The annual interest rate.
To find the annual interest rate r that will allow your balance to reach $2000 in 10 years, we need to use the formula for continuously compounded interest: A = Pert, where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the time in years.
We are given that P = $1000, A = $2000, and t = 10 years. Plugging these values into the formula, we get:
$2000 = $1000e10r
Dividing both sides by $1000, we get:
2 = e10r
Taking the natural logarithm of both sides, we get:
ln(2) = 10r
Dividing both sides by 10, we get:
r = ln(2)/10 ≈ 0.0693
Therefore, the annual interest rate r that will allow your balance to reach $2000 in 10 years is approximately 6.93%.
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Shawn’s science class starts at 11:25 a. M. It ends at 12:45 p. M. How long is Shawn’s science class?
Shawn’s science class takes 1 and half hour.
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.
Shawn’s science class starts at 11:25 a. M.
It ends at 12:45 p. M.
Now, to find the How long is Shawn’s science class we have to find the time difference as
= 12: 45 pm - 11: 25 am
So, From 11:25 am to 12:25 pm it is one hour and additional of 30 minutes or half an hour.
This, the class is 1 and half hour long.
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Kneaders in Lehi sold 4000 rolls at Thanksgiving time last year. This year they expect a 22% increase in sales...
How many rolls will Kneaders in Lehi bake this Thanksgiving rounded to the nearest whole roll?
Step-by-step explanation:
If Kneaders in Lehi sold 4000 rolls last year and expects a 22% increase in sales this year, the number of rolls they will bake this Thanksgiving can be calculated as follows:
Calculate the 22% increase in sales:
22% of 4000 = 0.22 x 4000 = 880
Add the increase to last year's sales to get the total expected sales this year:
4000 + 880 = 4880
Therefore, Kneaders in Lehi will bake approximately 4880 rolls this Thanksgiving rounded to the nearest whole roll.
Answer:
4,880 rolls, see explanation below :)
Step-by-step explanation:
1.22(4000)= 4,880
and you instantly get your answer.
if you don't understand I basically did 1.22 times 4000 and got 4,880.
Formula: X + %increase/decrease x orginal amount/amount sold last year of rolls, (we can assume there is an invisible 1 in front of the x)
Basically Everything Behind This, Kind of (sorry I'm not the best explainer! :( ;
Here in this case 22% as a decimal is 0.22, how we get to a decimal from a percent: 22 divided by a 100= 0.22. and we got the decimal for 22%!
So X + 0.22= 1.22, and remember the X has an invisible 1 in front of it. so 1 + 0.22= 1.22 in other words.
Now the other value we have is 4000, so we multiply it by 1.22 and get 4,880. And this is how we got to our answer.
The latest online craze is a new game, Khan on Seven. You get 100 points for playing the game. In addition, you get 50 points for each seven-letter word you make with the ten letters you receive. Sal wants to break the record, and he needs 18,000 or more points to do so. Write an inequality to determine the number of seven-letter words, w, Sal could make to break the record.
Graph the solution set to this inequality
The required inequality expression is 2 + w ≥ 360.
Inequalities:In mathematics, an inequality is a statement that compares two quantities or expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
An inequality states that one quantity is either less than or greater than the other, but not necessarily equal to it.
Here we have
You get 100 points for playing the game. In addition, you get 50 points for each seven-letter word you make with the ten letters you receive.
Sal wants to break the record, and he needs 18,000 or more points.
Let's assume Sal does 'w' number of seven-letter words
Then total points that Sal will gain = 100 + 50(w)
To break the record Sal wants 18000 points or more
=> 100 + 50w ≥ 18000
=> 2 + w ≥ 360
Therefore,
The required inequality expression is 2 + w ≥ 360.
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Write the transformed equation for f(x)-5, calling it h(x)
pls solve right away need desperately 20 point question
Transformed equation for f(x)-5 is the function h(x)=2x-4.
what is functionA functional equation in mathematics is, broadly speaking, an equation that has one or more functions as variable. A functional equation, however, is frequently used in a more narrow sense, where it refers to an equation that connects many values of the same function.
What is transformationAn equation that transforms into another equation and has roots that are the opposite of those in the given equation is said to be a transformation. To grasp the transformation equation, this transformation process must be made easy.
Given:f(x)=2x+1
Transforming the function f(x)-5, we get
h(x)=2x+1-5
h(x)=2x-4
h(x) is a function which is made by shifting f(x) 5 units downward.
Hence, transformed equation for f(x)-5 is h(x)=2x-4.
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2. In how many ways can the 18 members of a Boy Scout troop elect a president, a vice-president, and a secretary, assuming that no member can hold more than one office?
3. If a family has three children, find the probability that the two of the children are girls?
4. In how many ways can we seat 7 people at a round table with a certain 3 people side by side?
5. In testing an HP printer, the Quality Inspector found that 25% of the printers fail to pass the test
print. Of the next 15 printers tested, find the probability that fewer than 4 fail to pass the test print.
1. There are 4896 possible ways for the 18 members of a Boy Scout troop to elect a president, a vice-president, and a secretary, assuming that no member can hold more than one office.
2. The probability that two of the three children are girls is 3/8.
3. There are 144 possible ways to seat 7 people at a round table with a certain 3 people side by side.
4. The probability that fewer than 4 out of the 15 printers tested fail to pass the test print is 0.8539.
1. The number of ways to elect a president, vice-president, and secretary from 18 members is 18 * 17 * 16 = 4896. This is because there are 18 choices for president, 17 choices for vice-president (since one person has already been chosen for president), and 16 choices for secretary (since two people have already been chosen for the other offices).
2. The probability of having two girls out of three children is 3/8. This is because there are eight possible outcomes for the genders of three children (BBB, BBG, BGB, GBB, GGB, GBG, BGG, GGG), and three of these outcomes have two girls (BBG, BGG, GBG).
3. The number of ways to seat 7 people at a round table with a certain 3 people side by side is 4! * 3! = 144. This is because there are 4! ways to arrange the other 4 people around the table, and 3! ways to arrange the 3 people who are side by side.
4. The probability that fewer than 4 out of 15 printers fail to pass the test print is 0.8539. This can be found using the binomial probability formula: P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = (15 choose 0)(0.25^0)(0.75^15) + (15 choose 1)(0.25^1)(0.75^14) + (15 choose 2)(0.25^2)(0.75^13) + (15 choose 3)(0.25^3)(0.75^12) = 0.8539.
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what is 1/10 - 30 =
can some one help me
The simplified form of the expression ( 1/10 ) - 30 is -299/10 or -29 9/10.
What is the simplified form of the expression?Given the expression in the question;
( 1/10 ) - 30
To solve the expression (1/10) - 30, we need to first find a common denominator for the two terms in the expression.
The common denominator between 1/10 and 30 is 300, so we can rewrite the expression as:
(1/10) - 300/10
Now we can combine the two terms by subtracting the second term from the first:
(1/10) - 300/10 =
(1 - 300 )/10
-299/10
Convert -299/10 to mixed fraction
-29 9/10
Therefore, the solution to (1/10) - 30 is -299/10 or -29 9/10.
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Write a C++ program that prints a table showing the square and square root of x starting from 1 to 5, with an increment of 0.5. Display x in one decimal place, its square in 2 decimal places and its square root in 4 decimal places. All numbers are to be right justified. The columns of the table should have appropriate headings.
To write a C++ program that prints a table showing the square and square root of x starting from 1 to 5, with an increment of 0.5, you can use the following code:
#include <iostream>This program will print a table showing the square and square root of x starting from 1 to 5, with an increment of 0.5. The table will display x in one decimal place, its square in 2 decimal places and its square root in 4 decimal places, with all numbers being right justified. The columns of the table will have appropriate headings.
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The question is in the screenshot:
the complete question in the attached figure
Part 1) find sec (theta)
we know that
sec (theta)=1/ cos (theta)
cos (theta)=adjacent side angle theta/hypotenuse
adjacent side angle theta=5
hypotenuse=13
so
cos (theta)=5/13
sec (theta)=1/(5/13)-------> sec (theta)=13/5
the answer Part 1) is
sec (theta) = 13/5
Part 2)simplify sec(theta)*cos (theta)
sec (theta)=13/5
cos (theta)=5/13
so
sec(theta)*cos (theta)=(13/5)*(5/13)----> 1
the answer part 2) is 1
Part 3)simplify cot(theta)/cos(theta)
cot (theta)=5/12
cos (theta)=5/13
so
cot(theta)/cos(theta)=(5/12)/(5/13)----> 13/12
we know that
sin (theta)=opposite angle theta/hypotenuse
opposite side angle theta=12
hypotenuse=13
sin (theta)=12/13
csc (theta)=1/sin (theta)------> csc (theta)=1/(12/13)----> csc (theta)=13/12
therefore
cot(theta)/cos(theta)=csc (theta)
the answer Part 3) is
csc (theta)
Part 4)simplify cot(theta)*sin(theta)
cot (theta)=5/12
sin (theta)=12/13
so
cot(theta)*sin(theta)=(5/12)*(12/13)----> 5/13
cos (theta) =5/13
therefore
cot(theta)*sin(theta)=cos (theta)
the answer part 4) is
cos (theta)
What are the quotient and remainder when 3x^(4)-x^(2) is divided by x^(3)-x^(2)+1 ?
The quotient and remainder when 3x^(4)-x^(2) is divided by x^(3)-x^(2)+1 is x+1 and 2x^2-3, respectively.
To find the quotient and remainder, use long division. First, divide the leading terms of both polynomials. 3x^4 divided by x^3 gives x.
Next, multiply the quotient by the divisor and subtract from the dividend. x(x^3-x^2+1) subtract from 3x^4-x^2 gives x+1.
Finally, divide the remainder by the divisor to get the remainder. x+1 divided by x^3-x^2+1 gives 2x^2-3. Therefore, the quotient and remainder when 3x^(4)-x^(2) is divided by x^(3)-x^(2)+1 is x+1 and 2x^2-3, respectively.
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A car factory made 24 cars with a sunroof and 18 cars without a sunroof. What is the ratio of the number of cars with a sunroof to the total number of cars?
Answer:
4:7
Step-by-step explanation:
We know
A car factory made 24 cars with a sunroof and 18 cars without a sunroof.
What is the ratio of the number of cars with a sunroof to the total number of cars?
We find the total number of cars by taking
24 + 18 = 42 cars
The ratio of the number of cars with a sunroof to the total number of cars is
24:42
Simplify by 6, we get the ratio
4:7
"1.find the result of 4/5-1/3-1/15
a.1/5
b. 2/3
c. 7/15
d. 3/4
e.4/5"
Answer:
See below.
Step-by-step explanation:
We are asked to find the result of the expression.
We have 3 proper fractions, and they don't have a common denominator.
Meaning, that in order to simply subtract the Numerators, we should have the same Denominator for each.
We can find the Denominator simplify by finding the LCM.
What is the Least Common Multiple (LCM)?
The LCM is the smallest multiple that 2 or more numbers share.
We can easily find the LCM by making a list of numbers that adds the number to itself. The previous explanation is simpler, but what really is happening is we're multiplying the number with a number that grows by 1 each time; A common multiple.
The list should look like;
[tex]4; 4 \times 1 ,\ 4 \times 2, \ 4 \times 3, \ 4 \times 4, \ 4 \times 5, \ 4 \times 6, \ 4 \times 7.\\4; 4, 8, 12, 16, 20, 24, 28.[/tex]
Let's find the LCM of 5, 3, and 15:
[tex]5; 5, 10, [15], 20, 25\\3; 3, 6, 9, 12, [15]\\15; [15], 30, 45, 60, 75[/tex]
These numbers share a LCM of 15.
Multiply the fractions by setting up a proportion:
[tex]\frac{4}{5} -\frac{1}{3} -\frac{1}{15} \\\frac{4 \times 3}{5 \times 3} = \frac{12}{15} \checkmark \\\frac{1 \times 5}{3 \times 5} = \frac{5}{15} \checkmark\\\frac{1}{15} \ stays \frac{1}{15} \checkmark[/tex]
Subtract:
[tex]\frac{12}{15} - \frac{5}{15} - \frac{1}{15} = \frac{6 \div 3}{15 \div 3} = \frac{2}{5} .[/tex]
Your final answer is [tex]\frac{2}{5} .[/tex]
The correct answer is c. 7/15.
To find the result of 4/5 - 1/3 - 1/15, you need to first find a common denominator for all three fractions. The smallest common denominator for these fractions is 15.
Next, you need to convert each fraction to an equivalent fraction with a denominator of 15.
4/5 = 12/15
1/3 = 5/15
1/15 = 1/15
Now you can subtract the numerators of each fraction and keep the common denominator of 15.
12/15 - 5/15 - 1/15 = 6/15 - 1/15 = 5/15
Finally, you can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 5.
5/15 = 1/3
So the result of 4/5 - 1/3 - 1/15 is 7/15, which is answer choice c.
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The code for a lock consists of 4 digits. The last number cannot be 0 or 1. How many different codes are possible?
The total number of codes possible is 9 × 10 × 10 × 8.
To find the total number of codes possible, we need to multiply the number of choices for each digit.
For the first digit, there are 9 choices (0 is not allowed).
For the second and third digits, there are 10 choices each (0-9).
For the last digit, there are 8 choices (0 and 1 are not allowed).
So the total number of codes possible is 9 × 10 × 10 × 8 = 7200.
Therefore, there are 7200 different codes possible for the lock.
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Write an equation in slope intercept form for a line that passes through (10,-1) and a y intercept of -6
The equation in slope intercept form for a line that passes through (10,-1) and a y intercept of -6 is y = -1/10x - 6.
What is equation?Equation is a mathematical statement that expresses the equality of two expressions. It typically consists of two expressions that are separated by an equals sign (=), and the equation is true if and only if both expressions have the same value.
Slope intercept form is a way to express a linear equation in the form of y = mx + b, where m is the slope of the line and b is the y intercept. In this equation, m is equal to -1/10 (the slope of the line between the two given points) and b is equal to -6 (the given y intercept). This equation can be used to describe the line that passes through (10,-1) and has a y intercept of -6.
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QUESTION 2 Find a polynomial function with the following properties: It has a triple zero at x = -1, double zero at x = 1 and zero at x = 3, and passes through the point (2, 27)
The polynomial function is f(x) = (x + 1)³(x - 1)²(x - 3). A polynomial function is a mathematical expression that consists of variables, constants, and exponents that are combined using the operations of addition, subtraction, multiplication, and division.
The zeros of a polynomial function are the values of x that make the function equal to zero. The given polynomial function has a triple zero at x = -1,
double zero at x = 1, and zero at x = 3.
This means that the factors of the polynomial function are (x + 1)³, (x - 1)², and (x - 3).
Multiplying these factors together gives us the polynomial function:f(x) = (x + 1)³(x - 1)²(x - 3).
To find the value of the constant term, we can use the given point (2, 27). Substituting x = 2 and f(x) = 27 into the polynomial function gives us:
27 = (2 + 1)³(2 - 1)²(2 - 3)27
3³(1)²(-1)27 = 27(-1)27
= -27
To make the function pass through the point (2, 27), we need to multiply the polynomial function by -1:
f(x) = -1(x + 1)³(x - 1)²(x - 3)f(x)
= -(x + 1)³(x - 1)²(x - 3)
Therefore, the polynomial function is f(x) = -(x + 1)³(x - 1)²(x - 3).
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Let u = 2i + 3j and v = 4i + B j. Determine B such that:
a.) u and v are orthogonal.
b.) u and v are parallel.
c.) the angle between u and v is π/6
a) B = -8/3.
b) B = 3.
c) B = √(13 - 8) = √5.
a), u and v are orthogonal if and only if their dot product is 0. To calculate the dot product, multiply the corresponding components of u and v and then add them together. Therefore, u · v = 2i · 4i + 3j · Bj = 8 + 3B = 0, so B = -8/3.
b), u and v are parallel if and only if all components are equal. Therefore, 2i = 4i and 3j = Bj. To solve for B, we have B = 3.
c), the angle between u and v is π/6 if and only if their dot product is equal to the product of their magnitudes. The magnitude of u is |u| = √(2^2 + 3^2) = √13 and the magnitude of v is |v| = √(4^2 + B^2) = √(16 + B^2). To solve for B, we have u · v = √13 · √(16 + B^2) = 2cos(π/6), so B = √(13 - 8) = √5.
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What is the fourth vertex of the rectangle with vertices at (1,4), (1,−4), and (−5,−4)?
Group of answer choices
(4,4)
(4,-5)
(-5,-5)
(-5,4)
The fourth vertex of the rectangle is obtained as (-5, 4).
What is a rectangle?A quadrilateral with parallel sides that are equivalent to one another and four equal vertices is known as a rectangle. It is also known as an equiangular rectangle for this reason.
To find the fourth vertex of the rectangle, we can use the fact that opposite sides of a rectangle are parallel and equal in length.
The given vertices are (1, 4), (1, -4), and (-5, -4).
Apply the midpoint theorem of diagonals of a rectangle -
Midpoint of BD = Midpoint of AC
(x,y) = , [(1 - 5)/2 , (4 - 4)/2)
(x,y) = (-2, 0)
Now, the fourth vertex of the rectangle is -
(-2,0) = [(x + 1)/2 , (y - 4)/2)
-2 = (x + 1)/2
-4 = x + 1
x = -5
0 = (y - 4)/2
y = 4
So, the fourth vertex of the rectangle is (-5, 4).
Therefore, the points are is (-5, 4).
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Write the formula for the parabola that has x-intercepts (−2,0) and (4. 6,0), and y-intercept (0,1. 5)
The equation of the parabola can be written as
y=-0.16(x+2.0)(x-4.6)
A parabola is a curve made from the conic section whose eccentricity is 1 and is defined by the linear equation,
y=a(x-h)²+k, where a is an arbitrary constant and (h,k) denotes the vertex of the parabola.
According to the Intercept form of a parabola, if two x-intercepts (h1, 0), (h2, 0) are given, then the equation of parabola can be written as,
y=a(x+h1)(x-h2)
In this question,
h1 = 2.0
h2 = 4.6
So, the equation of the parabola would be,
y=a(x+2.0)(x-4.6)
Now, to find the value of the arbitrary constant "a", we can plug the point (0, 1.5) in this equation,
1.5 = a(0+2.0)(0-4.6)
1.5 = a(-9.2)
a = -0.16
So, the equation of the parabola can be written as,
y=-0.16(x+2.0)(x-4.6)
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A city has a population of 1.5 million people. If the monthly incomes of these inhabitants follow a normal distribution with a mean of £2,075 and a standard deviation of £162, how many people from this city will have a monthly income between £2,000 and £2,300?
a. Between 260,000 and 270,000 people
b. Between 620,000 and 630,000 people
c. None of the above
d. Exactly half of the population
e. Between 890,000 and 900,000 people
The correct answer is (e) Between 890,000 and 900,000 people.
To find out how many people from this city will have a monthly income between £2,000 and £2,300, we need to use the z-score formula:
z = (x - μ) / σ
where x is the value we are interested in, μ is the mean, and σ is the standard deviation.
First, we'll find the z-score for £2,000:
z = (2000 - 2075) / 162 = -0.46
Next, we'll find the z-score for £2,300:
z = (2300 - 2075) / 162 = 1.39
Using a z-table, we can find the corresponding probabilities for these z-scores. The probability for a z-score of -0.46 is 0.3228, and the probability for a z-score of 1.39 is 0.9177.
To find the probability of having a monthly income between £2,000 and £2,300, we need to subtract the smaller probability from the larger probability:
0.9177 - 0.3228 = 0.5949
This means that approximately 59.49% of the population will have a monthly income between £2,000 and £2,300. To find out how many people this represents, we'll multiply the probability by the total population:
0.5949 * 1,500,000 = 892,350
Therefore, the answer is (e) Between 890,000 and 900,000 people.
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he weighs 280 lbs. After 6 months, he now weighs 238 lbs. By what percent did his weight decrease?
The percent decrease in student's weight is 15%.
To calculate this, take the difference between his starting and ending weight and divide it by his starting weight. Multiply the result by 100 to express it as a percent.
To find the percent decrease in his weight, we can use the formula:
percent decrease = (original weight - new weight) / original weight * 100
First, let's plug in the given values:
percent decrease = (280 - 238) / 280 * 100
Next, we can simplify the numerator:
percent decrease = 42 / 280 * 100
Then, we can divide 42 by 280 to get 0.15:
percent decrease = 0.15 * 100
Finally, we can multiply 0.15 by 100 to get the percent decrease:
percent decrease = 15%
Therefore, his weight decreased by 15%.
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Write a number to complete each sentence. The polynomial 7x^(7)-9x^(5)+3x^(4)+12x+1 has roots.
The polynomial 7x^(7)-9x^(5)+3x^(4)+12x+1 has four roots. Roots are the values of x that make the polynomial equal to zero. To find these values, one can use a variety of methods, such as factoring, graphing, and the quadratic formula.
Factoring is the simplest method to use, and it involves breaking the polynomial down into simpler terms. In this case, the polynomial can be broken down into the product of two linear polynomials (7x^(7)-9x^(5) and 3x^(4)+12x+1). By setting each factor equal to zero and solving for x, you can find the roots.
Graphing is also a useful tool for finding the roots of a polynomial. By graphing the polynomial, you can see the x-intercepts, which are the values at which the graph crosses the x-axis. These are the roots.
Finally, the quadratic formula can be used to find the roots of this polynomial. This formula is a general solution for any quadratic equation, and it can be applied to the polynomial by replacing the coefficients of x^2 with those of x^7 and solving for x.
In conclusion, the polynomial 7x^(7)-9x^(5)+3x^(4)+12x+1 has four roots. These can be found using factoring, graphing, or the quadratic formula.
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PT2 really need help
The value of x for each rectangle is given as follows:
5) x = 7.
7) x = 10.
How to obtain the area of a rectangle?The area of a rectangle of base b and height h is given by the multiplication of these two dimensions, as follows:
A = bh.
Hence, for item 5, the value of x is given as follows:
3(5x - 2) = 99
5x - 2 = 33
5x = 35
x = 7.
For item 7, the value of x is obtained as follows:
3(4x - 3) = 111
4x - 3 = 37
4x = 40
x = 40/4
x = 10.
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Question 1 The weekly eaming X (in thousand AED) of a small store has the following cumulative distribution function. F(x)=0; for x<0 F(x) = x^3/64 for 04
a) Find the density function of X b) Find the expected value and the variance of X. c) lt is known that the weekly not profit. Y of this store, is 10% of the coming minus the fixed cost of one thousand AED. Compute the mean and the standard deviation of the net profit
Question 1
a) The density function of X is given by f(x)= 3x^2/64 for 0 ≤ x ≤ 4 and f(x) = 0 otherwise.
b) The expected value of X is E(X)= 3/2 and the variance of X is Var(X)= 3/8.
c) The mean of the net profit Y is given by E(Y) = 0.1E(X) - 1000 = -950 and the standard deviation is given by σY = 0.1σX = 0.1(√3/2) = 0.1825.
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Dan's reading group has read 168 books this year. His reading group has 6 members. Each member read the same amount of books. How many books did each member read?
Answer:
To find out how many books each member read, we can divide the total number of books by the number of members in the reading group:
168 books ÷ 6 members = 28 books per member
Therefore, each member of Dan's reading group read 28 books this year.
168/6 = 28
28 books per member
From a hot-air balloon, Violet measures a 27° angle of depression to a landmark
that's 790 feet away, measuring horizontally. What's the balloon's vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary. Do NOT say 402.53 - says it’s wrong.
Answer:
358.65
Step-by-step explanation:
sin27 = x/790
so x = sin27 × 790 = 358.65
The pizza shown has a radius of 13 cm. What is the approximate area of the pizza? (Use 3.14 for .)
Answer:
530.66 cm²
Step-by-step explanation:
Pizza has a circle shape
The formula for the area of the circle is
A = π · r²
r = 13 cm
π = 3.14
3.14 x 13² = 3.14 x 169 = 530.66 cm²
So, the area of the pizza is 530.66 cm²
Answer:
530.66cm^2
Step-by-step explanation:
since a pizza is in the shape of a circle, we can use the formula π[tex]r^{2}[/tex] and here the radius is r which is 13cm, and since you asked to use 3.14 as pi's value,
=3.14*(13^2)cm
=3.14*169cm
is approximately = 530.66cm^2
Help with geometry. How would I solve this problem with parallelograms?
Answer:
see attached
Step-by-step explanation:
Given some of the angles in a parallelogram with diagonals shown, you want the measures of missing angles.
Missing anglesThe measures of missing angles are found by making use of triangle and parallelogram angle relations:
the sum of angles in a triangle is 180°alternate interior angles are congruentangles of a linear pair are supplementaryadjacent angles of a parallelogram are supplementaryan exterior angle is equal to the sum of the remote interior anglesIn the attached diagram, the given angles are shown in red. The requested angles are shown in blue.
∠BDC = 40°, congruent to alternate interior angle ABD
∠DEA = 78°, supplementary to adjacent angle AEB
∠BDA = 70°, congruent to alternate interior angle DBC
∠BCD = 70°, supplementary to adjacent angle ABC = 40°+70°.
We can see here that solving the parallelogram, we have:
∠BDC = 40°, congruent to alternate interior ∠ABD ∠BDA = 70°, congruent to alternate interior ∠DBC ∠DEA = 78°, supplementary to adjacent ∠AEB∠BCD = 70°, supplementary to adjacent ∠ABC = 40°+70°.What is a parallelogram?A parallelogram is a quadrilateral (a polygon with four sides) in which opposite sides are parallel to each other. This means that the opposite sides of a parallelogram have the same slope and will never intersect, even if extended infinitely.
A parallelogram has four sides, four angles, and two pairs of opposite sides that are equal in length. The opposite angles of a parallelogram are also equal in measure.
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Keith will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $40 and costs an additional $0. 60 per mile driven. The second plan has no initial fee but costs $0. 80 per mile driven
200 miles is covered by Keith when the plans have the same price. When both plans have the same price, the cost is $160.
Two rents plans and the costs, the miles traveled by Keith when the two plans cost the same and the cost when the two plans cost the same, quadratic equations will be
Let the total miles covered for each plan be
The cost of the first plan would be
cost of the plan A=40+0.60x
The cost of the second plan would be
Cost of second plan=0.80x
If the two cost is the same, then
[tex]0.80x=40+0.60x[/tex]
Solve for x by collecting like terms
[tex]0.80x-0.60x=40[/tex]
[tex]0.20x=40[/tex]
[tex]x=\frac{40}{0.20}[/tex]
[tex]x=200[/tex]
The cost when the two plans cost the same would be
[tex]0.80x=0.80(200)=160[/tex]
or
[tex]40+0.60x=40+0.60(200)=160[/tex]
Hence, the miles covered when the plans cost the same is 200 miles.
The cost when the two plans cost the same is $160.
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mplify. Write "undefined" for expr [[-2,-2,4],[-6,-2,5],[-5,-1,5]]+[[5,2,2],[2,-4,-2],[4,5,-5]]
The simplified expression is [[3,0,6], [-4,-6,3], [-1,4,0]].
The given expression is [[-2,-2,4],[-6,-2,5],[-5,-1,5]] + [[5,2,2],[2,-4,-2],[4,5,-5]]. To simplify it, add the corresponding elements of each matrix:
[[-2,-2,4] + [5,2,2] = [3,0,6],
[-6,-2,5] + [2,-4,-2] = [-4,-6,3],
[-5,-1,5] + [4,5,-5] = [-1,4,0]]
Therefore, the simplified expression is [[3,0,6], [-4,-6,3], [-1,4,0]].
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Question 19 (4 Points) Saving. Enter A Whole Number. If You Are "Charged" 3¢ For Each Use Of A Straightedge And 5¢ For Each Use Of A Compass, Performing The Cheapest) Straightedge And Compass Construction Of Two Perpendicular Straight Lines Will Cost You
A/ Any Time You Must Move The Straightedge Or Compass, You Incur A New Charge.
The cheapest straightedge and compass construction of two perpendicular straight lines will cost you 11¢. This is because each use of the straightedge costs 3¢, and each use of the compass costs 5¢. Therefore, it takes three uses of the straightedge (3 x 3¢ = 9¢) and two uses of the compass (2 x 5¢ = 10¢) to create the two perpendicular straight lines, for a total of 11¢. So it will cost you 11¢
To create the perpendicular lines, first move the straightedge to create a line segment with one endpoint at the origin. Next, place the compass at one endpoint of the line segment and draw an arc with the desired radius, cutting the line segment at another point. Then, repeat this process with the straightedge and compass, but with the compass at the new endpoint and draw a perpendicular arc, intersecting the original arc. This will create the two perpendicular lines.
Each time you move the straightedge or compass, you incur a new charge. As outlined above, it will take three moves of the straightedge and two moves of the compass, for a total of five moves and a cost of 11¢.
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Identify the initial value and rate of change for the graph shown. (4 points) A coordinate plane graph is shown. A line passes through the y-intercept at 1 and through the point 5 comma 4. a Initial value: 1, rate of change 3 over 5. b Initial value: 3 over 5., rate of change: 0 c Initial value: 1, rate of change 5 over 3. d Initial value: 5 over 3., rate of change: 0
The correct answer is c: Initial value: 1, rate of change 5 over 3. In this case, the change in y is 3 (from 1 to 4) and the change in x is 5 (from 0 to 5).
What is a linear equation?A linear equation is an equation that describes a straight line when it is graphed. It has the form y = mx + b, where m is the slope of the line and b is the y-intercept. Linear equations are used to describe many real-world situations, such as the height of a ball thrown in the air, the distance traveled by a car, or the height of a person over time.
This question is asking for the initial value and rate of change for a linear equation. The initial value is the y-intercept, which is the point at which the line crosses the y-axis. In this case, the y-intercept is 1, so the initial value is 1. The rate of change is the slope of the line, which can be found by calculating the change in y over the change in x. In this case, the change in y is 3 (from 1 to 4) and the change in x is 5 (from 0 to 5). Therefore, the rate of change is 5 over 3, so the correct answer is c: Initial value: 1, rate of change 5 over 3.
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