There are three basic methods for solving quadratic equations: factoring, using the quadratic formula, and completing the square.
quadratic equations
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax^2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).
factoring
factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
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Marvin used the money he received from high school graduation gifts to start a new savings account with a simple interest rate of 7. 5%. After 12 years, the account had earned $288. If there were no other deposits or withdrawals, what was the original amount placed in the account?
The original amount placed in the account is $320.
What is simple interest ?
Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.
The simplest way to compute interest is as a percentage of the principal. For instance, if you borrow $100 from a friend and agree to pay back the money with 5% interest, the interest you would have to pay would simply be 5% of $100, or $5.
Simple Interest is the amount repaid for using the borrowed funds over a predetermined amount of time.
The interest earned is calculated as follows:
I = P*r*t
Where:
I = Interest
P = initial principal balance
r = interest rate
t = time
Marvin is saving money in a savings account with a simple interest rate of r=7.5%=0.075. It's known that after t=12 years, the account had earned $288 interest.
Substituting in the formula:
288 = P*0.075*12
Calculating:
288 = 0.9P
Dividing by 0.9:
P = $320
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please help:
find BP
Answer:
so i will be honest I've done this before and it may be 64 or 120
Step-by-step explanation:
It may be one of these answers I'm doing as much as I can to help
A performance score on the normally distributed WAIS Test that is higher than all but 2 percent of all scores earns an intelligence score of:
Scores earns an intelligence score of 130
What percentage of WAIS scores fall into this range?According to the 68-95-99.7 rule, 68% of persons have WAIS scores ranging from 100-15 to 100+15. WAIS scores between 85 and 115 are obtained by 99.7% of the population. As a result, 32% of adults have WAIS scores of 85 or above. Factor Analysis is a statistical process used to discover clusters of similar questions (called factors) on a test; it is used to identify multiple levels of performance that underpin one’s overall score.
The WAIS categories are shown below and are based on a mean of 100: Scores of 130 and higher are deemed talented. Scores between 120 and 129 are regarded extremely intelligent. Normal intellect is defined as a score between 110 and 119.
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Complete question is: A performance score on the WAIS that is higher than all but 2 percent of all scores earns an intelligence score of:
115.120.130.145.A solution of 60 quarts of sugar and water is 20% sugar. How much water must be added to make a solution that is 5% sugar
On solving the provided question we can say that by equation 180 water must be added to make a solution that is 5% sugar
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
here, the equation is -
1200=300+5x
900 = 5x
x=180
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simpelest form of the ratio 2 weeks to 30 days
Answer:
7:15 ,2 weeks=14 days and 30 days divide by 2 = 7 and 15 put them to a ratio and you'll get 7:15.
Blanca runs 8 laps around the track each day to train for an endurance race. She times each lap to practice her pacing for the race. The table shows the lap times, in seconds, for three days of practice. Which histogram represents Blanca’s lap times for the three days of practice?
A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and the number of laps on the vertical axis. 1 lap was 82 to 84 seconds. 4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 5 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 0 laps were 96 to 98 seconds
What is endurance race?
A type of motorsport racing known as endurance racing is designed to test both the participants' and the equipment's endurance. Teams of several drivers attempt to travel a long distance in a single race while being allowed to change drivers at any time.
The given table is attached below.
The number of laps in the range 82 to 84 seconds = 1
The number of laps in the range 84 to 86 seconds = 4
The number of laps in the range 86 to 88 seconds = 2
The number of laps in the range 88 to 90 seconds = 4
The number of laps in the range 90 to 92 seconds = 6
The number of laps in the range 92 to 94 seconds = 5
The number of laps in the range 94 to 96 seconds = 2
The number of laps in the range 96 to 98 seconds = 0
Therefore, the histogram that represents Blanca's lap times for the three days of practice is described as follows;
A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and the number of laps on the vertical axis. 1 lap was 82 to 84 seconds. 4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 5 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 0 laps were 96 to 98 seconds.
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Answer:A
Step-by-step explanation:
Consider the differential equation dy/dx=xy^4.
(b) Find ⅆ2yⅆx2 in terms of x and y. Determine the concavity of all solution curves for the given differential equation in Quadrant II. Give a reason for your answer.
(c) Find the particular solution y=f(x) to the given differential equation with initial condition f(4)=−1.
The differential equation [tex]\frac{dy}{dx} = xy^{4}[/tex] is considered and the solutions for the following questions are found.
What is a differential equation?
A differential equation is an equation that links the derivatives of one or more unknown functions. Differential equations contain derivatives, which might be either partial derivatives or ordinary derivatives.
The differential equation describes a relationship between the variable that is constantly varying with respect to the change in another quantity, and the derivative represents a rate of change.
Given,
[tex]\frac{dy}{dx} = xy^{4}[/tex]
a) Now finding [tex]\frac{d^{2} y}{dx^{2} }[/tex] = [tex]y^{4} + 4xy^{3} \frac{dy}{dx}[/tex] = [tex]y^{4} + 4xy^3 (xy^4) = y^4 + 4x^2y^7[/tex]
In quadrant II, the values of x < 0 and the values of y >0.
So [tex]\frac{d^{2} y}{dx^{2} }[/tex] = [tex]y^4 + 4x^2y^7[/tex] > 0 for all values of x and y in quadrant II.
Therefore the concavity is up for of all solution curves of the given differential equation.
b)
[tex]\frac{dy}{dx} = xy^{4}\\\\\frac{dy}{y^4} =x dx\\\\\int {\frac{dy}{y^4} } \, = \int {x} \, dx \\\\\frac{y^{-4+1} }{-4+1} = \frac{x^{2} }{2} + c\\\\\frac{y^{-3} }{-3} = \frac{x^{2} }{2} +c[/tex]
Now it is given that initial condition is f(4) = -1
So substituting x =4 and y = -1 is the above equation to find c, we get
[tex]\frac{-1^{-3} }{-3} = \frac{4^2}{2} +c \\\\\frac{1}{3} = 8 + c\\\\c = \frac{1}{3} - 8 = \frac{-23}{8}[/tex]
Therefore the solution y = f(x) is to the given differential equation with initial condition f(4)=−1.
[tex]\frac{y^{-3} }{-3} = \frac{x^{2} }{2} -\frac{23}{8}\\ \\ \frac{1}{3y^3} = \frac{46 - 8x^2 }{16} = \frac{23 - 4x^2 }{8}\\\\y = \sqrt[3]{\frac{8}{3(23-4x^2)} }[/tex]
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Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. He has to option of beginning to repay the loan in 4.5 years. He also knows that during the time he is not making payments, interest will be charged at 4.29%. If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period. What will his monthly payments be? Round to the nearest cent.
If Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. His monthly payment is $87.31.
What is monthly payment?Monthly payment can be defined as the amount a person received on a monthly basis.
Now let find the monthly payment
Monthly payment = 7900 (0.0429/12) ( 1+ 0.0429/12)^12×10 ÷ ( 1+ 0.0429/12)^12×10 -1
Monthly payment = 7900 (0.003575) ( 1+ 0.003575)^120÷ ( 1+ 0.003575)^120 -1
Monthly payment =7900 (0.003575) ( 1.003575)^120 ÷ ( 1.003575)^120 -1
Monthly payment = $87.31
Therefore the monthly payment is $87.31.
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The complete question is:
Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. He has to option of beginning to repay the loan in 4.5 years. He also knows that during the time he is not making payments, interest will be charged at 4.29%. If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period. Suppose that Rich had decided to apply for a private loan rather than a federal loan. He is considering a 10-year lo"an with an interest rate of 5.9% .What will his monthly payments be?
help i have 5 mins left
Answer: c = P - a - 5
Step-by-step explanation:
P= a + 5 + c
P - a - 5= c
What is the relationship between the line of reflection and the segments connecting the corresponding points?
The relationship between the line of reflection and the segments connecting the corresponding points is perpendicular bisector.
Here we have to find the relationship between the line of reflection and the segments connecting the corresponding points
In order to find the relationship we must know what is meant by line of reflection.
The term line of reflection is defined as a line that lies in a position between two identical mirror images so that any point on one image is the same distance from the line as the same point on the other flipped image.
As per the definition of the term we have identified that the relationship between these two element is perpendicular to the segment and bisects it. Because the line of reflection is the perpendicular bisector of the segment joining corresponding points of the preimage and image.
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Sara's mom takes the parkway to work. It takes her 30 minutes to travel from mile marker 88 where she enters to her exit at mile marker 121. What is her average speed
Sara's mom average speed is 66mph. The next step is to divide the distance by the time: 33/0.5 = 66 mph.
What is average speed ?You may estimate the average pace at which an object will go a distance by looking at its average speed. Average speed is calculated by dividing a quantity by the time required to obtain that quantity.
Finding the distance and the time is necessary to calculate speed.
In this situation, you must deduct mile marker 88 from 121 to determine the distance.
121 - 88 = 33mile
Even though the time is 30 minutes, you're probably interested in miles per hour. 30 minutes must be converted to 0.5 hours.
The next step is to divide the distance by the time: 33/0.5 = 66 mph.
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\frac { 32 x ^ { 2 } } { y } + \frac { 108 y ^ { 2 } } { x } y 32x 2 + x 108y 2
Therefore , the solution of the given problem of fraction comes out to be 4((2x)³ + (3y)³) /xy.
What exactly is a fraction?To represent a whole, divide it into any number of comparable parts, or fractions. How many units of a particular size there are is expression using fractions in standard English. 8, 3/4. Parts of a whole are included. Numbers in mathematics are stated as a ratio of the fraction to the denominator. These are each simple fractions that represent an integer. A fraction is contained in the exponent or population of a complicated fraction. When a fraction is true, its numerators are less than its denominators. An amount that makes up a fraction of a whole is called a fraction. You can assess the whole by dissecting it into smaller pieces. For instance, 12 is used to denote half of a total number or item.
Here,
Given : 32x²/y + 108y²/x
=> (32x³+ 108y³ ) /xy
=> 4(8x³ + 27y³) /xy
=> 4((2x)³ + (3y)³) /xy
Therefore , the solution of the given problem of fraction comes out to be
4((2x)³ + (3y)³) /xy.
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How do you graph a slope of 3 4?
if the y-intercept is (0,5), you have:
y = (3/4)x + 5
How to slope a graph?To graph a line with a slope of 3/4, you can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
Since the slope is 3/4, the equation of the line is y = (3/4)x + b.
To find the y-intercept, you can plug in the coordinates (0,b) into the equation. So if the y-intercept is (0,5), you have:
y = (3/4)x + 5
You can then plot the point (0,5) on the graph, and use the slope of 3/4 to find the next point by going up 3 and right 4.
Another way is to pick two points on the line and plot them, you can use the slope formula (rise over run) to find the next point on the line.
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4. Find the probability that a randomly chosen point lies inside the shaded region. 4.
Express your answer as a decimal rounded to the nearest hundredth.
0.167 or 0.17 rounded to the nearest hundredth.
How do you round off decimal to the nearest hundredth?
When rounding to the nearest hundredth, you want to look at the third decimal place, the one to the right of the hundredth place. If the value in the third decimal place is less than 5, you truncate everything to the right of the hundredth place, leaving the number unchanged.
If the value in the third decimal place is greater than or equal to 5, you add one to the number in the hundredth place.
The total area of the rectangle is 15*5 = 75 square feet.
The area of the triangle inside the rectangle is (1/2)25 = 12.5 square feet.
The shaded region is the area of the triangle, so the probability that a randomly chosen point lies inside the shaded region is
12.5/75 = 0.167 or 0.17 rounded to the nearest hundredth.
Hence, 0.167 or 0.17 is rounded to the nearest hundredth.
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Fwam went shopping for a new phone. Sales tax where he lives is 9%. The price of the phone is $33. Find the total price including tax. Round to the nearest cent.
Answer:
$35.97
Step-by-step explanation:
33 × .09 = 2.97
33 + 2.97 = $ 35.97
The diameter of a circle is 34 inches.What is the area of the circle in square inches?Use 3.14 as pi
Answer: 907.46 inches squared
Step-by-step explanation:
The formula for the area of the circle is:
[tex]A = \pi r^{2}[/tex]
In this question, pi is 3.14. The radius of a circle is half of its diameter. So:
[tex]\frac{34}{2} =17[/tex]
Plug these values into the equation:
[tex]A = (3.14)(17)^2[/tex]
Simplify:
[tex]A = 907.46[/tex]
The area of the circle is 907.46 inches squared.
(d) At a football match, there are 29 800 people, correct to the nearest 100. (i) At the end of the football match, the people leave at a rate of 400 people per minute, correct to the nearest 50 people. Calculate the lower bound for the number of minutes it takes for all the people to leave.
The lower bound for the number of minutes that it takes for all people to leave is of:
70 minutes.
How to obtain the lower bound for the number of minutes that it takes for each person to leave?At a football match, there are 29 800 people, correct to the nearest 100. The fewest number of people that can be there, hence, is of:
29,750.
(as 29749 would be rounded to 29,700).
At the end of the football match, the people leave at a rate of 400 people per minute, correct to the nearest 50 people, hence the fastest rate is given as follows:
424 people per minute.
(as 425 people would be rounded to 450).
Hence the time it would take is obtained applying the proportion as follows:
29750/424 = 70 minutes.
(lower bound is fewest time, hence lowest number of people leaving at the fastest rate).
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Finn jumped 200 times in 10 hours. At what rate, how many times would he jumped in 12 minutes?
Answer: 4 times
Step-by-step explanation: I got 4 times. Here's how to solve it:
Set up a proportional relationship, but first, we need to convert 10 hrs into mins:
1 hour = 60 mins
To find how many minutes are in 10 hours, we multiply 60 by 10, which equals 600.
So, therefore there are 600 mins in 10 hours. Now, we can set up our proportional relationship:
[tex]\frac{200}{60} = \frac{?}{12}[/tex]
So, if we know 12 is a factor of 60, we should divide 60 by 12, and we should get 5. So, now we do the same with the 200. We do 200 / 50, and we get 4. I hope this helps!
consider the fahrenheit thermometer. what does zero mean in this context
minuscule temperature. There are a number of tales of how he initially created his scale, but the original publication states that the lower Fahrenheit defining point, 0 °F, was set as the freezing temperature of a brine solution made from a combination of water, ice, and ammonium chloride (a salt).
How do Fahrenheit and Celsius compare?Thus, the difference between Celsius and Fahrenheit is 1.8 times. In other words, 1 degree Fahrenheit is equivalent to 5/9 degree Celsius. These two temperature scales overlap at -40 degrees, which means that -40 degrees Fahrenheit is equivalent to -40 degrees Celsius despite their quite significant discrepancies.
How hot or chilly is Celsius?°C) is a different unit of measurement for temperature. Except for the United States, most nations use Celsius as their unit of measurement. 0 degrees Celsius is really chilly. 40 degrees is a scorching temperature!
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What's the domain of a logarithmic function?
Answer:
all positive numbers
Step-by-step explanation:
You want to know the domain of the log function.
Log functionThe log function ln(x) is defined for all x > 0. A log function with any other base is similarly defined.
log function domain: all positive numbers
A parent log function has a vertical asymptote at x=0, and an x-intercept at x=1. Its vertical scaling will depend on the base of the logarithm. Like any function, it can be translated and scaled horizontally and vertically.
__
Additional comment
In the field of complex numbers, the log function is defined for any non-zero number. For example, ln(-1) = πi.
The range is all real numbers.
Juanita changed $20 into euros when the exchange rate was €1=$1.2685.
How many euros did she receive?
Give your answer correct to 2 decimal places.
An instructor gives four -hour exams and one final exam, which counts as three -hour exams. Find a student's grade if she received , , , and on the -hour exams and on the final exam. Round your answer to one decimal place if necessary.
One final test that lasts three hours is given in addition to four-hour exams that are given by the teacher. The student's last grade is an 83.29.
What is students final average ?The final exam result was an 80, which counts as 31 hour examinations if the exam scores range from 60 to 81, which totals to 97,87. In order to accomplish this, we must multiply three eighty by 62, 81, 97, and 87, which equals a 31-hour exam.
The whole time for the final exam, which is 31 hours, will be added up and divided by 7, giving us an average final grade for the student of 81.To reduce the number's number of significant digits in order to approximate it. Rounding down from 15.4 to 15.5, from 15.51 to 15.5 or 16, from 0.499 to 0, and from 970,000 to 1 million.
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DIG DEEPER! A cube is removed from a rectangular prism. Find the surface area of the figure after removing the cube.
A rectangular prism with length 9 feet, width 8 feet, and height 5 feet. A cubic hollow runs to the height of the rectangular prism and has the side length of 5 feet.
The surface area is ______ square feet
The surface area of the figure after a cubic hollow runs to the height of the rectangular prism is 364 square feet.
The surface area is 364 square feet.
Find the surface area of the rectangular prism.
To do this, use the formula for the surface area of a rectangular prism:
(2 x length x width) + (2 x width x height) + (2 x length x height)
In this case, the length is 9 feet, the width is 8 feet, and the height is 5 feet. Plugging these values into the formula gives:
= (2 × 9 × 5) + (2 × 8 × 5) + (2 × 9 × 8)
= 314 square feet
When a cubic hollow runs to the height of the rectangular prism and has the side length of 5 feet, 2 cubic faces is removed and 4 cubic faces added to the surface area of the resultant solid. So
surface area = 314 - 2×5² + 4×5²
= 314 + 2×5²
= 314 + 50
= 364 square feet
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the cost of kens car wash was $23.95. if he wants to givve his detailer a 15% tip,about how much of a tip should he leave
Ken should leave a $3.59 tip.
We will discuss algebra, a branch of mathematics that deals with symbols and the rules for manipulating them, in the context of algebra word problem worksheets.
They represent variables or quantities without set values. Our abilities to construct and solve equations must be combined in order to solve algebraic word problems.
It is crucial to start by converting verbal descriptions into algebraic formulas before tackling word issues.
To find the amount of tip he should give, we note that 15% is equal to 0.15 as a decimal.
23.95 * 0.15= 3.5925≈3.59 (approximately)
Therefore, Ken should leave a $3.59 tip.
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The width of a rectangle is 5x-1.5 feet and the length is 1.5x+5 feet. Find the perimeter of the rectangle.
7th grade
The perimeter of the rectangle is 13x+7 feet
What is the area of the rectangle?The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.
Given here: The width of a rectangle is 5x-1.5 feet and the length is 1.5x+5 feet. Therefore the perimeter of the rectangle is given by
= 2(5x-1.5+1.5x+5)
=2(6.5x+3.5)
= 13x+7
Hence, The perimeter of the rectangle is 13x+7 feet
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Which strategies can be used to find the product of 1,587 x 1,000? Select two options
Answer:
Step-by-step explanation:
you can multiple and get 1,587,000]and then you divide to get 8 [tex]\sqrt{1587000[/tex]N is an integer such that
3n+4 <19 and 10n/n^2+16Find all the possible values of n.
N is the integer between {3,4,5}.so we can find all possible values of n is 2 and 8.
What is an integer?An integer is a whole number that can be positive, negative or zero. Examples of integers are -5, 1, 5, 8, 97, and 3,043.The integers are generated from the set of counting numbers and the operation.
What are the steps to solving inequalities?Subtract the same number from both sides. Multiply both sides by the same positive number. Divide both sides by the same positive number. Multiply both sides by the same negative number and reverse the sign.
Now we solve
3n+4 <19
3n+4-4<19-4
3n<15
n<5
so n is less than and equal to 5 it will be {3, 4, 5].
10n/[tex]n^{2}[/tex]+16 >1
10n> [tex]n^{2}[/tex] +16
0> [tex]n^{2}[/tex]-10n +16
0>[tex]n^{2}[/tex] -8n -2n +16
0> n(n-8)-2(n-8)
0> (n-8) (n-2)
So n-2<0 n-8<0
n<2 n<8
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tan took Lily to his friend’s restaurant on a date. The friend told the waiter to remove the $12 dessert from Stan’s bill. Stan tipped the waiter 20% on the reduced bill, which was a $15 tip. Fill in the blanks to write an equation that will determine the amount of the original bill, b.(2 points)
___(b −___) = ___
$b+$12 is the equation that will determine the amount of the original bill
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that The friend told the waiter to remove the $12 dessert from Stan’s bill.
Stan tipped the waiter 20% on the reduced bill, which was a $15 tip
We need to write an equation that will determine the amount of the original bill b.
Let us find what 20% of amount will be 15
20/100×b=15
0.2x=15
b=15/0.2=75
The reduced bill is $75.
As before $12 is removed
$b+$12=$87
$87 is the original bill and 15 is the tip.
Hence, $87 is the original bill.
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A karaoke machine regularly costs $146 and is on sale for 35% off. What is the discount?
Answer:51.1
Step-by-step explanation:
How do you know if 3 measures can make a triangle?
To determine if three measures can make a triangle, use the Triangle Inequality Theorem. This theorem states that the sum of any two sides of a triangle must be greater than the measure of the third side.
for example
side 1 = 6
side 2 = 8
side 3 = 10
6 + 8 = 14 > 10,
therefore the three sides can make a triangle.
1. Gather the three measures of the triangle.
2. Add the two smallest side lengths together.
3. Compare the sum of the two smallest sides to the longest side.
4. If the sum of the two smallest sides is greater than the longest side, then the three measures can make a triangle.
5. If the sum of the two smallest sides is not greater than the longest side, then the three measures cannot make a triangle.
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