Answers
x2 - 3x - 5 = 0 has a unique solution of type -11, which is what the equation entails.
what is discriminant ?The "discriminant" is the value that aids in identifying the many types of solutions when using the quadratic formula to solve a problem. It is a unique function of a co-efficient in a mathematical equation (a quadratic equation), and the value it yields provides details about the roots of the equation. Calculating the discriminant involves square rooting the "b" term and subtracting four times the "a" term from the "c" term. Alongside "D," there is a (delta) that represents discrimination. A quadratic equation with two distinct real number solutions is said to have a positive discriminant. A quadratic equation with a discriminant of zero has repeated real number solutions. Both of the solutions are not real numbers, as indicated by a negative discriminant.
given
x2 - 3x - 5 = 0
D=b2−4ac
D= −32−4×1×5
D=92−20
D= −11
x2 - 3x - 5 = 0 has a unique solution of type -11, which is what the equation entails.
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Related Questions
Multiply the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending powers of x. (8x 3)(4x 7)
Answers
The product of the two polynomials is (8x³)(4x⁷) = 32x¹⁰.
THE POLYNOMIALSWhen we multiply two polynomials together, we add the exponents of the x's in each term. In this case, we have 8x³ and 4x⁷. The x in 8x³ has an exponent of 3, and the x in 4x⁷ has an exponent of 7. To find the product of the two polynomials, we add the exponents of the x's in each term, so 3 + 7 = 10. The x in the product will have an exponent of 10. The coefficient, or the number in front of the x, is also multiplied together, so 8 × 4 = 32.So the final answer is 32x¹⁰, where 32 is the coefficient and 10 is the exponent of x.The polynomial 32x¹⁰ is an example of a polynomial, but it's not a characteristic of a polynomial.A polynomial is a mathematical expression involving a sum of powers in one or more variables (such as x, y, z) with non-negative integer exponents and real or complex coefficients. A polynomial can have one or more terms, and each term is separated by a plus or minus sign.Learn more about polynomial here:
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Stefan sells Jin a bicycle for $146 and a helmet for $19. The total cost for Jin is 150% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Answers
Stefan spend price $110 and made price $60 by selling bicycle and helmet to Jin.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Here, given that,
Selling price of bicycle = $146
Selling price of helmet = $19
Total = 146+19= $165
Let,
x represents the original cost Stefan to buy the bike and helmet.
150% of x = $165
1.5x=$165
Dividing both sides by 1.5
we get ,
x=$110
Stefan bought bicycle and helmet for $110.
Profit made by Stefan = Selling price - buying price
Profit made by Stefan = 165-110= 55
Hence, Stefan spend price $110 and, made $55 by selling bicycle and helmet to Jin.
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What is BPT Theoram please solve
Answers
In a triangle, a line is drawn parallel to one side of the triangle. Then it ratio of the two similar triangles will be con
What is the Basic Proportionality theorem?The Basic Proportionality Theorem, often known as the Thales Theorem, was developed by the eminent Greek mathematician Thales. He asserted that the ratio of any two matching sides is constant for any two equiangular triangles. He developed the basic proportionality theorem based on this idea (BPT). Similar triangles have presented this idea. When two triangles resemble one another.
Think about the triangle ΔABC in the given illustration. A line PQ connecting the sides AB and AC of P and Q in this triangle is drawn parallel to the side BC of the triangle.
AP/PB = AQ/QC
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What is the coefficient of y² in the expression 2x²y 10xy² 5y?
Answers
The coefficient of yA² for the three given expressions are 2, 10 and 5 respectively.
What is expression?
It is a mathematical statement that defines a mathematical concept as well as the system of a mathematical operation express in a symbolic form.
Mathematical expression is made up of at least two numerical terms along with a sign or at least two terms along with a sign. The expression having two or more numerical terms is called numerical expression.
As example 4 + 3 or 100÷4
The expression which has both variables and numbers is called algebraic expression.
As example X+6 or 25+5y
What is coefficient?
In an expression, the numbers which are accompanied by variables is called coefficient. As example, 24 + 3y, where 3 is the coefficient of y
but 24 is a constant number.
How can we determine the coefficient from the given expression?
We are given three expressions, these are 2xA²y, 10xyA² and 5yA²
for the 1st expression, 2 is the coefficient of A²y
for the 2nd expression, 10 is the coefficient
for the last 5 is the coefficient.
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What does using the if __ name __ == '__ main __' syntax allow programmers to do?
Answers
The if __name__ == '__main__' syntax allows a programmer to specify that certain code should only be executed when the script is run directly, rather than when it is imported as a module into another script.
This can be useful for running code that you only want to execute when you're running the script for testing or development, rather than when you're using it as a library in another program. It also allows to use the same code in multiple script without running the main code.
When a Python script is run, the interpreter assigns the name __main__ to the script's global namespace. Therefore, when the script is run directly, __name__ will be set to __main__. When the script is imported as a module into another script, __name__ will be set to the name of the module, rather than __main__.
So, when a programmer uses the if __name__ == '__main__' syntax, they are essentially checking whether the script is being run directly or imported as a module. If the script is being run directly, the code within the if block will be executed. If the script is being imported as a module, the code within the if block will not be executed.
This allows the programmer to separate code that should only be run when the script is executed directly from code that is intended to be used as a library when the script is imported as a module. It also allows to use the same code in multiple script without running the main code.
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What does += mean in Python?
Answers
In Python an operator += is an assignment operator which adds the value on its right to the variable and assigns the result to the variable on its left.
We know that an operator is a symbol that represents a mathematical or logical process.
We know that in Python the operator += provides a convenient way to add a value to an existing variable and assign the new value back to the same variable.
If p += q
This means, the variable p the left side is getting added to the value on the right side (q), and the result is then reassigned to the variable on the left.
i.e., p = p + q
+= is an assignment operator.
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Which of the following is the graph of y=-4 square root x
Answers
In the second graph, these points are located. As a result, the second graph is the function's correct graph.
what is function ?In mathematics, the term "linear function" refers to two different but related ideas. In calculus and related fields, a quadratic variable of grade 0 or 1 is a linear function if its graph is a direct line. A straight line on a reference system is a representation of a linear function. For instance, the linear function y = 3x - 2 is a straight line just on coordinate plane, hence it is a linear function. Since f(x) may be connected to y, the function can be represented by f(x) = 3x - 2.
given
The function provided is
This function is defined for any x values that are positive, including 0.
The radical expression x has a constant positive value. Given that is a function, it is always negative.
At x=0, = 0
At x=1, = -4
At x=4, = -8
This indicates that the graph of the specified function traveling through the points (0,0), (1,-4) and (4,-8).
In the second graph, these points are located. As a result, the second graph is the function's correct graph.
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√
18
−
√
2 simplify far as possible
Answers
Answer:
2[tex]\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\sqrt{2x9}[/tex] - [tex]\sqrt{2}[/tex] = 3[tex]\sqrt{2}[/tex] - [tex]\sqrt{2}[/tex] = 2[tex]\sqrt{2}[/tex]
How do you find the dilation of a function?
Answers
Finding the dilation's center point is the first step in determining the scale factor. Next, we measure the distances between the center point and various points on the preimage and the image. The scale factor is equal to the ratio of these distances.
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.
A graph's form is altered by dilations, frequently leading to "movement" in the process. In the figure above, the green curve has been "transformed" into the red curve. It has been three times "dilated" (or stretched) horizontally. A dilatation is an axial stretching or contraction brought on by multiplication or division.
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Select all the pairs of operations that have inverse relationships.
Answers
The pairs of operations that have inverse relationships are subtraction and addition and multiplication and division. The correct options are A and D.
What are algebraic operations?Any of the common arithmetic operations, such as addition, subtraction, multiplication, division, raising to a whole number power, and taking roots, are considered basic algebraic operations in mathematics (fractional power).
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The inverse operations can be subtraction and addition and multiplication and division.
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Margo borrows $700, agreeing to pay it back with 8% annual interest after 16 months. How
much interest will she pay?
Answers
After 16 months, Margo will pay $74.67 interest
We know that the simple Interest Formula
I = P × r × t
Where: P = Principal Amount
I = Interest Amount
R = Rate of Interest as a percent
r = Rate of Interest in decimal
r = R/100
t = Time Periods involved
Here we have been given P = $700, t = 16 months and R = 8%
First we convert interest rate R percent to r a decimal
r = R/100
= 0.08 per year,
Now we convert time from months to years .
16 months ÷ 12 months/year
= 1.333333 years,
Using above formula of simple interest,
I = P × r × t
I = 700 × 0.08 × 1.333333
I = $ 74.67
Hence, the simple interest accumulated on a principal of $ 700.00 at a rate of 8% per year for 16 months is $ 74.67.
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The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.
Answers
The solution of the system of equations is:
x = 5t - 4
y = -5t + 1
z = t
Option B is the correct answer.
What is a matrix?A matrix is a set of numbers arranges in rows and columns such that it form a rectangular array.
We have,
From the row-echelon form of the augmented matrix of a system of equations, we get,
x + 0y -5z = -4
x - 5z = -4
x = 5z - 4
0x + y + 5z = 1
y + 5z = 1
y = -5z + 1
0x + 0y + 0z = 0
Now,
Put z = t (any real number)
We get,
x = 5t - 4
y = -5t + 1
Thus,
The solutions are:
x = 5t - 4
y = -5t + 1
z = t
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A newsletter publisher believes that more than 47% of their readers own a personal computer. Is there sufficient evidence at the 0.05 level to substantiate the publisher's claim?
Answers
There is no sufficient evidence at the 0.05 level to substantiate the publisher's claim
How to determine the substantial claim?The parameters for the claim is more than 47% of their readers own a personal computer0.05 level of significanceNote that the significance level, also known as alpha or α, is a measure of the strength of the evidence that must be present in your sample before you will reject the null hypothesis and conclude that the effect is statistically significant
In conclusion, the advertiser failed to reject the null hypotenuse so this would mean there is not sufficient evidence at the 0.02 level of significance to say that the percentage of people who own a Rolls Royce is higher than 47%
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x^5 multiplied by x^3 /x^4
Answers
Answer:
x^4
Step-by-step explanation:
[tex]x {}^{5} \times \frac{x {}^{3} }{x {}^{4 \\ } } \\ \\ \frac{ {x}^{8} }{x {}^{4} } \\ \\ x {}^{8 \: - \: 4} \\ {x}^{4} [/tex]
Raina is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices. Company A charges and allows unlimited mileage. Company B has an initial fee of and charges an additional for every mile driven. For what mileages will Company A charge less than Company B
Answers
For mileages of 40 or less, Company A will charge less than Company B. For mileages above 40, Company B will charge less than Company A.
To compare the prices of the two companies, we need to determine the total cost for each company at different mileage.
For Company A, the total cost is the initial fee of $50. This is a fixed price, regardless of the mileage driven.
For Company B, the total cost is the initial fee of $30 plus the additional cost per mile driven. To calculate this, we can use the formula:
Total cost = initial fee + (mileage * additional cost per mile)
For Company B, this would be:
Total cost = $30 + (mileage * $0.50)
To find out when Company A charges less than Company B, we need to compare the total costs of the two companies at different mileage. We can set up the following inequality:
$50 <= $30 + (mileage * $0.50)
To solve for mileage, we need to isolate it on one side of the inequality. To do this, we can subtract $30 from both sides:
$20 <= (mileage * $0.50)
Then, we can divide both sides by $0.50:
40 <= mileage
So for mileages of 40 or less, Company A will charge less than Company B. For mileages above 40, Company B will charge less than Company A.
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It takes 34 of an hour to paint a single shutter. It takes 9 hours to paint 12 pairs of shutters. The number of hours, y, that it takes to paint xshutters shows either a direct or inverse variation. What is the equation that relates x and y?
Answers
The equation that relates x and y for the given data is y = (3/4)x.
The relationship between the number of shutters (x) and the number of hours (y) is an inverse variation because as the number of shutters increases, the number of hours required to paint them decreases and vice versa.
An inverse variation is a relationship between two variables in which their product is always equal to a constant value. Mathematically, it can be represented by the equation: y = k/x where k is a constant and x and y are the variables in question.
Hence, the equation that relates x and y can be found using the information given:
y = (9 hours) / (12 shutters) * x shutters
y = (3/4)x is the required equation.
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How to determine if a triangle is right acute or obtuse based on side lengths calculator?
Answers
A triangle is said to be acute if the sum of the squares of its two shorter sides is greater than the square of its longest side.
How do you know if its right obtuse or acute?Less than 90 degree angles are considered acute. Right angles have a 90 degree angle. Angles that are obtuse exceed 90 degrees.
See samples of various angles and learn about them. If and only if side lengths a, b, and c satisfy a2 + b = c2, a right triangle will be formed. These numbers are referred to as a Pythagorean triple. When the square of a triangle's longest side equals the sum of the squares of its other two sides, the triangle is said to be a right triangle. So, in the ABC equation, if c2=a2+b2, then C is a right triangle, with PQR serving as the right angle.
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Solve for x : 4x-6=x+9
Answers
4x - 6 = x + 9
4x - x = 9 + 6
3x = 15
[tex]x = \frac{15}{3} \\ [/tex]
x = 5 ...
Answer:
[tex]x =5[/tex]
Step-by-step explanation:
[tex]4x - 6=x+9[/tex]
Subtract x from both sides
[tex]4x -6-x=x+9-x[/tex]
[tex]3x-6=9[/tex]
Add 6 to both sides
[tex]3x-6+6=9+6[/tex]
[tex]3x=15[/tex]
Divide both sides by 3
[tex]\frac{3x}{3} = \frac{15}{3}[/tex]
[tex]x = 5[/tex]
Karl invests $100 in a savings account, which earns interest yearly.
Select the TWO changes that would earn Karl more money from this savings account.
Answers
The two changes that would Karl earn more money are "Karl increases his initial investment" and "Karl deposits more money into the account every year" (options B and D).
What factors affect the amount of money Karl can get?In this case, the amount of money Karl can get depends on both the amount of money he invest and the interest rate. Here are some examples:
If he invest $100 and the interest rate is 10% he will get $10
If the invest $1000 and the interst rate is the same (10%) he will get $1000
Moreover, if the interste rate increases he can get more money: If the invest $100 but the interst rate is 12% he gets $12
This means he can get more profit if the investment is higher or the rate increases. Based on this, the two options that would increase his amount of money are increasing the initial investment or depositing more money (option B and D).
Note: This question is incomplete; here is the missing section:
A. The bank decreases the interest rate.
B. Karl increases his initial investment.
C. The bank adds a fee to keep the account active.
D. Karl deposits more money into the account every year.
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50 POINTS!!!! urgent!!!!!!
Mary is collecting cup cakes for the school fair. She will make 12 cupcakes to start it off. She plans to collect 24 cupcakes each
day from her surrounding neighborhood for the next 3 days. If you model this word problem for Mary as y=mx+b then match the
corrects pairs.
a. 12
b. 84
c. 3
d. 24
1. m
2. y
3. x
4. b
Answers
Since the problem is about linear equation in the form of y = mx + b, initial number represents the value of b = 12, the number of days represents the value of x = 3, the daily collection of cupcakes represent the slope m = 24, then the value of y is:
y = 24*3 + 12 = 72 + 12 = 84So the matching pairs are:
a ⇔ 4, b ⇔ 2,c ⇔ 3,d ⇔ 1 .What is the equation of the Y axis?
Answers
Answer:
x=0
Step-by-step explanation:
The general form of the equation of y-axis is x = 0. hence, the equation of line parallel to the y-axis is given by the equation: x = k.
3x-3y=-6
3x+y=10 use subtraction please help thank you
need an ordered pair
Answers
Answer:
x=2, y=4. (2, 4).
Step-by-step explanation:
3x-3y=-6 implies 3(x-y)=3(-2), so x-y=-2.
-----------------------------
x-y=-2
3x+y=10
---------------
4x=8
x=8/4=2
2-y=-2
y=2-(-2)=2+2=4
Solve equations - two sides
(135a)
Solve
2x - 7=7x +5
Answers
Answer:
x=-12/5
Step-by-step explanation:
2x-7=7x+5
2x-7x=5-(-7)
-5x=5+7
x=12/-5
x=-12/5
How many times smaller is 1.2 × 106 than 1.38 × 107?
Answers
The number 1.2 × 10⁶ is 11.5 times smaller in comparison to the number 1.38 × 10⁷.
The two given numbers here have been written using the method of powers of 10. In this method, very large or very small numbers are easily simplified and written by denoting the powers of 10. These power are integral in nature. Very large numbers are of the form y × 10ⁿ and very small numbers can be expressed in the form z × 10⁻ⁿ.
In the given problem, we have the numbers 1.2 × 10⁶ and 1.38 × 10⁷ and we have to tell how much the former number is from the latter. For this, we divide the two and easily find our solution. Before this, we have to make the powers of 10 in both numbers the same. We can rewrite the 1.38 × 10⁷ as 13.8 × 10⁶. Now, we divide the two and get-
⇒ 11.5
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Answer: B. 11.5
Step-by-step explanation: I took the test
The data below shows the orders that were placed at a local paint shop. 1 2 3 4 Paint orders 5 6 Gallons 7 8 9 10 Solve for the MEAN of this data set. If needed, round to the nearest tenth.
Answers
To find the MEAN of Natural numbers, such as 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, a + b + c3 is the sum of the three numbers a, b, and c. Therefore, 5.5 is the MEAN of the first 10 natural numbers.
Find the MEAN Of Data setFirstly The Given set of numbers Represents Natural numbers,
A natural number is an integer greater than 0. Natural numbers begin at 1 and increment to infinity: 1, 2, 3, 4, 5, etc.
Therefore, the first ten natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
And the mean of three numbers a, b, c is a + b + c3
Then the mean of 10 numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is:-
⇒1+2+3+4+5+6+7+8+9+1010
Adding and dividing we get the value of the above term as,
⇒1+2+3+4+5+6+7+8+9+1010=5510=5.5
Hence, the mean of the first 10 natural numbers is 5.5.
Note: To solve this problem, you must understand that the integers greater than zero are natural numbers and that the mean of the three numbers a, b, and c equals a + b + c3. Knowing how to calculate the average number of elements and being familiar with natural numbers can help you arrive at the correct conclusion.
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Write the explicit formula for the sequence below:
Answers
The explicit formula for the sequence -28, -31, -34, -37, ..., is aₙ= -28 -3d.
What is an arithmetic sequence?A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given:
-28, -31, -34, -37, ...
The general formula of an arithmetic sequence:
aₙ= a₁ + (n)d,
where a₁ is the first term and d is the common difference.
First, we will find the common difference between consecutive terms.
Here,
a₁ = -28
To find the common difference:
a₂ - a₁ = -31 + 28 = -3
a₃ - a₂ = -34 + 31 = 3
a₄ - a₃ = -37 + 34 = 3
Hence, d = -3.
Substitute the values to the formula,
aₙ= a₁ + (n)d,
aₙ= -28 + (-3)d,
aₙ= -28 -3d
Therefore, aₙ= -28 -3d is the required sequence.
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Jayden has been reading a 275275275-page book for English class. On average, he has read about 101010 pages in 151515 minutes (\text{min})(min)(, start text, m, i, n, end text, ). With a deadline looming, Jayden realizes that he won't finish in time unless he skims through the rest of the book. If he skims the book, he can cover 151515 pages in 10\,\text{min}10min10, start text, m, i, n, end text. If it takes Jayden 555 hours and 50\,\text{min}50min50, start text, m, i, n, end text to finish the book (reading and skimming combined), how many pages did Jayden have to skim through
Answers
Jayden had to skim through an amount of 75 pages, in the given word problem.
What is word problem?A word problem is a few sentences that describe a "real-life" scenario in which a problem must be solved using a mathematical calculation.
Word problems are regarded as an important part of the primary curriculum because they require children to apply their knowledge of various concepts to'real-life' scenarios.
Let S = no. of skimmed pages
Let R = no. of read pages
Then S + R = 275
So R = 275 - S
Reading rate = 15 min/10 pages
Skimming rate = 10 min/15 pages
Total time to finish book = 350 min
So,
(R)(Reading rate) + (S)(Skimming rate) = 350 minutes
Substituting the values:
(275-S)(15/10) + (S)(10/15)=350
Multiplying equation through by 30 yields:
12375 - 45S + 20S = 10500
Combine terms
1875=25S
S = 75
Thus, Jayden had to skim through an amount of 75 pages.
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Order the set of numbers from least to greatest: 5, -19, -25, 7, 22, -4, -15
Answers
Answer:
-25, -19, -15, -4, 5, 7, 22
Step-by-step explanation:
-25, -19, -15, -4, 5, 7, 22 is the order from least to greatest
The bigger the negative number, the smaller it is; that is why the order is
-25, -19, -15, -4, 5, 7, 22
Please help if you can or and know how to do this pls! Can
Answers
Answer:
m<1=50
m<2=130
m<3=50
m<4=130
m<5=40
m<6=40
m<7=90
m<8=140
Step-by-step explanation:
what part of 3$ is the sum of 7 dimes, 1 nickel and 3 pennies?
Answers
Answer:
7/60
Step-by-step explanation:
First, we would need to add up all of the coins and know their values.
1 dime (d) = 10¢
1 nickel (n) = 5¢
1 penny (p) = 1¢
An equation we can use will look something like this:
(d × 7) + (n × 1) + (p × 3) =?
Now just add the numbers and solve.
(10 × 7) + (5 × 1) + (1 × 3) = 78
Therefore, the total amount is 78¢.
Now to figure out how much 78¢ is out of $3, we can use an equation that looks something like this:
3 ÷ 0.78 = 3.84615385 or 7/60
So, this means that with 7 dimes, 1 nickel and 3 pennies it is 7/60 of $3.