Select the correct answer. Consider the given quadratic equation. y=x2 + 4x +5 Use the discriminant to determine which graph could represent the equation.
A. A graph shows a downward parabola vertex at the first quadrant and intercepts at x-axis 2 points
B. A graph shows an upward parabola vertex at x-axis and intercepts at y-axis on one side
C. A graph shows upward parabola intercepts x-axis at 2 points and passes through y-axis at 1 point
D. A graph shows an upward parabola vertex at the second quadrant and intercepts at y-axis 1 side
Answers
the correct answer is option B, which describes an upward parabola with vertex at the x-axis and intercepts at the y-axis on one side.
What is quadratic?In mathematics, a quadratic is a polynomial function of the form:
\(f(x) = ax^2 + bx + c\)
where a, b, and c are constants, and x is the variable.
The term "quadratic" comes from the Latin word "quadratus," which means "square." This is because the highest power of the variable x in a quadratic function is 2, which corresponds to the area of a square.
by the question.
The quadratic equation \(y = x^2 + 4x + 5\) can be written in the standard form. \(ax^2 + bx + c = 0\), where a = 1, b = 4, and c = 5.
The discriminant of the quadratic equation is. \(b^2 - 4ac = 4^2 - 4(1)(5) = -4.\)
Since the discriminant is negative, the quadratic equation has no real roots. This means that the graph of the equation does not intersect the x-axis, and it either opens upwards or downwards depending on the sign of the coefficient of \(x^2\).
In this case, since the coefficient of \(x^2\) is positive, the graph opens upwards.
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Related Questions
Which of the following functions has a graph with a vertex that is a translation 6 units horizontally to the left of the vertex of the graph of f(x) = (x − 4)2 + 8?
Answers
suppose that the number of log-ons to a computer network follow a poisson process with an average of three counts per minute, a. what is the mean time between counts? b. what is the standard deviation of the time between counts?
Answers
a) Mean time between counts is 0.3333 minutes.
b) Standard deviation of time between counts is 0.5774 minutes.
a. Mean time between counts: The mean time between counts can be computed as the inverse of the Poisson rate parameter (λ): Mean time between counts = 1/λ.
The average of 3 counts per minute is the same as the rate parameter λ in a Poisson process. Thus, the mean time between counts is: Mean time between counts = 1/λ = 1/3 = 0.3333 minutes (20 seconds approximately).
b. Standard deviation of the time between counts: The standard deviation of a Poisson process is equal to the square root of the mean.
Therefore, the standard deviation of the time between counts can be calculated as follows: Standard deviation of time between counts = sqrt(mean) = sqrt(1/λ) = sqrt(1/3) = 0.5774 minutes (approximately 35 seconds).
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*97 POINTS*
Use the numerals representing cardinalities in the Venn diagram, shown on the right, to give the cardinality of the set
A' ∩ B' ∩ C. '
n(A' ∩ B' ∩ C')= ___________
Answers
Answer:
19
Step-by-step explanation:
A' represents everything out A
B' represents everything out B
C' represents everything out C
So only the outside is left hope this helps
I NEED HELP PLEASE PLEASE PLEASE HELP MEE !!!!
Answers
Answer:
The second step involves getting rid of the number closest to the variable x
Which pair shows equivalent expressions?
A B C OR D???
Answers
A toy company has 6 different heights of its best-selling action figure, labeled versions 1 through 6. Each version is modeled from clay molding of the action figure. Version 1 is 125% taller than the clay molding of the action figure. The heights of action figure versions 2 through 6 are each 125% taller than the previous version of the action figure. The clay molding of the action figure is 4 inches tall. Which function can be used to find the height in inches of each version of action figure, where 1 ≤ v ≤ 6?
h(v) = 1.25(v+ 4)
h(v) = 4(1.25)v
h(v) = 1.25(4)v
h(v) = 4(v + 1.25)
Answers
Answer:
a
Step-by-step explanation:
a
What is the equation in slope-intercept form of the line that passes through the point (12, 5) and is perpendicular to the line represented by y=34x−8?
Answers
Answer:
The equation in slope-intercept form of the line that passes through the point (12, 5) and is perpendicular to the line is:
\(y=-\frac{1}{34}x+\frac{91}{17}\)Step-by-step explanation:
We know the slope-intercept form of the line equation
\(y=mx+b\)
where m is the slope and b is the y-intercept
Given the line
\(y=34x-8\)
comparing with the slope-intercept form of the line equation
The slope m = 34
We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:
slope = m = 34
Thus, the slope of the the new perpendicular line = – 1/m = -1/34 = -1/34
Using the point-slope form
\(y-y_1=m\left(x-x_1\right)\)
where m is the slope of the line and (x₁, y₁) is the point
substituting the values of slope = -1/35 and the point (12, 5)
\(y-y_1=m\left(x-x_1\right)\)
\(y-5=-\frac{1}{34}\left(x-12\right)\)
Add 5 to both sides
\(y-5+5=-\frac{1}{34}\left(x-12\right)+5\)
\(y=-\frac{1}{34}x+\frac{91}{17}\)
Therefore, the equation in slope-intercept form of the line that passes through the point (12, 5) and is perpendicular to the line is:
\(y=-\frac{1}{34}x+\frac{91}{17}\)Let n be a positive integer. z^n is the set of all lists of length n whose
entries are in z. prove that z^n is countable. (hint: find a bijection
between z^(n−1) × zand z^n and then use induction.)
Answers
ASAP! exponent rules
Answers
Answer:
C: 9
Step-by-step explanation:
3^4/3^2
3*3*3*3/3*3 cancel out 2 threes from the bottom and top.
3*3=9
A researcher wondered what the average SAT score is for all current students at the University of Michigan. Based on a random sample of 30 students, she reports that the average SAT score for all current students at the University of Michigan is 1222 with a margin of error of 30.
1. Is the average of 1222 reported by the student calculated from a sample or the whole population?
2. Use the margin of error to give an interval of possible values for the true mean of the whole population.
3. Do we know that every current student at the University of Michigan has an SAT score within the interval you constructed in #2? Explain.
4. Why do we need to report a margin of error along with the estimate? Answer each item with a yes or no.
• Some students might have lied when asked about their SAT score.
• The researcher may have recorded the wrong values for some of the SAT scores.
• Due to sampling variability. Every random sample produces different estimates.
Answers
1. The average of 1222 is calculated from a sample, not the whole population.
2. The interval of possible values for the true mean of the whole population, given the margin of error, is 1192 to 1252.
3. No, we don't know that every current student at the University of Michigan has an SAT score within this interval.
Yes, a margin of error is reported due to:
Potential dishonesty from students.Possible recording errors by the researcher.Inherent sampling variability.How to find the intervalNo, we don't know that every current student at the University of Michigan has an SAT score within this interval. The interval only estimates the average SAT score for the entire student population, not individual scores.
Yes, a margin of error is reported due to:
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determine the angle between 0 and 2π that is coterminal with 17pi/4
Answers
the angle between 0 and 2π that is coterminal with 17π/4 is π/4.
To find the angle between 0 and 2π that is coterminal with 17π/4, we need to find an equivalent angle within that range.
Coterminal angles are angles that have the same initial and terminal sides but differ by a multiple of 2π.
To determine the coterminal angle with 17π/4, we can subtract or add multiples of 2π until we obtain an angle within the range of 0 to 2π.
Starting with 17π/4, we can subtract 4π to bring it within the range:
17π/4 - 4π = π/4
The angle π/4 is between 0 and 2π and is coterminal with 17π/4.
what is equivalent'?
In mathematics, the term "equivalent" is used to describe two things that have the same value, meaning, or effect. When two mathematical expressions, equations, or statements are equivalent, it means that they are interchangeable and represent the same mathematical concept or relationship.
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How many cups of water would you need for 9 cups of oats?
Oats (cups) Water (cups)
6 18
1
3
1
1 3
9
Answers
For 9 cups of oats, 27 cup water is needed.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Let for 9 cups of oats x cup of water is required.
Given that,
For 6 cups of oats, 18 cup of water is required.
To solve for the value of x, use ratio property
6 cups of oats= 18 cup water
⇒1 cup of oats = 3 cup water
⇒9 cup of oats = 27 cup water
For 9 cups of oats, there will be 27 cup water required.
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Andrew buys a laptop for $450. The store increases its purchase price by 40%? What is the new price of the laptop?
Answers
Answer:
630
Step-by-step explanation:
450 x 0.4 = 180
180 + 450 = 630
You can also do 450 x 1.4 = 630 because this will find the increased price with 140% of 450
john has walked 15% of the way home from school. if he has walked 54 yards so far, how far does he walk home from school
Answers
Answer: John walks a total of 360 yards from school.
Step-by-step explanation:
Let's represent the total distance John walks from school as "x".
According to the problem, John has already walked 15% of the way, which can be written as:
0.15x
We also know that he has walked 54 yards so far, which means:
0.15x = 54
To find the total distance John walks from school, we can solve for "x" by dividing both sides of the equation by 0.15:
x = 54 ÷ 0.15
x = 360
Therefore, John walks a total of 360 yards from school.
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Please helpppp!!!!!!!! And if u can show alll your work and I will give you brainliest!!
And 10 points and a thanks and 5 stars ✨
Answers
Answer:
10cm, 5cm, 7cm.
Step-by-step explanation:
So basically what I did was I pretended the line was a ruler that was in centemeters, and all the lines were centimeters, so then I added it up to get my answer, as you can see in the picture
A history professor decides to give a 12-question true-false quiz. She wants to choose the passing grade such that the probability of passing a student who guesses on every question is less than 0.10. What score should be set as the lowest passing grade? Group of answer choices
Answers
Answer:
we can set the 9 as a benchmark to be the score for the passing grade so that probability of passing a student who guesses every question is less than 0.10
Step-by-step explanation:
From the given information;
Sample size n = 12
the probability of passing a student who guesses on every question is less than 0.10
In a alternative - response question (true/false) question, the probability of answering a question correctly = 1/2 = 0.5
Let X be the random variable that is represent number of correct answers out of 12.
The X \(\sim\) BInomial (12, 0.5)
The probability mass function :
\(P(X = k) = \dfrac{n!}{k!(n-k)!} \times p^k\times (1-p)^{n-k}\)
\(P(X = 12) = \dfrac{12!}{12!(12-12)!} \times 0.5^{12}\times (1-0.5)^{12-12}\)
P(X = 12) = 2.44 × 10⁻⁴
\(P(X = 11) = \dfrac{12!}{11!(12-11)!} \times 0.5^{11}\times (1-0.5)^{12-11}\)
P(X =11 ) = 0.00293
\(P(X = 10) = \dfrac{12!}{10!(12-10)!} \times 0.5^{10}\times (1-0.5)^{12-10}\)
P(X = 10) = 0.01611
\(P(X = 9) = \dfrac{12!}{9!(12-9)!} \times 0.5^{19}\times (1-0.5)^{12-9}\)
P(X = 9) = 0.0537
\(P(X = 8) = \dfrac{12!}{8!(12-8)!} \times 0.5^{8}\times (1-0.5)^{12-8}\)
P(X = 8) = 0.12085
\(P(X = 7) = \dfrac{12!}{7!(12-7)!} \times 0.5^{7}\times (1-0.5)^{12-7}\)
P(X = 7) = 0.19335
.........
We can see that,a t P(X = 9) , the probability is 0.0537 which less than 0.10 but starting from P(X = 8) downwards the probability is more than 0.01
As such, we can set the 9 as a benchmark to be the score for the passing grade so that probability of passing a student who guesses every question is less than 0.10
a spinner is divided into 15 identical sectors and labeled 1 through 15 how many spins are expected for a multip;le of 4 to be spun 30 times
Answers
We need to spin the spinner 150 times, to expect a multiple of 4 to be spun 30 times.
In the question, we are given that a spinner is divided into 15 identical sectors and labeled 1 through 15.
We are asked the number of times the spinner must be spun to expect a multiple of 4 30 times.
The possible outcomes of a multiple of 4 are 4, 8, and 12.
Thus, the number of possible outcomes are 3.
The total number of outcomes are 15.
Thus, the probability of getting a multiple of 4 in one spin = 3/15 = 1/5.
Thus, to expect a multiple of 4 once, we need to spin the spinner 5 times.
Thus, to expect a multiple of 4 30 times, we need to spin the spinner 5 * 30 = 150 times.
Thus, we need to spin the spinner 150 times, to expect a multiple of 4 to be spun 30 times.
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Answer:
The spinner is expected to spin 150 times for a multiple of 4 to be spun 30 times.
from the question, given that a spinner is divided into 15 identical sectors and labeled 1 through 15.
now, find the how many spins are expected for a multiple of 4 to be spun 30 times.
The multiple of 4 are 8, 12 and 15.
so the number of favourable outcomes be 3.
the total number of outcomes is 15.
Now the
\(probability = 3 \div 5 = 1 \div 5\)
so for 30 times of multiple of 4, we need to the spinner \(5 \times 30 = 150 \: times\)
Therefore,The spinner is expected to spin 150 times for a multiple of 4 to be spun 30 times.
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Imagine you are given a set of data with 10 points and record the mean of the data. The
mean of that data is 18.
If you add an 11th piece of data to the data set, what should the size of the number be for
the mean to remain unchanged?
Responses
Answers
If we add an 11th data point with a value of 0, the mean of the 11 data points will still be 18.
What is mean?
In mathematics and statistics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is also commonly known as the arithmetic mean.
If the mean of a set of 10 data points is 18, then the sum of those data points is 10*18 = 180.
To keep the mean unchanged when adding an 11th data point, the sum of the 11 data points should be:
sum of 11 data points = sum of the original 10 data points + the 11th data point
To keep the mean unchanged, the sum of the 11 data points should still be 180. So we have:
sum of 11 data points = 180
sum of the original 10 data points + the 11th data point = 180
10*18 + the 11th data point = 180
Simplifying this equation, we get:
the 11th data point = 180 - 10*18
the 11th data point = 180 - 180
the 11th data point = 0
Therefore, if we add an 11th data point with a value of 0, the mean of the 11 data points will still be 18.
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Refer to pictures above real help please
Answers
Answer:
38.7°
Step-by-step explanation:
∆ = Tan-1(opposite/ Adjacent)
=Tan-1(8/10)
= 38.66°
= 38.7° to n nearest tenth
It is one question the three images are the options for answers to the question.
Answers
write the lengths in order from greatest to least
12.7 ( 12 7/10) 12 3/5 12 3/4
Answers
what is the equation of a line that is perpendicular to y=3x-2 and passes through the point (6 8) ANSWERS
Answers
The equation of the line that is perpendicular to y = 3x - 2 is: y - 8 = -1/3(x - 6) [point-slope form] or y = -1/3x + 10 (slope-intercept form).
How to Find the Equation of a Perpendicular Line?Two lines will have slope values that are negative reciprocals if both lines are perpendicular to each other.
If an equation of a line is given in the form of, y = mx + b, the slope of the line is the value of m.
Given the equation of a line as y = 3x - 2, the slope of the line is 3.
The negative reciprocal of 3 is -1/3, because (3)(-1/3) = -1. Therefore, the slope (m) of the line that is perpendicular to it is -1/3.
To write the equation of the line, substitute m = -1/3 and (a, b) = (6, 8) into y - b = m(x - a):
y - 8 = -1/3(x - 6) [point-slope form]
Rewrite in slope-intercept form:
y - 8 = -1/3x + 2
y = -1/3x + 2 + 8
y = -1/3x + 10 (slope-intercept form)
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Find the area.
4m
6m
6m
Answers
What is the description of <2 as it relates to the situation shown?
Answers
Consider the following example.
IN here, we have angles 1 and 2 measured with respect the horizontal line that passes through point A. Note that angle 2 is related to points A and C. In this case, angle is under the horizontal line that passes through A. Then, angle 2 is the angle of depression from point A to point C. Every angle that is under the horizontal line would receive the name of angle of depression. In the same manner, since angle 1 is above the horizontal line, then it is an elevation angle from point A to point C. In fact, every angle that is above the horizontal line, would receive the name of elevation angle.
Coming back to our problem, we can see that angle 2 is formed by the horizontal line that passes through the radar and the line that connects the plane to the radar. This angle would be above the horizontal line of the radar. Then, according to our previous explanation, this means that angle 2 is an elevation angle from the radar to the plane.
PLEASE I NEED HELP RNNN!!!!!!!
Answers
multiply the numbers
The area of a triangle with the given base and height is 9.5625 square inches.
What is the area of a triangle?The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.
From the given triangle, height is 2.5 inches.
By using Pythagoras theorem,
3²=x²+2.5²
9=x²+6.25
x²=9-6.25
x²=2.75
x=1.65 inches
So, the base = 6+1.65=7.65 inches
Area of a triangle = 1/2 ×7.65×2.5
= 0.5×7.65×2.5
= 9.5625 square inches.
Therefore, the area is 9.5625 square inches.
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I am in need of help plz and thank you:
Answers
Answer:
x ≥ 1
Step-by-step explanation:
-30 + 8x ≥ -22
Add 30 to both sides.
8x ≥ 8
Divide both sides by 8.
x ≥ 1.
On the number line, click and hold in the middle of 0 and 2 (1) and drag all the way to the right to 12.
The ___ of a hyperbola is one of two points such that the difference of the distances from any point on the hyperbola to the foci is a constant.
Answers
The POINT of a hyperbola is one of two points such that the difference of the distances from any point on the hyperbola to the foci is a constant.
What is hyperbola?A hyperbola is a significant conic section in mathematics that is created by the intersection of a double cone with a plane surface, though not always at the center. A hyperbola is symmetric along its conjugate axis and resembles the ellipse in many ways. A hyperbola is subject to concepts like foci, directrix, latus rectus, and eccentricity. Examples of hyperbola that are frequently seen include the path taken by the tip of a sundial's shadow, the scattering trajectory of subatomic particles, etc.Here, we'll use instances that have been solved to better grasp the definition, formula, derivation, and standard forms of hyperbolas.Hence, The POINT of a hyperbola is one of two points such that the difference of the distances from any point on the hyperbola to the foci is a constant.
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A 4th grade class took a field trip to a science museum. There are 24 students in the class. Each student purchased a $9dollar sign, 9 ticket for the museum and a box lunch, which was also $9dollar sign,
Estimate the total cost of the field trip
Answers
Estimate the total cost of the field trip to a science museum is equals to the$432.
We have, a field trip to a science museum of a 4th grade class .
Total number of students in class = 24
Purchased amount by each student for 9 tickets of museum = $9
The purchased amount for a box lunch for each student= $9
Let the total cost of field trip and cost spent by one student on field trip be "$y" and "$x " respectively. Now, dollars spent by one student on field trip to science museum, x = purchased amount of trip + purchased amount of lunch box
=> x = $9 + $9 = $18
There is total 24 students so, total cost of field trip to science museum = total number of students × cost spent by one student on trip
=> y = 24 × x
=> y = 24× 18
=> y = 432 dollars.
So, required value of y is $432.
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Find N ′
(11) Round to the nearest whole number. A. 15 B. 14,018 C. 480 D. 18 Find N ′
(11) Round to the nearest whole number. A. 15 B. 14,018 C. 480 D. 18
Answers
The value of N'(11) approximating to a whole number is: N'(11) = 18
How to find the derivative of the function?The given function is:
N(a) = 14,000 + 200 In a,
where:
N(a) represents the number of units sold.
a denotes the amount spent on advertising in thousands.
Now, the derivative will be found by applying calculus differentiation to get:
dN/da = 200/a
Thus:
N'(a) = 200/a
Thus:
N'(11) = 200/11
N'(11) = 18.18
Approximating to a whole number gives N'(11) = 18
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The complete question is:
A model for advertising response is given by N(a) = 14,000 + 200 In a, a ≥ 1, where N(a) = the number of units sold and a = amount spent on advertising in thousands.
Find N ′(11) Round to the nearest whole number.
A. 15 B. 14,018 C. 480 D. 18
4. Drew is going to try out for the basketball team, so he decides to shoot free throws every day at the park. On the first day, he shoots 15 free throws. On the second day, he shoots 25 free throws. On the third day, he shoots 35 free throws, Drew continues to increase the number of free throws he shoots each day by the same amount. a) If Drew continues to follow this pattern, how many free throws will Drew shoot on the 20th day? b) What is the total number of free throws Drew shot during those 20 days?
Answers
Answer:
He shot a total of 2,415 free throws. He shot 255 on the 20th day.
Step-by-step explanation: