How do you solve this problem? I’m really stressed and don’t know how, can someone take me step by step through it? It’s really hard for me
An equation for the depreciation of a car is given by y = A(1 – r)t , where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately how old is the car?
3.3 years
5.0 years
5.6 years
6.6 years
Answer:
D; 6.6 years.
Step-by-step explanation:
We know that the equation for the depreciation of the car is:
[tex]y=A(1-r)^t[/tex]
Where y is the current cost, A is the original cost, r is the rate of depreciation, and t is the time, in years.
We are told that the value of the car now is half of what it originally cost. So:
[tex]\displaystyle y=\frac{1}{2}A[/tex]
Substitute this for y:
[tex]\displaystyle \frac{1}{2}A=A(1-r)^t[/tex]
We also know that the rate of depreciation is 10% or 0.1. Substitute 0.1 for r:
[tex]\displaystyle \frac{1}{2}A=A(1-0.1)^t[/tex]
So, let's solve for t. Divide both sides by A:
[tex]\displaystyle \frac{1}{2}=(1-0.1)^t[/tex]
Subtract within the parentheses:
[tex]\displaystyle \frac{1}{2}=(0.9)^t[/tex]
Take the natural log of both sides:
[tex]\displaystyle \ln\left(\frac{1}{2}\right)=\ln((0.9)^t})[/tex]
Using the properties of logarithms, we can move the t to the front:
[tex]\displaystyle \ln\left(\frac{1}{2}\right)=t\ln(0.9)[/tex]
Divide both sides by ln(0.9):
[tex]\displaystyle t=\frac{\ln(0.5)}{\ln(0.9)}[/tex]
Use a calculator. So, the car is approximately:
[tex]t\approx6.6\text{ years old}[/tex]
Our answer is D.
And we're done!
Which is equal to (2+3i) + (-4+i)
Answer:
-2 + 4i
Step-by-step explanation:
Step 1: Write expression
(2 + 3i) + (-4 + i)
Step 2: Combine like terms
-2 + 4i
Explain, with at least 2 sentences, how to determine if a graph is increasing or decreasing based on the x- and y-values.
Answer:
Two sentences below
Step-by-step explanation:
A graph is increasing if the Y value increases as the X value increases. A graph is declining if the Y value decreases as the X value increases.
1. Determine Linda's bonus using the following formula: 2 weeks' salary plus 3 percent of gross sales.
annual salary: $88,600.00
gross sales: $314,000.00
what anti hero
A
ghost rider
b
deadpool
c
venom
d
magneto
Answer:
b
Step-by-step explanation:
b bc its the besttt!!!!
Find the distance UV between the points U (7,-4) and V(-3,-6). Round your answers to the nearest tenth,if necessary
Answer:
The answer is 10.2 unitsStep-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\[/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
U (7,-4) and V(-3,-6)
The distance between them is
[tex] |UV| = \sqrt{( {7 + 3})^{2} + ( { - 4 + 6})^{2} } \\ = \sqrt{ {10}^{2} + {2}^{2} } \\ = \sqrt{100 + 4} \: \\ = \sqrt{104} \: \: \: \: \: \: \: \: \\ = 2 \sqrt{26} \: \: \: \: \: \: \: \: \\ = 10.1980...[/tex]
We have the final answer as
10.2 units to the nearest tenthHope this helps you
Determine the value of X
D o,k (X,9) —> (-10,-6)
A. 5
B. 7
C. 12
D. 15
Answer:
7
Step-by-step explanation:
that is the answer if it may help you
Katrina said that the lines y=-2/3x + 5 and y = -3/2x + 2 are perpendicular. Explain Katrina's error.
Answer:
product of gradients of the two lines = 1 does not imply the lines being perpendicular, the product of gradients have to instead be equal to -1.
For the given lines to be perpendicular Katrina mistakenly put a negative sign on the slope of the second line.
What is a slope?The slope is the rate of change of y-axis with respect to x axis.
We know in terms of the slope we can determine if two lines are perpendicular when their slopes are negative reciprocals of each other means if a line has a slope of 'm' the line perpendicular to it will have a slope of '-1/m'.
Given are two lines in slope intercept form which is y = mx + b.
One is y = -(2/3)x + 5 and another line is y = -(3/2)x + 2.
As we can observe the first line has a slope of -(2/3) and the second line has a slope of -(3/2) which should be (3/2) which is the negative reciprocal of -(2/3).
learn more about slope here :
https://brainly.com/question/3605446
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mr. Smith is traveling north from Houston Texas to Dallas Texas it takes 4 hours to make the 224 mile trip what is his velocity
Answer:
56mph
Step-by-step explanation:
Speed = distance/ time
= 224/4
= 56
56mph
Answer:
56mph
Step-by-step explanation:
if f(x) = -3x-2 find f(-7)
please helppppp!
-x - 5y = -13 y = 7x - 19
Using substitution
Answer:
x = 3
y = 2
Step-by-step explanation:
Step 1: Define
-x - 5y = -13
y = 7x - 19
Step 2: Substitute and solve for x
Substitute: -x - 5(7x - 19) = -13Distribute -5: -x - 35x + 95 = -13Combine like terms: -36x + 95 = -13Subtract 95 on both sides: -36x = -108Divide both sides by -36: x = 3Step 3: Substitute x to find y
Substitute: y = 7(3) - 19Multiply: y = 21 - 19Subtract: y = 2Step 4: Check
Plug in x and y to verify it's a solution set.
2 = 7(3) - 19
2 = 21 - 19
2 = 2
Which is equivalent to(6 - i)-(3 –8i)?
The expression equivalent to (6 - i) - (3 - 8i) is 3 + 7i.
What are Complex Numbers?Complex numbers are numbers which are of the form [tex]a+bi[/tex] where a and b are real numbers and i is the imaginary number called iota whose value is [tex]i^{2}[/tex] = -1.
The given expression is (6 - i) - (3 - 8i).
Subtraction of complex numbers are done by subtracting the real numbers and subtracting the imaginary numbers separately.
(6 - i) - (3 - 8i) = 6 - i - 3 + 8i
= (6 - 3) + (8i - i)
= 3 + 7i
Hence the resulting value of the difference of the complex numbers 6 - i and 3 - 8i is 3 + 7i.
To learn more about Complex Numbers, click on the link given :
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given the function f(x)=-9x²-3, which of the following best represents the value of f(-2)?
F. 78
G. 321
H. 33
J. 39
Answer:
78
Step-by-step explanation:
Find the value of x.
Answer:
14
Step-by-step explanation:
add both values and equals them to 180.then solve the equation and find X you will get 14
Answer: I think x = 14
Step-by-step explanation:
7x - 1 + 6x - 1 + 7x -1 + 6x -1
(vertically opposite angles are equal)
collect like terms:
26x - 4 = 360
(angles around a point = 360 degrees)
+4 to both sides
26x = 364
x = 14
A dinner theater sold 270 tickets in 3 hours. At this rate, how many tickets will be sold in 8 hours
Answer:
720 tickets in 8 hours
Step-by-step explanation:
you know that the theatre sold 270 tickets in 3 hours. you have to find the hourly rate of tickets sold. so you divide 3 into 270 and get 90. you take the hourly rate of tickets and multiply it by the 8 hours and get 720. Hope this helps!! :)
Answer: 720 in 8 hours
Step-by-step explanation:
Troy uses 2 pints of stain on each table that he makes. How many tables can he paint with 1
gallon of stain?
Answer:
4 Tables
Step-by-step explanation:
there are 8 pints in one gallon and it uses two pints per table. 8/2= 4
here are prices for cans of juice that are the same brand and the same size at different store offers the best deal explain your resoning.
what is (3 x 8 x 16 x 7) + 37 - (77 x 3) - 44 ÷ 20 - 0.8 + 9
IM GIVING 25 POINTS
Answer:
use calculator
follow DMAS rule
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The area of North Carolina is about 5.3 ×104 square miles. The area of Rhode Island, the smallest state, is about 1.3 × 103square miles. Approximately how many times greater is the area of North Carolina as compared to the area of Rhode Island?
jaasnajaksnsbkakanajridjsjsjaaaana
Can someone please help me
Answer:
G
Step-by-step explanation:
ʙʀᴀɪɴʟɪᴇsᴛ!
Solve for h:
h/4 = -7
HELP PLS I GIVE 20 BRAINLIST
The first song performed during a concert was more than 60 seconds longer than the final song. The first song was 190 seconds long. The inequality 190 > 60 + f represents the situation when f is the length of the final song, in seconds. f is in the center of a line. Which value should point f on the number line be?
1. 250
2. 190
3. 130
Which best describes the appearance of the graph?
1. open circle at f, shaded right
2. open circle at f, shaded left
3. closed circle at f, shaded right
4. closed circle at f , shaded left
Answer:
3. 130
2. Open Circle at f, shaded left.
Step-by-step explanation:
Edg. 2020
Answer:
3. 130
2. Open Circle at f, shaded left.
Step-by-step explanation:
WHO IS REALLY GOOD AT WRITING ESSAYS i promise you wont regret answering this!!!
12 divided by 264, long division.
Answer:0.04545454545 or 1/22
Step-by-step explanation:
Michelle delivers books to school libraries. Her truck has a slide out ramp for unloading the books. The top of the ramp is 3 feet above the ground. The ramp itself is 5.2 feet long. What is the horizontal distance the ramp reaches?
Round to the nearest tenths
GET BRAINLY IF ANSWERED CORRECT
Answer:
8.2
Step-by-step explanation:
Answer:
imma trying to figure it out too to late i know
Step-by-step explanation:
Kara wants to rent out a party venue for Halloween. The venue charges a deposit of $200 plus $8 per person. Determine the total cost if Kara invites 35 people. *
$235
$280
$480
$7,008
Roxy decided to start a t-shirt business. She spent $25.50 on supplies for her t-shirt designs. In the month of August, she sold 32 t-shirts at $7.25 per t-shirt. Roxy plans to set aside one-fourth of her earnings towards supplies for the next month. What was Roxanne's profit in the month of August? (Profit is the amount a person earns after they subtract their expenses)
Answer:
$199.8 (This is what I personally got it could be wrong)
Step-by-step explanation
7.25 x 32 = 232
232 x 1/4 = 58
58 - 25.50 = 32.5
232 - 32.5 = 199.8
Answer: $199.8 in profit
Which of the sets shown include the elements of Set Z that are both even numbers and multiples of 3? Z = {–12, –10, –9, –1, 3, 6, 8, 15} A. {6} B. {–12, 6} C. {–12, –9, 3, 6, 15} D. {–12, –10, –9, –1, 3, 6, 8, 15}
Answer:
B. -12,6
Step-by-step explanation:
