Answer: ABC is isosceles
Step-by-step explanation:
The coordinate of points given are:
A(1,-4)
B(-1, -2 )
C ( -2 , -5 )
For ABC to be isosceles , then AB must be equal to BC or AB = AC
The next thing to do is to find the value of AB , BC and AC using the formula for finding distance between two points which is given by:
D = [tex]\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2}-y_{1}) ^{2}}[/tex]
Calculating AB first , we have
[tex]\sqrt{(-1-1)^{2}+(-2+4)^{2} }[/tex]
= [tex]\sqrt{4+4}[/tex]
=[tex]\sqrt{8}[/tex]
Therefore:
AB = [tex]\sqrt{8}[/tex]
Calculating BC , we have :
D = [tex]\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2}-y_{1}) ^{2}}[/tex]
D = [tex]\sqrt{(-2+1)^{2}+(-5+2)^{2} }[/tex]
D = [tex]\sqrt{10}[/tex]
Therefore:
BC = [tex]\sqrt{10}[/tex]
Calculating AC , we have :
D = [tex]\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2}-y_{1}) ^{2}}[/tex]
D = [tex]\sqrt{(-2-1)^{2}+(-5+4)^{2} }[/tex]
D = [tex]\sqrt{10}[/tex]
Therefore:
AC = [tex]\sqrt{10}[/tex]
Since AC = BC then triangle ABC is isosceles
Practice Analytic Geometry
1. Find the midpoint of the line segment defined by the points: (sqrt 2, 0) and (0, -sqrt 2)
Answer is ((sqrt 2)/2, (-sqrt2)/2)
2. Find the distance of the line segment joining the two points: (5,4) and (-2,1)
Answer is sqrt 58
3. Find the distance of the line segment joining the two points: (1/2, -5/2) and (-4/3, -1/6)
Answer is (sqrt 317)/6
4. Given triangle ABC with vertices at A (1,-4), B (-1, -2), and C (-2,-5), prove or disprove that triangle ABC is an isosceles
Answer triangle ABC is isosceles since AB = sqrt 8, BC = sqrt 10, and AC = sqrt 10
Find the unit rate in each case. 4 pounds of red chilies cost $5
If A = {x | x = 3n, n € {2,3,4}} and
B = {x x = 4m - 3, m = {1,2,3}},
what element exists in the
intersection of these two sets?
Answer: 9
====================================
Explanation:
The intersection of the two sets is the list of all values that are in both sets at the same time.
Let's convert set A into roster notation. Roster notation means we just list out all the members (use ellipses if there are a lot of values you don't want to write out; luckily these sets are small). Plug n = 2 into x = 3n and you'll find that x = 6. Repeat for n = 3, and you get x = 9. Repeat for n = 4 and you get x = 12.
Set A looks like this: {6, 9, 12}
-------
Repeat the same basic steps for set B. We'll plug m = 1 into x = 4m-3 to get x = 1. Plug m = 2 into that same equation to get x = 5. Finally m = 3 leads to x = 9
Set B = {1, 5, 9}
-------
In summary,
A = {6, 9, 12}
B = {1, 5, 9}
We see that only 9 is in both sets at the same time.
Therefore, [tex]A \cap B = \left\{ 9 \right\}[/tex] which says "the intersection of set A and set B is the set { 9 } ".
The Venn Diagram shown below has the single element 9 in the overlapping region of the two circles. The other values are in their proper respective circles, but not inside the overlapping region. Set U is the universal set.
Can two fractions with the same numerator and different denominators can be equal.
Nope!
They cannot be equal if they have the same numerator but different denominators. they need to be able to reduce into the same number
No, two fractions with the same numerator and different denominators can not be equal.
The numerator simply means the number that's on top of a fraction. The denominator simply means the number that's under the fraction.
Two fractions with the same numerator and different denominators can not be equal. An example is 1/4 and 1/6 aren't equal.
Read related link on:
https://brainly.com/question/13674561
A rectangle is 10 cm longer than it is wide. If its length and width are both decreased by 2 cm, its area
is decreased by 48 cm'. Find the dimension of the original rectangle.
Answer:
Step-by-step explanation:
Yeah it right thank sweetheart
The original width of the rectangle is 8 cm and the original length is 18 cm. These dimensions are found by setting up an equation based on the change in area when both dimensions are reduced by 2 cm.
Finding Original Dimensions of a Rectangle
Let's denote the width of the rectangle as w, and the length will then be w + 10 cm. The area of the original rectangle is w(w + 10) square centimeters. Now, by decreasing each dimension by 2 cm, the new width becomes w - 2 cm and the new length becomes (w - 2) + 10 cm = w + 8 cm. The area of the new rectangle is (w - 2)(w + 8) square centimeters.
The problem states that the area of the rectangle is decreased by 48 cm2 when the dimensions are reduced. This gives us the equation:
w(w + 10) - (w - 2)(w + 8) = 48
Expanding the terms and solving for w will provide us with the width of the original rectangle. After finding w, we can calculate the original length by adding 10 cm to the width. To solve for w, we proceed with the calculation:
[tex]w_2 + 10w - (w_2[/tex] + 6w - 16) = 48
w2 + 10w - w2 - 6w + 16 = 48
4w + 16 = 48
4w = 32
w = 8 cm.
Therefore, the original width is 8 cm and the original length is 18 cm (that is, 8 cm + 10 cm).
Solve for c 9c-7=7c-11
Answer:
c = -2Step-by-step explanation:
[tex]9c-7=7c-11\qquad\text{add 7 to both sides}\\\\9c-7+7=7c-11+7\\\\9c=7c-4\qquad\text{subtract}\ 7c\ \text{from both sides}\\\\9c-7c=7c-7c-4\\\\2c=-4\qquad\text{divide both sides by 2}\\\\\dfrac{2c}{2}=\dfrac{-4}{2}\\\\c=-2[/tex]
Answer:
2
Step-by-step explanation:
Simplifying
9c + -7 = 7c + -11
Reorder the terms:
-7 + 9c = 7c + -11
Reorder the terms:
-7 + 9c = -11 + 7c
Solving
-7 + 9c = -11 + 7c
Solving for variable 'c'.
Move all terms containing c to the left, all other terms to the right.
Add '-7c' to each side of the equation.
-7 + 9c + -7c = -11 + 7c + -7c
Combine like terms: 9c + -7c = 2c
-7 + 2c = -11 + 7c + -7c
Combine like terms: 7c + -7c = 0
-7 + 2c = -11 + 0
-7 + 2c = -11
Add '7' to each side of the equation.
-7 + 7 + 2c = -11 + 7
Combine like terms: -7 + 7 = 0
0 + 2c = -11 + 7
2c = -11 + 7
Combine like terms: -11 + 7 = -4
2c = -4
Divide each side by '2'.
c = -2
Simplifying
c = -2
What are the answers to these questions?
The high school soccer booster club sells tickets to the varsity matches for $4 for students and $8 for adults. The booster club hopes to earn $200 at each match. Which equation could be used to represent the total amount the booster club would like to earn from ticket sales at each match? a
y = 4x + 8
b
4x + 8y = 200
c
12x = 200
d
y - 4 = 8(x - 200
The correct equation for the booster club aiming to earn $200 per match from student and adult tickets priced at $4 and $8, respectively, is 4x + 8y = 200. This represents the sum of $4 per student ticket (x) and $8 per adult ticket (y) sold to reach the goal.
Explanation:To solve the problem presented by the high school soccer booster club, we need to formulate a linear equation that represents their goal for ticket sales revenue from students and adults. The tickets are priced at $4 for students and $8 for adults. If we let x represent the number of student tickets sold and y the number of adult tickets sold, the total revenue T would be expressed as the sum of $4 per student ticket and $8 per adult ticket.
The booster club aims to earn $200 per match, which gives us the equation for their goal: 4x + 8y = 200. Here, the 4 and 8 are the prices of the tickets for students and adults, respectively, and x and y are the numbers of tickets sold. This clearly aligns with option b from the choices you've provided.
To illustrate with an example similar to your situation, a tutoring school equation of y = 3000x + 500 combines a one-time enrollment fee of $500 with a tuition of $3000 per year. In this case, y represents the total cost of attendance and x the number of years a student is enrolled.
ANSWER CORRECTLY!
Which factor inspired the resurgence of the KKK in the 1920s?
A. increased immigration from Eastern Europe and Asia
B. pseudo-scientific racism
C. the film The Birth of a Nation
D. All answers are correct.
Answer:
D. All answers are correct
Step-by-step explanation:
The film The Birth of a Nation promoted the KKK.
There was pseudo-scientific racism also going on.
From these two facts, we know that the answer definitely is D. Also, generally when there is "All of the above" as an answer, "All of the above" is correct.
| Sample Response: Linear relationships can be
compared using their initial values, or y-intercepts, and
their rates of change, or slopes. Initial values can tell
you which relationship started with a greater value.
Comparing slopes can tell you which relationship is
rising or falling faster.
Which of the following did you include in your
response? Check all that apply.
initial value (y-intercept) of each function
rate of change (slope) of each function
initial value to compare starting points
slope to compare rise or fall
Answer:
Initial value (y-intercept) of each function.
Rate of change (slope) of each function.
Initial value to compare starting points.
Slope to compare rise or fall. (Answer)
Step-by-step explanation:
Sample Response: Linear relationships can be compared using their initial values, or y-intercepts, and their rates of change, or slopes. Initial values can tell you which relationship started with a greater value. Comparing slopes can tell you which relationship is rising or falling faster.
Therefore, I included in the response
Initial value (y-intercept) of each function.
Rate of change (slope) of each function.
Initial value to compare starting points.
Slope to compare rise or fall. (Answer)
There are between 24 and 40 students in the class
the ratio for boys to girls is 4:7
how many students are in the class
Answer:
33 Students
Step-by-step explanation:
4+7=11 so the number of students in the class must be a multiple of 11. The only multiple of 11 between 24 and 40 is 33.
Answer:
33
Step-by-step explanation:
Let's take the constant of proportionality to be X
4x+7x=between 24 to 40
11x= 24 to 40
X should be a natural number therefore the number of students should be multiple of 11
Only multiple of 11 between 24 and 40 is 33
Using the numbers 4.3, -1.07 and -2.971, write an expression using addition and subtraction coming out to a negative answer.
The expression is ( – 1.07 ) + ( - 2.971 ) – ( 4.3 )
Solution:Given that, we have to use the numbers 4.3 , - 1.07 and – 2.971 such that the value of the expression with the given numbers and the either addition or subtraction operation between them to be negative value.
So, now take the numbers.
If we add the negative numbers and subtract the positive number from it, we will always get a negative number
So, expression will be ( – 1.07 ) + ( - 2.971 ) – ( 4.3 )
- 1.07 – 2.971 – 4.3
- 8.341
Here the result is negative value.
Hence, the expression is ( – 1.07 ) + ( - 2.971 ) – ( 4.3 )
An airplane traveled 11,760 miles in 21 hours. On average, how many miles per hour did it fly?
Answer:
560mph
Step-by-step explanation:
11,760÷21=560
label- 560mph
Answer:
560 MILES
Step-by-step explanation:
11760/21=560
6rs — 7bc (-) 9rs — 7bc simplify
Final answer:
To simplify the expression (6rs - 7bc )-( 9rs - 7bc), distribute the negative sign, combine like terms, and simplify to get -3rs.
Explanation:
To simplify the expression (6rs - 7bc )-( 9rs - 7bc), you can start by distributing the negative sign to the terms inside the second set of parentheses. This will change the signs of both terms inside it, making the expression become 6rs - 7bc - 9rs + 7bc. You can then combine like terms. Notice that -7bc and +7bc are like terms and cancel each other out, as do 6rs and -9rs. Simplifying these terms, you get -3rs.
Here is the step-by-step process:
Distribute the negative sign: 6rs - 7bc - 9rs + 7bc.
Combine like terms: (6rs - 9rs) + (-7bc + 7bc).
Simplify the expression: -3rs + 0.
Final answer: -3rs.
It's often helpful to eliminate terms wherever possible to simplify the algebra and then check the answer to ensure it is reasonable.
Which of the following represents the area of a rectangle whose length is 3x + 5 and whose width is x − 2?
The area of the rectangle with dimensions (3x + 5) by (x - 2) is represented by the algebraic expression 3x² - x - 10.
The area of a rectangle is found by multiplying its length by its width. Given a rectangle with length (3x + 5) and width (x - 2), we can find its area by using the formula for the area of a rectangle, which is length × width.
Area = (3x + 5)(x - 2)
By expanding this, we use the distributive property:
Area = 3x(x) + 3x(-2) + 5(x) + 5(-2)
Area = 3x² - 6x + 5x - 10
By combining like terms, we get:
Area = 3x² - x - 10
please draw accurately much appreciated
Answer:
draw a square
Step-by-step explanation:
draw a square then write 32mm on all sides
draw a triangle with a wide bottom a small side a medium side
Help me please I need an explanation.!
Answer:
A
Step-by-step explanation:
An ordered pair is a point on a coordinate graph that represents data. The x represents an independent variable and the y a dependent. Your y is your vertical axis. Each square on this graph represents 50 feet. The line on your graph hits the intersection between 2 minutes and 100 feet. Therefore (2,100) Is an ordered pair
15+3x=45 solve the equation
Answer:
x= 10
Step-by-step explanation:
45-15=30
30/3=10
One lunch table can hold 10 students. There are 60 students in 3rd grade. How many lunch tables are needed so that every student in 3rd grade can eat lunch at the same time?
Answer:
6 lunch tables
Step-by-step explanation:
Since one lunch table can hold 10 students and 60 students are needed to hold,
60 ÷ 10 = 6 lunch tables
Answer:
6
Step-by-step explanation:
1 table is 10
60 divided by 10= 6
A woman bought some large frames for $10 each and some small frames for $5 each add a closeout sale if she bought 20 frames for $135 find how many of each type she bought
Answer:
The quantity of large frames is 7
The quantity of small frames is 13
Step-by-step explanation:
Given as :
The price of each large frames = $ 10
The price of each small frames = $ 5
The total number of both frames bought = 20
The price for both the frames = $ 135
Now,
Let the quantity of large frames = L
And The quantity of small frames = S
So , According to question
The total number of both frames bought = 20
Or, The quantity of large frames + the quantity of small frame = 135
Or, L + S = 20 ......A
And $ 10 L + $ 5 S = $ 135 ................B
Or, $ 10× ( L + S ) = $ 10× 20
Or, $ 10 L + $ 10 S = $ 200
( $ 10 L + $ 10 S ) - ( $ 10 L + $ 5 S ) = $ 200 - $ 135
Or , ( $ 10 L - $ 10 L ) + ( $ 10 S - $ 5 S ) = $ 65
Or, 0 + 5 S = 65
∴ S = [tex]\frac{65}{5}[/tex]
I.e S = 13
So, The quantity of small frames = S = 13
Put the Value of S in eq A
So , L + S = 20
Or, L = 20 - S
Or, L = 20 - 13
∴ L = 7
So, The quantity of large frames = L = 7
Hence The quantity of large frames is 7
And The quantity of small frames is 13 Answer
Alex wants to buy the same number of stamps and envelops. Stamps are sold in packs of 14 and envelops are sold in the packs of 10.
What is the least number of each he could buy to have the same number of stamps and envelops?
Answer:
5 numbers of stamp packs and 7 number of envelop packs that Alex has to buy.
Step-by-step explanation:
Alex wants to buy the same number of stamps and envelops.
Stamps are sold in packs of 14 and envelop are sold in the packs of 10.
Now, we have to find the least number of stamp packs and envelop packs that Alex should buy to get an equal number of stamps and envelops.
The least common multiple of 14 and 10 will give the result.
14 has multiples 14, 28, 42, 56, 70, .......
And 10 has multiples 10, 20, 30, 40, 50, 60, 70, ........
Therefore, 70 is the least common multiple.
In that case 5 numbers of stamp packs and 7 number of envelop packs that Alex has to buy to get 70 stamps and 70 envelop. (Answer)
The least number of stamps and envelopes Alex can buy to have the same number is 70 of each, which he can get by purchasing five packs of each.
Explanation:Alex wants to buy the same number of stamps and envelopes. To find the least number of each he could buy to have the same number, we need to find the least common multiple (LCM) of the two pack sizes, 14 (stamps) and 10 (envelopes).
The multiples of 14 are 14, 28, 42, 56, 70, etc., and the multiples of 10 are 10, 20, 30, 40, 50, 60, 70, etc. The first common multiple they share is 70.
Therefore, Alex can buy five packs of envelopes (5 x 10 = 50 envelopes) and five packs of stamps (5 x 14 = 70 stamps) to have the same number of each, which is 70.
Match the real-world problem to its constant of proportionality.
a. $18.36 for 3 pizzas [box]
b. $4.17 for 3 pounds of bananas [box]
c. $16.48 for 4 pounds of potatoes [box]
d. 2 cups of flour to make 24 cookies [box]
Place in the box 12 4.12 6.12 1.39
WIN BRAINLIEST
Answer:
a. $18.36 for 3 pizzas : k = 6.12
b. $4.17 for 3 pounds of bananas . k = 1.39
c. $16.48 for 4 pounds of potatoes . k = 4.12
d. 2 cups of flour to make 24 cookie . k = 12
Step-by-step explanation:
PROPORTIONALITY:
Two quantities x and y are said to proportional to each other
if for x ∝ y , x = y k.
Here, k is called the PROPORTIONALITY CONSTANT.
⇒ [tex]x\propto y \implies k = \frac{x}{y}[/tex]
Now, for the given quantities:
a. $18.36 for 3 pizzas [box]
Here, [tex]k = \frac{18.36}{3} = 6.12[/tex]
So, the proportionality constant is 6.12.
b. $4.17 for 3 pounds of bananas [box]
Here, [tex]k = \frac{4.17}{3} = 1.39[/tex]
So, the proportionality constant is 1.39.
c. $16.48 for 4 pounds of potatoes [box]
Here, [tex]k = \frac{16.48}{4} = 4.12[/tex]
So, the proportionality constant is 4.12.
d. 2 cups of flour to make 24 cookies
Here, [tex]k = \frac{24}{2} = 12[/tex]
So, the proportionality constant is 12
Can anyone help me solve this problem below:
3x2−5x−2
___________ <0
x2−9
Answer:
[tex]-\frac{1}{3} < x < 2[/tex] and -3 < x < 3
Step-by-step explanation:
The inequality equation is
3x² - 5x - 2 < 0
⇒ 3x² - 6x + x - 2 < 0
⇒ (x - 2)(3x + 1) < 0
Therefore, either (x - 2) > 0 and (3x + 1) < 0
⇒ x > 2 and [tex]x < -\frac{1}{3}[/tex] which is not possible for any particular value of x.
or, (x - 2) < 0 and (3x + 1) > 0
⇒ x < 2 and [tex]x > -\frac{1}{3}[/tex] which is valid.
So, the solution is [tex]-\frac{1}{3} < x < 2[/tex] (Answer)
Now, another inequality is
x² - 9 < 0
⇒ x² < 9
Therefore, -3 < x < 3 is the solution. (Answer)
Which rational number will result in a repeating decimal?
A 141/4
B 268/8
C 316/5
D 158/6
Answer:
D. 158/6
Step-by-step explanation:
If you divide 158/6 you get 26.3333333333 which is a repeating decimal, and makes it a rational number.
PLEASE HELP ASAP!!!!
2. Compose two dependent clauses. Do not use any of the clauses given above.
Example: after the meal was served
Answer:
A subordinate clause—also called a dependent clause—will begin with a subordinate conjunction or a relative pronoun and will contain both a subject and a verb. This combination of words will not form a complete sentence. It will instead make a reader want additional information to finish the thought.
what's 1/4 × 2/3 in simplest form
Answer: 1/6
Step-by-step explanation: To multiply fractions, first multiply across the numerators, then multiply across the denominators.
So here, we have 1 × 2 which is 2 and 4 × 3 which is 12. So now we have the fraction 2/12.
Notice however that 2/12 is not in lowest terms so we need to divide the numerator and the denominator by the greatest common factor of 2 and 12 which is 2.
So if we divide the numerator and the denominator by 2, we get 1/6.
Therefore, 1/4 × 2/3 = 1/6.
Answer:
1/6
Step-by-step explanation:
For fraction multiplication, multiply the numerators and then multiply the denominators to get
1 x 2 2
------- = --------
4 x 3 12
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 2 and 12. GCF(2,12) = 2
2 divided by 2 1
------------------------ = ----
12 divided by 2 6
So...
1/4 x 2/3 = 1/6
Simplify the expression: (6 + 4i) − (5 + i). 1 + 3i 1 + 5i 11 + 3i 11 + 5i
Answer:
1+3i
Step-by-step explanation:
(6+4i)-(5+i)
6+4i-5-i
1+4i-i
1+3i
Answer: 1+3i
Step-by-step explanation:
(6 + 4i) − (5 + i)
Before solving further, note that :
Minus × Minus = Plus
Plus × Minus = Minus
Plus × Plus = Plus
(6 + 4i) − (5 + i)
Open the bracket
= 6 + 4i - 5 - i
Collect like terms
= 6 - 5 + 4i - I
= 1 + 3i
pint is 16 ounces and the price is $3.98 and quart is 32 ounces and the price is $5.98 and gallon is 128 and the price is $34.99 what is the unit rate to the neatest cent per ounce for each
Answer:
3.98/16= 0.24875 round up to make 0.25
5.98/32= 0.186875 round up to make 0.19
34.99/128= 0.273359375 = 0.27
Step-by-step explanation:
3.98/16= 0.24875 round up to make 0.25
5.98/32= 0.186875 round up to make 0.19
34.99/128= 0.273359375
8 parentheses y -9 close parentheses equals -32
Answer:
y = 5
Step-by-step explanation:
Divide each side by 8 to get (y-9) = -4.
Add 9 to each side to isolate the variable y. This leaves you with y = 5
Answer:
y = 5Step-by-step explanation:
[tex]\bold{METHOD\ 1:}[/tex]
[tex]8(y-9)=-32\qquad\text{divide both sides by 8}\\\\\dfrac{8\!\!\!\!\diagup(y-9)}{8\!\!\!\!\diagup}=\dfrac{-32\!\!\!\!\!\diagup^4}{8\!\!\!\!\diagup_1}\\\\y-9=-4\qquad\text{add 9 to both sides}\\\\y-9+9=-4+9\\\\y=5[/tex]
[tex]\bold{METHOD\ 2:}[/tex]
[tex]8(y-9)=-32\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(8)(y)+(8)(-9)=-32\\\\8y-72=-32\qquad\text{add 72 to both sides}\\\\8y-72+72=-32+72\\\\8y=40\qquad\text{divide both sides by 8}\\\\\dfrac{8y}{8}=\dfrac{40}{8}\\\\y=5[/tex]
Which of the following is the area of a trapezoid whose dimensions are base one = 10 cm, base two = 5 cm, and height = 2 cm?
30 squared cm
30 cm
15 cm
15 squared cm
Answer:
The correct answer is D. 15 squared centimeters.
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Base one = 10 centimeters
Base two = 5 centimeters
Height = 2 centimeters
2. Let's find out the area of the trapezoid, using the following formula:
Area = 1/2 (Base one + Base two) * Height
Replacing with real values:
Area = 1/2 (10 + 5) * 2
Area = 1/2 (15 * 2) = 1/2 (30)
Area = 15 centimeters ²
The correct answer is D. 15 squared centimeters.
How much money should be deposited today in an account that earns 7% compounded semiannually so that it will accumulate to $11,000 in three years?
The amount of money that should be deposited is $ N
(Round up to the nearest cent.)
Answer:
$8950.37
Step-by-step explanation:
Use the compound amount formula A = P(1 + r/n)^(nt), in which P is the initial amount of money (the principal), r is the interest rate as a decimal fraction, n is the number of times per year that interest is compounded, and t is the number of years.
Here we have A = $11,000, n = 2, r = 0.07 and t = 3, and so:
$11,000 = P(1 + 0.07/2)^(2*3), or
$11,000 = P (1.035)^6
$11,000 $11,000
Solving for P, we get P = ---------------- = ------------- = $8950.37
1.035^6 1.229
Depositing $8950.37 with terms as follows will result in an accumulation of $11,000 after 3 years.
To determine how much money should be deposited today in an account that earns 7% compounded semiannually to accumulate to $11,000 in three years, one needs to apply the formula for compounded interest and solve for the principle amount.
Explanation:The subject in question pertains to compounded interest under the domain of financial mathematics. In this context, the student wants to determine how much money needs to be deposited today to accumulate a given amount, in this case, $11,000, in an account that earns 7% compounded semiannually in three years. It's important to note that when interest is compounded, it's added to the principal, and future interest calculations are based on this adjusted amount.
Applying the formula for compounded interest: A = P(1 + r/n)^(nt)
Where:
A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount you borrow or deposit). r is the annual interest rate (in decimal form). n is the number of times that interest is compounded per year. t is the time the money is invested or borrowed for, in years.
our aim is to find P (the principal amount or the amount to be deposited today), which can be mathematically rearranged from the formula above as follows:
**P = A / [(1 + r/n)^(nt)]**
Substituting A = $11,000, r = 7% (or 0.07 in decimal form), n = 2 (since the interest is compounded semiannually), and t = 3, we calculate P (the amount to be deposited today).
Learn more about Compounded Interest here:https://brainly.com/question/14295570
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