Yes , the toll company is correct to give the teacher a ticket.
Mean Value Theorem for a function f(x): [a,b]→ R such that f(x) is continuous and differentiable over the interval.
(i) f(x) is continuous on [a,b].
(ii) f(x) is differentiable on (a,b).
(iii) There exist a point c in (a,b) such that f'(c)=f(b)-f(a)/(b-a).
In the given question
Speed Limit = 60 mph
Time of entrance on toll road = 6:00
Time of exit from toll road = 7:00
Total time on toll road = 1 hr
Mile marker on entry in toll road = 15 mile
Mile marker on exit from toll road = 100 mile
Total distance travelled on toll road = 100-15= 85 miles
[tex]Average.Speed=\frac{total . distance}{total.time}[/tex]
Substituting the values we get .
Avg Speed = 85/1 = 85 mph
Overspeed = Avg Speed - Speed Limit
=85-60
=25 mph
The teacher over speed by 25 mph.
Since 85 mph is the average speed , it means that for some instance he was travelling below the average speed and for some instance he was travelling above the average speed.
By Mean value Theorem , it is clear that there have been at least one point where the teacher was travelling above 85 mph , which means he was over speeding .
Therefore , Yes , the toll company is correct to give the teacher a ticket.
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Moussa has a collection of vintage action figures that is worth $390. If the collection appreciates at a rate of 3% per year, which equation represents the value of the collection after 3 years?
The equation representing the future value of the collection is given by V=390(1.03)³ as the value appreciates by 3%.
When a value appreciates at a certain percentage means the value of the collection increases by that percentage each year.
The equation that represents such an appreciation is in the form of an exponential equation.
The general equation for calculating future value with appreciation is:
[tex]V = P (1 + r)^n[/tex] where
V = Future value
P = Present value
r = appreciation rate
n = number of years
Given P = $390 , r= 3%=0.03 , n = 3
Now we substitute the given values in the equation to get:
V=390(1+0.03)³
or, V= 390(1.03)³
or, V= 426.16 dollars approximately .
Hence the required equation is V= 390(1.03)³ .
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solve the equation -27=3/4w
Answer: w = -32
Step-by-step explanation:
Start isolating the variable by getting rid of 3/4. You can do this by multiplying by its reciprocal.
That leaves us with 3/4 times -27
The product is -32.
Hope this helps!
Tim wants to enclose a 12ft x 8ft plot of land for his garden. How much fencing does he need?
Tim needs 40ft fencing.
For fencing the square garden we need to ascertain perimeter of the square.
Perimeter of plot = 2*(a+b)
Where a = length of the plot
b=width of plot
length =12ft
width=8ft
Perimeter of plot = 2*(a+b) = 2*(12+8)ft=40ft
He needs 40ft fencing.
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What is the center of dilation?
Answer:
Point Y
Step-by-step explanation:
This dilation is an expansion, so in order for it to expand, the center of dilation need to be in the middle or near the middle of the pre-image.
What is a pre-image?
Noun. preimage (plural preimages) (mathematics) For a given function, the set of all elements of the domain that are mapped into a given subset of the codomain; (formally) given a function ƒ : X → Y and a subset B ⊆ Y, the set ƒ−1(B) = {x ∈ X : ƒ(x) ∈ B}.
What is an Image?
The new position of a point, a line, a line segment, or a figure after a transformation is called its image.
Center of Dilation:
The center of a dilation is a fixed point in the plane about which all points are expanded or contracted. The center is the only invariant (not changing) point under a dilation (k ≠1), and may be located inside, outside, or on a figure.
I hope this helps! :)
the graphs of y=-4x and y = -4x + 2 are shown. Use the drop down menus to complete the statements The ratios of y/x are the same for the graph of ________ the ratios of y/x are NOT the same for the graph of ______
The ratios of y/x are the same for the graph of y = -4x and y = -4x + 2 because they both represent parallel lines.
What are parallel lines?Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
The condition for two parallel lines.In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts. This ultimately implies that, two (2) lines are parallel under the following conditions:
m₁ = m₂
Note: m is the slope and it is given by this mathematical expression, slope, m = Δy/Δx.
In this context, we can reasonably infer and logically deduce that the ratios of y/x are the same for the graph of y = -4x and y = -4x + 2 because they both represent parallel lines.
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What is the slope of the line that passes through the points (2, 3) and (0, 11)? Write
your answer in simplest form.
Answer:
-4
Step-by-step explanation:
If you graph the two coordinates the line is going down, so the answer is going to be negative. The slope is -4/1 but simplified is -4. Hope this helps. Have a great night.
Which method do you think is easier to use to find the gradient of the line joining R(-50, 460) and S(115, 55)? Explain your answer.
The gradient of the line joining R(-50, 460) and S(115, 55) is -2.45
How to find the gradient of the line joining R(-50, 460) and S(115, 55)?The points on the line are given as
R = (-50, 460)
S = (115, 55)
The gradient of the line joining R(-50, 460) and S(115, 55) is calculated using
Gradient = (y2 - y1)/(x2 - x1)
This gives
Gradient = (460 - 55)/(-50 - 115)
Evaluate
Gradient = -2.45
Hence, the gradient of the line joining R(-50, 460) and S(115, 55) is -2.45
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dana said that 0.6 divided by 30 = 0.02. is she correct? explain.
Answer:
It can be said that Dana is correct when she says that 0.6 divided by 30 gives 0.02 as a reminder.
Step-by-step explanation:
It is given that we need to rectify whether 0.6 divided by 30 = 0.02 or not.
Firstly, let us understand how does simplification work;
In mathematics, the operation and interpretation of a function to make it simple or easier to grasp is known as simplifying, and the process is known as simplification.
Now, let us understand what exactly is arithmetic;
According to the assertions, it deals with a number of operations in mathematics. Addition, subtraction, multiplication, and division are the four main arithmetic operators.
Now, let us equate the given condition that is;
=> 0.6 can also be expressed as 6/10
Now, let us divide the above numbers with each other as given in the question;
=> (6/10) ÷ 30
=> 6/300
On dividing both the numbers with each other we get;
=> 0.02 which can be expressed as 2/100
Therefore, it can be said that Dana is correct when she says that 0.6 divided by 30 gives 0.02 as a reminder.
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Answer:
Step-by-step explanation:
work out 7+8 over 5-2
Answer:
[tex]6\frac{3}{5}[/tex]
Step-by-step explanation:
[tex]8 \div 5 = 1\frac{3}{5} \\\\1\frac{3}{5} + 7 = 8\frac{3}{5}\\\\8\frac{3}{5} - 2 = 6\frac{3}{5}[/tex]
A person invests 9000 dollars in a bank. The bank pays 4.25% interest compounded
semi-annually. To the nearest tenth of a year, how long must the person leave the
money in the bank until it reaches 14200 dollars?
The time taken to reach $14200 in the bank with 4.25% interest compounded is 50 years
The time taken to reach 14200 with interest compounded semi-annually can be calculated by
[tex]A = P (1 +\frac{R}{100n})^{nT}[/tex]
where A is the total amount at the end of the period
P is the principal amount
R is the rate of interest
n is the no. of interest compounded per year
T is the time period
We know that A = 14200
P = 9000
R = 4.25%
n = 2
By substituting these values, we get
14200 = 9000 [1 + (4.25 /200[tex]]^{2T}[/tex]
14200/9000 = [tex](1+0.02125)^{2T}[/tex]
1.5778 = [tex](1+0.02125)^{2T}[/tex]
1.5778 = [tex](1+0.02125)^{2T}[/tex]
1.5778 =[tex](1 +0.02125)^{2T}[/tex]
Taking logs on both sides,
log (1.5778) = log [tex](1+0.02125)^{2T}[/tex]
log (1.5778) = 2T log(1 +0.02125)
0.198 = 2T log(1.02125)
0.198 = 2T (0.00913)
0.918 = 0.01826 T
T = 0.918 / 0.01826
T = 50.27 yrs
T ≅ 50 years
Therefore, the time taken to reach $14200 in the bank with 4.25% interest compounded is 50 years
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How do I do this ???
Answer:
(-1,4)
(0,0)
(1,-4)
(1,-8)
Step-by-step explanation:
Substitute the value of x in the equation and find the corresponding y value.
y = -4x
When x = -1 ; y = -4*(-1) = 4.
When x = 0 ; y = 0
When x = 1 ; y = -4*1 = -4
When x = 2 ; y = -4*2 = -8
What is the final version of this supposed to look like?
The graph of the inequality expressions is added as an attachment
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to determine the graph of the inequality expression?The inequality expressions are given as
y ≥ 2
x + y ≤ 4
y ≤ 2x + 2
Next, we interpret each inequality expression
First expression: y ≥ 2
The inequality symbol in the above inequality expression is ≥
This implies that the inequality expression is a greater than or equal to
When an inequality expression has a sign of equal to, then the line of the inequality graph will be a solid line
Also, the inequality symbol implies that the upper part is shaded
Second expression: x + y ≤ 4
The inequality symbol in the above inequality expression is ≤
This implies that the inequality expression is a less than or equal to
When an inequality expression has a sign of equal to, then the line of the inequality graph will be a solid line
Also, the inequality symbol implies that the bottom part is shaded
Third expression: y ≤ 2x + 2
The inequality symbol in the above inequality expression is ≤
This implies that the inequality expression is a less than or equal to and the inequality symbol implies that the bottom part is shaded
See attachment for the graph of the inequality expressions
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The graph of y = f(X) is shown.
b) Find the roots of f(X) = 0
c) Find f(0)
A) The roots of the graph f(x) are; x = -2 and x = -1
B) The value of the function at f(0) is; 2
How to find the roots of a quadratic graph?
a) We want to find f(0) of the graph.
Now, f(0) simply refers to the y-values when x = 0.
This is the point at which the graph crosses the y-axis
From the graph we can see that the value here is 2. Thus;
f(0) = 2
b) To find the roots of f(x) , we simply find the points at which the plot crosses the x-axis.
From the graph, the roots are at x = -2 and x = -1
Thus, the roots of the equation are x = -2 and x = -1
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what is the answer to the problem.
Answer:
0
Step-by-step explanation:
Because there is no question only
Jerica sells used motorcycles. she makes $300 per week plus $75 for each bicycle sold. she wants to earn $1059?per week. write an equation to find out how many motorcycles she must sell each week to accomplish this.
Answer: $684
Step-by-step explanation: Add 300 to 75 and you have 375, next subtract the total payment she wants to have per week (which is 1059) so, subtract 1059 to 375 then you have $684. To check your answer, add 684 to 375 and you come up with 1059.
The force F of gravity on a rocket varies directly with its mass m and inversely with the square of its distance d from Earth. Write a model for this combined variation. Write an equation to find the mass of the rocket in terms of F and d .
Model for the Combined variation is [tex]F = \frac{km}{d^{2} }[/tex]
Equation to find the mass of the rocket in terms of F and d is :
[tex]m=\frac{F d^{2} }{k}[/tex]
What is Force ?A force is the quantity that change the motion of the object. Force is that influence which can cause any object having some mass, to change it's position or to accelerate from it's original position.
Force (F) and mass (m) of any object are directly proportional to each other. More the mass of the object , more the force will require to accelerate it.
Mathematically, we can write the equation of force as :
F = m . a
where , m = mass of the object
a = constant value
In the statement given,
As, force of gravity varies directly with its mass
Therefore, F= k m , where k is a constant
Also force is inversely varies with square of distance d
Thus, F = k / d²
Combining both equations :
[tex]F = \frac{km}{d^{2} }[/tex]
and the equation of mass in terms of F and d can be written as :
[tex]m=\frac{F d^{2} }{k}[/tex]
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g(t)=−9t−4g, left parenthesis, t, right parenthesis, equals, minus, 9, t, minus, 4
g\Big(g(g, left parenthesis
\Big)=23)=23
The resulting expression if the value of t is 23 is g(23) = -4g - 207
Function and valuesA function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given the function below;
g(t)=−9t−4g
We are to determine the value of g(23). Substitute t = 23;
g(t)=−9t−4g
g(23) = -9(23) - 4g
g(23) = -207 - 4g
g(23) = -4g - 207
Hence the resulting expression if the value of t is 23 is g(23) = -4g - 207
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HELP ME PLSSSSSS , MY DEADLINE IS NOW PLS HELPPP
Multiple choice :
A) 0
B) 2
C) -1.5
D) 4
E) 0.5
=======================================================
Explanation:
The given equation is in the form of ax^2+bx+c = 0
The coefficients are
a = 2b = kc = -3According to Vieta's formula, we know that the roots of a quadratic multiply to c/a
In this case, the roots multiply to -3/2
Let p and q be the two roots. We're told that -3 is one of the roots, so p = -3. Let's find q.
pq = c/a
-3q = -3/2
q = (-3/2)*(-3/1)
q = 1/2
q = 0.5
The other root is 0.5
The product of the roots is -3*0.5 = -1.5 = -3/2 to confirm the answer.
-------------
The longer way to solve would be to plug x = -3 into the equation and solve for k. You should get k = 5
Once you know the value of k, use the quadratic formula to find the two roots. You should get -3 and 1/2 = 0.5 as the two roots.
Simplify each number. 100⁴.⁵
The result of simplifying each number 100⁴.⁵ using the exponent rules is
10⁽⁴⁰⁾
To solve this exercise we have to resolve algebraic operations following the exponent rules.
100⁴.⁵
Base= 100 = 10²
The base number 100 is the same that: 10², then we get:
(10²)⁴.⁵
Using the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:
10⁽²*⁴*⁵⁾
10⁽⁸*⁵⁾
10⁽⁴⁰⁾
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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Juan and Houa are reading the same book. At the beginning of the month, Juan was on page 45 and Houa was on page 9. Juan will read 15 pages per day and Houa will read 18 pages per day. Let J represent the page of the book that Juan is on at the end of t days into the month, and let H represent the page of the book that Houa is on at the end of t days into the month. Write an equation for each situation, in terms of t, and determine what page Juan and Houa will be on on the day they are both on the same page.
The page they will be on is 225.
What page will they be on?The page that both Juan and Houa would be on at the end of the month is a function of the page they are at the beginning of the month and the page they read per day.
Pages they are in t days:
J = 45 + 15t
H = 9 + 18t
When they are on the same page, both equations would be equal
45 + 15t = 9 + 18t
45 - 9 = 18t - 15t
36 = 3t
t = 36 / 3
t = 12
Page they would be in 12 days: 45 + 15(12)
45 + 180 = 225
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help me
please show your solution
Answer:
[tex] a_{1} = 5[/tex]
Step-by-step explanation:
check the attached image for explanation
Giải Phương trình
(x-3)^2+x^4= -y^2+6y-4
Answer:
Solution on screen
Step-by-step explanation:
Don't worry it's okay
The product of 3 and a number x is 23.
What is the value of x?
x=7/3
x=2/9
x=2
x=2 1/3
Answer:
D.
Step-by-step explanation:
x=2 1/3
That is the answer
Find the least integer greater than each number. Do not use a calculator.
log₅1/47
The least integer greater than each number for log₅1/47 = -3
All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.
Let y = log₅1/47
We know, logₐ x = y, only if a^y= x
Therefore, 5^y = 1/47
So, we must find an integer y such that 5 > 1/47
5^y > 1/47
5^{-3} > 1/47
(As, 5² = 25; 5³ = 125) (Since, 5² < 47, the answer will be 5³ as 5³ > 47)In this case, y = -3 will be the least integer to satisfy this inequality.
Therefore, the ultimate answer to the equation is log₅1/47 = -3
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What is the value of 1742 divided by 4.16
Answer:
1742 is divided by 2.16 than answer is 418.75
Simplify each expression.
10 ln e
10 (ln (e)) = 10, by the definition of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
By property of logarithm, ln (e) = 1
Thus, in the expression 10 (ln (e)) = 10 (1) = 10.
Hence, 10 (ln (e)) = 10, by the definition of logarithm.
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The price of a train ticket consists of an initial fee of $5 plus a fee of $2.75 per stop. Julia has
$21 and would like to travel 50 kilometers. She wants to know the largest number of stops she
can afford to buy on a ticket.
Let S represent the number of stops that Julia buys.
1) Which inequality describes this scenario?
Choose 1 answer:
5 + 2.75 . S € 21
5 + 2.75 - 5 > 21
(C
5 + 2.75 - 5 = 50
5 + 2.75. S > 50
Considering the definition of an inequality, the inequality 5 + 2.75×S ≤21 describes the scenario.
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Inequality in this caseIn this case, you know that:
The price of a train ticket consists of an initial fee of $5 plus a fee of $2.75 per stop. Julia has $21 and would like to travel 50 kilometers. She wants to know the largest number of stops she can afford to buy on a ticket.Being "S" the number of stops that Julia buys, the inequality that expresses the previous relationship is
5 + 2.75×S ≤21
Finally, the inequality 5 + 2.75×S ≤21 describes the scenario.
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Write each expression in simplest form. (x⁻²/₃ / y⁻¹/₃)¹⁵
The given expression is a fraction raised to a power and will be solved by multiplication of exponents for both numerator and denominator.
When in an expression, the base is a fraction raised to a number (exponent), the exponent is applied to both numerator and denominator.
In this case, the base is x^-2/3/y^-1/3 and the exponent is 15.
Since (x^a)^b=x^ab
Multiplication of exponent applied to both numerator and denominator,
(x^⁻²/₃/y^⁻¹/₃)^¹⁵=x^⁻²/₃*15/y^⁻¹/₃*15
Simplifying,
x^⁻²/₃*15/y^⁻¹/₃*15=x^-10/y^-5
Since both numerator and denominator have negative exponents, it is not yet in the simplest form.
According to negative exponents rule, x^-a=1/x^a
To remove the negative exponent, the fraction should be reversed.
x^-10/y^-5=y^5/x^10
The simplest form of the expression (x^⁻²/₃/y^⁻¹/₃)^¹⁵ is y^5/x^10
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rearrange x=3g+2 make g the subject
Answer:
3g=x-2
Step-by-step explanation:
3g+2=x then, move 2 to the other side(nb*change to negative) then it will be 3g=x-2 finally divide both sides by 3 then it will be g=x-2
3
9x +8y=40 written in slope-intercept form.
Answer: Slope = 2.250/2.000 = 1.125
x-intercept = 40/9 = 4.44444
y-intercept = 40/-8 = 5/-1 = -5.00000
Step-by-step explanation:
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -5.000 and for x=2.000, the value of y is -2.750. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -2.750 - (-5.000) = 2.250 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
ttttttgyygyyAnswer:
Step-by-step explanation:
gtgtggtgyyyhhyhyy