The system of equations is graphed on the coordinate plane.

y=x−1
y=−2x−4

Enter the coordinates of the solution to the system of equations in the boxes.

The System Of Equations Is Graphed On The Coordinate Plane.y=x1y=2x4Enter The Coordinates Of The Solution

Answers

Answer 1

Answer:

(-1,-2)

Step-by-step explanation:

Hello!

The solution to the system is at the intersection between the two graphed lines.

Remember that a coordinate is written in (x,y) format, so we take the x-value of the points and the y-value of the point.

The coordinate is (-1, -2).

Answer 2
Answer is (-1, -2)
Step by step
You have two equations
y= x -1 (we will call equation A)
y= -2x-4 (we will call equation B)
Substitute equation A for the “y” value in equation B

x-1 = -2x -4
We need to isolate x to one side of the = so first we will add 1 to both sides
x-1+1 = -2x -4 +1
Combine like terms
x = -2x -3
Now add 2x to both sides
2x + x = -2x +2x -3
Combine like terms
3x = -3
Now solve for x by dividing both sides by 3
3/3x = -3/3
X= -1

Now we can solve for “y” by substituting our “x” value into equation A

y = -1 -1
y = -2

Now you can check your work by substituting your x and y values into with equation

A (-2) = -1 -1
A -2 = -2

B -2 = -2(-1) -4
B -2 = -2

Problem solved and graph is correct - see attached

The System Of Equations Is Graphed On The Coordinate Plane.y=x1y=2x4Enter The Coordinates Of The Solution

Related Questions

Ali has X paintings He buys two more paintings.
How many Paintings does he now have?

Answers

Answer:

X+2

Hope this helps

The box plots show the data distributions for the number of customers who used a coupon each hour for two days of a store sale. What is the difference of the medians? 0 2 4 7

Answers

The difference of medians is given as follows:

2.

What does a box and whisker plot shows?

A box and whisker plots shows these five metrics from a data-set, listed and explained as follows:

The minimum non-outlier value.The 25th percentile, representing the value which 25% of the data-set is less than and 75% is greater than.The median, which is the middle value of the data-set, the value which 50% of the data-set is less than and 50% is greater than%.The 75th percentile, representing the value which 75% of the data-set is less than and 25% is greater than.The maximum non-outlier value.

The median for each day is given as follows:

Day 1: 6.Day 2: 8.

Hence the difference is given as follows:

8 - 6 = 2.

Missing Information

The box plot is given by the image presented at the end of the answer.

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Alfred says that the line shown on the scatter plot is a good line of fit because the line goes through the middle of all the data points. Do you agree? Explain your reasoning

Answers

No, I disagree because a good line of fit has to minimize the sum of the squared distance between all the points in the data.

Line of fit

A line of fit is used to mathematically model the relationship between variables in a data. A line of fit is drawn such that the best line would minimize the sum of the squared distances between the plotted points.

This means that, the line of fit should not aim to go through the middle of the data points but minimize the sum of the squared distances between them.

Hence, Alfred's reasoning is Incorrect .

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the martins bought a condominium for $85,000. assuming that the value of the condo will appreciate at most 5% a year, how much will the condo be worth in 5 years?

Answers

Answer:

Step-by-step explanation:

Answer:181,250

Step-by-step explanation:

Basically, the cost would go up 5 percent, and you’re asking how much it would go up in 5 years. So 5x5=25, so you’d multiply 145,000 by 25%, which is 36,250. So, you’d add that to 145,000 which would get you 181,250.

One of the authors received a credit card bill for $2,559, but it included a charge of $1,825 th
values of the absolute and relative errors.
The value of the absolute error is $
The value of the relative error is%. (Round to the nearest integer as needed)

Answers

The absolute error is $1825, the relative error is 2

What is an absolute and relative error?

An absolute error is a determinant of how large an error is. A relative error defines how good or bad an error is.

The formula for determining an absolute error is;

Absolute error = measured value - actual value

The formula for determining a relative error is:

Relative error = absolute error ÷ actual value

From the parameters given:

The absolute error can be computed as:

Absolute error = 2559 - (2559 - 1825)

Absolute error = 2559 - 734

Absolute error = $1825

The relative error = 1825 ÷ 734

The relative error = 2.4

The relative error ≅ 2 (as an integer)

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Raj purchases a new home for $150,000. The value of the home increases by 9% every 3 years.
Determine the value of the home after 5 years.

Answers

The value of the home after 5 years would be $194,415.

How to calculate the value of the home after 5 years

First, let's calculate the increase in value for each 3-year period:

After the first 3 years:

Increase = 9% of $150,000 = 0.09 * $150,000 = $13,500

After the second 3 years:

Increase = 9% of ($150,000 + $13,500) = 0.09 * ($150,000 + $13,500) = $14,850

After the third 3 years:

Increase = 9% of ($150,000 + $13,500 + $14,850) = 0.09 * ($150,000 + $13,500 + $14,850) = $16,065

Now, let's add these increases to the initial value of the home to find the value after 5 years:

Value after 5 years = $150,000 + $13,500 + $14,850 + $16,065 = $194,415

Therefore, the value of the home after 5 years would be $194,415.

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Please help me find the function that explains how to get the output from the input

Answers

Answer:

The equation for those inputs and outputs is:
0.25 *input - 151.75 = Output  

Step-by-step explanation:

For this, first search for the Slope of the funtion
THe slope can be found by calculating this :
(y2-y1)/(x2-x1)  or in this case (output2 - output1)/ (input2 - input1)

IT continues as follows:
( -48.5 - 24)  / (-413 - (-703) ) =
= (-72.5) / (290)
= -0.25

The slope is -0.25. If the function is a line then the equation is

-0.25*input + B = output

with any of the choices we can determine B.
  -0.25 * (-703) + B    = 24

   175.75 + B              = 24
175.75 +B - 175.75    = 24 - 175.75

               B                 = - 151.75

The equation for those inputs and outputs is:
0.25 *input - 151.75 = Output  

Please help. Is the answer even there?

Answers

The critical values t₀ for a two-sample t-test is ± 2.0.6

To find the critical values t₀ for a two-sample t-test to test the claim that the population means are equal (i.e., µ₁ = µ₂), we need to use the following formula:

t₀ = ± t_(α/2, df)

where t_(α/2, df) is the critical t-value with α/2 area in the right tail and df degrees of freedom.

The degrees of freedom are calculated as:

df = (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)]

n₁ = 14, n₂ = 12, X₁ = 6,X₂ = 7, s₁ = 2.5 and s₂ = 2.8

α = 0.05 (two-tailed)

First, we need to calculate the degrees of freedom:

df = (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)]

= (2.5²/14 + 2.8²/12)² / [(2.5²/14)²/13 + (2.8²/12)²/11]

= 24.27

Since this is a two-tailed test with α = 0.05, we need to find the t-value with an area of 0.025 in each tail and df = 24.27.

From a t-distribution table, we find:

t_(0.025, 24.27) = 2.0639 (rounded to four decimal places)

Finally, we can calculate the critical values t₀:

t₀ = ± t_(α/2, df) = ± 2.0639

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22. Which of the following is NOT a rational expression?
O(x+3)(2x-1)
x+3
O3x²+3x
4x+5
3x+4√x-7
2x+2
2x²-3x³+5
5x

Answers

The correct expression which is not a rational expression,

⇒ (x+3)(2x-1) / (x+3)

We have to given that;

All the expressions are,

⇒ (x+3)(2x-1) / (x+3)

⇒ (3x²+3x) / (4x+5)

⇒ (3x+4√x-7) / (2x+2)

⇒ (2x²-3x³+5) / 5x

Since, A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.

Hence, We can simplify all the expressions as,

⇒ (x+3)(2x-1) / (x+3)

⇒ (2x - 1)

Hence, It is not a rational expression.

⇒ (3x²+3x) / (4x+5)

⇒ 3x (x + 1) / (4x + 5)

Hence, It is a rational expression.

⇒ (3x+4√x-7) / (2x+2)

⇒ (3x + 4√x - 7) / 2 (x + 1)

Hence, It is a rational expression.

⇒ (2x²-3x³+5) / 5x

Hence, It is a rational expression.

Thus, The correct expression which is not a rational expression,

⇒ (x+3)(2x-1) / (x+3)

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The graph below displays a fire department's
response time, which measures the time from when
the alarm is sounded at the firehouse to the time the
first fire engine leaves the station.
Fire Department Response Times
0.4
Relative Frequency
10
02
0
10
20 30 40 50 60 70 80 90
Response Time (Seconds)
Which of the following correctly describes the shape of
the distribution?
uniform
skewed left
skewed right
roughly symmetric

Answers

The correct description of the shape of the distribution is D. Roughly Symmetric.

What is a symmetric distribution ?

Symmetric distribution is an often-referenced term in statistics, representing a type of probability with data segments evenly dispersed around the mean. This denotes the perfect mirror image of the right and left halves when the distribution is split; arriving at an equal size and shape on either side when drawn at the midpoint of the line.

Looking at the distribution of a fire department's response time, we can see that the distribution is roughly symmetric because the values on the left seem to match those on the right.

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Gabe learns more than just
math in Mrs. Zemla's class. Today he
learned that buying a car is a bad
investment because a car's value decreases
each year. So when Gabe was looking to
buy a 2024 Porsche Boxster for $54792,
he also reasearched the projected resale
value of the vehicle. He found that the
vehicle is expeced depreciate 19% each
year after the car is purchased. What is
the expected vaule of the car 7 years after
it was purchased?

Answers

The expected value of the car 7 years after it was purchased is $47,029.12.

To solve this problem, we need to calculate the expected value of the car after 7 years. To do this, we need to use the formula for calculating the value of a depreciating asset:

Value after n years = Initial Value - (Initial Value × (Depreciation Rate/100)×n)

In this case, the initial value of the car is $54792, the depreciation rate is 19%, and n = 7. Thus, the expected value of the car 7 years after it was purchased is:

Value after 7 years = 54792 - (54792 × (19/100)×7)

Value after 7 years = 54792 - (54792 × 0.19×7)

Value after 7 years = 54792 - 7762.88

Value after 7 years = $47,029.12

Therefore, the expected value of the car 7 years after it was purchased is $47,029.12.

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A cruise ship can cover 19 nautical miles in 437 minutes. How many nautical miles will it travel in 345 minutes?

Answers

The cruise ship will travel approximately 15 nautical miles in 345 minutes.

How did we get the value?

Use a proportion to solve this problem. Let "d" be the number of nautical miles the cruise ship will travel in 345 minutes. Then:

19 nautical miles / 437 minutes = d nautical miles / 345 minutes

To solve for "d", cross-multiply:

19 nautical miles x 345 minutes = d nautical miles x 437 minutes

Then, divide both sides by 437 minutes to isolate "d":

d nautical miles = (19 nautical miles x 345 minutes) / 437 minutes

Simplifying this expression, we get:

d nautical miles = 15 nautical miles (rounded to the nearest whole number)

Therefore, the cruise ship will travel approximately 15 nautical miles in 345 minutes.

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Help me with this question pls. And do it fast I have to submit it soon in 3 minutes

Answers

The perimeter of the dilated rectangle M'N'O'P' is 54 centimeters.

If the area of the original rectangle is A, and the area of the dilated rectangle is A', then the relationship between their areas is:

A' = k² × A

Similarly, the relationship between their perimeters is:

P' = k × P

The original rectangle has an area of 14 square centimeters.

The dilated rectangle has an area of 126 square centimeters.

We need to find the perimeter of the dilated rectangle.

Let's denote the scale factor as "k."

126 = k² × 14

Dividing both sides by 14, we get:

9 =  k²

k = 3

Now, we can find the perimeter of the dilated rectangle using the perimeter relationship:

P' = k × P

The original rectangle has a perimeter of 18 centimeters, so:

P' = 3 × 18

P' = 54 centimeters

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The question is :

Which expression is a factor of both
x^2-9 and x^2+8x+15

Can you please explain this to me like you are talking to an elementary schooler, i kinda get it but im honestly so confused.

Answers

The expression that is a factor of both x² - 9 and x² + 8x + 15 is (x + 3).

What is the common factor between the given polynomials?

Given the polynomials in the question:

x² - 9

x² + 8x + 15

To find a factor that is common to both x² - 9 and x² + 8x + 15, we can factorize the two expressions and look for any common factors.

First, factorize x² - 9:

Using the difference of sqaure formula

a² - b² = ( a + b )( a - b )

x² - 9

x² - 3² = (x - 3)(x + 3)

Next, factorize x² + 8x + 15:

Using AC method

( x + 3 )( x + 5 )

From the factorizations, we can see that both expressions have a common factor of (x + 3).

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Which equation choice could represent the graph shown below?
1) F(x) = (x - 4)(x + 1)(x - 6)
2) F(x) = (x - 4)(x - 1)(x - 6)
3) F(x) = (x - 4)(x - 1)(x + 6)
4) F (x) = (x + 4(x - 1)(x - 6)

Answers

The algebraic equation of the cubic function set on Cartesian plane is f(x) = (x + 6) · (x - 1) · (x - 4). (Correct choice: 3)

What equation does represent a cubic function?

In this problem we find the representation of a cubic function set on Cartesian plane, whose definition as algebraic equation is shown below:

f(x) = a · (x - r₁) · (x - r₂) · (x - r₃)

Where:

a - Lead coefficient.r₁, r₂, r₃ - Roots of the polynomial.

Graphically speaking, the roots of the polynomials are the points of the curve on x-axis. If we know that a = 1, r₁ = - 6, r₂ = 1 and r₃ = 4, then the algebraic equation of the cubic function is:

f(x) = (x + 6) · (x - 1) · (x - 4)

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Answer:

3)  f(x) = (x - 4)(x - 1)(x + 6)

Step-by-step explanation:

The x-intercepts of a function are the points at which the curve crosses the x-axis, so when f(x) = 0.

From inspection of the given graph, the curve crosses the x-axis at:

x = -6x = 1x = 4

According to the Factor Theorem, if f(x) is a polynomial and f(a) = 0, then (x - a) is a factor of f(x).

Therefore, as f(x) = 0 when x = -6, x = 1 and x = 4, then (x + 6) and (x - 1) and (x - 4) are factors of the polynomial.

Therefore, the equation of the function is:

f(x) = (x - 4)(x - 1)(x + 6)

At a football game, a vender sold a combined total of 233 sodas and hot dogs. The number of hot dogs sold was 51 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.​

Answers

The vendor sold 142 sodas and 91 hotdogs.

According to the question:

The vendor sold 233 sodas and hotdogs combined

The number of hot dogs sold was 51 less number of sodas sold

To find:

Number of sodas sold(S)

Number of hotdogs sold(H)

From the question, it is clear that:

S + H = 233 ...(i)

S - H = 51 ...(ii)

These two are simultaneous linear equations.

Adding equations (i) and (ii):

S + H + S - H = 233 + 51

2S = 284

S = 284/2

S = 142

Substitute this value of S in equation (i):

142 + H = 233

H = 233 - 142

H = 91

Therefore, the vendor sold 142 sodas and 91 hotdogs.

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x+3 is a factor of p(x)=x^3-7x^2+15x-9
true or false

Answers

The statement "x + 3 is a factor of p(x) = [tex]x^3 - 7x^2 + 15x - 9[/tex]" is false.

To determine whether x + 3 is a factor of p(x) = [tex]x^3 - 7x^2 + 15x - 9[/tex], we can use the factor theorem.

According to the factor theorem, if a polynomial p(x) has a factor (x - a), then p(a) = 0.

In this case, we have x + 3 as a possible factor. To check if it is indeed a factor, we substitute -3 for x in the polynomial p(x):

[tex]p(-3) = (-3)^3 - 7(-3)^2 + 15(-3) - 9[/tex]

= -27 - 63 - 45 - 9

= -144

Since p(-3) is not equal to zero, we conclude that x + 3 is not a factor of p(x).

Therefore, the statement "x + 3 is a factor of [tex]p(x) = x^3 - 7x^2 + 15x - 9[/tex]" is false.

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4 3/8 + 5 1/2= in fractions

Answers

Answer:

9 7/8

Step-by-step explanation:

1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.

2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.

3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.

At the farmers' market, Tom bought 11/12 of a pound of string beans and 1/2 of a pound of
lima beans. How many more pounds of string beans did Tom purchase?
Write your answer as a fraction or as a whole or mixed number.
pounds

Answers

He bought 5/12 of a pound more string beans.

You can change 1/2 to 6/12 by multiplying both the top and bottom number by 6. Then you subtract 6/12 from 11/12 and you get 5/12.

Suppose the prices of a certain model of new homes are normally distributed with a mean of 150,000 use the 68 9599.7 route to find the percentage of buyers who paid between 150,000 and 153,300 if the standard deviation is 1100

Answers

The percentage of buyers who paid between 150,000 and 153,300 is approximately 68% + 2.5% = 70.5%.

To solve this problem, we can use the properties of the normal distribution and the empirical rule (also known as the 68-95-99.7 rule) to estimate the percentage of buyers who paid between 150,000 and 153,300.

According to the empirical rule, given a normal distribution:

approximately 68% of the data falls within one standard deviation of the mean approximately 95% of the  three standard deviations of the mean, the data are contained.

In this case, we want to find the percentage of buyers who paid between 150,000 and 153,300, which is one interval of length 3300 above the mean. To use the empirical rule, we need to standardize this interval by subtracting the mean and dividing by the standard deviation:

z1 = (150,000 - 150,000) / 1100 = 0

z2 = (153,300 - 150,000) / 1100 = 3

Here, z1 represents the number of standard deviations between 150,000 and the mean, and z2 represents the number of standard deviations between 153,300 and the mean.

Since the interval we are interested in is within three standard deviations of the mean (z2 <= 3), we can use the empirical rule to estimate the percentage of buyers who paid between 150,000 and 153,300:

Approximately 68% of the buyers paid within one standard deviation of the mean, which is between 149,000 and 151,000 (using z-scores of -1 and 1).

Approximately 95% of the buyers paid within two standard deviations of the mean, which is between 148,000 and 152,000 (using z-scores of -2 and 2).

Therefore, the remaining percentage of buyers who paid between 152,000 and 153,300 is approximately (100% - 95%) / 2 = 2.5%.

So, the percentage of buyers who paid between 150,000 and 153,300 is approximately 68% + 2.5% = 70.5%.

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ill mark brainliest !

Answers

Answer:

Since the line is vertical and passes through the point (3, -5), it is a vertical line with undefined slope.

Step-by-step explanation:

This may be hard to put together, but I need help with an angle equation. I'm looking for example equations and how to do these types of equations. *please note that this equation is completely random and probably ends with an ugly number. it's just an example of a type of problem*

Answers

Example: (2x - 4) x=7 so (2x (x=7) - 4) =18

Can someone please answer and provide an explanation for these problems?

Answers

The area of the sector is: 21) 177.0 cm² 22) 58.6 in.²

The missing sides are: 23) 12     24) 8

How to Find the Area of a Sector of a Circle?

The area of the sector of any circle is given as:

Area = ∅/360 * πr², where r is the radius.

21. ∅ = 120°

r = 13 cm

Substitute:

Area = 120/360 * π * 13² = 177.0 cm²

22. ∅ = 105°

r = 8 in.

Substitute:

Area = 105/360 * π * 8² = 58.6 in.²

Since the lines appear tangents in the circles given, then the triangle formed is a right triangle, therefore, we will apply the Pythagorean Theorem in each case:

23. Missing side = √[(9 + 6)² - 9²]

Missing side = 12

24. Let the missing side be x. Therefore, we have:

12 + x = √(16² + 12²)

12 + x = 20

12 + x - 12 = 20 - 12

x = 8

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The photo is kinda blurry but please help me with it

Answers

The perimeter of rectangle M'N'O'P' is given as follows:

54 cm.

What is a dilation?

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The ratio between the areas is given as follows:

126/14 = 9.

The area is measure in square units, while the perimeter is measured in units, hence the ratio of the perimeters is the square root of the ratio of the areas, that is:

3.

Hence the perimeter of rectangle M'N'O'P' is given as follows:

3 x 18 = 54 cm.

Missing Information

The complete problem is:

Rectangle MNOP has a perimeter of 18 cm and an area of 14 cm2. After rectangle MNOP is dilated, rectangle M'N'O'P' has an area of 126 cm2. What is the perimeter of rectangle M'N'O'P'?

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Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra $22,000 over the next 3 years. What amount must be deposited quarterly into an account that earns 4.7% interest, compounded quarterly, in order to reach your goal? Round your answer to the nearest cent, if necessary.

Answers

The initial deposit needed for the account is given as follows:

$19,257.37.

What is compound interest?

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.

The parameters for this problem are given as follows:

[tex]A = 22000, t = 3, r = 0.0447, n = 4[/tex]

Hence the initial deposit P is obtained as follows:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]22000 = P\left(1 + \frac{0.0447}{4}\right)^{4 \times 3}[/tex]

1.142657P = 22000

P = 22000/1.142657

P = $19,257.37.

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Your brain needs caffeine! You decide to walk from home to the coffee shop located at point (-8,-5). What coordinate would you be standing on if you stood on a point “K” so that it directed the line segment in a ratio of 5:2?

Answers

The coordinates you would be standing on would be coordinate (-5.71, -3.57).

How to calculate the coordinates

To discover the arrangement of point "K" that partitions the line section interfacing the beginning point to the coffee shop in a proportion of 5:2, we are able to utilize the concept of the area equation.

We should expect the starting point to be meant as A with orchestrates (- x1, - y1), and the café is implied as B with works with (- x2, - y2). The ratio of 5:2 suggests that segment AB is divided into two parts and five parts, each accounting for 7 percent of the length.

The x-direction of point K can be determined as:

xK = (5 * x2 + 2 * x1)/7

Basically, the y-direction of point K can be determined as:

yK = (5 * y2 + 2 * y1) / 7

Stopping within the arranges of the coffee shop (-8, -5) as (-x2, -y2) and accepting the beginning point as the beginning (0, 0), we have:

xK = (5 * (-8) + 2 * 0) / 7 = -40/7 ≈ -5.71

yK = (5 * (-5) + 2 * 0) / 7 = -25/7 ≈ -3.57

Hence, in case you stood on point K, you'd be around at coordinate (-5.71, -3.57).

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Tommy looks around at an assembly. He notices his younger sister to his right and his older brother 4 meters ahead of him. If Tommy's brother and sister are 5 meters apart, how far apart are Tommy and his younger sister?

Answers

Answer: Tommy's sister is four meters away from him.

Step-by-step explanation:

If Tommy's older brother is 4 meters ahead and he is 5 meters from his sister,subtract 1 from that since it is described she is right next to him,and you get four.

This is my first time answering anyone so I hope it helps.

100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

Answers

The value of side TS is,

⇒ TS = 28

First, we are going to divide the figure and named new points X and Y as:

Now, we know that TS is the sum of TX and XS.

TS = TX + XS

Additionally, TX has the same length of HJ, so:

TX = HJ = 14

Now, we want to know the length of YK, and we can calculate it using the following equation:

LK = LY + YK

LY = HJ,

so, LY = 14

And, 42 = 14 + YK

42 - 14 = YK

28 = YK

Finally, since T and S are midpoints, the length of XS is the half of the length of YK. It means that XS is:

XS = YK/2

XS = 28/2

XS = 14

Therefore, TS is equal to:

TS = TX + XS

TS = 14 + 14

TS = 28

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Find the amount accumulated after
investing a principle P for t years at an
interest rate compounded k times per year.
P = $40,500 r = 3.8% t = 20 k = 12
Hint: A = P(1 + £)kt
A = $[?]

Answers

The solution is: the amount accumulated after investing a principle P for t years at an interest rate compounded k times per year is $86496.26.

Here, we know,

The whole sum borrowed (or invested), exclusive of interest and dividends.

We have,

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

The formula for the amount A accumulated after investing a principle P for t years at an annual interest rate r compounded k times per year is:

A = P * (1+r / k)^kt

given that,

P = $40,500 r = 3.8% t = 20 k = 12

Substituting the given values into this formula, we have:

A = $40,500 * (1 + 0.038 / 12)^12*20

A = $40,500 * 2.1357

A = $86496.2599

A = $86496.26 (rounded to the nearest cent)

Therefore,  the amount accumulated after investing a principle P for t years at an interest rate compounded k times per year is $86496.26.

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(Worth 100 Brainly points help fast)Solve the following system of equations and show all work.
y = 2x²
y = -3x -1

Answers

The solutions are : solution of the following system of equations are:

(- 1/2, 1/2)

(- 1, 2)

Here, we have,

The given system of equations is expressed as

y = 2x²- - - - - - - - - - - - - - -1

y = - 3x - 1- - - - - - - - - -- - - -2

We would apply the method of substitution by substituting equation 1 into equation 2. It becomes

2x² = - 3x - 1

2x² + 3x + 1 = 0

We would find two numbers such that their sum or difference is 3x and their product is 2x².

The two numbers are 2x and x. Therefore,

2x² + 2x + x + 1 = 0

2x(x + 1) + 1(x + 1) = 0

2x + 1 = 0 or x + 1 = 0

x = - 1/2 or x = - 1

Substituting x = - 1/2 into equation 1, it becomes

y = 2(-1/2)² = 1/2

Substituting x = - 1 into equation 1, it becomes

y = 2(-1)² = 2

Hence, The solutions are : solution of the following system of equations are:

(- 1/2, 1/2)

(- 1, 2)

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