The depreciating value of a semi-truck can be modeled by y = Ao(0.83)x, where y is the remaining value of the semi, x is the time in years, and it depreciates at 17% per year.
An exponential function comes down from the positive infinity and passes through the points zero comma seventy thousand. The graph is approaching the x-axis. What is the value of the truck initially, Ao, and how would the graph change if the initial value was only $50,000?
$70,000, and the graph would have a y-intercept at 50,000
$60,000, and the graph would have a y-intercept at 70,000
$70,000, and the graph would fall at a slower rate to the right
$70,000, and the graph would fall at a faster rate to the right
Answer:
Option A is correct.
Step-by-step explanation:
We are given that, the model for the depreciating value of a semi-truck is,
[tex]y = A_{O}(0.83)^x[/tex]
1. It is required to find the value of the truck initially i.e. when x= 0.
So, substituting x= 0, we have,
[tex]y = A_{O}(0.83)^0[/tex]
i.e. [tex]y = A_{O}\times 1[/tex]
i.e. [tex]y = A_{O}[/tex]
Since, the graph passes through the point (0,70,000).
Thus, we get, [tex]A_{O}=70,000[/tex]
Hence, the initial value is 70,000.
2. It is required to find the value of the truck initially i.e. when x= 50,000
That is, when x= 0, the value of y= 50,000.
Graphically, it means that the graph would cut y-axis at the point (0,50,000).
Thus, the y-intercept would be at 50,000.
Change in the initial value will not have any affect on the rate of the graph.
So, from the above, we get,
Option A is correct.
Given 5n² + 6n + 7 = n² - 4n : a. Find the value of the discriminant. b. State the number and type of roots/solutions/zeros.[2 real, 2 imaginary, 1 real]
A new truck that sells for 29,000 depreciates 12% each year. What is the decay factor b?
The second term in a geometric sequence is 20. The fourth term in the same sequence is 11.25. What is the common ratio
Which mathematical statement represents “17 more than a number is 26”?
17 + x = 26
17 +n = 26
n + 17 = 26
something like those, you didn't give options to choose from.
Answer:
x + 17 = 26
Step-by-step explanation:
mathematical statement represents “17 more than a number is 26”
Let x be the unknown number
17 more means we add 17 with the unknown number x
so it becomes x+17
'is' represents an = sign
So the equation for the mathematical statement “17 more than a number is 26” becomes x + 17 = 26
Write the expression in standard form.
three divided by quantity three minus twelve i.
Answer:
What was the answer?!?!!?!? >-<
The point $(r,\theta)$ in polar coordinates is $(7,5)$ in rectangular coordinates. what is the point $\left( 2r, \theta + \frac{\pi}{2} \right)$ in rectangular coordinates?
Final Answer:
The rectangular coordinates of the point[tex]$\left( 2r, \theta + \frac{\pi}{2} \right)$[/tex], where [tex]$(r, \theta)$[/tex] corresponds to the polar coordinates (7, 5), are approximately (-13.59, 11.54).
Step-by-step explanation:
In polar coordinates, a point is represented as [tex]$(r, \theta)$[/tex] , where [tex]$r$[/tex] is the distance from the origin, and $\theta$ is the angle with respect to the positive x-axis. In rectangular coordinates, the point is represented as (x, y).
Given that the point [tex]$(r, \theta)$[/tex] in polar coordinates is equivalent to the point (7, 5) in rectangular coordinates, we can express this relationship as:
[tex]\[ x = r \cos(\theta) \][/tex]
[tex]\[ y = r \sin(\theta) \][/tex]
For the given point $(7, 5)$, we have:
[tex]\[ x = 7 \cos(5) \][/tex]
[tex]\[ y = 7 \sin(5) \][/tex]
Now, you want to find the point [tex]$\left( 2r, \theta + \frac{\pi}{2} \right)$[/tex] in rectangular coordinates. This can be expressed as:
[tex]\[ x' = 2r \cos\left(\theta + \frac{\pi}{2}\right) \][/tex]
[tex]\[ y' = 2r \sin\left(\theta + \frac{\pi}{2}\right) \][/tex]
We know that [tex]$\cos\left(\theta + \frac{\pi}{2}\right) = -\sin(\theta)$[/tex] and [tex]$\sin\left(\theta + \frac{\pi}{2}\right) = \cos(\theta)$[/tex]. Substituting these into the equations:
[tex]\[ x' = -2r \sin(\theta) \][/tex]
[tex]\[ y' = 2r \cos(\theta) \][/tex]
Now, if we substitute the values of [tex]$r$[/tex] and [tex]$\theta$[/tex] from the given point (7, 5):
[tex]\[ x' = -2 \times 7 \times \sin(5) \][/tex]
[tex]\[ y' = 2 \times 7 \times \cos(5) \][/tex]
Calculating these values will give you the rectangular coordinates of the point $\left( 2r, \theta + \frac{\pi}{2} \right)$.
If triangle CDF ∼ triangle MKP, what is the value of x?
0.2
1.6
4.8
5.4
Answer:
The value of x is 1.6
Step-by-step explanation:
We have been given that triangle CDF ∼ triangle MKP.
Therefore, the ratio of the corresponding sides are equal.
Hence, we have
[tex]\frac{DC}{MK}=\frac{CF}{MP}[/tex]
Plugging the known values, we get
[tex]\frac{9}{1.8}=\frac{8}{0.x}[/tex]
Cross multiplying, we get
[tex]9x=8\times1.8[/tex]
Divide both sides by 9
[tex]x=\frac{8\times1.8}{9}[/tex]
Simplifying, we get
[tex]x=8\times10.2\\\\x=1.6[/tex]
The value of x is 1.6
Using the given zero, 2 - 4i, find one other zero of f(x) = x4 - 4x3 + 21x2 - 4x + 20
The conjugate of the given zero 2 - 4i is 2 + 4i, which must also be a zero of the polynomial f(x) due to the Complex Conjugate Root Theorem.
Given the zero 2 - 4i of the polynomial function f(x) = [tex]x^4 - 4x^3 + 21x^2 - 4x + 20,[/tex] we know by the Complex Conjugate Root Theorem that if a polynomial has real coefficients, then any complex zeros must occur in conjugate pairs. Therefore, the conjugate of 2 - 4i, which is 2 + 4i, must also be a zero of the polynomial function.
As a result, the polynomial can be factored to include the factors (x - (2 - 4i)) and (x - (2 + 4i)). When these factors are multiplied out, they will give you a quadratic factor of the polynomial, which when multiplied with the remaining factors, will result in the original polynomial f(x). The two factors, when multiplied together, yield a quadratic with real coefficients, which means any remaining zeros must also satisfy this quadratic equation.
A circle has its center at (5, -2) and a radius of 3 units. What is the equation of the circle?
A quadratic equation is shown below:
4x^2 − 12x + 10 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 2x^2 − 13x + 21 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
Suppose? 30% of the people in your town talk on their cell phones and drive at the same time. if you stood on a busy street corner and watched 50 people drive? by, about what proportion would you expect to see talking on their cell? phones?
There are 9 different positions on a baseball team. if a team has 18 players how many different line-ups can the team make?
Final answer:
To find the number of different line-ups a team can make, we use permutations. Using the formula for permutations, we arrive at the answer of 437,760 different line-ups.
Explanation:
To find the number of different line-ups a team can make, we need to use the concept of permutations. Since there are 9 positions on a baseball team and 18 players, we can arrange the players in a line-up using the formula for permutations:
P(n, r) = n! / (n-r)!
Where n is the total number of players (18) and r is the number of positions (9). Substituting the values, we get:
P(18, 9) = 18! / (18-9)! = 18!/9! = 437,760.
Therefore, there are 437,760 different line-ups that the team can make.
Use the remainder theorem to determine the remainder when d4 + 2d2 + 5d − 10 is divided by d + 4.
The remainder theorem states that the answer when d + 4 is substituted into the whole equation, the remainder would be the answer divided by d + 4. Therefore:
d + 4 = 0
d = -4
Evaluating when d = -4:
d^4 + 2 * d^2 + 5 * d − 10
= (- 4)^4 + 2 * (- 4)^2 + 5 * (- 4) – 10
= 256 + 2 * 16 – 20 – 10
= 256 + 32 – 30
= 258
Therefore basing on the remainder theorem, the remainder would then be:
Remainder = 258 / (d + 4) ---> Answer
Determine whether the forces are pulling at right angles to each other. Explain. 3.5 lb, 6.2 lb, resultant force 9.1 lb
A. yes; 3.52 + 6.22 = 9.12
B. no; a + b > c
C. no; 3.52 + 6.22 ≠ 9.12
D. yes; a + b > c
Solve the inequality. 4(p – 4) > 12
What important information must be included to find a sum of a series?
Answer:
Important information like the common difference, 1st term, the # of terms; the last term must be included to find the sum of a series.
If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)?
Answer:
Given the functions: [tex]f(x)= -x^2 +3x+5[/tex] and [tex]g(x) = x^2+2x[/tex]
Now, calculate first [tex](f+g)(x)[/tex] ;
[tex](f+g)(x) = f(x) + g(x)[/tex]
Substitute the given values we have;
[tex](f+g)(x) = -x^2+3x+5+x^2+2x[/tex]
Combine like terms;
[tex](f+g)(x) =5x+5[/tex]
Let y = [tex](f+g)(x)[/tex]
Then, we have y = 5x+5
Now, Graph the equation of the line y =5x +5
Using slope intercept form: An equation of line is given by :
y = mx +b ; where m is the slope of the line and b is the y-intercept.
On comparing we get;
m = 5 (Since, slope is positive which means a line moves upward on a graph from left to right)
Now, find the intercepts of the equation: y=5x+5;
x-intercepts: The graph or line crosses the x-axis i.,e
Substitute y = 0 and solve for x;
0 = 5x +5
Subtract 5 on both sides we get;
-5 = 5x
Divide both sides by 5 we get;
x = -1
x-intercepts= = (-1, 0)
Similarly for y-intercept:
Substitute the value of x= 0 and solve for y;
y = 5(0)+5
y = 5
y-intercepts = (0, 5)
Now, using these point we can draw a graph of function [tex](f+g)(x) =5x+5[/tex] as shown below in the attachment.
Anderson has $50 in his savings account. He deposits $5 every week. His father also deposits $20 into the account every time Anderson mows the lawn. His savings account balance can be shown with the following expression:
50 + 5w + 20m
Part A: Identify a coefficient, a variable, and a constant in this expression. (3 points)
Part B: If Anderson saves for 10 weeks and mows the lawn 2 times, how much will he have in his account? Show your work to receive full credit. (4 points)
Part C: If Anderson had $85 in his savings account, would the coefficient, variable, or constant in the expression change? Why? (3 points)
A county has been experiencing a mean of 35.935.9 motor vehicle deaths each year. Use the Poisson distribution to answer the following. a. Find the mean number of deaths per day. b. Find the probability that on a given day, there are more than 2 motor vehicle deaths. c. Is it unusual to have more than 2 motor vehicle deaths on the same day
Convert 0.00001 to a power of 10.
104
10−4
105
10−5
In scientific notation, 0.00001 is equal to 1 × 10⁻⁵.
FURTHER EXPLANATIONScientific notation is a way of expressing very big or very small numbers conveniently and with the appropriate number of significant figures. The general expression for the scientific notation is shown below:
M × 10ⁿ
M is a number that is greater than or equal to 1 but less than 10 and n is the number of times you have to multiply M by 10 to get the number.
The value of n can be easily determined by looking at the decimal point and counting the number of times it is moved to the left or to the right until a proper value of M is obtained.
The steps are as follows:
Locate the decimal point in the given. If it's a whole number, there is an implied decimal point at the end or to the right of the last digit.Move the decimal point to the right or to the left until you get a number that is greater than or equal to 1 but less than 10. This will be the value of M.Count how many decimal places you moved through to get the value of M. This will be the numerical value of the exponent, n.NOTE: If the decimal point was moved to the left, then the
exponent n will be written as positive (+x).
If the decimal point was moved to the right, then the
exponent n will be written as negative (-x).
Applying the steps to the problem:
STEP 1: 0.00001
The decimal point is four places away from the digit 1.
STEP 2: To get a number M that is greater than or equal to 1 but less than 10, the decimal point must be moved five places to the right and placed after the digit 1. (000001 or 1)
STEP 3: Since the decimal point was moved five places to the right, the exponent should have a magnitude of 5 and a negative sign. (1 × 10⁻⁵)
LEARN MORE significant figures brainly.com/question/11905420 standard notation brainly.com/question/296147 operation in scientific notation brainly.com/question/169955Keywords: scientific notation, exponential notation
Scientific notation is a form that can be used to represent very large or very small numbers
The option that gives the correct representation of 0.00001 is scientific notation (standard form) is the option;
10⁻⁵Reason:
Required: To convert 0.00001 to a power of 10
Solution:
The method to convert a decimal to a scientific notation is given by moving the decimal point to the right of the first significant digit then multiply the result by 10 raised to the negative of the number of places the decimal point is moved
The general form of the scientific notation is [tex]a \times 10^b[/tex]Where;
a = The number having only one digit to the left of the decimal point
b = The number of places the decimal point is moved (b is positive moving left and negative for moving right)
The given decimal number is 0.00001
Therefore, the decimal can be moved 5 places to the right to give;
0.00001 = 1.0 × 10⁻⁵ = 10⁻⁵
The correct option is 10⁻⁵Learn more here:
https://brainly.com/question/17478191
Solve x2 – 4 = 5 by graphing the related function.
Answer:
Refer graph attached below
Step-by-step explanation:
Given equation [tex]x^2-4=5[/tex]
We have to Solve the given equation [tex]x^2-4=5[/tex] graphically.
We first solve the given equation [tex]x^2-4=5[/tex]
Consider the given equation [tex]x^2-4=5[/tex]
Adding 4 both sides, we have
[tex]\Rightarrow x^2-4+4=5+4[/tex]
Simplify, we get,
[tex]\Rightarrow x^2=9[/tex]
[tex]\Rightarrow x^2-9=0[/tex]
To plot the graph let [tex]x^2-9=y[/tex] be the equation
It will be a parabola with vertex (0,9).
Refer graph attached below
Find an exact value. cosine of negative seven pi divided by twelve
Answer:
(the square root of 2 minus the square root of 6) / 4
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Two lines, A and B, are represented by the following equations:
Line A: 3x + 3y = 12
Line B: x + y = 4
Which statement is true about the solution to the set of equations? (4 points)
It is (12, 4).
There are infinitely many solutions.
It is (4, 12).
There is no solution.
Terry earns $22,500 annually. What is the total amount of each paycheck if she is paid biweekly?
52 weeks per year
biweekly means she gets paid every 2 weeks
so 52/2 = 27
22500/27 = 833.33 each paycheck
Marisol receives total employee benefits that are 14.5% of her gross annual pay. If Marisol has a gross annual pay of $50,000, how much in total employee benefits does she receive?
If Marisol has a gross annual pay of $50,000 and receives total employee benefits of 14.5% of her gross annual pay, then you can find how many benefits she receives, using proportion:
[tex] \$50,000 - 100\%,\\ \$x - 14,5\% [/tex].
Then
[tex] \dfrac{50000}{x} =\dfrac{100}{14.5} ,\\\\ x=\dfrac{50000\cdot 14.5}{100}=500\cdot 14.5=7250 [/tex].
In total she will receive $50,000+$7250=$57250.
Answer: $57250.
Write an algebraic equation for the following. The product of three and a squared number is twice the sum of the number and four.
Exit Felix was given $125 for his birthday from his grandmother. He plans to put this money toward the purchase of a $250 skateboard. The remainder of the money he plans to earn mowing lawns for the rate of $35 each. What is the least number of lawns Felix will have to mow in order to have enough to buy the skateboard?
4th term of (4x-y)^9