To find the total amount paid for the car after 2 years, we use the compound interest formula [tex]A = P(1 + r)^n[/tex], where P is the initial loan amount, r is the interest rate, and n is the number of years. Substitute in the given values to calculate the final amount.
Explanation:To calculate the total amount paid for the car after 2 years, we apply the formula for compound interest. The formula is[tex]A = P(1 + r)^n[/tex], where A is the final amount, P is the principal (or initial amount), r is the interest rate, and n is the number of periods. In this case, P = $54200, r = 15.1% or 0.151, and n = 2.
Plugging these values into the formula:
[tex]A = $54200 * (1 + 0.151)^2[/tex].
Once you solve the equation, you will find the total amount paid for the car after 2 years.
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Final answer:
Using the compound interest formula, you will have paid $71,787.31 for a $54,200 car loan at 15.1% interest compounded annually after 2 years.
Explanation:
To calculate the total amount paid for a car after 2 years on a loan of $54,200 with an interest rate of 15.1% compounded annually, we'll use the formula for compound interest:
[tex]A = P (1 + r/n)^{(nt)}[/tex]
Where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money)r is the annual interest rate (decimal)n is the number of times that interest is compounded per yeart is the time in yearsFor this car loan:
P = $54,200r = 15.1% = 0.151n = 1 (since interest is compounded annually)t = 2 yearsSubstitute the values into the formula:
A = $54,200 (1 + 0.151/1)^(1*2)
A = $54,200 (1 + 0.151)^2
A = $54,200 (1.151)^2
Calculate the amount:
A = $54,200 * (1.151)^2
A = $54,200 * 1.324301
A = $71,787.31
After 2 years, you will have paid $71,787.31 for your car.
What is x for unknown angle problems algebra?
Step-by-step explanation:
If two lines cross each other the angles opposite of each other are the same. So left=right and top=bottom. Knowing this the bottom angle must be 120°. if 3x=120° then x=40°
PLZZZ HELP!!!!!!!!!!!!
Two angles are a linear pair. The measure of one angle is 5 more than 3/4 of the other. Find the measure of both angles.
Answer:
Angle 1: 100
Angle 2: 80
Step-by-step explanation:
A linear pair of angles is formed when two lines intersect. The measure of a straight angle is 180 degrees, so a linear pair of angles is equal to 180 degrees.
Angle 1: x
Angle 2: (x * 3/4) + 5
x + (x * 3/4) + 5 = 180
x + 3/4x + 5 = 180
1 3/4x + 5 - 5 = 180 - 5
1 3/4x = 175
1 3/4x / 1 3/4 = 175 / 1 3/4
x = 100
Check:
(x * 3/4) + 5
(100 * 3/4) + 5
75 + 5
80
100 + 80 = 180
To find the measure of both angles that form a linear pair, set up an equation and solve for x.
Explanation:To find the measure of both angles, let's assume that one angle is x degrees. According to the given information, the other angle is 3/4 of x degrees plus 5. So the measure of the other angle is (3/4)x + 5 degrees. Since the two angles form a linear pair, their measures sum up to 180 degrees. Therefore, we can write the equation: x + (3/4)x + 5 = 180. Solving this equation, we can find the value of x and then calculate the measures of both angles.
The price decreased by nine dollars
Answer: -9
Step-by-step explanation: it is a negative because it is minus 9$ from the price just like adding -9
Answer:
t - 9 = ?
Step-by-step explanation:
Find the cosine of L
Answer:
0.42
Step-by-step explanation:
use the attached as reference
recall that for a right (90°) triangle, with any acute angle θ,
cos θ = length of adjacent side / length of hypotenuse
in our case, for angle I, the adjacent side is HI = 36 units and the hypotenuse is IJ = 85 units
by the above formula,
cos I = length of adjacent side / length of hypotenuse
= 36 / 85
= 0.42353
= 0.42 (rounded to nearest hundredth)
Car A and car B are traveling opposite directions st the same speed. Car A drove for 17 minutes and car B drove for 32 minutes. Car B drove 12 miles more than car A. How fast were the cars driving?
Answer: 0.8mile/min
Step-by-step explanation:please see attachment for explanation
-16t^2+vt+h Find a function
Answer:
Step-by-step explanation:
what's the nth term of this sequence 16,8,4,2,1,
Answer:
Step-by-step explanation:
This Sequence is Geometric Progression
a = 16
r = 8/16 = 1/2
nth term = ar^(n-1) = 16*(1/2)^(n-1)
The nth term of the geometric sequence 16, 8, 4, 2, 1 can be found using the formula an = 16 * (1/2)^(n-1), where n is the position of the term in the sequence.
The sequence given is 16, 8, 4, 2, 1, which is a geometric sequence where each term is half of the previous term. This means the common ratio r is 1/2. The nth term of a geometric sequence is given by the formula a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.
To find the nth term for our sequence, we plug in the values: a_1 = 16 and r = 1/2. Thus, the formula for the nth term becomes an = 16 * (1/2)^(n-1).
Does anyone know what this answer is?
0.3x − 2.7 =
Answer:
the answer is 9
Step-by-step explanation:
why it 9 Add '2.7' to each side of the equation.
-2.7 + 2.7 + 0.3x = 9 + 2.7
Combine like terms: -2.7 + 2.7 = 0.0
0.0 + 0.3x = 9 + 2.7
0.3x = 9 + 2.7
Combine like terms: 9 + 2.7 = 11.7
0.3x = 11.7
Divide each side by '0.3'.
x = 39
Simplifying
x = 39
Marco scored 1,753 points
when playing his video game.
Jasmine only scored 877
points. How many more points
did Marco score than Jasmine?
Marco scored 876 more points than Jasmine.
Explanation:To find how many more points Marco scored than Jasmine, we subtract Jasmine's score from Marco's score.
Marco scored 1,753 points while Jasmine scored 877 points.
Thus, Marco scored 1,753 - 877 = 876 more points than Jasmine.
how can you come up with a tree diagram
Answer:
Create a tree diagram
1. Click File > New > Templates > General, and then open Block Diagram.
2. From the Blocks and Blocks Raised stencils, drag block shapes onto the drawing 3.page to represent stages in a tree structure.
5 .To add text to a shape, select the shape, and then type.
6. Indicate relationships between the blocks by connecting the shapes:
Step-by-step explanation:
And kind of like this but you can do whatever get creative:) here’s the picture
A tree diagram is a form of graphical representation that visually displays possible outcomes of an experiment or event. It is particularly useful in solving complex probability problems. An example would be if you were to draw balls from an urn multiple times and wanted to visualize all the possible outcomes.
Explanation:A tree diagram is a graphical representation used to determine the outcomes of an experiment. It consists of multiple branches, typically representing different possible outcomes or choices.
As an example, let's consider an urn with 11 balls: 3 red and 8 blue. If you were to draw two balls, one at a time, with replacement (putting the first ball back before the second draw), a tree diagram would show all possible outcomes. Your first set of branches would represent the color of the first ball drawn (red or blue) and from each of those branches, a second set would signify the color of the second ball drawn.
So branch one could show red for the first draw, and from that branch you would have two further branches, red and blue, showing the possibilities for the second draw. The same would be done for the first draw being blue. This tree diagram illustrates the different scenarios of this experiment.
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Parallelograms partner challenge
Step-by-step explanation:
parallelogram is a simple quadrilateral with 2 pairs of. parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
Thanks..... hope it helped.
x + y = -9
5x - 2y = 32
The solution is x = 2 and y = -11
Solution:
Given system of equations are:
x + y = -9 --------- eqn 1
5x - 2y = 32 ------------- eqn 2
We have to solve the system of equations
We can solve the system by substitution method
From eqn 1,
x + y = -9
Isolate "y" to one side
y = -9 - x ---------- eqn 3
Substitute eqn 3 in eqn 2
5x -2(-9 - x) = 32
5x + 18 + 2x = 32
Combine the like terms
7x = 32 - 18
7x = 14
x = 2
Substitute x = 2 in eqn 3
y = - 9 - 2
y = -11
Thus the solution is x = 2 and y = -11
PLEASE HELP I REALLY NEED IT
The lines a and b intersect at point D.
What is the value of z?
Enter your answer in the box.
z =
Answer: 12 I saw your comment lol
−2(2x+3)=−4(x+1)−2
x = ___
(type your answer as a number, "no solution" or "infinite solutions")
Answer:
infinite solutions
Step-by-step explanation:
−2(2x+3)=−4(x+1)−2 multiply -2 and -4 with inside the parenthesis
-4x -6 = -4x -4 -2 now add like terms
-4x -6 = -4x -6 ➡ -4x +4x = -6+6
that makes equation 0 = 0 this is called infinite solutions which means whatever number you use instead of x there will always be a solution.
What is the solution of the system of equations?
y = -2x + 5
-5y = 10x + 20
(1,3)
no solution
infinitely many solutions
(0, 20)
The correct answer is "no solution."
Let's first rewrite the second equation in the system in slope-intercept form (y = mx + b) to make it easier to work with:
[tex]\[ -5y = 10x + 20 \][/tex]
Divide both sides by -5:
[tex]\[ y = -2x - 4 \][/tex]
Now we have the system of equations:
[tex]\[ y = -2x + 5 \][/tex]
[tex]\[ y = -2x - 4 \][/tex]
To find the solution to the system, we can set the two equations equal to each other since they both equal y:
[tex]\[ -2x + 5 = -2x - 4 \][/tex]
Now, we can solve for x:
[tex]\[ 5 = -4 \][/tex]
This equation is not true, which means there is no value of x that satisfies both equations simultaneously. Therefore, the system has no solution.
Express 60 as the product of its prime factors. Write the prime factors in ascending order and give your answer in index form.
Answer: 2.2.3.5 = 60 are the prime factors in ascending order
(1.6z+4) -4(-0.5+5z) no parentheses
Answer:
-18.4z+6
Step-by-step explanation:
Solve the system of equations.
2x + 3y = 1
5x + 2 = 8
What is the solution?
Answer:
x = 2, y = -1
Step-by-step explanation:
2x + 3y = 1.....(1)
5x + 2y = 8.....(2)
multiply equation (1) by 5 and equation (2) by 2
10x + 15y = 5 .......(3)
10x + 4y = 16......(4)
solving by elimination method
we subtract equation (4) from (3)
hence ...
11y = -11
dividing both sides by 11
y = -1
substituting y = -1 in equation (1) to solve for the value of x
2x + 3(-1) = 1
2x - 3 = 1
rearranging,
2x = 3 + 1
2x = 4
dividing both sides by 2
x = 2
Briana has 1,438 likes for the picture posted online of her dog dressed up like a superhero.How many more likes does Briana need to reach 2,000 likes?
Answer:Briana needs 562likes to reach 2000
Step-by-step explanation:
The number of likes Briana has = 1438
The number of likes Briana wants to reach = 2000
The remaining of likes she needs= 2000-1438 = 562
Hence, Briana needs 562 more likes to reach 2000likes on her picture
Final answer:
Briana needs 562 more likes to reach 2,000 likes on her dog's picture, calculated by subtracting her current likes from the target amount.
Explanation:
Briana currently has 1,438 likes on a picture of her dog dressed as a superhero. To determine how many more likes Briana needs to reach 2,000 likes, we perform a simple subtraction operation:
2,000 (desired amount of likes) - 1,438 (current amount of likes) = 562 more likes needed.
Therefore, Briana needs 562 additional likes to reach her goal of 2,000 likes on the picture of her dog.
solve for x
4x = -48
Answer:
-12
Step-by-step explanation:
4x=-48. use inverse operations here so divide -48 by 4
x=-12
Find the coordinates of a point on the directed segment from (3,-2) to (8,0) that divides it into a ratio of 3:1.
a.
(6.75,-0.5)
b.
(6, -0.75)
c.
(4, -1.5)
d.
(5, -1.5)
The coordinates of a point on the directed segment from (3,-2) to (8,0) that divides it into a ratio of 3:1 is (6.75, -0.5). The correct option is A.
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
Let the line be represented as AB, therefore, the coordinates of points A and B are (3,-2) and (8,0), respectively. The coordinate of the point m that divides the line AB in a ratio of 3:1 is,
x = [(x₂×m)+(x₁×n)]/(m+n)
x = [(8×3)+(3×1)]/(3+1)
= (24+3)/4
= 6.75
y = [(y₂×m)+(y₁×n)]/(m+n)
y = [(0×3)+(-2×1)]/(3+1)
= (0-2)/4
= -0.5
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Final answer:
The coordinates of the point that divides the directed segment from (3,-2) to (8,0) in the ratio of 3:1 are a) (6.75, -0.5), using the section formula.
Explanation:
When finding the coordinates of a point on a directed segment that divides it into a specific ratio, such as 3:1, the formula for the section formula in coordinate geometry is used. This formula allows us to calculate the coordinates of the point that divides the segment internally or externally in a given ratio (m:n) using the coordinates of the endpoints (x1,y1) and (x2,y2). The formula for the point (x, y) that divides the segment internally in the ratio m:n is:
x = (mx2 + nx1) / (m + n)
y = (my2 + ny1) / (m + n)
For the directed segment from (3, -2) to (8, 0) and a ratio of 3:1, we find the point by this method:
x = (3×8 + 1×3) / (3 + 1) = (24 + 3) / 4 = 27 / 4 = 6.75
y = (3×0 + 1×(-2)) / (3 + 1) = (0 - 2) / 4 = -2 / 4 = -0.5
Thus, the coordinates of the point that divides the segment in the ratio 3:1 are a) (6.75, -0.5).
(-22) - 14 - (-22) + 14
Answer:
-28
Step-by-step explanation:
(-22)-14= -36. (-22)+14= -8. -36-(-8)= -28.
The product of (a + b)(a − b) is a2 − b2. (1 point)
Group of answer choices
Sometimes
Always
Never
Flag this Question
Question 21 pts
(07.07)
Find the product of (x − 7)2. (1 point)
Group of answer choices
x2 − 14x + 49
x2 + 14x + 49
x2 − 49
x2 + 49
Flag this Question
Question 31 pts
(07.07)
Find the product of (x + 5)2. (1 point)
Group of answer choices
x2 − 10x + 25
x2 − 25
x2 + 25
x2 + 10x + 25
Flag this Question
Question 41 pts
(07.07)
Find the product of (x + 3)(x − 3). (1 point)
Group of answer choices
x2 − 6x + 9
x2 + 6x + 9
x2 + 9
x2 − 9
Flag this Question
Question 52 pts
(07.07)
Find the product of (4x − 3y)2. (2 points)
Group of answer choices
16x2 + 24xy + 9y2
16x2 − 9y2
16x2 − 24xy + 9y2
16x2 + 9y2
Flag this Question
Question 62 pts
(07.07)
Find the product of (2x + 5y)2. (2 points)
Group of answer choices
4x2 + 20xy + 25y2
4x2 − 20xy + 25y2
4x2 − 25y2
4x2 + 25y2
Flag this Question
Question 72 pts
(07.07)
Find the product of (3x + 7y)(3x − 7y). (2 points)
Group of answer choices
9x2 − 42xy + 49y2
9x2 + 42xy + 49y2
9x2 − 49y2
9x2 + 49y2
1. Always
2. x^2 − 14x + 49
3. x^2 + 10x + 25
4. x^2 − 9
5. 16x^2 − 24xy + 9y^2
6. 4x^2 + 20xy + 25y^2
7. 9x^2 − 49y^2
Some of these may be incorrect as you didn't probably right down the problems... I had to guess what was exponents/ <3
What is 4/5(1/4c-5)? By using distributive property and collecting like terms.
Answer:
The simplified expression is
[tex]\frac{4}{5}(\frac{1}{4}c-5)=\frac{c}{5}-4[/tex]
Step-by-step explanation:
Given expression is
[tex]\frac{4}{5}(\frac{1}{4}c-5)[/tex]
To simplify the given expression:
[tex]\frac{4}{5}(\frac{1}{4}c-5)[/tex]
[tex]\frac{4}{5}(\frac{1}{4}c-5)=(\frac{4}{5}\times \frac{1}{4}c)-(\frac{4}{5}\times 5)[/tex] ( here using the distributive property )
[tex]=(\frac{1}{5}c)-(4\times 1)[/tex] (simplify the factors )
[tex]=\frac{1}{5}c-4[/tex] or
[tex]=\frac{c}{5}-4[/tex]
Therefore the simplified expression is
[tex]\frac{4}{5}(\frac{1}{4}c-5)=\frac{c}{5}-4[/tex]
Which of the following is a source of water pollution?
a. sewage
b. oil spills
C. fertilizers
d. all of the above
Answer:
D
Step-by-step explanation:
all of the above
The solution is Option D.
The sources of water pollution are sewage , oil spills and fertilizers
What is water pollution?Water contamination is the tainting of bodies of water, typically as a result of human activity, which has a detrimental impact on their uses. Aquifers, reservoirs, lakes, rivers, seas, and groundwater are all examples of bodies of water. When contaminants are introduced into these water bodies, water contamination results. It causes illnesses: consuming contaminated water can lead to serious health problems. From diarrhoea, cholera, hepatitis A, typhoid, to death.
Given data ,
Water scarcity is the situation when available water is not sufficient
And , the sources of water pollution are mainly sewage , oil spills and fertilizers thrown out into the ocean and other water bodies by humans
Toxic substances from farms, towns, and factories readily dissolve into and mix with it, causing water pollution.
Ground water , surface water and ocean water pollution are the three water bodies caused by water pollution
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What is the solution for 3x-4=-1/2x+3
Answer:
2
Step-by-step explanation:
3x-4 =-1/2x+3
3x+1/2x=3+4
6x+x/2=7
6x+x=14
7x=14
x=14/2
x= 2
Answer:
X = 2
Step-by-step explanation:
- Add 1/2 to both sides
3x - 4 + 1/2x = -1/2x + 3 + 1/2x
7/2x - 4 = 3
- Add 4 to both sides
7/2x - 4 + 4 = 3 + 4
7/2x = 7
- Multiply both sides by 2/7
(2/7) X (7/2x) = (2/7) X (7)
x = 2
A sporting goods store regularly sell shoes for $17.49 their ad for a sale says *Save 25%* what is the sale price of the shoes
Answer:
The price of the shoes should be $13.12
A: twice a number minus seven is eight greater than three times a number
B: how many solutions does this equation have?
The equation has only one solution that is x = -15
Step-by-step explanation:
We have to convert the given statement in form of equation to find the number
Let x be the number
then
According to given statement,
[tex]2x-7 = 3x+8\\-7 = 3x-2x+8\\-7 = x+8\\x = -7-8\\x = -15[/tex]
The equation has only one solution that is x = -15
Keywords: Linear equation, variables
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Final answer:
The equation 'twice a number minus seven equals eight greater than three times the number' simplifies to 2x - 7 = 3x + 8, which has one solution: x = -15.
Explanation:
The original question asks us to solve an algebraic equation where twice a number minus seven is equal to eight greater than three times that number.
To translate this into an algebraic expression, let the unknown number be x.
This gives us the equation 2x - 7 = 3x + 8.
To solve this equation, we can subtract 2x from both sides to get -7 = x + 8 and then subtract 8 from both sides to isolate x, resulting in x = -15.
To answer part B, this type of linear equation will only have one solution because it’s a linear equation with a non-zero coefficient in front of the variable x.
Help me with this please!
Answer:
Step-by-step explanation:
Increases weight = 80 - 40 = 40 lbs
Percent increase = (40/40)*100 = 1*100 = 100%
Answer:
The percent change is 50%.
Step-by-step explanation
1) 80-40=40
2) 40 divided by 80 which equals 0.5
3) 0.5 multiplied by 100
4) 0.5 x 100=50
The formula for percent change is change divided by the original amount then multiply the answer from that problem by 100.
What is 2(4f+2g) equal