The value of the car will be £2,621 after 5 years.
What is exponential decay?Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time.
Given that, The value of a second-hand car is £8,000. Each year it loses 20% of its value, we are asked to find its value after 5 years.
This is a situation of exponential decay.
Hence, using the exponential decay formula =
A = P(1-r)ⁿ
Where A is final value, P is principal value, r is rate of decrease and n is the number of years.
Here, we will find A, and we have,
P = £8,000.
r = 20% = 0.20
t = 5
Therefore,
A = 8000(1-0.20)⁵
A = 8000(0.80)⁵
A = 8000(0.32768)
A ≈ 2,621
Hence, the value of the car will be £2,621 after 5 years.
For more references on exponential decay, click;
https://brainly.com/question/2193799
#SPJ1
What is the slope of the line with the equation of y = =*
Ex that passes through the point (2, 1)?
A.) - 2/3
B.) - 3/2
C.) 2/3
D.) 3/2
Anna and Sharon both construct a triangle. Anna begins by drawing a segment with a length of 3 inches. Starting from one vertex, she draws another segment with a length of 5 inches so that the two segments have an included angle of 35°. Sharon constructs her triangle by drawing a segment with a length of 5 inches, measuring a 35° angle, and drawing a ray from one vertex. Then she measures and terminates the ray at 3 inches. Do Anna and Sharon create congruent triangles? Explain.
Answer:
Yes, Anna and Sharon both created triangles that are congruent. Their triangles are congruent because they have 2 corresponding, congruent side-lengths and an included angle that is congruent. Therefore, their triangles are congruent by SAS (Side-Angle-Side).
Need help on these problems
Answer:
1.) x = 50 2.) x = 70
Step-by-step explanation:
These angles are complementary angles meaning the angles add up to 90°. Therefore, we can set up equations to solve for the variables.
1.)
x + 40 = 90
x = 50
2.)
x + 20 = 90
x = 70
Answer:
x = 50°
x = 70°
Step-by-step explanation:
90° - 40° = 50°
x = 50°
90° - 20° = 70°
x = 70°
consider the trinomial 15x² - 34x - 16.
List all the factor pairs for -240.
Answer: To find the factor pairs for -240, we can use the following steps:
Find the prime factorization of -240: -240 = (-2) * (-2) * (-2) * (-3) * (-5)
For each prime factor, there are two possible factor pairs: (-1) and (1), and (-n) and (n). For example, for the factor -2, the possible factor pairs are (-1) and (1), and (-2) and (2).
The factor pairs for -240 are: (-1) and (1), (-2) and (2), (-3) and (3), (-5) and (5), (-6) and (6), (-10) and (10), (-15) and (15), (-30) and (30).
Thus, the factor pairs for -240 are: (-1, 1), (-2, 2), (-3, 3), (-5, 5), (-6, 6), (-10, 10), (-15, 15), and (-30, 30).
Step-by-step explanation:
A sample of radioactive element follows the law of exponential decay. if there are 50g of the element at noon 30g at 3:00 pm that same day then how many grams will there be at 9:00 pm that same day?
Answer:
10.8 g
Step-by-step explanation:
Exponential decay equation: [tex]A=A_0e^{-rt}[/tex]
[tex]A_0[/tex] is the initial amount (at time t = 0, "noon")
r is the decay rate
You have two pieces of information:
Noon t = 0 [tex]A_0=50[/tex]
3:00 pm t = 3 [tex]A=30[/tex]
Plug those in to get [tex]30=50e^{-r(3)}[/tex]
Divide by 50.
[tex]0.6=e^{-3r}[/tex]
Take the natural log of both sides.
[tex]\ln(0.6)=-3r[/tex]
Divide by -3.
[tex]\frac{\ln{(0.6)}}{-3}=r\\\\r \approx .17027[/tex]
Now, for 9:00 pm, use this value of r and t = 9.
[tex]A=50e^{-.17027(9)} \approx 10.8[/tex]
Find y'' for x² + y⁴ = 20
now, this is implicit differentiation, so it comes with the assumption that "y" is a function in "x terms", as opposed to a plain vanilla variable, whilst "x" is just that, so
[tex]\cfrac{d}{dx}[x^2+y^4=20]\implies 2x+\stackrel{chain~rule}{4y^3\cdot \cfrac{dy}{dx}}=0\hspace{5em}\cfrac{d}{dx}\left[ 2x+4y^3\cdot \cfrac{dy}{dx}=0 \right] \\\\\\ 2+\stackrel{product~rule}{\left( 12y^2\cdot \cfrac{dy}{dx}+4y^3\cdot \cfrac{d^2y}{dx^2} \right)}=0\implies 2+12y^2\cdot \cfrac{dy}{dx}+4y^3\cdot \cfrac{d^2y}{dx^2}=0 \\\\\\ 2+12y^2\cdot \cfrac{dy}{dx}=-4y^3\cdot \cfrac{d^2y}{dx^2}\implies {\Large \begin{array}{llll} \cfrac{2+12y^2\cdot \frac{dy}{dx}}{-4y^3}=\cfrac{d^2y}{dx^2} \end{array}}[/tex]
Cones A and B both have volume 48pi cubic units, but have different dimensions. Cone A has radius 6 units and height 4 units. Find one possible radius and height for Cone B.
The possible radius and height for Cone B are 3 units and 16 units respectively
How to determine the radius and height of the cone
The formula for calculating the volume of a cone is expressed mathematically;
Volume = 1/3 πr²h
Given that;
π takes the value 3.1 4r is the radius of the coneh is the height of the coneFrom the information given, we have that;
Both cone A and B have volume of 48πCone A has 6 units and height of 4 unitsNow, let the height of cone B be 16 units
Substitute the value into the formula, we have;
48π = 1/ 3 × π × r² × 16
multiply the values, we have
48 = 16r²/3
cross multiply
16r² = 144
Divide both sides by 16
r² = 144/16
r² =9
Find the square root of both sides
r = 3units
Hence, the values are 3 units and 16 units
Learn more about cones here:
https://brainly.com/question/6613758
#SPJ1
Find the value of x.
30°
105°
xo
Exterior angle of triangle x has a value of 135 in this sentence.
What is the simplest technique to measure angles?A protractor can be used to measure angles precisely. Angles are measured in degrees, hence the term "degree measure." Since one full revolution is equivalent to 360 degrees, it is divided into 360 segments.
What exactly is the triangle rule?According to the "sides of a triangle rule," any two sides of a triangle must add up to be longer than the third side.
By extending one side of the triangle, an external angle is formed. An exterior angle is the angle formed by the stretched side and the side that is immediately adjacent.
Practice. Triangle Angle Measurement
via the triangle's external angle characteristic, x = 105 + 30 = 135.
To know more about triangle visit:-
https://brainly.com/question/2773823
#SPJ1
Please help triangle similarity
9514 1404 393
Answer:
(C) SAS
Step-by-step explanation:
The obtuse angles in each triangle are "corresponding" with respect to the segments marked parallel and the horizontal transversal.
Those angles are between pairs of proportional sides:
60/42 = 40/28 = 10/7
so, the applicable theorem is SAS. The triangles can be proven similar using the SAS theorem.
An initial amount of $1300 is invested in an account at an interest rate of 1% per year, compounded continuously. Find the amount in the account after five years. Round your answer to the nearest cent.
Answer:
65, given the amount of $1300 times 0.01 percent times 5 years would equal $65 over 5 years, to break it down, multiply 1300 times 0.01 times 5.
Step-by-step explanation:
Corin measures the apparent height of a tower 800 feet away by holding a ruler in front
of her eye and observing that the tower appears to be 9 inches tall. The apparent height h
(in inches) varies inversely with Corin's distance d (in feet) from the tower. Write an
equation that gives d as a function of h. How tall would the apparent height of the tower
be if she was standing 2000 feet away from the tower? Show your work.
Answer:
Since the apparent height h of the tower varies inversely with Corin's distance d from the tower, we know that h and d are inversely proportional. This means that the product of h and d is constant. We can write this relationship as:
hd = k
where k is a constant.
We can find the value of k by substituting the known values of h and d:
9 inches * 800 feet = k
Solving for k, we find that k = 7200 inches * feet.
Since h and d are inversely proportional, we can write the inverse relationship as:
d = k / h
Substituting the value of k that we found earlier, we have:
d = 7200 inches * feet / h
To find the apparent height of the tower if Corin is standing 2000 feet away, we can substitute 2000 for d in the equation above:
h = 7200 inches * feet / 2000 feet = 3.6 inches
Therefore, the apparent height of the tower would be 3.6 inches if Corin is standing 2000 feet away.
Step-by-step explanation:
12 feet below the surface of the water. What is the pool's depth in feet?
Answer:
Step-by-step explanation:
-12
If I ate 300 apples and there were 29 left how many were there in the start. Or before I ate the apples.
How much did the population change between 1970 and 1980? population change between 1990 and 1995? What was the average annual change for that period?
Hint: Calculate the changes, then calculate the mean, or average, by dividing by the number of years. State the units clearly. The units are listed on the chart.
The population change for each period is given as follows:
1970 to 1980: 0.748 billion.1990 to 1995: 0.407 billion.Hence the average annual change for the period between 1970 and 1995 is given as follows:
7,932,000 people a year.
How to obtain the population change?The population change over a period is given by the subtraction of the population at the end of the period by the population at the beginning of the period.
The population data for each year is given by the table on the image presented at the end of the answer.
Hence the changes are obtained as follows:
1970 to 1980: 4.456 - 3.708 = 0.748 billion.1990 to 1995: 5.691 - 5.284 = 0.407 billion.The change between 1970 and 1995 is of:
5.691 - 3.708 = 1.983 billion.
This period is composed by 25 years, hence the average annual change is of:
1.983/25 = 0.07932 billion people a year = 7,932,000 people a year.
Missing InformationThe chart is given by the image presented at the end of the answer.
More can be learned about the average rate of change at https://brainly.com/question/11627203
#SPJ1
to solve 2/5 x = 14, you multiply both sides of the equation by 5/2. your friend divides both sides of the equation by 2/5. who is right? explain.
Answer:
both are right
Step-by-step explanation:
2/5x = 14
multiply both sides by 5/2:
(5/2)(2/5)x = 14(5/2)
x = 70/2 = 35
However, dividing by 2/5 is the same as multiplying by 5/2, so you are BOTH right. Dividing by a fraction is the same as multiplying by the reciprocal of the fraction.
Ramon invested a total $9,700 into two accounts, account 1 earns 6% simple interest and account 2 earns 4% simple interest. After one year, the total interest earned from both accounts was $466. Let X be the amount you invested in account 1 and y be the amount invested in account 2
Answer:
In the account that paid 3% Ramon put $800
In the account that paid 6% Ramon put $1,600
Step-by-step explanation:
Answer:
x+y= 9700 & 0.06x + 0.04y=466
Step-by-step explanation:
let X & Y be each account. Together, they are $9,700.
So, x+y=9700
thus, account 1 (x) earns 6 %. which converted to decimal is 0.06
account 2 (y) earns 4 % which converted is 0.04
It also said that both accounts were $466, after 1 year.
0.06x+0.04y=466
John needs to print 36 copies of his colored poster. His HP printer can print 16 copies in 5 minutes. His Epson printer can print 4 copies in 1 minute.
9a) Enter an equation that can be used to find the number of minutes, t, John would take to make 36 copies if he used both printers. Enter your response in the first response box. (DO NOT PUT SPACE IN YOUR ANSWER. USE t AS YOUR VARIABLE. Write fractions using the correct order of operations.)Plz help
Answer:
It would probably be 36t
Step-by-step explanation:
because if you think about It.
It is mainly asking you how long it is going to take, so you need a a equation to find the answer.
-John needs 36 copies
- Hp printers out 16 in 5 minutes
- Epson printer out 4 in 1 minutes
so 36 x t or 36t
Select all of the following that are quadratic equations.
3x ^2 + 5x - 7 = 0
x ^3 - 2x ^2 + 1 = 0
2x - 1 = 0
5x ^2+ 15x = 0
6x - 1 = 4x + 7
x ^2 - 4x = 4x + 7
Answer:
3x ^2 + 5x - 7 = 0
5x ^2+ 15x = 0
x ^2 - 4x = 4x + 7
Step-by-step explanation:
Just find a equation with a degree of 2 and boosh
A 94-ft tree casts a shadow that is 110 ft long. What is the angle of elevation of the sun?
Answer:
Step-by-step explanation:
Setting up a diagram would be helpful here, so we should have the vertical leg representing the 84-ft. tree and the horizontal leg representing the 120 ft. shadow. With the two measurements we are given, we should use the tangent ratio, opp/adj, to set up an equation to solve for the angle of elevation. So the equation will be:
tan θ = 84/120. Using the tan inverse function on the calculator, we have tan-1( 84/120) = θ and, rounding our decimal value to the nearest 10th, we have θ =35°.
Pls help me answer the question down in the image below
Using the concept of proportion to find the value of x in the similar triangle, x is equal to 6.67
What is Similar Triangle TheoremSimilar triangle theorem states that if two triangles have corresponding angles that are equal, then the sides of the triangles are proportional to each other. This theorem can be used to solve problems involving triangles, such as finding the lengths of missing sides.
We can use the concept of ratio to find the value of x.
12 / 5 = 16 / x
Cross multiply both sides and solve for x
12 × x = 16 × 5
12x = 80
x = 80 / 12
x = 6.67
The value of x is 6.67
Learn more on similar triangle theorem here;
https://brainly.com/question/3168048
#SPJ1
Please help quick (timed)
What isometric transformation was Applied to triangle XYZ ?
Translation ?
Reflection ?
Dilation ?
Rotation ?
Answer:
Rotation
Step-by-step explanation:
What is the length of the altitude of the equilateral triangle below? A. 6 B. 2 C. 2/3 D. /48 E. 36 F. 6 /3
Answer:
Step-by-step explanation:
It’s A
The length of the altitude of the right triangle given is 6.
What is Right Angled Triangle?Right angled triangle are those triangle for which one of the angle is 90 degrees.
The given triangle is an equilateral triangle.
All the sides are equal.
Each of the side = 4√3
Altitude divides one of the side in to two equal halves.
Using Pythagoras theorem,
Altitude = √(4√3)² - (2√3)²
= √(16×3) - (4 × 3)
= √48 - 12
= √36
= 6
Hence the altitude of the triangle is 6.
Learn more about Pythagoras theorem here :
https://brainly.com/question/343682
#SPJ7
find the order pairs for y=-5x-4
Answer:
(0,-4),(1,1)(2,6)
Step-by-step explanation:
19) Write in Ascending Order
7613 m , 7.6 km , 7.59km ____________________
7.6 km,7.59 km, 7613 m
O 7613 m , 7.59 km , 7.6 km
O 7.59 km , 7.6 km, 7613 m
checking account a charges a montly service fee of 3 and a per check fee of .02 while checking account b charges a montly service fee of 2 and a per check fee of .03 how many checks would a person have to write for the two accounts to cost the same
Answer:
good morning I was just asking when will I be
Help me with this question
9514 1404 393
Answer:
A. (0, -1)
Step-by-step explanation:
The x-coordinate of the y-intercept is always zero (eliminates choices B and D. Here, we can see that extending the given line will make it cross the y-axis below the x-axis, where y-values are negative (eliminates choice C).
We can see that the slope of the line is a rise of 1 for a run of 2 units to the right. The point that is 1 above and 2 right of (-2, -2) is (0, -1), the y-intercept.
What’s the answer ?
Solve |2x - 3| ≥7
Answer:
x ≤ −2 or x ≥ 5
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
— 12 – 6р – (-2)
help pls
Answer: -6P - 10
Step-by-step explanation:
STEP 1. -12 - 6P + 2
STEP 2. -6P + ( -12 + 2 )
STEP 3. -6P - 10
Read the situations in the table below. Then drag a graph and equation to represent each situation. Indicate whether each of the relationships is proportional or non-proportional.
The equation for situation 1 is y=4x and is directly proportional and the situation two will have equation y=x+4 and is not proportional.
What are linear equations?
Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here, graph 1 varies 4 times the x value every time there is an increase of 1 in the x-axis and in graph 2 it is a linear equation with intercept at 4 and thus the graph increases with +4 and A proportional relationship exists between two values x and y when they can be expressed in the general form y = kx,
Hence, The equation for situation 1 is y=4x and is directly proportional and the situation two will have equation y=x+4 and is not proportional.
Learn more about linear equations here:
https://brainly.com/question/29739212
#SPJ1
how to figure out how many data points are in a data set
Answer:
Step-by-step explanation:
read the data numbers