Answers
(y_final-y_start)/(x_final-x_start) (also for physics!)
In your case:
average rate of change is:
(-1-(-3))/(3-2) = 2/1=2
You can see it's +, so increasing (yeah).
if you would make the interval very small, from x=2 to x=2.00001, and so n, you'd get the concept of slope and derivative (but that's just to let u know)
Answer:
The average rate of change from x = 2 to x = 3 is 2. Therefore first option is correct.
Step-by-step explanation:
The average rate of a function f(x) on the interval [a,b] is defined as
[tex]m=\frac{f(b)-f(a)}{b-a}[/tex]
The average rate of change from x = 2 to x = 3 is
[tex]m=\frac{f(3)-f(2)}{3-2}[/tex] .... (1)
From the given graph it is clear that the value of the function is -3 at x=2 and -1 at x=3. It means f(2)=-3 and f(3)=-1.
Put f(2)=-3 and f(3)=-1 in equation (1).
[tex]m=\frac{-1-(-3)}{3-2}[/tex]
[tex]m=\frac{-1+3}{1}[/tex]
[tex]m=\frac{2}{1}[/tex]
[tex]m=2[/tex]
The average rate of change from x = 2 to x = 3 is 2. Therefore first option is correct.
Related Questions
Which algebraic expression represents “the difference of 54 and a number”?
Answers
For this case, the first thing we should do is define a variable.
We have then:
x: unknown number
Then, we write the algebraic expression that models the following problem:
the difference of 54 and a number.
We have then:
[tex]54-x[/tex]
Answer:
An algebraic expression that represents "the difference of 54 and a number" is:
[tex]54-x[/tex]
Answer:
A
Step-by-step explanation:
The volume of a cube depends on the length of its sides. This can be written in function notation as v(s). What is the best interpretation of v(4)=64
Answers
True or false the center of the circumscribed circle about a triangle is equidistant to the vertices of the inscribed triangle
Answers
Answer:
True
Step-by-step explanation:
Consider triangle ABC inscribed in the circle with center at point O. Point O is a point of intersection of perpendicular bisectors of sides AC, AB and BC. According to the attached diagram, points E, F and G are midpoints of sides BC, AC and AB, respectively.
Then
EB=EC;FC=FA;GA=GB.Since segments OE, OF and OG are perpendicular bisectors of sides BC, AC and AB, then
m∠OBE=m∠OCE=90°;m∠OCF=m∠OAF=90°;m∠OBG=m∠OAG=90°.You get three pairs of congruent triangles:
ΔOBE≅ΔOCE;ΔOCF≅ΔOAF;ΔOBG≅ΔOAG.This gives you that
[tex]OB=OC=OA.[/tex]
Each of these segments is a radius of the circumscribed circle about a triangle ABC, then the center of the circumscribed circle about a triangle is equidistant to the vertices of the inscribed triangle.
From 75 campsites to 120 campsites
Answers
subtract 75 from 120
120-75 =45 more campsites
Applying the distributive property, the expression becomes (3x)(–x) + (3x)(4) + (–5)(–x) + (–5)(4). What is the simplified product in standard form?
Answers
= -3x^2 + 12x + 5x - 20
= -3x^2 + 17x - 20
hope it helps
Julio checked the temperature of a bag of frozen peas and found it was at −13°C. After he left the bag out of the freezer for an hour, its temperature rose to 8°C. What was the change in temperature in an hour?
a)−21°C
b)21°C
c)5°C
d)−5°C
Answers
ΔT = final temperature - initial temperature = 8°C - ( -13°C) = 8°C + 13°C = 21 °C.
So, the temperature raised 21 °C, and that is the change in temperature.
Answer: change = option b) 21°C.
Bryce is testing whether school is more enjoyable when students are making high grades. He asked 100 students if they enjoyed school and whether their GPA was above or below 3.0. He found that 33 of the 40 students with a GPA above 3.0 reported that they enjoyed school, and 5 of the 60 students with a GPA below 3.0 reported that they enjoyed school. What is the probability that a student with a GPA below 3.0 does not enjoy school?
85%
92%
65%
75%
Answers
55/60 which is 0.916666666666
This is rounded to 92%! :)
Answer:
The answer is 92%.
Step-by-step explanation:
5 of the 60 students reported that they like school. This means that the other 55 don't like school. You then divide 55/60 and you get 92%. So, therefore, your answer is 52%.
Solve 2x + 5y = −13
3x − 4y = −8
Answers
3x-4y=-8
Rearrange the first equation to solve for x in terms of y. This will be needed to apply the substition method.
2x+5y=-13
2x=-5y-13
x=-5/2y-13/2
Now plug this in for x in the second equation.
3(-5/2y-13/2)-4y=-8
-15/2y-39/2-4y=-8
-23/2y-39/2=-8
-23/2y=11.5
y=-1
Now plug this y value in to one of the original equations.
2x+5(-1)=-13
2x-5=-13
2x=-8
x=-4
Final answer: (-4,-1). <=============
To check:
2(-4)+5(-1)=-13
-8+5(-1)=-13
-8-5=-13
-13=-13
True
3(-4)-4(-1)=-8
-12-4(-1)=-8
-12+4=-8
-8=-8
True
A tea bag is shaped like a regular square pyramid. Each leg of the base is 4 cm, and the slant height is 5 cm. Find the VOLUME of the tea bag.
Answers
So, the area of the base is 4x4, which is 16, then you multiply it by the height, 5, and 16x5 is 80, and 80/3 is approximately 26.6
The answer would be 26.6 cm^3
If there are 52 ounces of cereal in 2 boxes, how many ounces are there in 5 boxes?
Answers
26 * 5 = 130 ounces of cereal in 5 boxes
Answer:
If there are 52 ounces of cereal in 2 boxes, how many ounces are there in 5 boxes?
Step-by-step explanation:
If we have 52 ounces in 2 boxes, in 1 box we have: 52/2 = 26 ounces.
If we have 5 boxes and 26 ounces in each, we have: 5 x 26 = 130 ounces in total.
Write an equation for the translation of the function. y = cos x; translated 6 units up
Answers
Answer:
[tex]y=cos(x)+6[/tex].
Step-by-step explanation:
We are asked to write an equation for the translation of the function [tex]y=cos(x)[/tex] to 6 units upwards.
Let us recall transformation rules.
[tex]f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}[/tex]
[tex]f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}[/tex]
[tex]f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}[/tex]
[tex]f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}[/tex]
Since we need to shift our given function 6 units upwards, so we will add 6 to our given function outside the parenthesis as:
[tex]y=cos(x)+6[/tex]
Therefore, our required equation would be [tex]y=cos(x)+6[/tex].
The sum of two numbers is 54 . the smaller number is 12 less than the larger number. what are the numbers?
Answers
Someone help me please !!!
Answers
Answer:
1. 10
2. 12
3. Sqrt 130
4. Sqrt 45
Step-by-step explanation:
To find the missing side of a right triangle, use the Pythagorean Theorem. The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex] where a and b are the legs with a being the smallest and c is the hypotenuse.
1. a=6, b=8, c=?
[tex]6^2+8^2=c^2\\36+64=c^2\\100=c^2\\10=c[/tex]
2. a=5, b=?, c=13
[tex]5^2+b^2=13^2\\25+b^2=169\\169-25=b^2\\144=b^2\\12=b[/tex]
3. a=7, b=9, c=?
[tex]7^2+9^2=c^2\\49+81=c^2\\130=c^2\\\sqrt{130}=c[/tex]
4. a=2, b=?, c=7
[tex]2^2+b^2=7^2\\4+b^2=49\\49-4=b^2\\45=b^2\\\sqrt{45}=b[/tex]
(05.05)What is the rate of change of the linear relationship modeled in the table?
x y
1 2
3 5
5 8
7 11
negative three over two
two over three
one
1 three over two
Answers
slope (rate of change) = (5 - 2) / (3 - 1) = 3/2 <==
Answer: three over two
Step-by-step explanation:
We know that the rate of change of a function [tex]y=f(x)[/tex] is given by :-
[tex]k=\dfrac{\text{change in y}}{\text{change in x}}[/tex]
From the consecutive values in the table, the change in x = [tex]3-1=2[/tex]
Change in y = [tex]5-2=3[/tex]
Now, the rate of change of the linear relationship modeled in the table will be ;-
[tex]k=\dfrac{3}{\text{2}}[/tex]
Find the area of the larger regular pentagon if the smaller pentagon has an area of 43.01 inches^2. The side length of the small pentagon is 5 and the side length of the large pentagon is 8.
Answers
Please help me !!!!!!!!
Answers
side xy = square root 81 = 9
cosine(X) = Adj / Hypo
cosine(X) = 9/41
answer
C. 9/41
Rectangular prisms A and B are similar.
The edge of prism B is 3 times that of prism A. How many times the volume of prism A is the volume of prism B?
Answers
[tex]\bf \textit{let's say the edge of A is \underline{k} long, then B's is \underline{3k}} \\\\\\ \cfrac{A}{B}\qquad \cfrac{k}{3k}\implies \cfrac{1}{3}\implies \cfrac{s}{s}\qquad thus \\\\\\ \cfrac{A}{B}\qquad \cfrac{1}{3}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{1}{3}=\sqrt[3]{\cfrac{s^3}{s^3}}\implies \left( \cfrac{1}{3} \right)^3=\cfrac{s^3}{s^3}\implies \cfrac{1^3}{3^3}=\cfrac{s^3}{s^3} \\\\\\ \cfrac{1}{27}=\cfrac{s^3}{s^3}[/tex]
20 POINTS, PLEASE HELP ASAP!!!!
Answers
17 minutes ⇒ 1 revolution = 2π
1 minute ⇒ 2π/17
Angle of rotation is 2π/17 per minute
Question c)
The period of the rotation is 2π/17
The wheel starts rotating from the height of 5 meters from the ground and the maximum height is 125 meter from the ground.
The amplitude is 125 - 5 = 120 ÷ 2 = 60
The midline of the rotation is at 125 - 5= 120 ÷2 = 60 + 5 = 65 (this is the location of the centre of the wheel). This value is a shift of 65 from the zero midlines (which in this case would be the ground)
Question C
The movement of the wheel can be described as starting from 0° then reaching its peak at 180° and come back to its original position as it stops and it makes a complete circular turn 360°.
If we sketch this on a graph, we will obtain a curve of -cos(x)
We need to apply the period, the amplitude and the shift produced by this rotation into the equation [tex]y = -cos(x)[/tex]
The period is [tex] \frac{2 \pi }{7} [/tex] ⇒ [tex]f(t)=-cos( \frac{2 \pi }{7}t) [/tex]
The amplitude of 60 ⇒ [tex]f(t)=-60cos( \frac{2 \pi }{7}t) [/tex]
The shift of the midline by 65 units upwards ⇒ [tex]f(t) = -60cos( \frac{2 \pi }{7}t)+65 [/tex]
The final equation is
[tex]f(t) = -60cos( \frac{2 \pi }{7}t)+65 [/tex]
and the graph is shown in the third picture below
if a radius of a circle is perpendicular to a chord, then it _____ that chord.
a. is equal in length to
b. bisects
c. is congruent to
d. parallels
Answers
If a radius of a circle is perpendicular to a chord, then it _bisects____ that chord.
What is radius of circle?
In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin radius, meaning ray but also the spoke of a chariot wheel.
What is chord?
A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. The infinite line extension of a chord is a secant line, or just secant. More generally, a chord is a line segment joining two points on any curve, for instance, an ellipse.
According to question, we have to fill in the blank.
The property of the circle is that if a radius of a circle is perpendicular to a chord, then it bisects that chord.
Hence we can conclude that Option(B) is correct.
Learn more about chord of circle here:
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Final answer:
A radius of a circle that is perpendicular to a chord bisects the chord, dividing it into two equal segments.(Option b)
Explanation:
If a radius of a circle is perpendicular to a chord, then it bisects that chord. This statement is supported by a theorem in geometry which states that, in a circle, the radius bisecting an angle at the centre is perpendicular to the chord which subtends the angle and also bisects this chord. Therefore, by drawing a radius from the center of a circle to the midpoint of a chord, you create two equal segments, effectively bisecting the chord.
Thus, a perpendicular radius drawn from the center of a circle to a chord's midpoint ensures that the chord is bisected into two equal segments. This geometric principle facilitates chord division and enhances the understanding of circle properties.
I have 3 questions here , one of them I just need my answer checked on and the other two I really need help with. Thank you!!
Answers
The narrowest graph happens when the leading coefficient is furthest from 0. In this case, that happens to be 4 which is the coefficient in choice B.
See the attached image "figure1" for the graph. The functions are color coded
y = -x^2 is in red
y = 4x^2 is in blue
y = (1/4)x^2 is in green (note: 1/4 = 0.25; so y = (1/4)x^2 is the same as y = 0.25x^2)
y = (1/9)x^2 is in purple (note: 1/9 = 0.11 approximately; so y = (1/9)x^2 is roughly the same as y = 0.11x^2)
As you can see in figure1, the blue graph corresponding to y = 4x^2 is the most narrowest.
----------------------------------------------------------------------------------------------
Problem 2)
See figure2 for the graph. The image is also attached along with figure1.
Figure2 shows a parabola that opens upward and the lowest point is at (0,2) which is the vertex. This point is shown in red as point A.
y = x^2+2 is the same as y = 1(x-0)^2 + 2. That second equation is in the form y = a(x-h)^2 + k where a = 1, h = 0, k = 2
So the vertex is (h,k) = (0,2). The fact that 'a' is positive (a = 1) indicates that the parabola opens upward and this implies the vertex is the lowest point.
Therefore the vertex (0,2) is the minimum
----------------------------------------------------------------------------------------------
Problem 3)
You have the correct answer here. Nice work.
A quiz has 4 multiple-choice questions with 4 possible answer choices each. for each question, there is only 1 correct answer.a student guesses each answer at random. what is the probability of getting exactly 3 questions correct, to the nearest percent?(3 correct and 1 incorrect)
Answers
The probability of getting 3 correct and 1 wrong in one of these ways is
1/4 * 1/4 * 1/4 * 3/4 = 3/256
So required probability = 4 * 3/256 = 12/256 = 4.69 %
5% to nearest percent.
Answer: (quartered spinner) (4) (1/256)
Driving on the North West Express-way, Debbie averaged 62 miles per hour for 3 & one fourth hours. How far did she drive?
Answers
1/4 = 0.25
s0 3 1/4 = 3.25
62x3.25 = 201.50 miles = 201 1/2 if you need it in fraction form
In 45-45-90 right triangle, what is the ratio of the length of one leg to the length of the other leg
Answers
Answer: it’s 1:1
Step-by-step explanation:
Twenty times the square of a non-zero number is equal to 15 times the number
Answers
20x^2 - 15x = 0
5x(4x - 3) = 0
5x = 0, x =0
4x -3 = 0, x = 3/4
answer
non-zero number is 3/4
Which is heavier 9 5/8 pounds or 9 3/4 pounds
Answers
The cells of a certain culture of bacteria double every 6 minutes. If the culture contains 100 cells in the beginning, then the total number of cells P in this culture after t minutes is given by the exponential equation P = 100(2)t/6. Identify the number of minutes it will take for the number of cells to exceed 50,000.
A) 53 min
B) 49 min
C) 48 min
D) 54 min
Answers
Since the growth is exponential, therefore I believe the correct form of the equation is:
P = 100 (2)^(t / 6)
Where t / 6 is the exponent of 2
So to find for the amount of time needed to exceed the population of 50,000, all we have to do is to plug in that value in the equation and find for t. Therefore:
P = 100 (2)^(t / 6)
50000 = 100 (2)^(t / 6)
500 = 2^(t / 6)
log 500 = (t / 6) log 2
t / 6 = log 500 / log 2
t = 6 * 8.96578
t = 53.8 mins = 54 mins
Answer:
D. 54 min
The cells of a certain culture of bacteria triple every 2 minutes. If there are 40 cells in the beginning, in how many minutes will there be more than 9500 cells?
A) 4 min
B) 5 min
C) 11 min
D) 10 min
Answers
Answer: 10 min
Step-by-step explanation:
Final answer:
The bacterial culture that triples every 2 minutes will surpass 9500 cells just after 10 minutes. Since we cannot have a fraction of a minute in this context, the answer is 11 minutes (Option C).
Explanation:
The student is asking about exponential growth, specifically in a bacterial culture that triples every 2 minutes. To find out how many minutes it will take for the initial 40 cells to grow to more than 9500, we can use the formula for exponential growth:
N = N0 × 3t/2
Where N is the final number of cells, N0 is the initial number of cells (40 in this case), and t is the time in minutes.
We want N to be greater than 9500, so we solve the inequality:
9500 < 40 × 3t/2
Dividing both sides by 40 gives:
237.5 < 3t/2
Next, we find the smallest t for which the inequality holds by applying logarithms and solving:
t > 2 × (log3(237.5))
Calculating the right side, we get:
t > 10.096
So, the culture will have more than 9500 cells just after 10 minutes. The smallest whole number of minutes greater than 10.096 is 11, hence the answer is: C) 11 min
Find the area of a sector that has a central angle of 40 and a radius of 2 cm. Round your answer to the nearest 100th. Use 3.14=
Answers
What is -11-8-13(-10)? And how did you get you're answer
Answers
First, multiply since multiplication goes before subtraction according to the order of operations.
-11-8+130
Then add and subtract from left to right.
-11-8= -19
-19+130=111
Final answer: 111
The sum of two numbers is 33. Twice the first number minus the second number equals 18. Find both numbers.
Answers
y = 33 - x
SO
2x - 33 + x = 18
3x = 51
x = 17
Now, we know x. We can use this to find y:
x + y = 33
17 + y = 33
y = 16
So, the numbers are 16 and 17.
The both numbers are = 17 and 16
Solving for the unknown numbersThe sum of two numbers = 33
Let the two numbers be X and y.
therefore X + y = 33 ----> equation 1
Twice the first number minus the second number= 18.
That is,
2x - y = 18 -----> equation 2
From equation 1 make X the subject of formula;
X = 33 – y
substitute X into equation 2,
2(33 – y) - y = 18
66 – 2y – y = 18
66 – 3y = 18
66 – 18 = 3y
48 = 3y
y = 48/3
y = 16
Substitute y = 16 into equation 1
Therefore, X +16 = 33
X = 33 –16
X = 17
Therefore, he both numbers are = 17 and 16
Learn more about summation here:
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