x² - 116x + 23 = 0.
Which is a quadratic equation with the coefficients given as follows:
a = 5, b = -116, c = 23.
Using a quadratic equation calculator, the solutions are given as follows:
x = 0.2 -> extraneous, as the length 3x - 9 would be negative.x = 23.More can be learned about the tangent-secant theorem at https://brainly.com/question/9132922
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Eric took out an 80/20 mortgage to buy a $175,000 house. The first (80%)
mortgage has an interest rate of 4.75%, and the second (20%) mortgage has
an interest rate of 7.525%. Both mortgages are 30-year fixed-rate mortgages..
What is the total mortgage payment for this house?
Answer:
The total monthly mortgage payment for the house is $975.63
Step-by-step explanation:
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Answer: [tex]h(x)=549(0.7)^{x}[/tex]
Step-by-step explanation:
What happens to y = x when the slope is changed to a negative number?
If the slope is a negative number for example, y = - x then it would go up one and to the left one because it's a negative number. Negative slopes will always go through the coordinate plant II and IV
Aretha had $180 in her bank
account at the end of the week. She
wrote a check for $120, deposited
$250, and spent $75 on groceries
during the week. How much was
in her account at the start of the
week?
should be about $625
Just add all the number up and then subtract the answer you got with the same number except 180 since that's what she has left over. correct me if I'm wrong.
Prehistoric cave painting were discovered. The paint contained 5% of the original carbon-14. Estimate the age of the paintings using the exponential decay model for carbon-14, A=A_0e ^-0.000121t (round to the nearest whole number as needed.)
About 24 ,758 years have passed since the cave drawings were created.
What is the age formula?If one's age is x now, one's age will be nx in the future. Age n years from now equals x + n if the age at currently is x. Age n years ago equals x - n if the current age is x. The ages will be ax and bx in the ratio a: b.
What is the measure age?The time since birth, which is typically expressed as an exact number of years or a finished number of years, is known as a person's chronological age.
A is the current sum.
A0 is the original sum.
A0 = A0 A0 = A0 0.05 e-0.000121t
A / A0 = e-0.000121t
0.05 = e-0.000121t, 0.05 = ln e-0.000121t, 0.05 = -0.000121t, 0.05 = e, and 0.05 = -0.000121t, respectively.
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The artwork is 24,758 years old, according to the exponential equation's solution.
Is power equivalent to exponential?Exponents are frequently referred to as strengths or indices. In plain English, a power expression is one that depicts the same number being multiplied repeatedly, whereas an exponent is a quantity that depicts the powers to which the value is increased.
Briefing:A = current amount
A₀ = original amount
0.05 A₀ = A
A = A₀ [tex]e^{-0.000121t}[/tex]
A / A₀ = [tex]e^{-0.000121t}[/tex]
0.05 = [tex]e^{-0.000121t}[/tex]
ln 0.05 = ln [tex]e^{-0.000121t}[/tex]
ln 0.05 = -0.000121t ln e
ln 0.05 = -0.000121t
-2.9957 ≈ -0.000121t
24758.11 ≈ t
About 24,758 years have passed since the cave drawings were created.
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What is the scale factor of the geometric sequence?
4, −12, 36, −108, . . .
Enter your answer in the box.
Answer:
Step-by-step expl
The first three terms of an arithmetic sequence are as follows 17,13,9
Henry has a rope that is 5 meters long. He cuts away a piece that is 1.27 meters long. How long is the remaining piece of rope?
need it now pls
The length of the remaining rope is 3.73 meters.
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,
Length of the rope = 5 meters
Length of the rope that is cut away = 1.27 meters
The remaining length of the rope.
= 5 - 1.27
= 3.73 meters
Thus,
The remaining length of the rope is 3.73 meters.
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y=-2x coordinate plane
Answer:
The Y=-2x coordinate plane is a two-dimensional plane that represents all possible points with coordinates that satisfy the equation Y=-2x. The Y axis is the vertical axis, and the X axis is the horizontal axis. A point on the Y=-2x coordinate plane can be represented by an ordered pair (x, y), where x is the distance of the point from the Y axis, and y is the distance of the point from the X axis. In the Y=-2x coordinate plane, the Y coordinate of a point is always equal to -2 times the X coordinate of that point.
Step-by-step explanation:
Select all of the algebraic expressions that could represent the phrase below.
"nine more than the product of 5 times the number of tires t"
Answer:
a,b,d
Step-by-step explanation:
Answer:
Option A: 9 + 5t
Option B: 5 · t + 9
Option D: (5 × t) + 9
Step-by-step explanation:
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A metallurgist has one alloy containing 28% aluminum and another containing 59% aluminum. How many pounds of each alloy must he use to make 42 pounds of a third alloy containing 30%
The number of pounds from one alloy is 2.71.
The number of pounds from another alloy is 39.29.
What is an equation?An equation is a mathematical statement of two expressions connected by an equal sign.
We have,
x = pounds from one alloy
y = pounds from the second alloy
Two equation.
28% of x + 59% of y = 30% of 42
0.28x + 0.59y = 0.30 x 42 ______(1)
x + y = 42 _____(2)
Now,
x = 42 - y ________ (3)
Putting (3) in (2)
0.28(42 - y) + 0.59y = 0.30 x 42
11.76 - 0.28y + 0.59y = 12.6
11.76 + 0.31y = 12.6
0.31y = 12.6 - 11.76
0.31y = 0.84
y = 2.71
Now,
x = 42 - y
x = 42 - 2.71
x = 39.29
Thus,
The number of pounds of each alloy is 2.71 and 39.29.
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- Write a two-step problem that contains a hidden question about buying something at the mall. Tell what the hidden question is and solve your problem. Use $8.95 somewhere in your equation. Write your answer in a complete sentence.
The hidden question (that uses $8.95 in the equation) along with the answer is mentioned below.
What is a function? What is equation modelling? What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the functionEquation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is to write a two-step problem that contains a hidden question about buying something at the mall.
The problem is as follows -
You are visiting a mall where you bought 10 chocolates each of $8.95. You had $100 with yourself. If you are left with with $x, then find x.
Answer to the problem -
We can write the equation for [x] as -
x = 100 - (8.95 x 10)
x = 100 - 89.5
x = 10.5
Therefore, the hidden question along with the answer is given above.
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Thomas earned $46.50 in 4 hours at his job today. How much can he earn tomorrow if he works 10 hours at the same hourly rate? Do NOT include a dollar sign in your answer.
Answer:
116.25 0r 116.30
Step-by-step explanation:
To find the hourly rate, divide the pay by the number of hours
So 46.50/4 = 11.625
You should round that to 11.63
Then, multiply the hourly rate by the number of hours worked the next day.
So 11.63 x 10 = 116.30
Write an equation of a line passing through the point (-4, -11) and perpendicular to the line 4x + 5y = -45.
The required equation of the line is given as y = 5x -6.
To determine the equation of a line passing through the point (-4, -11) and perpendicular to the line 4x + 5y = -45.
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The slope of the given line
4x + 5y = -45
y = -4/5 - 45
m = -4/5
The equation of the perpendicular line is given as,
y - y₁ = -1/m (x - x₁)
Substitute the value in the above equation,
y + 11 = -1 / -4/5 (x + 4)
y = 5/4(x + 4) - 11
y = 5x + 5 - 11
y = 5x -6
As a result, the needed equation for the line is y = 5x -6.
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Rewrite 26/9 as a mixed number
( What value of h makes the equation true? )
-1/8 (2h + 4) + 1/2 = -7/4
. H = ?
. Please explain step by step!!
Which of the following properly expresses the
verbal
statement "The square root of a number, x, is 5
less than
the sum of the number and 2" ?
F. √x = 5-(x + 2)
G√√√x = (x + 2)-5
Answer:F. √x = 5-(x + 2)
Step-by-step explanation:
explain the pattern you found on the table
Picture 1 has 5 green squares. It is one square with a square coming out from each corner.
Describe the table pattern you noticed ? Picture 2 adds an additional square extending out from each corner square, making a total of 9 squares. This pattern continues, adding 4 green squares total each time. This means Picture 3 has 13 squares, Picture 4 has 17 squares, and Picture 5 will have 21 green squares.Picture one has 5 green squares. It is one square with a square coming out from each corner. Picture 2 adds an additional square extending out from each corner square, making a total of 9 squares. This pattern continues, adding 4 squares total each time. This means Picture 3 has 13 squares, Picture 4 has 17 squares, and Picture 5 will have 21 squares.To learn more about table pattern refer
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Given quadrilateral ABCD with A(-4,-2), B(-3,2), C(2,4) and D(4,-3). Find the area in square units.
The area of the quadrilateral ABCD, with the vertices coordinates A(-4, -2), B(-3, 2), C(2, 4), and D(4, -3), is 18 square units
What is a quadrilateral?A quadrilateral is a four sided polygon, that has a sum of the interior angles of 360°
The area of the quadrilateral can be calculated as comprising of the area of two triangles, with vertices; B(-3, 2), C(2, 4), D(4, -3), and B(-3, 2), C(2, 4), A(-4, -2)
The area of a triangle with known coordinates of the vertices is precented as follows;
Let (x₁, y₁), (x₂, y₂), (x₃, y₃) represent, the vertices of the triangle, we get;
A = 0.5×|x₁·y₂ - x₂·y₁ + x₂·y₃ - x₃·y₂ + x₃·y₁ - x₁·y₃|
Therefore;
The area, A₁ of the triangle ΔBCD with vertices at the coordinates (-3, 2), (2, 4), (4, -3), is found as follows;
A₁ = 0.5 × |(-3)×4 - 2×2 + 2 ×(-3) - 4 × 4 + 4×2 - (-3)×4| = 9
Similarly, the area, A₂, of the triangle, ΔBCA with vertices (-3, 2), (2, 4), (-4, -2), is found as follows;
A₂ = 0.5 × |(-3)×4 - 2×2 + 2 ×(-2) - (-4) × 4 + (-4)×2 - (-3)×(-2)| = 9
The area of the quadrilateral, A = A₁ + A₂, is therefore;
The area of the A = 9 + 9 = 18
The area of the quadrilateral ABCD is 18 square units
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please help! I'm almost out of time on my assignment
The functions f and h are defined as follows:
f(x) = (x + 5)/(x - 7) and h(x) = (x + 5)(x - 7).
Explain why the functions f and h are not the same function.
The functions f and h are not the same because they are composed of different operations.
What is Function?A function is a block of code that performs a specific task. It can accept input in the form of parameters, and may return an output. Functions are an important part of programming, as they allow for the repetition of code without having to write the same lines multiple times. This increases code readability and eliminates the need to debug multiple lines of code. Functions can also be reusable, meaning they can be called and used over and over again with different parameters.
Function f takes the ratio of two terms while function h takes the product of two terms. Additionally, the terms in the two functions are different. Function f takes the sum of x and 5 and the difference of x and 7 while function h takes the sum and the difference of the same two terms. As a result, the functions f and h will generate different outputs for the same input.
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