Step-by-step explanation:
the zeros are the x-intercepts. because these are x values, when y (= f(x)) = 0.
a quadratic equation has 2 zeros (even if they are equal or complex numbers).
a quadratic equation
ax² + bx + c = 0
can always be solved by
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (-14 ± sqrt(14² - 4×2×20))/(2×2) =
= (-14 ± sqrt(196 - 160))/4 =
= (-14 ± sqrt(36))/4 = (-14 ± 6)/4
x1 = (-14 + 6)/4 = -8/4 = -2
x2 = (-14 - 6)/4 = -20/4 = -5
these are the 2 zeros (x-intercepts).
if you need the explicit points :
(-5, 0) and (-2, 0)
the y-intercept is the y-value when x = 0
y = 2×0² + 14×0 + 20 = 20
the explicit point : (0, 20)
Please find the degree of angle x!
Answer:22.61 degrees
Step-by-step explanation:
Use reverse tangent
(-2, 2) and (4, -1) lie on a line, what is the equation of the line?
As (-2, 2) and (4, -1) lie on a line the equation of the line is: y = (-1/2)x + 1
We can use the slope-intercept form of a linear equation,
which is y = mx + b, where m is the slope and b is the y-intercept.
First, we need to find the slope of the line using the two given points. The slope formula is:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Plugging in the values, we get:
m = (-1 - 2) / (4 - (-2)) = -3/6 = -1/2
Now we have the slope (m = -1/2), and we can use either of the two given points to find the y-intercept (b).
Let's use the first point (-2, 2):
y = mx + b
2 = (-1/2)(-2) + b
2 = 1 + b
b = 1
So the equation of the line is:
y = (-1/2)x + 1
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a box contains 12 balls of which some are red in colour. if 6 more red balls are put in the box and a ball is drawn at random the probability of drawing a red ball doubles than what it was before. find the number of red balls in the bag.
We are told that the probability of drawing a red ball doubles when an extra 6 red balls are added.
Let's assume that there are initially "x" red balls in the box. This means that there are (12 - x) non-red balls in the box.
When 6 more red balls are added, the total number of red balls becomes (x + 6), and the total number of balls in the box becomes (12 + 6) = 18.
We are told that the probability of drawing a red ball doubles when an extra 6 red balls are added. This means that the probability of drawing a red ball before the extra balls were added was:
P(red) = x / 12
And the probability of drawing a red ball after the extra balls were added is:
P(red) = (x + 6) / 18
We are also told that the second probability is twice the first:
(x + 6) / 18 = 2 * (x / 12)
Simplifying this equation, we get:
(x + 6) / 9 = x / 6
Multiplying both sides by 18, we get:
2(x + 6) = 3x
Expanding the left-hand side, we get:
2x + 12 = 3x
Subtracting 2x from both sides, we get:
12 = x
Therefore, there are initially 12 red balls in the box.
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Ms. Rod rolls a 6-sided die . If she rolls the die 57 times, how many times should she expect to roll a composite number?
By understanding what composite numbers are and how they relate to rolling a die, we can determine the expected number of times Ms. Rod will roll a composite number in 57 rolls.
A composite number is a positive integer that has at least one positive divisor other than one or itself. In other words, a composite number is a number that can be factored into smaller positive integers.
To find the number of times Ms. Rod should expect to roll a composite number, we need to know how many numbers from 1 to 6 are composite. Only two numbers are prime in this range, namely 2 and 3. This means that the other four numbers (4, 5, and 6) are composite. Therefore, out of the 6 possible outcomes of rolling the die, 4 of them are composite numbers.
We can use this information to calculate the expected number of times Ms. Rod will roll a composite number. We know that she is rolling the die 57 times, and each roll has a probability of 4/6 (or 2/3) of resulting in a composite number. Therefore, we can use the formula for the expected value of a discrete random variable, which is:
Expected value = (number of trials) x (probability of success)
Plugging in the values, we get:
Expected value = 57 x 2/3
Expected value = 38
Therefore, we can expect Ms. Rod to roll a composite number about 38 times out of 57 rolls. However, it's important to note that this is just an expected value, and the actual number of times she rolls a composite number may vary.
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g hich is more affected by extreme observations, the mean or median? and how about the standard deviation or iqr? mean, standard deviation mean, iqr median, standard deviation median, iqr
The combinations that are more affected by extreme observations are mean and standard deviation, while the combinations that are less affected are median and IQR.
The mean is more affected by extreme observations, because it takes into account the value of every observation in the data set, whereas the median only considers the middle value(s) and is therefore less sensitive to extreme values.
The standard deviation is more affected by extreme observations, because it takes into account the difference between each observation and the mean of the data set. A single extreme value can have a large impact on the mean, and therefore on the standard deviation.
On the other hand, the interquartile range (IQR) is less affected by extreme observations, because it only considers the range of the middle 50% of the data. The median and IQR are often used together to describe a data set that has extreme values or is not normally distributed.
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What is the area of this figure? Please show your work.
Answer:
112.13 square mm
Step-by-step explanation:
Decompose the composite figure into familiar shapes. One such decomposition is shown in the attached figure
There are four familiar shapes
A semicircle and 3 rectangles
The diameter of the semicircle = 6 mm and therefore its radius is 3mm
Area of the semicircle = 1/2 x area of circle = 1/2 x π x 3²
= 1/2 x 3.14 x 9
= 14.13 square mm
The rectangle below the semi circle has height 5 mm and width 10 mm
Area of this rectangle= 5 x 10 = 50 square mm
The rectangle at the bottom left has width = 6 mm and height = 7mm
Area of this rectangle = 6 x 7 = 42 square mm
The bottom right rectangle has width 2 mm and height 3 mm
Area of this rectangle = 2 x 3 = 6 square mm
Area of the three rectangles = 50 + 42 + 6 = 98 square mm
Total area of composite figure
= Area of 3 rectangles + Area of semicircle
= 98 + 14.13
= 112.13 square mm
hi can have help with this please i can’t figure out what c is :)
Answer: octagon
Step-by-step explanation:
Answer:
Step-by-step explanation:
No. c will be decagon because it has 10 sides
the lengths of human pregnancies (gestation) can be modeled by a bell-shaped distribution with mean 266 days and standard deviation 16 days. a certain pregnancy had a z-score of -2.5 (negative 2.5). how many days did this pregnancy last?
If a certain pregnancy had a z-score of -2.5 with mean 266 days and standard deviation 16 days , the pregnancy lasted 230 days.
We know that the length of human pregnancies can be modeled by a normal distribution with a mean of 266 days and a standard deviation of 16 days.
We are also given that a certain pregnancy had a z-score of -2.5. The z-score is a measure of how many standard deviations a data point is away from the mean. A negative z-score means that the data point is below the mean.
We can use the formula for converting a z-score to an actual value in a normal distribution:
z = (x - mu) / sigma
where z is the z-score, x is the actual value we want to find, mu is the mean, and sigma is the standard deviation.
Plugging in the given values, we get:
-2.5 = (x - 266) / 16
Solving for x, we get:
x = (-2.5 * 16) + 266 = 230
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Please Help! I Have Limited Time! A scatter plot is shown on the coordinate plane.
Which two points would a line of fit go through to best fit the data?
A. (3, 6) and (7, 3)
B. (3, 7) and (9, 1)
C. (1, 9) and (10, 1)
D. (1, 7) and (2, 5)
The two points that a line of fit will go through to best fit the data are;
B: ( 3, 7) and (9, 1)
How to Interpret the Scatter Plot?Scatter plots are defined as the graphs that present the relationship between two variables in a data-set. It is used to represent data points on a two-dimensional plane or on a Cartesian system. The independent variable or attribute is plotted on the X-axis, while the dependent variable is plotted on the Y-axis.
A line of best fit is a straight line drawn through the maximum number of points on a scatter plot. It should have an equal number of points above and below that line. This is best represented on the blue line on the attached graph. It touched 4 points and is between the green and red line.
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What number to the power of three is 500000?
The number that, when raised to the power of three, equals 500000 is approximately 100.
To find this number, we can use the cube root function:
x^3 = 500000
x = cube root of (500000)
x = approximately 100
So, the number that, when raised to the power of three, equals 500000 is approximately 100.
Tanya went to the store and bought a box of spaghetti noodles for $4. She also bought x pounds of ground beef for $3.52 per pound. The total amount of money Tanya spent can be represented by the equation 18 = 3.52x + 4. How many pounds of ground beef did Tanya buy?
Answer:
Answer is in the attached photo.
Step-by-step explanation:
SolutionThe solution is in the attached photo, do take note for this question, we will have to make x the subject and solve for x.
at a cricket match there are 27500 people correct to the nearest 100
calculate the upper bound for the difference between the number of people at the football match and at the cricket match
The upper bound for the difference between the number of people at the football match and at the cricket match is 29750<=p<=29849 .
p = number of people
The true value of p is unknown, but we know that it rounds to 29800 when rounding to the nearest hundred people.
The smallest p could be is 29750 since that rounds to 29800.
The largest is 29849; note that 29850 rounds to 29900.
We have this interval 29750<=p<=29849
r = the rate in which the people leave
This rate is in "people per minute".
Like p, the true value of r is unknown.
The midpoint of 350 and 400 is (350+400)/2 = 375, which represents the smallest value r could be if we round to the nearest 50.
The value 374 would round to 350.
On the other side of the spectrum, (400+450)/2-1 = 425-1 = 424 rounds to 400 as well when rounding to the nearest 50.
The value 425 rounds to 450.
To wrap this section up, you have this interval 375<=r<=424
Summary so far:
29750<=p<=29849
375<=r<=424
where p is the number of people and r is the rate in which they leave (in people per minute).
If we have the smallest number of people (29750) and the highest rate in which they leave (424), then we'll get the lower bound of how long it takes everyone to leave.
This can be thought of as the floor value.
time = (number of people)/(rate)
time = (29750)/(424)
time = 70.1650943396227
time = 70.165
Hence, the upper bound for the difference between the number of people at the football match and at the cricket match is 29750<=p<=29849 .
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Shawna is playing a game that involves rolling a black numbered cube and a red numbered cube. The result of a red numbered cube represents a negative number, and the result of a black numbered cube represents a positive number. Shawna’s current score is 4. Then, Shawna rolls a red 5 and a black 3. Write and solve an equation to represent Shawna’s new score
Shawna's new score can be represented by the equation is New Score = Current Score + (Result of Black Cube) + (Result of Red Cube). So, Shawna's new score is 2.
In the game that Shawna is playing, rolling the black cube results in a positive number, while rolling the red cube results in a negative number. We are told that Shawna's current score is 4, which means that she has accumulated 4 points up to this point in the game.
Next, we are told that Shawna rolls a red 5 and a black 3. This means that the red cube resulted in a negative 5 and the black cube resulted in a positive 3.
To calculate Shawna's new score, we can add the results of these two rolls to her current score. However, we need to be careful to subtract the negative number, rather than adding it. This is because a negative number is actually a decrease in score.
Therefore, we can use the following equation to calculate Shawna's new score:
New Score = Current Score + (Result of Black Cube) + (Result of Red Cube)
Substituting in the values that we know, we get:
New Score = 4 + 3 + (-5)
Simplifying, we can combine the positive and negative numbers:
New Score = 4 - 2
Therefore, Shawna's new score is 2. This means that after rolling a red 5 and a black 3, her score has decreased by 2 points from her original score of 4.
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question 3 a highschool teacher in new york wants to know how students in her class did on their last test. the teacher asks the 10 students sitting in the front row to state their latest test score. she concludes from their report that the class did extremely well. what is the population and what is the sample? a. population: all of the students in the highschool sample: the 10 students selected from the front row b. population: all highschool students within the country sample: all of the students who took the test c. population: all of the students in the class sample: the 10 students selected from the front row d. population: highschool students in new york sample: the students in the class who took the test
The population and the sample is option a population: all of the students in the high school sample: the 10 students selected from the front row
In this scenario, the population refers to the entire group of students that the teacher is interested in studying. The population could be all students in the high school, all high school students within the country, all students in the class, or high school students in New York, depending on the research question.
A sample, on the other hand, is a smaller subset of the population that is actually observed or measured. The teacher selected 10 students from the front row as the sample for her study.
It's important to note that the accuracy of the conclusions drawn from a sample depends on how well the sample represents the population. In this case, the teacher may have concluded that the class did extremely well based on the scores reported by the 10 students in the front row. However, it's possible that the front row students are not representative of the entire class or the entire population, which could lead to inaccurate conclusions.
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25kg= blank lb i need help plese i have 2 min left
Answer: 25,000 grams
Step-by-step explanation:Really sorry if im wrong.
How can I find the population of the town? Many thanks
The large tank begins with 600 gallons of oil. The flow rate is recorded as –4 gallons per minute. After a period of 32 minutes, how much oil has been moved and to which tank?
After a period of 32 minutes 128 gallons of oil is moved from a large tank to a small one.
What is the flow rate?
The quantification of bulk fluid movement is called flow measurement. The mass of a material that moves per unit of time is known as the mass flow rate. The amount of fluid moving per unit of time is known as the volumetric flow rate.
Here, we have
Given that the flow rate is recorded at -4 gallons per minute, which is negative.
It means that the oil is flowing in the small tank.
The rate of flow, r is 4 gallons per minute, here work is oil flowing into a tank
Rate of flow, r = oil flown in a tank/time taken
Given that time, t = 32 minutes
∴ rate of flow × time taken = Oil flown in small tank
⇒ r× t = oil flown in small tank = 4 × 32 = 128 gallons
Hence, after a period of 32 minutes 128 gallons of oil is moved from a large tank to a small one.
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what would the shape of the graph b if the speed of the objects decreased from 50m/s at 30s to 30m/s at 40s
The shape of the graph b will be linear with an immediate decrease in speed.
What is a position vs time graph?In Mathematics, a position vs time graph can be defined as a type of graph that is used to graphically represent the distance traveled by an object from its starting position with respect to the time when it is started moving.
Generally speaking, the position or distance traveled by a physical object in a position vs time graph is always plotted on the y-coordinate while time is always plotted on the x-coordinate (x-axis).
In this scenario, the rate of change of the shape's position can be calculated as follows:
Rate of change = (30 - 50)/(40 - 30)
Rate of change = -20/10
Rate of change = -2.
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Need some helppp on this question will give 20 points
[tex]\cfrac{\sqrt[3]{27xy^3}}{5x^{\frac{4}{3}}y^2}\implies \cfrac{\sqrt[3]{3^3 xy^3}}{5x^{\frac{4}{3}}y^2}\implies \cfrac{(3^3 xy^3)^{\frac{1}{3}}}{5x^{\frac{4}{3}}y^2}\implies \cfrac{3^{3\cdot \frac{1}{3}}x^{\frac{1}{3}}y^{3\cdot \frac{1}{3}}}{5x^{\frac{4}{3}}y^2}\implies \cfrac{3x^{\frac{1}{3}}y}{5x^{\frac{4}{3}}y^2}[/tex]
[tex]\cfrac{3}{5}\cdot \cfrac{x^{\frac{1}{3}}y}{x^{\frac{4}{3}}y^2}\implies \cfrac{3}{5}\cdot x^{\frac{1}{3}}yx^{-\frac{4}{3}}y^{-2}\implies \cfrac{3}{5}\cdot x^{\frac{1}{3}}x^{-\frac{4}{3}}yy^{-2}\implies \cfrac{3}{5}\cdot x^{\frac{1}{3}-\frac{4}{3}} y^{1-2} \\\\\\ ~\hfill {\Large \begin{array}{llll} \stackrel{a ~~~~ b ~~ ~~ c}{0.6 x^{-1}y^{-1}} \end{array}}~\hfill[/tex]
Can some one help me find y I have already found x
Step-by-step explanation:
Since y is on a straight line, it'll be easy
The degree of a straightine is 180
You have one angle of 57, so all we do is subtract 57 from 180
180-57 = 123
Hayden use 2.25 cups of water in his lemonade mixture that serves nine people Christian use 3.75 cups of water in his own lemonade mixture that serves 10 people how much more water is in one serving of Christians lemonade.
One serving of Christian's lemonade has 0.125 cups more water than one serving of Hayden's lemonade.
What is lemonade?Lemonade is a sweetened beverage made from lemon juice, water, and sugar. It is typically served cold, and may also include other ingredients such as fruit, herbs, or carbonated water. Lemonade is a popular summer drink that is enjoyed in many parts of the world.
First, we can find the amount of water per serving in Hayden's lemonade by dividing the total amount of water (2.25 cups) by the number of servings (9 people):
Water per serving in Hayden's lemonade = 2.25 cups / 9 = 0.25 cups per serving
Next, we can find the amount of water per serving in Christian's lemonade by dividing the total amount of water (3.75 cups) by the number of servings (10 people):
Water per serving in Christian's lemonade = 3.75 cups / 10 = 0.375 cups per serving
To find how much more water is in one serving of Christian's lemonade compared to one serving of Hayden's lemonade, we can subtract the water per serving in Hayden's lemonade from the water per serving in Christian's lemonade:
Water per serving difference = 0.375 cups per serving - 0.25 cups per serving = 0.125 cups per serving
Therefore, one serving of Christian's lemonade has 0.125 cups more water than one serving of Hayden's lemonade.
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This year 116 kangaroos were adopted from a shelter. This is 24 fewer than twice the number that were adopted last year. Write an equation that you can use to find the number of pets adopted last year?
Answer:
70
Step-by-step explanation:
Let x be the number of kangaroos adopted last year.
Twice the number adopted last year is 2x.
So, the number adopted this year is 2x - 24.
Equating this to the given number of kangaroos adopted this year, we have:
2x - 24 = 116
Adding 24 to both sides, we get:
2x = 140
Dividing both sides by 2, we get:
x = 70
So, the number of kangaroos adopted last year was 70.
Heidi contributes 11% of her monthly salary towards her 401(k) and her employer matches her contribution up to 6% of her salary. If the interest rate of her 401(k) is 6.25% compounded monthly and her monthly salary is $3,250, determine the amount in her account after 15 years. Round to the nearest cent.
Answer:
The amount that will be in Heidi’s account after 15 years is option A. $164,146.52.What is Future Value?It can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:FV = M (((1 + r)^n - 1) / r)Where;FV = Future value of the amount need to findM = total monthly contribution which is Heidi’s monthly contribution of 11% of her monthly salary + Employer monthly contribution of 6% of Heidi’s monthly salary can be calculated as;= (11% of Heidi’s monthly salary + 6.25% of Heidi’s monthly salary) = (11% of $3,250) + (6.25% x $3,250) = $552.50r = Monthly interest rate= Annual interest rate of 401(k) / 12 = 6.25% / 12 = 0.0625 / 12 r = 0.00520833333333333n = number of months = Number of years x 12 = 15 x 12 n= 180Substituting all the values into equation (1), we have;FV = $552.50 (((1 + 0.00520833333333333)^180 - 1) / 0.00520833333333333)FV = $552.50 x 297.097770863934FV = $164,146.518402324Rounding to the nearest cent, we get;FV = $164,146.52Therefore, the amount that will be in Heidi’s account after 15 years is option A. $164,146.52.
Step-by-step explanation:
.
For a classical infinite square-well potential of width a. How does the classical result compare with the quantu
For small particles such as atoms and subatomic particles, quantum mechanics produces more accurate results than classical mechanics. As the particle size decreases, the differences between classical and quantum mechanical results become more pronounced.
The particle in an infinite square well potential is treated as a point particle with well-defined position and momentum in classical mechanics. The classical solution to the infinite square well problem involves a particle bouncing back and forth between the well's walls, its energy being provided by the kinetic energy associated with its motion inside the well.
In quantum mechanics, on the other hand, the particle in an infinite square well potential is treated as a wave function that solves the Schrödinger equation. The probability distribution of the particle's position and momentum inside the well is described by the wave function. The allowed energy levels of the particle are quantized and can be calculated using the problem's boundary conditions.
The following formula gives the classical result for a particle's energy in an infinite square well potential:
[tex]n2*h2/(8ma2) = E n[/tex]
where n is an integer, h is Planck's constant, and m is the particle's mass. According to this formula, energy levels are continuous and can take any value.
The quantum mechanical result for a particle's energy in an infinite square well potential, on the other hand, is given by the formula:
[tex]E n = (n2 * pi2 * h2) / (2ma2).[/tex]
n must be a positive integer. According to this formula, energy levels are quantized and can only take on discrete values.
As a result, the classical result for the energy of a particle in an infinite square well potential differs greatly from the quantum mechanical result. The classical result predicts continuous energy levels, whereas the quantum mechanical result predicts quantized energy levels.
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Give m || n, find the value of x and y
(3x+5). (8x+10)
The value of x and y are not specified, but the result of the multiplication is 24x^2 + 76x + 50.
What do you mean by Expression?
In mathematics, an expression is a mathematical phrase that can contain numbers, variables, and operators. Expressions can be combined and simplified to solve problems, find relationships, and evaluate the truth of statements. For example, the expression "3 + 4" is a simple expression that represents the value 7 when evaluated.
Expressions can also be more complex, involving multiple operations, variables, and functions. For example, the expression "2x + 3y - z" is a more complex expression that involves three variables and three different operations.
Given the expression (3x + 5)(8x + 10), to find the value of x and y, we have to multiply the two expressions inside the parentheses and simplify the result.
Multiplication of the expressions:
(3x + 5)(8x + 10) = 24x^2 + 76x + 50
So, the value of x and y are not specified, but the result of the multiplication is 24x^2 + 76x + 50.
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draw a coordinate plane and find points A(-2;0) B(1;4) C(-5;-1) D(5;0) E(0;0)
pls help me
20 points
For each value of u, determine whether it is a solution to us 10.
u
8
4
10
13
Is it a solution?
Yes
O
No
X
Ś
For the given inequality, the values of u are:
u = 8 is a solution.u = 4 is a solution.u = 10 is a solution.u = 13 is not a solution.Which values of u are solutions of the inequality?We want to see which ones of the values are solutions of the inequality:
u ≤ 10
So u can be smaller than 10, or equal to 10.
For example, for the irst case u = 8.
8 ≤ 10
This is true, because 8 is smaller than 10.
Then:
u = 8 is a solution.
u = 4 is a solution.
u = 10 is a solution.
u = 13 is not a solution.
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Ashton just launched a new business page on social media. After one month, she has
35 followers. She decides to take a course that promises to triple her number of
followers each month for 6 months. After 7 months, how many followers will Ashton
have if this is true?
3
Step-by-step explanation:
35 times 3.sub
help pls, i dont get this
Answer:
Your already got it.
Step-by-step explanation:
I have no explanation for this.
La masse d’un atome est de 1,05•
Answer:La masse d'un atome de cuivre est de 1,05 x 10^-25 kg. Un atome de cuivre comporte 29 électrons. Ces electrons constituent le nuage electronique de l'atome. chaque electron a une masse de 9,11 x 10^-311.
Step-by-step explanation:
