Graph the following piecewise function and then find the range.
Answer:
The correct option is 3.
Step-by-step explanation:
The given piecewise function is
[tex]f(x)=\begin{cases}3x^2+1 & \text{ if } -4<x<6 \\ 6 & \text{ if } 6\leq x<9 \end{cases}[/tex]
Range is the set of output or y values.
The given function for 6 ≤ x < 9 is
[tex]f(x)=6[/tex]
It is a constant function, the value of function is 6 for all values of x.
Range = 6
The given function for -4 < x < 6 is
[tex]f(x)=3x^2+1[/tex] .... (1)
It is a quadratic function.
The vertex form of a quadratic function is
[tex]f(x)=a(x-h)^2+k[/tex] ....(2)
Where (h,k) is vertex and a is constant.
From (1) and (2), we get a=3,h=0,k=1.
The vertex of this function is (0,1), it means the range of this function is greater than or equal to 1. But this function is only defined for -4 < x < 6.
[tex]f(-4)=3(-4)^2+1=49[/tex]
[tex]f(6)=3(6)^2+1=109[/tex]
The maximum value of the maximum value of the function is 109 at x=6. Since 6 is not included in the interval -4 < x < 6, therefore 109 is not included in the range.
Range = [1,109)
When we combined the range of both functions we get
Range = [1,109)
Therefore the correct option is 3.
Lourenço analyzed prices of laptop
computers based on the speed of the
processor. He calculated the trend line to
be y = 101x + 207.85, where x is the
speed of the processor in gigahertz and
y is the price. Which amount below is
closest to the price of a laptop with a
processor speed of 2.5 gigahertz?
A. $309
B. $455
C. $460
D. $620
(Please show your work because I'm beyond confused
classify the polynomial 3x^2+x-6 by degree
A. cubic
B. quintic
C. quadratic
D. quartic
Keywords:
Polynomial, classify, degree, greatest exponent
For this case we have the following polynomial: [tex]Q (x) = 3x ^ 2 + x-6[/tex], we must classify the polynomial according to its degree. For this, we must bear in mind, that by definition, a polynomial is of the form:
[tex]P (x) = ax ^ n + bx ^ {n-1} + ... + cx ^ 3 + dx ^ 2 + ex + f[/tex]
Where:
a, b, c, d, e, f: They are the coefficients of the polynomial
n, n-1,3,2,1,0: They are the exponents. This polynomial is of degree "n", because "n" is the largest exponent.
x: It is the variable
Thus, [tex]Q(x) = 3x ^ 2 + x-6[/tex]is of degree "2" because "2" is the largest exponent.
Answer:
It is a quadratic polynomial
Option C
The correct classification for this polynomial is C. quadratic.
The polynomial 3x^2 + x - 6 is classified by its degree, a fundamental characteristic of polynomials determined by the highest power of the variable 'x.'
In this case, the highest power is 2, making it a quadratic polynomial. Quadratic polynomials represent a U-shaped graph when plotted, often described as a parabola.
They play a significant role in various areas of mathematics, science, and engineering, serving as fundamental models for various real-world phenomena.
Quadratic equations are commonly encountered in physics, engineering, economics, and other fields, making them essential for solving problems and making predictions. Thus, the correct classification for this polynomial is C. quadratic.
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A brick oven has an opening as shown. What is the area of the entire opening?
Answer:
[tex]13.93ft^{2}[/tex]
Step-by-step explanation:
The area of the opening will be the sum of the area of the two shapes shown which are rectangle and half ellipse:
[tex]Area =Area_{rectangle}+\frac{1}{2} Area_{Ellipse}[/tex]
The area of the rectangle is:
[tex]Area_{Rectangle}=a*b[/tex]
where:
[tex]a=4ft\\b=2\frac{1}{2}ft[/tex]
we replace values(we convert the mixed fraction to improper fraction by multiplying the whole number part by the fraction's denominator, then add that to the numerator then write the result on top of the denominator.):
[tex]Area_{Rectangle}=4*2\frac{1}{2} =4*\frac{5}{2}=10[/tex]
The area of the ellipse is:
[tex]Area_{Ellipse}=a*b*\pi[/tex]
where:
[tex]a=Radius1=1\frac{1}{4}ft\\b=Radius2=2ft\\[/tex]
Radius2 will be half the side of the rectangle
[tex]Radius2=\frac{4}{2}=2[/tex]
we replace the values:
[tex]Area_{Ellipse}=1\frac{1}{4} *2*\pi=\frac{5}{4}*2*\pi=\frac{5}{2}\pi =7.85[/tex]
we calculate now the total area:
[tex]Area =Area_{rectangle}+\frac{1}{2} Area_{Ellipse}\\Area=10+\frac{1}{2}(7.85)=10+3.93=13.93ft^{2}[/tex]
if N is an acute angle and sin N=12over13, evaluate cos N and tan N.
Which is a stretch of an exponential decay function?
f(x) =4/5(5/4)^x
f(x) =4/5(4/5 )^x
f(x) =5/4(4/5)^x
f(x) =5/4(5/4)^x
Select all of the coefficients in the expression.
12xy3 + 2x5y + 4x5y2 + 7x5y.
2
3
4
5
7
12
2,4,7,12 for edgynuity. the way you can tell is because you look at the front. 12xy3 + 2x5y + 4x5y2 + 7x5y. the 12 1 4 7 are the coefficients.
Final answer:
The coefficients in the algebraic expression are 12, 2, 4, and 7, which are the numerical multipliers of the variable terms.
Explanation:
The coefficients in the expression 12xy^3 + 2x^5y + 4x^5y^2 + 7x^5y are the numerical factors that multiply the variables x and y in each term of the polynomial expression. The coefficients in this expression are 12, 2, 4, and 7. These are the numbers in front of the variable terms and not the exponents or the variables themselves.
Someone please answer this
Melissa has scored 83 , 84 , 93 , 77 , and 85 on her previous five tests. what score does she need on her next test so that her average (mean) is 83 ?
83 x 6 = 498
all six of her scores need to equal at least 498 for an 83 average
83 + 84 + 93 + 77 + 85 = 422
498-422 = 76
she needs a 76
The domain of a relation is
the output (y) values of the relation
the input (x) values of the relation
a set of points that pair input values with output values
x and y values written in the form (x, y)
Answer:
the input (x) values of the relation
Step-by-step explanation:
(a) No, The output (y) values of the relation are called Range. So it is the wrong option.
(b) Yes, the input (x) values of the relation are called Domain. Thus, it is the correct option.
(c) No, it is not a definition of Domain. Thus, this is an incorrect option.
(d) No, it is not a definition of Domain. It is called the cartesian point. Thus it is also an incorrect option.
Further,
The Domain is the all possible input values of a function that gives defined values.
The Range is the all defined output values that we get from a function (or y).
Please help me with my geometry!
What is the discriminant of the polynomial below? 4x2 - 20x + 25
The discriminant of the given polynomial is 0, indicating one real root.
Explanation:The discriminant of a quadratic equation is a value that can be used to determine the nature of the solutions (roots) of the equation. It is calculated using the formula b^2 - 4ac, where a, b, and c are the coefficients of the equation.
In the given polynomial, the coefficients are a = 4, b = -20, and c = 25. Plugging these values into the formula, we get: (-20)^2 - 4(4)(25) = 400 - 400 = 0.
Since the discriminant is equal to zero, the polynomial has one real root.
The sum of twice a number and 7
What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 2.86 plus or minus .09 m?
Final answer:
To calculate the percent uncertainty in the volume of a spherical beach ball when the radius is uncertain, you multiply the square of the radius by four (surface area), by the uncertainty in the radius, and then compare this value to the total volume. The percent uncertainty is found to be approximately 2.62%.
Explanation:
To determine the percent uncertainty in the volume of a spherical beach ball with a radius of 2.86 1 0.09 meters, one must first calculate the volume's uncertainty, then relate this to the total volume, and finally convert this relationship into a percentage.
The formula for the volume of a sphere is [tex]V = (4/3)\pi(r^3)[/tex]. Since volume is proportional to the cube of the radius, any uncertainty in the radius dramatically affects the volume uncertainty. Using a function for the volume V(r) and applying the approximation for small changes in r, we have:
[tex]V = (4/3)\pi(r^2))(r)[/tex]
For a radius of 2.86 meters and an uncertainty of 0.09 meters, the uncertainty V in volume is 170 [tex]cm^3[/tex]. The volume is approximately V = [tex](4/3)(3.14)(2.86^3)[/tex] = 6538 [tex]cm^3[/tex]. Therefore, the volume expressed with its uncertainty is [tex]6500 \pm170[/tex] [tex]cm^3,[/tex] rounded to avoid false precision.
To find the percent uncertainty:
Convert the uncertainty to the same units as the ball's volume if needed (here both are in cm^3).
Divide the uncertainty by the volume: (170/6500) x 100%.
The percent uncertainty is approximately 2.62%.
A lab is trying to determine if a new medication is effective at reducing acne breakouts. The results are displayed in the Venn Diagram below: A Venn Diagram titled Acne medicine probabilities is shown with two circles labeled used the medicine and skin cleared. Inside the used the medicine area is 20. Inside the skin cleared area is 10. In the intersection of the two circles is 30. The area outside the two circles is labeled 40. What is the probability that the person's skin cleared up given that they used the medication?
Answer: 3/5 is the probability that person's skin cleared up given that they used the medication.
Step-by-step explanation:
let S represents skin cleared and M represents medicine used.
According to the given Venn diagram,
P(S) = 40
P(M)= 50
[tex]P(M\cap S) = 30[/tex]
Thus by the definition of conditional probability,
If it is given that the skin is cleared then the probability that persons used the medicine,
P(M/S)=[tex]\frac{P(M\cap S)}{P(S)}[/tex]=30/50= 3/5.
P(M/S)=3/5.
The probability that the person's skin will clear up given that they used the medication is:
3/5What is Probability?This refers to the likelihood of an event to occur based on certain conditions.
If we want to find the probability about whether the skin will clear up is:
We would assign S to represent the skin
M to represent medicine
Hence,
P(S) = 40P(M)= 50P(MnS) = 30
Using the conditional probability rule,
P9M/S)= P(MnS)/P(S) = 30/50
=3/5
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A state’s license plates consist of 3 letters followed by 3 numbers. What is the probability of randomly generating a license plate that reads AHW 304?
Answer: [tex]\frac{1}{17576000}[/tex]
Step-by-step explanation:
Given: A state’s license plates consist of 3 letters followed by 3 numbers.
Since, there are 26 letters in English alphabet and 10 digits in set of numbers(0,1,....,9).
Then , the total number of license plates can be generated (if repetition is allowed)=
[tex]26\times26\times26\times10\times10\times10=17576000[/tex]
In AHW304, each alphabet and number occurs only once, the number of license plate with this = 1
Now, the probability of randomly generating a license plate that reads AHW 304=[tex]\frac{1}{17576000}[/tex]
Answer:
1/17,576,000
Step-by-step explanation:
Write the equations in graphing form, then state the vertex of the parabola or the center and radius of the circle.
y=2x^2+16
The diagonal of the rectangle is 13 inches, and the side lengths of the triangles are Pythagorean triples. To the nearest tenth, what is the area of the shaded part of the figure?
May you help me please ? Thanks!
If the base of a square pyramid is 9 centimeters, and it has a volume of 324 cubic centimeters, what is the height of the pyramid?
V=1/3bh
324=1/3(9)* h
324=3h
h=324/3
h=108
height is 108cm
Answer: 12 cm
The other guy that answered didn't do it correctly, he didn't find the height. You have to do:
1/3 (9 • 9) (x) = 324
1/3 • 81x = 324
27x = 324
x = 12
Trust me, I just finished my quiz and got ths answer right.
what is a transformation that proportionally reduces or enlarges a figure.
Answer: Dilation is a transformation that proportionally reduces or enlarges a figure.
Step-by-step explanation:
A dilation a transformation that changes the size of the shape by using scale factor in particular ways .It stretches or shrinks the actual figure. It produces similar figures.
Since the corresponding sides of similar figures are in proportion.
⇒ It proportionally reduces or enlarges a figure.
Hence, A dilation is a transformation that proportionally reduces or enlarges a figure.
Final answer:
A scale transformation or dilation is a linear transformation that proportionally enlarges or reduces a figure, maintaining the proportional size relationships within the figure.
Explanation:
A transformation that proportionally reduces or enlarges a figure is known as a scale transformation or dilation. In such a transformation, lines are transformed into lines, and parallel lines remain parallel, consistent with the requirement for a transformation to be linear. This is important because it maintains the proportionality of the figure, meaning the size relationship of the parts of a figure to each other and to the whole figure remains constant, even though the overall size changes. Dilation can be characterized by a scale factor, which dictates how much larger or smaller the figure will become. If the scale factor is greater than 1, the figure enlarges; if it is between 0 and 1, the figure reduces in size.
A study conducted by a major milk manufacturer showed that 83% of American teenages prefer drinking milk to drinking soda. What are two reasons why this statistic cannot be trusted?
Please help me round 34,699 to the nearest ten thousand
Two parabolas are the graphs of the equations $y=2x^2-10x-10$ and $y=x^2-4x+6$. give all points where they intersect. list the points in order of increasing $x$-coordinate, separated by semicolons.
Answer:
(-2, 18) and (8, 38)
Step-by-step explanation:
First, set the two equations equal to each other to get $2x^2-10x-10=x^2-4x+6$. Combine like terms to get $x^2-6x=16$. To complete the square, we need to add $\left(\dfrac{6}{2}\right)^2=9$ to both sides, giving $(x-3)^2=16+9=25$.
So we have $x-3=\pm5$. Solving for $x$ gives us $x=-2$ or $8$. Using these in our original parabolas, we find the points of intersection to be $\boxed{(-2,18)}$ and $\boxed{(8,38)}$.
Credit: AoPs
For the function h defined by h(x)=2x2−2, find h(−12)
To find h(-12), substitute -12 into the function h(x)=2x²-2. The value of h(-12) is 286.
Explanation:To find h(-12), we substitute -12 into the function h(x)=2x²-2:
h(-12) = 2(-12)² - 2
h(-12) = 2(144) - 2
h(-12) = 288 - 2
h(-12) = 286
Therefore, h(-12) is equal to 286.
what is the greatest number of obtuse angles that a right triangle can contain
A) 3
B) 1
C) 0
D) 2
Answer:0
Step-by-step explanation:
A right triangle can have at most one obtuse angle since it already contains one right angle, and the sum of its angles must be 180 degrees according to geometrical axioms.
The question asks about the maximum number of obtuse angles that can be contained in a right triangle. In a right triangle, one angle is 90 degrees by definition, which is a right angle. According to Theorem 20, the sum of the angles of a triangle is two right angles, which equals 180 degrees. Having an obtuse angle, which is greater than 90 degrees, combined with a 90 degree angle, would exceed 180 degrees when the third angle is added, and this is not possible in a plane geometric figure. Therefore, a right triangle cannot have more than one right angle. As such, the option with the maximum number of obtuse angles a right triangle can contain is:
Answer: B) 1
One cell phone plan charges $20 per month plus $.15 per minute used. A second cell phone plan charges $35 per month plus $.10 per minute used. Write and solve an equation to find the number of minutes you must talk to have the same cost for both calling plans.
20+0.15x = 35+0.10x
0.15x=15+0.10x
0.05x=15
x= 15/0.05
x= 300minutes
check:
300*.015 = 45+20=65
300*0.10 = 30 + 35 = 65
they equal
so number of minutes would be 300
Find a function in the form of y = f(x) for the parametric equation:
x = 2t
y = t² - 6t
Which statistical test would be most appropriate for examining the relationship between temperature and the number of ice cream cones sold?
The most appropriate statistical test for examining the relationship between temperature and the number of ice cream cones sold would be a correlation analysis, specifically a Pearson correlation coefficient.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Correlation coefficient test measures the strength and direction of the linear relationship between two continuous variables, which is suitable for examining the relationship between temperature and the number of ice cream cones sold.
Additionally, a scatterplot could be used to visually assess the relationship between the two variables before conducting the statistical test.
Hence, statistical test for examining the relationship between temperature and the number of ice cream cones sold would be a correlation analysis
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An object is dropped from a height of 1,600 feet. The amount of time, in seconds, the object takes to hit the ground can be found by solving the equation −16t2+1,600=0. How many seconds will it take to hit the ground?
To find the time it takes for the object to hit the ground, we can solve the quadratic equation -16t^2 + 1600 = 0 using the quadratic formula. The positive solution to this equation gives us the time in seconds. Therefore, the object will take √102400/32 seconds to hit the ground.
Explanation:To find the time it takes for the object to hit the ground, we need to solve the equation -16t^2 + 1600 = 0. This is a quadratic equation, so we can use the quadratic formula. Plugging in the values, we get t = (-b ± √(b^2 - 4ac))/(2a). In this case, a = -16, b = 0, and c = 1600. Plugging in these values, we get t = (± √(0 - 4(-16)(1600)))/(2(-16)). Simplifying the equation further, we get t = (± √(0 + 102400))/(32). This gives us two possible values for t: t = √102400/32 and t = -√102400/32. Since time cannot be negative in this context, we can discard the negative solution. Therefore, the object will take √102400/32 seconds to hit the ground.