What is the solution to the following system of equations
4x+2y=6
X-y=3
Answer:
The solution of the equation 4x + 2y = 6 and x − y = 3 will be D. (2, –1)
Step-by-step explanation:
4x + 2y = 6 ....… (1)
x − y = 3 …..... (2)
Example, for equation 2 is:
x - y = 3
x = 3 + y
Put in equation 1:
4(y + 3) + 2y = 6
4y + 12 + 2y = 6
6y = -6
y = -6/6
y = -1
We have the value of y, then the value of x will be:
x = 3 + y
= 3 + (-1)
= 3 - 1
= 2
So, the solution of the equation 4x + 2y = 6 and x − y = 3 will be (2, –1)
what is the solution to the number sentence 18= b/-3 -4
Answer:
b = -66.
Step-by-step explanation:
[tex]18 = \frac{b}{ - 3} - 4 \\ = - 3(18) = - 3 \times \frac{b}{ - 3} - 4( - 3) \\ = - 54 = b + 12 \\ = - 54 - 12 = b \\ = - 66 = b[/tex]
2. The diagram shows a wall where the two shaded parts are painted in yellow. 20 m 12 m 16 m 15 m 0.1 litre of paint is required to paint an area of 1 m². What is the volume, in litres, of yellow paint required to paint the two shaded parts?
Answer: The two shaded parts of the wall have a combined area of 20m * 12m + 16m * 15m = 240 + 240 = 480 square meters.
Therefore, the volume of yellow paint required is 480 * 0.1 = 48 litres.
Step-by-step explanation:
Becky is making fruit salad with strawberries and cherries. She has 1.84 pounds of strawberries and 2.62 pounds of cherries. She mixes the two fruits together and then scoops out 0.25 pounds of fruit salad for each serving. What is the greatest number of 0.25 pound servings Becky can make?
The greatest number of 0.25 pound servings Becky can make is 18.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Becky has 1.84 pounds of strawberries and 2.62 pounds of cherries.
Now, number of pounds of salads
= 1.84+2.62
= 4.46 pounds
Becky mixes the two fruits together and then scoops out 0.25 pounds of fruit salad for each serving.
So, the number of servings = 4.46/0.25
= 17.84
≈ 18
Therefore, the greatest number of servings is 18.
To learn more about the unitary method visit:
brainly.com/question/22056199.
#SPJ9
f the following, which is the smallest sample size that will result in a margin of error of no more than 5 percentage points? responses 73 73 97 97 271 271 385 385 1,537 1,537 skip to navigation
The smallest sample size that will result in a margin of error of no more than 5% for a 95% confidence interval is given as follows:
385.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is modeled as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
We have no estimate, hence we consider that:
[tex]\pi = 0.5[/tex]
The minimum sample size is obtained as n when M = 0.05, hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.05\sqrt{n} = 1.96 \times 0.5[/tex]
[tex]\sqrt{n} = 1.96 \times 10[/tex] (0.5/0.05 = 10).
[tex](\sqrt{n})^2 = (1.96 \times 10)^2[/tex]
n = 384.16
Hence rounded to 385, as a sample size of 384 would have a margin of error slightly above 0.05.
More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ1
A truck that can carry no more than 6500lb is being used to transport refrigerators and upright pianos. Each refrigerator weighs 300lb and each piano weighs 475lb. Write and graph an inequality to show how many refrigerators and how many pianos the truck could carry. Will 10 refrigerators and 9 pianos overload the truck? Explain.
Answer:
We can write an inequality to represent the weight that the truck can carry:
Weight of Refrigerators + Weight of Pianos <= 6500
Let x be the number of refrigerators and y be the number of pianos. Then we can write:
300x + 475y <= 6500
To determine if 10 refrigerators and 9 pianos would overload the truck, we can substitute the values into the inequality:
300 * 10 + 475 * 9 <= 6500
3000 + 4275 <= 6500
7275 <= 6500
Since 7275 is greater than 6500, this means that 10 refrigerators and 9 pianos would overload the truck.
Graphically, we can plot the points representing the weight of the refrigerators and pianos on the x-y plane, and shade the region below the line representing the inequality to show the combinations of refrigerators and pianos that would not overload the truck. Any point above the line would represent a combination of refrigerators and pianos that would overload the truck.
Hope it helps! : )
Answer:
7275lb
Step-by-step explanation:
Let R be the number of refrigerators and P be the number of pianos. The total weight of the load can be represented as:
Weight = 300R + 475P
The weight must be less than or equal to 6500lb, so we have the inequality:
300R + 475P <= 6500
To graph this inequality, we can first rewrite it in slope-intercept form:
475P <= 6500 - 300R
P <= (6500 - 300R) / 475
Next, we can plot the points (0, 13.68), (22, 0) on the coordinate plane, where (0, 13.68) corresponds to the y-intercept and (22, 0) corresponds to the x-intercept. The graph will be a line that starts at the y-intercept and goes down to the right, passing through (22, 0).
The truck could carry up to 22 refrigerators (when R = 22, P = 0), or up to 13.68 pianos (when R = 0, P = 13.68), or any combination of refrigerators and pianos that results in a weight of less than or equal to 6500lb.
As for the specific case of 10 refrigerators and 9 pianos, the weight can be calculated as:
Weight = 300 * 10 + 475 * 9 = 3000 + 4275 = 7275
This would overload the truck, as the weight of 7275lb is greater than the maximum allowed weight of 6500lb.
Assume d varies directly as t and d = 180 when t = 3. Find t when d = 390.
The value of t is 6.5. The value of the constant is 60
What varies directly?
The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation. For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation if b is directly proportional to a. (where k is a constant).
Given that d varies directly as t.
The relation between d and t is
d = kt.
Given that d = 180 when t = 3.
Putting d = 180 and t = 3 in d = kt
180 = 3k
Divide both sides by 3:
k = 180/3
k = 60
Putting k = 60 in d = kt:
d = 60t
Now putting d = 390 in d = 60t:
390 = 60t
60t = 390
Divide both sides by 60
t = 6.5
To learn more about varies, click on the below link:
https://brainly.com/question/13585916
#SPJ1
Bob is interested in examining the relationship between the number of bedrooms in a home and its selling price. After downloading a valid data set from the internet, he calculates the correlation. The correlation value he calculates is only 0.05.What does Bob conclude?
A correlation coefficient of 0.05 indicates a very weak positive correlation between the number of bedrooms and selling price.
When Bob calculates the correlation between the number of bedrooms in a home and its selling price and obtains a value of only 0.05, he can conclude that there is little to no linear relationship between the two variables.
Correlation is a statistical measure that indicates the degree to which two variables are related and the direction of the relationship. A correlation coefficient ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.
A correlation coefficient of 0.05 is very close to 0, indicating that there is almost no linear relationship between the number of bedrooms in a home and its selling price.
However, it is important to note that a low correlation coefficient does not necessarily mean that there is no relationship between the variables, as there could be a non-linear relationship or other types of relationships that cannot be captured by a correlation coefficient.
Therefore, Bob should further analyze the data set and explore other statistical measures or techniques to fully understand the relationship between the number of bedrooms in a home and its selling price.
To learn more about correlation click on,
https://brainly.com/question/30631861
#SPJ4
A bag contains three blue counters and four yellow counters. Two counters are removed without replacement and X is the number of blue counters removed.
This is a probability problem. To find the probability of removing two blue counters, we need to calculate the number of possible outcomes of removing two blue counters out of seven counters (3 blue and 4 yellow).
The number of possible outcomes of removing two blue counters is 3C2 = 3! / (2! * (3-2)!) = 3.
So, the probability of removing two blue counters is 3/7C2 = 3/21.
To find the probability of X being equal to 2, we need to calculate the probability of removing two blue counters.
Therefore, the probability of X being equal to 2 is 3/21.
Pls answer quickly, make sure to answer all parts
Find the area of the region bounded by the line y =3x -6 and line y=-2x+8 and
a) the x-axis. b) the y-axis. c) the line y=6. d) the line x=5.
The area of the region between line y =3x -6 and line y=-2x+8 and
the x-axis with the help of integration will be 2.88 sq units.
What exactly is integration?
The process of computing an integral is known as integration. Mathematicians utilise integrals to compute a variety of useful quantities such as areas, volumes, displacement, and so on. When we talk about integrals, we usually imply definite integrals. Antiderivatives are represented by indefinite integrals. Integration, along with differentiation, is one of the two major calculus concepts in mathematics (which measure the rate of change of any function with respect to its variables).
Integral Fundamental
A definite integral is one that has both upper and lower bounds. For X to lie, only a true line may be utilised. The Definite Integral is also known as a Riemann Integral.
From a to b, use ∫f(x)dx
indefinite integral
Integrals are defined without upper and lower limits. It looks like this:
A indefinite Integral is written as:
∫f(x)dx = F(x) + C
Where C might be any constant and the function f(x) is referred to as the integrand.
Now,
As given in image
Area of the region will be =∫3x-6 dx from x=2 to 2.8 +∫-2x+8 from x=2.8 to 4.
=(3x²/2-6x) from x=2 to 2.8 + (-2x²/2+8x) from x=2.8 to 4.
=3*0.8*0.8/2-6*0.8-2*1.2*1.2+8*1.2
=2.88 sq units.
Hence,
The area of the region between line y =3x -6 and line y=-2x+8 and the x-axis with the help of integration will be 2.88 sq units.
To know more about Integration visit the link
https://brainly.com/question/18125359?referrer=searchResults
#SPJ1
PLEASE HELP ASAP??!!!
Andrew factored the polynomial 3x²y 6xy² as 3xy(x – 2y). Determine
if he is correct. If he is incorrect, help him fix his error. If he is correct, explain what
he did to get his answer.
Answer:
He is correct.
Step-by-step explanation:
Shown in picture.
Hope its clear.
5. Lucy rode her bike around the block 4 times for a total of 1 mile yesterday. Today she wants to ride her bike 3_ 4 of a mile. How many times will she need to ride her bike around the block
Answer:
3
Step-by-step explanation:
1 loop around the block is 1/4 of a mile. multiply both sides by three. 3 loops is 3/4 of a mile.
answer the question below please
The total surface area is π[(4/3)x]² + π(4/3)x². The base area is greater than the lateral area.
What is an equation?An equation is an expression that shows how numbers and variables are related using mathematical operations. Equations can be linear, quadratic, cubic and so on.
Given the cone. The surface area (SA) is given by the equation:
SA = πr² + πrs
where r is the radius of the cone and s is the slant height.
Given that the slant height is x and the radius of the cone is 4/3 the slant height = (4/3)x
Hence:
SA = πr² + πrs
substituting:
SA = π[(4/3)x]² + π(4/3)x(x)
SA = π[(4/3)x]² + π(4/3)x²
The base area = π[(4/3)x]², the lateral area = π(4/3)x²
The base area is greater than the lateral area.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Determine if the side lengths 9, 9, and 17 form a triangle. If it is a triangle, classify it by its sides.
equilateral triangle
It's not a triangle.
scalene triangle
isosceles triangle
Answer:
It's not a triangle
Step-by-step explanation:
What you do is add the two smallest numbers and hope it's smaller than the longer side
9 + 9 = 18
The longest side is 17, which is LESS than 18. That means it's not a triangle
Answer:
It isnt a triangle
Step-by-step explanation:
I did the quiz and this was the answer.
Miss carol spendmore is not good at budgeting her money. She initially haf $500 in the bank. She lent her friend $65 this month and she notices that her bank account is declining by $15 dollard per day. Determine the rate of cHange
Miss Carol's bank account is losing money at a daily rate of $15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.
We must calculate Miss Carol's account balance's daily decline in order to ascertain the rate of change in her bank account.
Since Miss Carol lent her friend $65 this month, her account balance is reduced by $65, leaving her with $500 - $65 = $435.
The information that her account is losing $15 every day can then be put to use. We can write this as:
Rate of change = -$15 per day
The negative symbol signifies a declining amount on her account.
Therefore, Miss Carol's bank account is losing money at a daily rate of
$15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.
To learn more about account balance, visit the link below:
https://brainly.com/question/28699225
#SPJ4
6.RP.3d-2016 (#39) Fei Yen's dog eats 8 ounces of dog food each day. Fei Yen bought a 28-pound bag of dog
food. How many 8-ounce servings are in a 28-pound bag of dog food?
A 14
B 56
C 224
D 448
There are 56 servings in a 28 pound bag of dog food.
What is Unitary Method ?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Each day Fei yen's dog eat dog food = 8 ounces
Fei yen bought a 28 pound bag of dog food.
And we know that 1 pound = 16 ounces
Then ,the food in ounces
= 28 x 16
= 448 ounces
Now, the number of 8 ounces servings are in a 28 pound bag of dog food
= 448 / 8
= 56
Learn more about Unitary Method here:
https://brainly.com/question/2565841
#SPJ9
Evaluate the expression.
[2³x (225+9)]-33
[2³ x (225 +9)] - 33 =
(Simplify your answer.)
URGENT URGENT
Pls this is needed urgently
1.) Common ailments of senior citizens are arthritis, arteriosclerosis and loss of hearing. A survey of 200 senior citizens found that 70 had arthritis, 60 had arteriosclerosis, 80 had loss of hearing, 35 had arthritis and arteriosclerosis, 33 had arthritis and loss of hearing, 31 had arteriosclerosis and loss of hearing and 15 had all three. How many of the senior citizens in the survey had; (1). none of these ailments, (f), arthritis but neither of the other two ailments, (iii), exactly one of these ailments, (iv). arteriosclerosis and loss of hearing but not arthritis, (v). arteriosclerosis or loss of hearing but not arthritis, (vi). exactly two of these ailments?
(i) none of these ailments, 26
(ii) arthritis but neither of the other two ailments, 17
(iii) exactly one of these ailments, 102
(iv) arteriosclerosis and loss of hearing but not arthritis, 16
We can use a Venn diagram to solve this problem.
Let A, B, and C represent the events of having arthritis, arteriosclerosis, and loss of hearing, respectively. Then, the given information can be represented as:
A = 70
B = 60
C = 80
A ∩ B = 35
A ∩ C = 33
B ∩ C = 31
A ∩ B ∩ C = 15
Using these values, we can find the answers to the questions:
(i) The number of senior citizens with none of these ailments is the complement of the union of A, B, and C. That is:
n(A ∪ B ∪ C)' = n(S) - n(A ∪ B ∪ C)
= 200 - (70 + 60 + 80 - 35 - 33 - 31 + 15)
= 26
Therefore, 26 senior citizens had none of these ailments.
(ii) The number of senior citizens with arthritis but neither of the other two ailments is:
n(A) - n(A ∩ B) - n(A ∩ C) + n(A ∩ B ∩ C)' = 70 - 35 - 33 + 15
= 17
Therefore, 17 senior citizens had arthritis but neither of the other two ailments.
(iii) The number of senior citizens with exactly one of these ailments is the sum of the complements of the intersections of the events. That is:
n(A' ∩ B ∩ C') + n(A ∩ B' ∩ C') + n(A' ∩ B' ∩ C) = (200 - 60 - 31 - 15 - 33) + (200 - 70 - 31 - 15 - 33) + (200 - 70 - 60 - 15 - 35) = 102
Therefore, 102 senior citizens had exactly one of these ailments.
(iv) The number of senior citizens with arteriosclerosis and loss of hearing but not arthritis is:
n(B ∩ C) - n(A ∩ B ∩ C) = 31 - 15 = 16
Therefore, 16 senior citizens had arteriosclerosis and loss of hearing but not arthritis.
To know more about Venn diagram check:
https://brainly.com/question/29301560
#SPJ1
Sarah used an equation to solve the problem below. Justify each step of her work. About 11% of people are left handed. How many people would you expect to be left handed in a class of 30 students?
Answer:
To solve the problem, Sarah used the equation:
Left-handed people = (11/100) * Total people
Step 1: Plug in the total number of people (30) into the equation.
Left-handed people = (11/100) * 30
Step 2: Simplify the right side of the equation.
Left-handed people = (11/100) * 30
Left-handed people = 3.3
Step 3: Round the answer to the nearest whole number.
Left-handed people = 3
So, Sarah expects 3 people in a class of 30 to be left-handed. Each step of Sarah's work is justified because she used the percentage formula to find the number of left-handed people in a class and rounded the answer to the nearest whole number.
Explain how you would find the value of x.
Find the value of x
please help!!
The measure of the angle x in the figure is 55 degrees
How to find the value of x.From the question, we have the following parameters that can be used in our computation:
The polygon and the external angles
The sum of the exterior angles of a polygon is 360°.
Using the above as a guide, we have the following:
5 * x + x + 30 = 360
Evaluate the like terms
So, we have
6x = 330
Divide by 6
x = 55
Hence, the value of x is 55
Read more about angles at
https://brainly.com/question/25716982
#SPJ1
Rob and Gina bought a decorative side table to put against their wall The table is a regular hexagon
Regular hexagon is a closed shape polygon having six equal sides and six equal angles.
Regular HexagonA regular hexagon is defined as a closed 2D shape made up of six equal sides and six equal angles.
Each angle of the regular hexagon measures 120 degrees.
A hexagon has six angles and the sum of all six interior angles is 720 degrees. In a regular hexagon, each interior angle measures 120 degrees.
Polygon
A polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides. It does not have curved sides. The sides of a polygon are also called its edges. The points where two sides meet are the vertices of a polygon.
learn more about hexagon here:-
https://brainly.com/question/3295271
#SPJ4
Yousuff deposits $2,500 into a savings account that has a simple interest rate of 3.8%.
5A) How much interest will Yousuff make in one year? Show your work!
5B) How much interest will Yousuff make after 8 years? Show your work!
5C) After 8 years, how much money will Yousuff have in his account? Remember to include both the original principal money AND the interest she made.
Step-by-step explanation:
Principal = $2,500
Rate = 3.8%
5A). The interest Yousuff make in one year
Therefore Time = 1 year.
Simple interest
[tex] = \frac{pincipal \times time \times rate}{100 \\ } \\ = \frac{2500 \times 1 \times 3.8}{100} \\ = 25 \times 1 \times 3.8 \\ = 95 .[/tex]
Therefore the interest Yousuff make in one year = $95.
5B). Interest Yousuff make in after 8 years
the time = 8 years
the interest
[tex] = \frac{pincipal \times time \times rate}{100} \\ = \frac{2500 \times 8 \times 3.8}{100} \\ = 25 \times 8 \times 3.8 \\ = 200 \times 3.8 \\ = 760 [/tex]
Therefore the interest Yousuff make after 8 years = $760.
5C). Principal - interest that Yousuff made after 8 years.
$2500 - $ 760
= $ 1,740.
Need step-by-step explanation. Will mark the brainliest. Basically explained this equation as if i am a 5 year old child. (with step of course)
attached is solution. please excuse handwriting.
break up summation into two smaller summation,
then use summation formula for E (x)
Multiply left-parenthesis x plus 2 right-parenthesis left-parenthesis x minus 6 right-parenthesis
Answer options
A.
x squared minus 8 x minus 12
B.
x squared plus 8 x minus 12
C.
x squared minus 4 x minus 12
D.
x squared plus 4 x minus 12
E.
x squared minus 4 x plus 12
Answer:
[tex]x^{2}-4x-12[/tex]
Step-by-step explanation:
(x+2)(x-6)
STEP 1 - USE FOIL
(FOIL is a standard way of multiplying 2 fractions, just multiply in the following order):
Forward
Outside
Inside
Last
(x+2)(x-6) becomes this when you FOIL it:
[tex](x^{2} )(-6x)(2x)(-12)[/tex]
STEP 2 - COMBINE ALL THE TERMS
[tex]x^{2}[/tex] has to stay by itself because there are no other squares. [tex]-6x+2x=-4x[/tex] because you're adding two to -6 which effectively is 6 - 2 but you're adding a negative sign. And [tex]-12[/tex] stays the same because there are no x's in it.
STEP 3 - WRITE THE SOLUTION
All in all, the final solution, once you put everything together, is:
[tex]x^{2} -4x-12[/tex]
Help, I got 2262, I dunno what I'm doing wrong.
The two states will never have the same median house value.
How to model the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.The intercepts are given by the values of each home in 1950, thus:
Idaho: 35500.Delaware: 55000.The slopes are given by the average change over the 50 years, hence:
Idaho: m = (106300 - 35500)/50 = 1416.Delaware: m = (130400 - 55000)/50 = 1508.As the number of years must be positive, Delaware starts with the higher income and has a higher yearly increase, the two states will never have the same median house value.
Solving 35500 + 1416x = 55000 + 1508x, we would end up with a negative value of x.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
It is given that the volume of the cylinder and the cuboid are the same. Find the value of x and give your answer correct to two decimal places.
who can help me pls
Answer: Sure, I can help you with that!
Let's assume that the height of the cylinder is h and its radius is r. The volume of the cylinder can be calculated using the formula:
V = πr^2h
Similarly, let's assume that the length, width and height of the cuboid are l, w and h respectively. The volume of the cuboid can be calculated using the formula:
V = lwh
As the volume of the cylinder and the cuboid are the same, we can set the two expressions equal to each other:
πr^2h = lwh
Now, let's assume that the radius of the cylinder is equal to the length of the cuboid (r = l). This means that:
πl^2h = lwh
Solving for h, we get:
h = (πl^2)/w
Finally, substituting the value of h back into the original equation:
πr^2h = πl^2h = lwh
πr^2 = lwh/w = lw
r^2 = lw
r = sqrt(lw)
So, the value of x (the radius of the cylinder) can be found by knowing the length (l) and width (w) of the cuboid. To two decimal places, x = sqrt(lw).
Step-by-step explanation:
what is the surface area, in square centimeters, of a cylinder with height of 10 cm and a radius of 6 cm
The surface area of the given cylinder is 602.88 square centimeters.
What is the surface area of a cylinder?The surface area of the cylinder is: A = 2πr(r+h)
where 'r' is the radius of the base (circle) of the cylinder
'h' is the height of the cylinder
The cylinder with a height of 10 cm and a radius of 6 cm.
⇒ A = 2πr(r+h)
Here h = 10 cm and r = 6 cm
Substitute the known values in the above formula,
⇒ A = 2(3.14)(6)(6+10)
⇒ A = (12.56)(6)(16)
Apply the multiplication operation, and we get
⇒ A = 602.88
Therefore, the surface area of the given cylinder is 602.88 cm².
Learn more about the surface area of a cylinder here :
brainly.com/question/14827013
#SPJ1
Anita puts $300.00 into an account to use for school expenses. The account earns 2%
interest, compounded continuously. How much will be in the account after 8 years?
Use the formula A = Pet, where A is the balance (final amount), P is the principal (starting
amount), e is the base of natural logarithms (2.71828), r is the interest rate expressed as a
decimal, and it is the time in years.
Round your answer to the nearest cent.
The amount in the account after 8 years will be $352.05.
What is Compound Interest?Compound interest is when you receive interest on both your interest income and your savings.
Given:
P = $300
R= 2%
T = 8 years
We have to use the function
A = P[tex]e^{rt[/tex]
A = 300.00[tex](2.71828)^{(0.02)(8)[/tex]
A = $352.05
Learn more about Compound Interest here:
https://brainly.com/question/28642748
#SPJ1
someone help me asap
Given one point and a slope:
(-3, - 4) and m = - 5To graph the line plot the given point first.
Then find the second point, consider the slope by adding 1 to the x-coordinate and -5 to the y-coordinate, this gives us:
x = - 3 + 1 = - 2y = - 4 - 5 = - 9Next, plot the second point (-2, - 9).
Now connect the two pints and extend either side. This is the line you need.
Chords AB and CD intersect at E and AE = EB. A semicircle is drawn with diameter CD. EF, perpendicular to CD, meets this semicircle at E. Prove that AE = EF.
help me pls.
The proof that AE = EF is done from the congruency theorem of triangles and the Pythagorean identity.
How can it be proved that AE = EF?In order to prove that AE = EF, note that angle CEF is a right angle since EF is perpendicular to the diameter CD and intersects it at E.
Since AE = EB, triangles AEB and CED are congruent (SAS theorem)
Therefore, angle EAF is congruent to angle ECF.
Also, angle EAF is a right angle, since it is inscribed in a semicircle with a diameter CD.
Therefore, triangles EAF and ECF are similar by the Angle-Angle (AA) theorem.
Since they are similar, the ratio of corresponding side lengths is the same.
Since AE = EB, we have that:
AE / EF = EC / CF
But we also know that EC = ED + DC = ED + 2EF, since CD is the diameter of the semicircle and EF meets it at E perpendicularly.
Similarly, we have CF = CD + DF
CF = 2EF + DF, where DF is the other leg of the right triangle CDF.
Substituting these expressions for EC and CF in the above equation, we get:
AE / EF = (ED + 2EF) / (2EF + DF)
Simplifying this equation, we get:
AE / EF = (ED/EF) + 2 / (2 + DF/EF)
But ED/EF = sin(DEF) and DF/EF = sin(EFD) by the definition of sine in right triangle DEF. Since the angles DEF and EFD add up to 90 degrees, their sines are complementary.
Therefore, we have that:
ED/EF = cos(EFD) and DF/EF = sin(DEF)
Substituting these expressions in the above equation, we get:
AE / EF = cos(EFD) + 2 / (2 + sin(DEF))
But cos(EFD) + 2 = sin(DEF) (Pythagorean identity).
Therefore, we have:
AE / EF = sin(DEF) / (2 + sin(DEF))
Multiplying both sides by (2 + sin(DEF)), we get:
AE = EF
Learn more about Pythagorean identity at: https://brainly.com/question/10285501
#SPJ1
