A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compareover the interval -2
Answers
To check the decay rate, we need to check the variation in y-axis.
Since our interval is
[tex]-2We need to evaluate both function at those limits.At x = -2, we have a value of 4 for both of them, at x = 0 we have 1 for the exponential function and 0 to the quadratic function. Let's call the exponential f(x), and the quadratic g(x).
[tex]\begin{gathered} f(-2)=g(-2)=4 \\ f(0)=1 \\ g(0)=0 \end{gathered}[/tex]To compare the decay rates we need to check the variation on the y-axis of both functions.
[tex]\begin{gathered} \Delta y_1=f(-2)-f(0)=4-1=3 \\ \Delta y_2=g(-2)-g(0)=4-0=4 \end{gathered}[/tex]Now, we calculate their ratio to find how they compare:
[tex]\frac{\Delta y_1}{\Delta y_2}=\frac{3}{4}[/tex]This tell us that the exponential function decays at three-fourths the rate of the quadratic function.
And this is the fourth option.
Related Questions
Drag each tile to the correct box.Arrange the functions in ascending order, starting with the function that eventually has the least value and ending with the function thateventually has the greatest value.3x + 8+4+3x² + 63x4*
Answers
To answer the question we are going to graph the functions given:
From the graph we notice that the order will be:
[tex]\begin{gathered} 3x \\ 3x+8 \\ x^2 \\ x^2+6 \\ 4^x \\ 4^x+3 \end{gathered}[/tex]use the information given to answer the question.consider the textbook and its mathematical label.part Awhich statement is true?the answer questions is in the image
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Solution:
Given the textbook and its mathematics label as shown below:
From the above shape of the book and label, the textbook takes the shape of a rectangular prism, while its label is rectangular in shape.
Thus, the textbook is best represented by a rectangular prism, while the label is best represented by a rectangle.
The third option is the correct answer.
What is the measure of ZBDC?What is the measure of arc length BC?
Answers
SOLUTION
Step 1:
To find the measure of
Step 2:
The angle subtended by an arc at the centre is twice the angle subtended at the circumference. More simply, the angle at the centre is double the angle at the circumference.
Step 3:
Dividing both sides by 2, we have;
[tex]\begin{gathered} <\text{BDC = }\frac{BOC}{2}\text{ = }\frac{138}{2} \\ \\Step 4:
We are to find the measure of arc length BC;
Angle BOC is given as 138
[tex]\begin{gathered} \frac{\theta}{360}\text{ x 2 }\pi\text{ r} \\ \\ \frac{138}{360}\text{ x 2 x 3.14 x r } \\ \\ 2.407r \end{gathered}[/tex]Note: Since the value of the radius was not given so we need to express our answer in term of r.
The measure of arc length BC is 2.407r, where r is the radius.
Answer To this question so that we can move on to the next question so we can get all this homework done
Answers
Commercial agents earn 5% of the cost of each product they sell. If an agent earsn $2000 for selling a product, what was the cost of the product?
Answers
Answer: 40,000
Step-by-step explanation: 5 (the earnings) times twenty is 100 (the total cost) and if we substitute 5 for 2000, the total is 40,000.
Answer: 40,000
Step-by-step explanation:
just because
Ever NL OP N 2 PN, and is the midst of MO. PALUN APON STATEMENTS REASONS: 2. Nisthe MO 1. Gren Given the following proof, what is the 5th reason? 2 MZ - OP 2. Given 3. IN EN 3. Given 2 MIN ON 4. Definition of midpoint 5 5. ALMN 2 APON SAS CPCTC SSS ASA
Answers
In this case, we have to use the SSS Postulate for the congruency of the triangles, that is, if three sides of a triangle are congruent to three sides of another triangle, then the triangles are congruent.
We have that all reasons are given congruent sides. The midpoint divides the segment into two equal parts, then the angles are congruent because of the reason: SSS ( SSS Postulate for congruency of triangles).
The sum of the ages of Darius and Brooke is 78 years. 7 years ago, Darius's age was 3 timesBrooke's age. How old is Darius now?
Answers
The sum of the ages of Darius and Brooke is 78 years. 7 years ago, Darius's age was 3 times
Brooke's age. How old is Darius now?
Let
x ------> darius's age
y -----> Brooke's age
we know that
x+y=78 ------> equation A
(x-7)=3(y-7) -----> equation B
solve the sytem of equations
isolate the variable x in the equation A
x=78-y -------> equation C
substitute equation C in equation B
78-y-7=3(y-7)
slve for y
71-y=3y-21
3y+y=71+21
4y=92
y=23
Find the value of x
x=78-y
x=78-23=55
therefore
Darius now is 55 year old
the table shows the number of hours worked and the total amount that each of the four people earned one weekendwhose pay rate was the best whose pay rate was the worst Based on the chart.
Answers
pay rate = money earned/hours worked
Gary's pay rate: $37/4 = $9.25 per hour
Tara's pay rate: $54.9/6 = $9.15 per hour
Lamont's pay rate: $27.6/3 = $9.2 per hour
Darius' pay rate: $46.5/5 = $9.3 per hour
best pay rate: Darius
worst pay rate: Tara
whstbis the area in square inches of the shaded part of the retangle below
Answers
The shaded area is trapezium with parallel sides as a = 10, b = 5 and height of trapezium is h = 18 in.
The formula for the area of trapezium is,
[tex]A=\frac{1}{2}\cdot(a+b)\cdot h[/tex]Determine the area of the tapezium.
[tex]\begin{gathered} A=\frac{1}{2}\cdot(10+5)\cdot18 \\ =15\cdot9 \\ =135 \end{gathered}[/tex]So area of shaded region is 135 square inch.
Which of the following expressions is equal to5 - 2(x + 2)?O -2x+1O 3x+6O -2x+2O 3x+2
Answers
Given:
an expression is given as 5 - 2(x + 2)
Find:
we have to simplify the expression and find correct expression from the options, which is equal to the given expression.
Explanation:
Now
5 - 2(x + 2) = 5 - 2x - 4 = - 2x + 1
Therefore, 5 - 2(x + 2) = - 2x + 1
2. The sum of the perimeters of similar quadrilaterals is 22.5 dm. Find the perimeters of the quadrilaterals if the similarity coefficient k = 1.25.
Answers
Given:
The sum of the perimeters of similar quadrilaterals is 22.5 dm. The similarity coefficient k = 1.25.
Required:
To find the perimeters of the quadrilaterals.
Explanation:
The quadrilaterals are similar and the similarity coefficient is k = 1.25.
If the quadrilateral is similar then the ratio of their corresponding sides is equal.
Let the perimeter of the one quadrilateral is x then the perimeter of the other quadrilateral will be 1.25x
Now
[tex]\begin{gathered} x+1.25x=22.5 \\ x(1+1.25)=22.5 \\ 2.25x=22.5 \\ x=\frac{22.5}{2.25} \\ x=10 \end{gathered}[/tex]Thus the perimeter of the one quadrilateral is 10dm.
The perimeter of the other quadrilateral = 1.25 x 10 = 12.5 dm
Final Answer:
Thus the perimeter of the quadrilaterals is 10dm and 12.5 dm.
y^(3)-27=9y^(2)-27y. could you please show steps
Answers
The solution to the algebraic expression is y =3
Algebraic expressionThis algebraic expression contain variable and constant along with unknow variables.
y^(3)-27=9y^(2)-27y
Add 27y to both sides
y^(3)-27 +27y =9y^(2)-27y +27y
Simplify
y^3-27 +27y =9y^2
Subtract 9y^2 from both sides
y^3-27 +27y-9y^2 =9y^2- 9y^2
y^3-27 +27y-9y^2= 0
Simplify
y^3 - 9y^2 + 27y - 27 =0
Factor by grouping y^3 - 9y^2 + 27y - 27 ; (y-3)^3
(y -3) (-y^2 + 6y -9) = 0
(y-3)^3 =0
Using the zero factor principle if ab = then a = 0 or b= 0
y-3= 0
Add 3 to both sides
y =3
Therefore, solution to the algebraic expression is y =3
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if m<10=77, m<7=47 and m<16=139, find the measure of the missing angle m<14=?
Answers
According to the diagram, angles 10 and 14 are supplementary, so they sum 180°.
[tex]\begin{gathered} m\angle10+m\angle14=180 \\ 77+m\angle14=180 \\ m\angle14=180-77 \\ m\angle14=103 \end{gathered}[/tex]Hence, angle 14 measures 103°.A business person invests $3,367 at 5% compounded semiannually for two years. What is the future value of the investment, and how much interest will they earn over the two-year period?
Answers
The future value of the investment will be $3712.1 and they will earn interest of $345.1 over the two-year period.
Given that business person invests $3,367 at 5% compounded semiannually for two years.
p = $3,367
r = 5%
t = 2 years
A = P(1+r/100)ⁿ
Substitute the values of p,r, and t in the formula,
A = 3,367(1 + 5/100)²
A = 3,367(1 + 0.05)²
A = 4.700 (1.05)²
A = 3712.1175
Rounded to the nearest cent
A = $3712.1
Total interest = A - p = 3712.1 - 3,367 = $345.1
Therefore, the future value of the investment will be $3712.1 and they will earn interest of $345.1 over the two-year period.
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Find the shape, or rate of change, from the following table?
Answers
ANSWER
C. -6
EXPLANATION
The rate of change is the change in the dependent variable when the independent variable changes 1 unit. In this case, all columns in the table have a change in the x variable of 1, so the difference between each column in the y-row is the rate of change,
[tex]m=-9-(-3)=-15-(-9)=-21-(-15)=-6[/tex]Hence, the rate of change is -6.
Find the values of A, B, and C in the table.Intervalfa) for a in Relation ofinterval fa) to x-axis(0, 1)f(-2)= -12below(-1, A)f(0)=Babove(A, 2)f (1.5) -0.6(2,)f(3) = 8above
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From the first line of the table, it shows
[tex]f(-2)=-12[/tex]This means that
when x = -2, y = -12,
so
[tex]a=-2[/tex]Now,
Yolanda is riding in a bike race that goes through a valley and a nearby mountain range,The table gives the altitude (in feet above sea level) for the five checkpoints in the race,Use the table to answer the questions,CheckpointAltitude(feet above sea level)12,2242- 13731,5714-305218(8) How much lower is Checkpoints than check out 2909 i lower
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Step 1
Write the given checkpoint altitude
Checkpoint 1 = 2224
Checkpoint 2 = -137
Checkpoint 3 = 1571
Checkpoint 4 = -39
Checkpoint 5 = -218
Step 2:
a) How much lower is checkpoint 5 than checkpoint 2
You will subtract checkpoint 5 altitude from checkpoint 2
[tex]\begin{gathered} =\text{ -137 - (-218)} \\ =\text{ -137 + 218} \\ =\text{ 81 f}eet \end{gathered}[/tex]b) Altitude of the top hill that is 365 above checkpoint 5.
[tex]\begin{gathered} \text{Altitude of the top hill = 365 - 218 } \\ \text{Altitude of the top hill 365 above checkpoint 5 = 147} \end{gathered}[/tex]"A quadrilateral is a square if and only if it has fourright angles."Which of the following terms provides acounterexample for why the biconditional statement is
Answers
Given statement: A quadrilateral is a square if and only if it has four right angles
Counterexample: A quadrilateral with four right angles can be also a rectangle. Then, not all quadrilaterals with four right angles are squares.
Answer: Rectangle
What is the value of x in the triangle?a right triangle with a short leg of length x and hypotenuse of length 3 times the square root of 2A. B. C. D. E.
Answers
Solution:
Given the right triangle below:
To solve for x, we use the trigonometric ratio.
In the above triangle, the angles at A and B are equal.
Thus, we have
[tex]\begin{gathered} \angle A+\angle B+\angle C=180(su\text{m of angles in a triangle\rparen} \\ \angle A=\angle B \\ thus, \\ 2\angle\text{B+90=180} \\ \Rightarrow2\angle\text{B=180-90} \\ 2\angle\text{B=90} \\ \Rightarrow\angle\text{B=45} \end{gathered}[/tex]From trigonometric ratio,
[tex]\sin\theta\text{=}\frac{opposite}{hypotenuse}[/tex]In this case, θ is the angle at B, which is 45; opposite is AC, and hypotenuse is AB.
Thus,
[tex]\begin{gathered} \sin45=\frac{x}{3\sqrt{2}} \\ \Rightarrow x=3\sqrt{2}\times\sin45 \\ =3\sqrt{2}\times\frac{1}{\sqrt{2}} \\ =3 \end{gathered}[/tex]Hence, the value of x is
[tex]3[/tex]The correct option is B
The polynomial P(x) = 5x^3 + 2x^2- 42 has ___ local maxima and minima
Answers
SOLUTION:
Case: Local maxima and local minima
Given:
[tex]P(x)=5x^3+2x^2-42^{}[/tex]Required: To find the local maxima and minima
Method:
[tex]\begin{gathered} P(x)=5x^3+2x^2-42^{} \\ \text{ } \end{gathered}[/tex]First the find the first derivative:
[tex]\begin{gathered} P^{\prime}(x)=15x^2+4x \\ we\text{ make P'(x) = 0} \\ 15x^2+4x=\text{ 0} \\ x(15x+4)=0_{} \\ x=0\text{ or 15x+4 =0} \\ x=\text{ 0 or x= }\frac{-4}{15} \end{gathered}[/tex]Let us take the points in the immediate neighbourhood of x = 0. The points are {-1, 1}.
[tex]\begin{gathered} \text{when x=-1} \\ P^{\prime}(x)=15x^2+4x \\ P^{\prime}(-1)=15(-1)^2+4(-1) \\ P^{\prime}(-1)=15(1)^2-4 \\ P^{\prime}(-1)=15^{}-4 \\ P^{\prime}(-1)=11 \\ \text{when x= 1} \\ P^{\prime}(x)=15x^2+4x \\ P^{\prime}(1)=15(1)^2+4(1) \\ P^{\prime}(1)=15^{}+4 \\ P^{\prime}(1)=19 \end{gathered}[/tex]Let us take the points in the immediate neighbourhood of x = -4/15. The points are {-1, 0}
[tex]\begin{gathered} \text{when x= 0} \\ P^{\prime}(x)=15x^2+4x \\ P^{\prime}(0)=15(0)^2+4(0) \\ P^{\prime}(0)=0^{}+0 \\ P^{\prime}(0)=0^{} \end{gathered}[/tex]Final answer:
The local minima is at x= 0 while the local maxima is at x= -4/15
Factor out the greatest common factor. Simplify the factors, if possible.6x4 - 42x3 + 12x2Select the correct choice below and fill in any answer boxes in your choice.O A. 6x4 - 42x3 + 12x2 =(Type your answer in factored form.)OB. There is no common factor other than 1.ih
Answers
You have to find the greatest common factor first.
To do so, do as follows:
[tex]6x^4-42x^3+12x^2[/tex]Factors of 6 are: 1, 2, 3, 6
Factors of 12 are: 1, 2, 3, 4, 6, 12
Factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
The greates common factor is the greatest common factor shared by all values, in this case is 6
Now to factor it out you have to divide each term of the equation by it.
[tex](\frac{6x^4}{6})=x^4[/tex][tex](\frac{42x^3}{6})=7x^3[/tex][tex](\frac{12x^2}{6})=2x^2[/tex]The expression with the GCF factorized is then:
[tex]6(x^4-7x^3+2x^2)[/tex]Hero and Lisa are photographers they take pictures of seniors for high school yearbooks they charge a standard fee for taking the pictures there’s also a charge for each set of prints ordered so the number sets of prints determine the total cost S stand for the sets of prints ordered right the rule that describes the students total cost
Answers
Given:
We get the points (0,30), (1,31),(2,32), and (3,33) from the table.
Required:
We need to find the total cost.
Explanation:
From the point(0,30).
There is an initial cost of $30 for print.
Let s be the number of sets of prints ordered.
Let k be the additional cost for each number of sets of print
The equation of the given model is
[tex]Total\text{ cost =ks+30}[/tex]Consider the point (1,31).
Substitute total cost =31 and s=1 in the equation.
[tex]31\text{=k\lparen1\rparen+30}[/tex][tex]31\text{=k+30}[/tex]Subtract 30 from both sides.
[tex]31-30\text{=k+30-30}[/tex][tex]1\text{=k}[/tex]Substitute k =1 in the equation.
[tex]Total\text{ cost =s+30}[/tex]Consider the point (2,32).
Substitute total cost =32 and s =2 in the equation.
[tex]32\text{ =2+30}[/tex]It is true, so the equation satisfies the values in the table,
Final answer:
[tex]Total\text{ cost =s+30}[/tex]Can you please help and Copy the pictures and put the answers
Answers
x = -1/2, y = -6
x = 0, y = -3
x = 1/2, y = -2
x = 1, y = -3
x = 3/2, y = -6
Explanation:We trace each point on the x-axis to the corresponding point on the y-axis to have the following
x = -1/2, y = -6
x = 0, y = -3
x = 1/2, y = -2
x = 1, y = -3
x = 3/2, y = -6
[tex]y = 3(x + 3)(x + 1)[/tex]Intercept form find the vertex
Answers
Answer:
(-2, -3)
Explanation:
If we have an equation with the form:
f(x) = ax² + bx + c
The vertex of the parabola is the point (-b/2a, f(-b,2a)).
So, to find the vertex, we need to write the equation y = 3(x + 3)(x + 1) as:
[tex]\begin{gathered} y=3(x+3)(x+1) \\ y=3(x^2+3x+x+3) \\ y=3(x^2+4x+3) \\ y=3x^2+12x+9 \end{gathered}[/tex]Then, the value of a is 3 and the value of b is 12. It means that -b/2a is equal to:
[tex]-\frac{b}{2a}=-\frac{12}{2(3)}=-\frac{12}{6}=-2[/tex]And f(-b/2a) = f(-2) is equal to:
[tex]\begin{gathered} y=3x^2+12x+9 \\ f(-2)=3(-2)^2+12(-2)+9 \\ f(-2)=3(4)-24+9 \\ f(-2)=12-24+9 \\ f(-2)=-3 \end{gathered}[/tex]Therefore, the vertex is the point (-2, -3)
it take Sarah to 1/2 AJ to make a birdhouse how much of the birdhouse will be built after 2/5 day choose the model that correctly illustrates the problem 2/5 ÷ 1/2
Answers
After 2/5 days Sarah can build 4/5 of a birdhouse.
It is given that Sarah can build birdhouses at the rate of 1/2 day per birdhouse.
Now let us use unitary method to calculate the number of birdhouses she can make in the given amount of time in a day.
Sarah takes 1/2 day to make 1 birdhouse
Sarah takes 1 day to make 1 ÷(1/2) birdhouse
Sarah takes 2/5 day to make 1÷ 1/2 × 2/5 birdhouse
Hence Sarah will make
= 1 ÷ 1/2 × 2/5
= 4/5 birdhouse
The unitary approach is a technique for solving problems that requires first figuring out how much one unit costs, then multiplying that amount to get the answer.
Therefore Sarah will take 2/5 days to make 4/5 of a birdhouse.
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What would be the equation for this line? 80 60 40 20 time in minutes 2 3 4 5 6 7 8 9 X distance in miles
Answers
the equation of the line is given as follows,
first we take points on this line
A(2,20)
and
B (4,40)
so, the equation of the line is,
[tex]y-20=\frac{40-20}{4-2}(x-2)[/tex][tex]\begin{gathered} y-20=\frac{20}{2}(x-2) \\ y-20=10x-20 \\ y=10x \end{gathered}[/tex]thus, the equation of the line is
y = 10x
A fuelling vehicle finished filling a plane with 12.40 tons of fuelat 10:35. If the fuelling rate is 0.20 ton of fuel per min, at whattime did the fuelling start? Give your answer in a 12-hour clockformat, such as 9:00.9:33xHmm, that wasn't the right answer. Let's give it one more try.
Answers
The angle of elevation to the top of a 10-story skyscraper ismeasured to be 3° from a point on the ground 2000 feet fromthe building. What is the height of the skyscraper to thenearest hundredth of a foot?
Answers
ANSWER :
The height is 104.82 feet
EXPLANATION :
The angle of elevation to the top of the building is 3 degrees from a point that is 2000 feet away from the building.
Using tangent function :
[tex]\tan\theta=\frac{\text{ opposite}}{\text{ adjacent}}[/tex]The opposide side to the angle is H and the adjacent side is 2000 feet.
Then :
[tex]\begin{gathered} \tan3=\frac{H}{2000} \\ \\ H=2000\tan3 \\ H=104.816\sim104.82\text{ }ft \end{gathered}[/tex]The length of a rectangle is 97 m and the width is 14 m find the area give your answer without units
Answers
The area of the rectangle is 1358
Explanation:length of the rectangle = 97m
width of the rectangle = 14m
Area of a rectangle = length × width
[tex]\begin{gathered} \text{Area = 97m }\times\text{ 14m} \\ Area\text{ }of\text{ the rectangle = }1358m^2 \end{gathered}[/tex]The area of the rectangle is 1358 (without units)
A teacher receivesa monthly salary of $2800.00 What isheraunnual salary?
Answers
The year has 12 months, since the teacher receives a monthly salary of $2800, then his annual salary is:
[tex]2800\times12=33600[/tex]Answer:
$33600