Identify whether the following real world examples should be modeled by a linear quadratic or exponential function
Answers
Solution
- Linear:
The general form of a linear function is
[tex]\begin{gathered} y=ax+b \\ where, \\ a,\text{ and b are constants} \end{gathered}[/tex]- Quadratic:
The general form of a quadratic function is:
[tex]\begin{gathered} y=ax^2+bx+c \\ where, \\ a,b,c\text{ are constants} \end{gathered}[/tex]- Exponential:
The general form of an exponential function is:
[tex]\begin{gathered} y=ab^x \\ where, \\ a,b\text{ are constants} \end{gathered}[/tex]- Now that we know the general forms of these functions, we can proceed to solve the question.
- The amount a person is paid per hour in wages is the amount that the person collects for every hour that he works
- Let us imagine that a person receives $a for every hour worked.
- This means that:
After 1 hour, the person makes $a
After 2 hours, the person makes $a + $a = $2a
After 3 hours, the person makes $a + $a +$a = $3a
- We can therefore generalize as follows:
Thus, after x hours, the person makes:
[tex]x\times a=\$ax[/tex]- Thus, the function representing the amount a person makes per hour of work is given by:
[tex]y=ax[/tex]- Comparing this result with the 3 function definitions above, we can see that this corresponds to a Linear function
Final Answer
The answer is Linear
Related Questions
What’s the correct answer answer asap for brainlist please
Answers
Answer:
A.it can't be endeavor.
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
Answers
Inga should use the first option that is [tex]2(x^2+6x+9)=3+18[/tex] to solve the quadratic equation.
Given equation:-
[tex]2x^2+12x-3=0[/tex]
We have to find which one of the given options are needed to solve the quadratic equation.
The given quadratic equation can be rewritten as:-
[tex]2x^2+12x[/tex]-3+3=0+3
[tex]\\2x^2+12x[/tex]-3 + 3 + 18=0 +3 +18
[tex]2x^2[/tex] + 12x + 18 = 0 + 3 + 18
Hence, the answer is the first option.
Quadratic equation
Quadratic equations are the polynomial equations of degree 2 in one variable of type [tex]f(x) = ax^2 + bx + c = 0[/tex]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). The values of x satisfying the quadratic equation are the roots of the quadratic equation (α, β).
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Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain. Given: XN NZ and NY = NW No; you cannot determine that the quadrilateral is a parallelogram. Yes; opposite sides are congruent. Yes; two opposite sides are both parallel and congruent. Yes; diagonals of a parallelogram bisect each other.
Answers
A parallelogram is a quadrilateral that has the following characteristics:
The opposite sides are parallel and congruent.
The opposite angles are congruent.
The consecutive angles are supplementary.
If any one of the angles is a right angle, then all the other angles will be at right angle.
The two diagonals bisect each other.
Since:
[tex]XN\cong NZ;NY\cong NW[/tex]We can conclude that the answer is:
Yes; diagonals of a parallelogram bisect each other.
lana 15:02If two events A and B are independent and you know that P(A) = 0.3, what is the value of P(A|B)?
Answers
Since the events are independent, we have the following property:
[tex]P(A)=P(A|B)[/tex]That is, the probability of A is the same as the probability of A given B (since the events are independent, event B does not affect event A).
So, if P(A) = 0.3, therefore P(A|B) is also equal to 0.3.
I need help answering the questions for person 2 on my group assignment
Answers
The equation for the relation of sides of triangle can be obtained by similar triangle property.
Consider triangle ABC and triangle DBE.
[tex]\begin{gathered} \angle CAB=\angle EDA\text{ (Each angle is right angle)} \\ \angle CBA=\angle EBD\text{ (common angle)} \\ \Delta CBA\cong\Delta EBD\text{ (By AA similarity condition)} \end{gathered}[/tex]Determine the ratio of corresponding sides of simillar triangle.
[tex]\frac{CB}{EB}=\frac{BA}{BD}=\frac{CA}{ED}[/tex]Thus similar triangle property is used to set up the equation.
A chef is going to use a mixture of two brands of italian dressing. the first brand contains 7% vinegar and the second brand contains 12% vinegar. the chef wants to make 280 milliliters of a dressing that is 9% vinegar. how much of each brand should she use
Answers
We know that
• The first brand contains 7% vinegar.
,• The second brand contains 12% vinegar.
,• The chef wants 280 milliliters with 9% vinegar.
Using the given information, we can express the following equation.
[tex]0.07x+0.12(280-x)=0.09(280)[/tex]Notice that 0.07x represents the first brand, 0.12(280-x) represents the second brand, and 0.08(280) represents the final product the chef wants to make.
Let's solve for x.
[tex]\begin{gathered} 0.07x+33.6-0.12x=25.2 \\ -0.05x=25.2-33.6 \\ -0.05x=-8.4 \\ x=\frac{-8.4}{-0.05} \\ x=168 \end{gathered}[/tex]Therefore, the chef needs 168 of the first brand and 112 of the second brand.Notice that 280-168 = 112.
rounded 425.652 to the hundredths place
Answers
Since the given number is 425.652
The hundredth digit is the 2nd number right at the decimal point
It is 5
To round to the nearest hundredth, we will look at the digit right to it
1. If it is 0, 1, 2, 3, or 4 we will ignore it and write the number without change except by canceling that digit
2. If it is 5, 6, 7, 8, or 9 we will cancel it and add the digit left to it 1
Since the right digit to the digit 5 is 2, then we will remove it and do not change the digit 5 (case 1), then
The number after rounding should be 425.65
The answer is 425.65
Identify the property of real numbers illustrated in the following equation.(-5) + (y · 7) = (y · 7) + (-5)
Answers
By definition, the commutative property of addition says that changing the order of addends does not change the sum, which is precisely what the equation is trying to show by changing the order of the sum, therefore, the property illustrated is the commutative property of addition.
Can you please help me with 44Please use all 3 forms of the expression such as : down/up. As _,_ And limits
Answers
Answer:
[tex]\begin{gathered} x-\text{intercept}=-3\text{ and 1} \\ y-\text{intercept}=\text{ -9} \end{gathered}[/tex][tex]\begin{gathered} x=1\text{ multiplicity 3} \\ x=-3\text{ multiplicity 2} \\ \lim _{x\rightarrow\infty}(x-1)^3(x+3)^2=\infty \\ \lim _{x\rightarrow-\infty}(x-1)^3(x+3)^2=-\infty \end{gathered}[/tex]Step-by-step explanation:
To find the x-intercepts factor the function to the simplest form:
[tex]h(x)=(x-1)^3(x+3)^2[/tex]As we can see the zeros to the function would be 1 and -3, then its:
[tex]\begin{gathered} x-\text{intercept}=-3\text{ and 1} \\ y-\text{intercept}=\text{ -9} \end{gathered}[/tex]Zero has a "multiplicity", which refers to the number of times that its associated factor appears in the polynomial. Therefore, this function has multiplicity:
[tex]\begin{gathered} x=1\text{ multiplicity 3} \\ x=-3\text{ multiplicity 2} \end{gathered}[/tex]For the end behavior:
down/up
As x approaches infinity f(x) approaches infinity
As x approaches -infinity f(x) approaches -infinity
[tex]\begin{gathered} \lim _{x\rightarrow\infty}(x-1)^3(x+3)^2=\infty \\ \lim _{x\rightarrow-\infty}(x-1)^3(x+3)^2=-\infty \end{gathered}[/tex]Find the degree measure of the central angle for sector C. (image attached)
Answers
We will determine the angle as follows:
We know that the whole circle contains 360°, so we determine the angle of 0.35 as follows:
[tex]C=\frac{0.35\ast360}{1}\Rightarrow C=126[/tex]So, the measure of the central angle for sector C is 126°.
(Algebra 1 Equivalent equations)
In a family, the middle child is 5 years older than the youngest child.
Tyler thinks the relationship between the ages of the ages of the children can be described with 2m-2y=10, where m is the age of the middle child and y is the age of the youngest.
Explain why Tyler is right.
Answers
Let the middle child is m and youngest is y.
The middle child is 5 years older than the youngest child, it can be shown as:
m - y = 5Tyler's equation is equivalent to ours since it can be obtained by multiplying both sides of our equation by 2:
2(m - y) = 2*52m - 2y = 10 ⇔ m - y = 5So Tyler is right.
What is the domain, range, and function? {(-3, 3), (1, 1), (0, -2), (1,4), (5, -1)}
Answers
The domain are all the inputs, that is; the x-values
Domain = { -3, 0, 1, 5}
The range are all the output, that is the y-values
Range = { 3, 1, -2, 4, -1}
This is just a relation and not a function, as we have more than 2 same value of x
which graph represents the solution to -1/2m>7/11
Answers
The graph of the inequality:
(-1/2)*m > 7/11
Can be seen in the image at the end.
Which graph represents the solution for the inequality?Here we have the following inequality:
(-1/2)*m > 7/11
First, let's solve this for m, this means that we need to isolate the variable in one side of the inequality.
If we multiply both sides by -2, we get:
-2*(-1/2)*m < -2*(7/11)
Where the direction of the symbol changes because we are multiplying by a negative number.
m < -14/11
The graph of this will be an open circle at -14/11 and an arrow that goes to the left, like the one below.
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We are reviewing a module and I don't remember how to do it.
Answers
The coordinate of point X which is 5/6 of the distance between P and Q is 5/11
Here, we want to calculate the coordinates of point X which is 5/6 of the distance between P and Q
Mathematically, we can use the internal division formula.
In this case, the coordinates of y is 0 in all cases
So the coordinates of P is (-5,0) while the coordinates of Q is (7,0)
Now, the coordinates of X divides the line PQ in the ratio 5 to 6
Using the internal divison formula, we have;
[tex](x,y)\text{ = }\frac{mx_2+nx_1}{m+\text{ n}},\text{ }\frac{my_2+ny_1}{m+\text{ n}}[/tex]In this case however, we are going to focus on the x-axis part of the question since the values of y at all points is 0
m , n are the division values which are 5 and 6 respectively in this case
x2 is 7 while x1 is -5
Substituting all of these, we have;
[tex]\begin{gathered} (x,y)\text{ = }\frac{5(7)\text{ + 6(-5)}}{11},\text{ 0} \\ \\ (x,y)\text{ = }\frac{35-30}{11},\text{ 0} \\ (x,y)\text{ = }\frac{5}{11},\text{ 0} \end{gathered}[/tex]So the coordinate of point X which is 5/6 of the distance between P and Q is 5/11
Jaylen used a 20% discount on a pair of jeans that cost $70 before tax. The sales tax is 6%. How much does the pair of jeans cost after tax? Show your work
Answers
If Jaylen used a 20% discount on a pair of jeans that cost $70 before tax, then the price of the jeans will be $70 - 20%.
Let's calculate the 20% of $70.
[tex]70\times20\%=14[/tex]So, the discounted price of the jeans before tax is $70 - $14 = $56.
Generally, sales tax is applied to the discounted price, so let's calculate the 6% of $56.
[tex]6\%\times56=3.36[/tex]The sales tax is $3.36.
Therefore, the cost of the pair of jeans after tax is $59.36.
[tex]56+3.36=59.36[/tex]If the correlation coefficient is 1, then the relation is a __________________.perfect positive correlationperfect negative correlationweak negative correlationweak positive correlation
Answers
Given:
The correlation coefficient is 1.
Required:
What type of correlation is it?
Explanation:
A coefficient of -1.0 indicates a perfect negative correlation, and a correlation of 1.0 indicates a perfect positive correlation.
Answer:
Hence, correlation coefficient is 1 then relation is perfect positive correlation.
An Integer is a number with a fractional part. True or False
Answers
An integer is a number with a fractional part is true statement.
HELP PLEASEEEEEEEE!!!
Answers
The rational number is -91/100 or -0.91.
What is Rational number?Any number of the form p/q, where p and q are integers and q is not equal to 0, is a rational number. The letter q stands for the set of rational numbers.
The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.
Given:
We have to find the rational number between -0.45 and -0.46
Now, make both decimal into fraction
-0.45 and -0.46
-45/100 and -46/100
Now, multiply 2
-45/100 x 2/2 and -46/100 x 2/2
-90/100 and - 92/100
Hence, the rational number is -91/100 or -0.91.
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The rational number is -91/100 or -0.91.
What is Rational number?Any number of the form p/q, where p and q are integers and q is not equal to 0, is a rational number. The letter q stands for the set of rational numbers.
The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.
Given:
We have to find the rational number between -0.45 and -0.46
Now, make both decimal into fraction
-0.45 and -0.46
-45/100 and -46/100
Now, multiply 2
-45/100 x 2/2 and -46/100 x 2/2
-90/100 and - 92/100
Hence, the rational number is -91/100 or -0.91.
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A spherical iron ball is coated with a layer of ice of uniform thickness. If the ice melts at the rate of 8 mL/min, how fast is the outer surface area of ice changing when the outer diameter of the ball with ice on it is 24 cm?
Answers
When the outer diameter of the ball with ice on it is 24 cm then the outer surface area of ice changes at the rate of 1/90cm²/sec.
As given in the question,
Spherical ball is coated with uniform thickness.
Ice melts at the rate of 8ml/min
= (8/60)cm³/sec
Consider r as the radius of given spherical ball
Diameter = 24cm
⇒Radius 'r' =12cm
Volume 'V' = (4/3)πr³
⇒ dV /dt = (4/3)π(3r²r')
⇒-(8/60) = (4/3)π(3 ×12²×r')
⇒r' =-(8/60)×(1/576π)
⇒r' = - 1/ 4320π
Rate at which change in surface area
A =4πr²
⇒A' = 4πrr'
⇒A' = 4π (12) ( - 1/ 4320π)
= -1/90 cm²/sec.
Decrease in surface area = 1/90 cm²/sec.
Therefore, when the outer diameter of the ball with ice on it is 24 cm then the outer surface area of ice changes at the rate of 1/90cm²/sec.
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The length of a rectangle is 6 cm more than the width. If the perimeter is 52 cm. What are the dimensions of the rectangle?
Answers
LA rectangle has two pairs of sides of the same length. If we call W to the width of the rectangle, we know that the length is 6cm more. If we call L the length of the rectangle:
[tex]L=W+6[/tex]The perimeter of a rectangle is twice the length plus twice the width:
[tex]Perimeter=2L+2W[/tex]Since we know that the perimeter is 52 cm, we can write the system of equations:
[tex]\begin{cases}L={W+6} \\ 2L+2W=52{}\end{cases}[/tex]We can substitute the first equation into the second one:
[tex]2(W+6)+2W=52[/tex]And solve:
[tex]2W+12+2W=52[/tex][tex]\begin{gathered} 4W=52-12 \\ . \\ W=\frac{40}{4}=10\text{ }cm \end{gathered}[/tex]We know that W = 10cm, we can now find L:
[tex]L=10+6=16\text{ }cm[/tex]Thus, the dimensions of the rectangle are:
Length: 16 cm
Width: 10 cm
How many and what type of solution(s) does the equation have?6p2 = 8p + 32 rational solutions1 rational solutionNo real solutions2 irrational solutions
Answers
We are going to solve the question using the quadratic formula
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{(b^2}-4ac)}{2a} \\ \text{where the quadratic equation is ax}^2+bx+c=0 \end{gathered}[/tex]The quadratic equation given is
[tex]\begin{gathered} 6p^2=8p+3 \\ 6p^2-8p-3=0 \\ \text{where a=6} \\ b=-8 \\ c=-3 \end{gathered}[/tex]By substitution we will have,
[tex]\begin{gathered} p=\frac{-(-8)\pm\sqrt[]{(-8)^2}-(4\times6\times-3)}{2\times6} \\ p=\frac{8\pm\sqrt[]{64+72}}{12} \\ p=\frac{8\pm\sqrt[]{136}}{12} \\ p=\frac{8\pm\sqrt[]{4\times34}}{12} \\ p=\frac{8\pm2\sqrt[]{34}}{12} \\ p=\frac{2(4\pm\sqrt[]{34)}}{12} \\ p=\frac{4\pm\sqrt[]{34}}{6} \\ p=\frac{4+\sqrt[]{34}}{6}\text{ or p=}\frac{4-\sqrt[]{34}}{6} \end{gathered}[/tex]Therefore,
With the roots gotten from the quadratic equation, we can therefore deduce that the solutions to the equation 6p²=8p+3 will give 2 irrational roots.
The correct answer is OPTION D
Given the following table of values determine the value of X where f(x) has a local minimum. Assume that f is continuous and differentiable for all reals
Answers
We have to find the value of x for which f(x) has a minimum.
Extreme values of f(x), like minimum or maximum values, correspond to values of its derivative equal to 0.
In this case f'(x) = 0 for x = -2 and x = 0.
We can find if this extreme value is a minimum if the second derivative f''(x) is greater than 0.
In this case, f'(x) = 0 and f''(x) > 1 for x = 0.
Then, x = 0 is a local minimum.
Answer: x = 0
Given Z VYX is bisected by YW, mZ VYX =(6r-18), and m2 VYW = 36. What is the value of r? A. 15 B. 30 C. 36 D. 72
Answers
A) 15
1) Let's sketch that
According to the Bisector Theorem, the bisected line equally divides the angle. So we can write:
∠VYW≅∠WYX
And:
6r-18 = 36+36
6r -18 = 72
6r= 90
r= 15
This chart shows the cost per pound of different fruits.
Answers
From the given data, the cost per pound of apple, CP=$1.89≈$2.
We have to estimate the cost of n=3.2≈3 pounds(lb) of apple.
The cost of n=3 lb of apple can be calculated as,
[tex]\begin{gathered} T=CP\times n \\ =2\times3\text{ lb} \\ =6 \end{gathered}[/tex]Therefore, the cost of 3. pounds of apples is about $6.048.
The area of a picture projected on a wall varies directly at the square of the distance from the projector to the wall if a 10ft distance produces a 16 feet squared (^2) picture, what is the area of the picture produced when the projection unit is moved to a distance 20 ft from the wall?
Answers
The new picture is 64 ft squared. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
What is area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
We are given the relation: Area of pic = constant * d^2, where d is distance from projector to wall.
For d = 10, we have A = 16 ft sqrd
Now given d = 20
what is A?
constant = 16/10*10
new A = [16/100] * 20*20 = 16 * 4 = 64 ft sqrd.
The new picture is 64 ft squared.
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A woman is floating in a
boat that is 175 feet from
the base of a cliff. The cliff
is 250 feet tall. What is the
angle of elevation from
the boat to the top of the
cliff?
Answers
The angle of depression between the cliff and the boat is 55.0
What is angle of depression?
The angle of depression is the angle between the horizontal line and the observation of the object of from the horizontal line. It's basically used to get the of distance of the two objects where the angles and an of object's distance from the ground are known to us.
A boat is moving 175 feet from the base and a women is in the boat.the height of the cliff is 259 feet tall. Here we have to find the angle between the cliff and the boat.
As per the given question
We have a right angled traingle where base is 175 ft and height is 250 ft.
Thus,
We know that tan theta =opposite/adjacent
250/175
So theta=tan^-1(250/175)
So theta = 55.0
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Find an equation of the line. Write the equation using function notation.
Through (4, -1); perpendicular to 4y=x-8
The equation of the line is f(x) =
Answers
The equation of line perpendicular to 4y = x-8 passing through (4,-1) is:
[tex]y = -4x+15[/tex].
What is a equation of line?These lines are written in the form y = mx + b, where m is the slope and b is the y-intercept. We know from the question that our slope is 3 and our y-intercept is –5, so plugging these values in we get the equation of our line to be y = 3x – 5.
Given equation of line is:
4y=x-8
We have to convert the given line in slope-intercept form to find the slope of the line
Dividing both sides by 4.
[tex]y = \frac{1}{4}x-2[/tex]
Let [tex]m_{1}[/tex] be the slope of given line
Then,
[tex]m_{1}[/tex] = [tex]\frac{1}{4}[/tex]
Let [tex]m_{2}[/tex] be the slope of line perpendicular to given line
As we know that product of slopes of two perpendicular lines is -1.
[tex]m_{1}*m_{2} = -1\\\frac{1}{4}*m_{2}=-1\\ m_{2} = -4[/tex]
The slope intercept form of line is given by
[tex]y = m_{2}x+c[/tex]
[tex]y = -4x+c[/tex]
to find the value of c, putting (4,-1) in equation
[tex]-1 = -4*4+c\\-1+16 = c\\c = 15[/tex]
Putting the value of c in the equation
[tex]y=-4x+15[/tex]
Hence, The equation of line perpendicular to 4y = x-8 passing through (4,-1) is [tex]y = -4x+15[/tex].
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Find a polynomial function of lowest degree with rational coefficients that has the
given numbers as some of its zeros.
√3,51
The polynomial function in expanded form is f(x) =
Answers
Answer: [tex]f(x)=x^3 -51x^2 -3x+153[/tex]
Step-by-step explanation:
By the conjugate root theorem, the roots are [tex]\sqrt{3}, -\sqrt{3}, 51[/tex].
Letting the leading coefficient be 1,
[tex]f(x)=(x-\sqrt{3})(x+\sqrt{3})(x-51)\\\\=(x^2 -3)(x-51)\\\\=x^3 -51x^2 -3x+153[/tex]
what is the solution set for the inequality
A. x ≤ -5
B. x ≤ 5
C. x ≤ 1
d. x ≤ -14
Answers
The solution set to the inequality, 4x + 12 ≤ -8, is determined as: A. x ≤ -5.
How to Find the Solution Set of an Inequality?The solution set is the value of x that would make an inequality statement true. To find the value of x, solve as you would solve a normal equation.
Using the key to the given model in the diagram, we can write the inequality as follows:
On the left, we would have, 4x + 12.
On the right, we would have, -8.
The inequality would be expressed as:
4x + 12 ≤ -8
Solve for x
4x + 12 - 12 ≤ -8 - 12 [subtraction property of equality]
4x ≤ -20
4x/4 ≤ -20/4
x ≤ -5
The solution set is: A. x ≤ -5.
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last night Danielle had a birthday party. 1/3 of the cake was left over.She wanted to share the left over cake with 4 friends the next day .How much of birthday cake would each get
Answers
Solution
For this case we have a total cake representing 1
We also know that 1/3 of the cake was left over so then 1/3
And we want to share to 4 friends so we can do this:
1/3 * 1/4 = 1/12
So then each friend will recieve 1/12
