Answer:
b) The bond Sandy purchased has a face value of $2500 and a coupon rate of 7%. The coupon rate is the interest rate paid on the bond, which is typically paid semiannually. To find how much interest Sandy will receive semiannually, we can use the formula:
Interest = Face value x Coupon rate / 2
Interest = $2500 x 7% / 2 = $87.50
So Sandy will receive $87.50 in interest semiannually from the bond.
c) The fund Sandy invested in is expected to grow by 3.5% per year. To find how long it will take for the fund to be worth $10,000, we can use the formula:
Future value = Present value x (1 + Interest rate)^Years
We can solve for Years by dividing both sides of the equation by the present value and taking the natural logarithm of both sides:
Years = ln(Future value/Present value) / ln(1 + Interest rate)
Years = ln(10000/5000) / ln(1.035)
Years = 7.19
Therefore, the fund will take about 7.19 years to be worth $10,000.
d) Sandy's gross annual income is $51,350. She is paid biweekly, and 5% of her paycheck is deducted for her 403(b). Her employer matches her deduction, up to 4%. To find how much is deposited into Sandy's 403(b) each payday, we can use the following formula:
Contribution = (Gross pay x Contribution rate) + (Employer match x Employee contribution)
Gross pay = $51,350/26 (for bi-weekly paycheck) = $1977.50
Contribution = ($1977.50 x 5%) + ($1977.50 x 5% x 4%) = $98.87
So, $98.87 is deposited into Sandy's 403(b) each payday.
A car dealership pays a wholesale price of $14,000 to purchase a vehicle. They sell the car for $16,100.
Answer:
15%
Step-by-step explanation:
markup = 16100 - 14000 = 2100
percent markup = 2100/14000 × 199% = 15%
Answer: The percent markup is 15%.
Polynominal 2x ^ 2 - 2 3x - 9 Name Using Degree Name Using Number of Terms - 3i ^ 2 - 6i + 9
Given polynomials are Binomial and Trinomial.
What are polynomials?
Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. An example of a polynomial with one variable is x^2+x-12. In this example, there are three terms: x^2, x and -12.
Based on the number of terms present in the expression, it is classified as
Monomial:-A monomial is an expression which contains only one term. For an expression to be a monomial, the single term should be a non-zero term. A Examples of monomials are: 5x,3.
Binomial:-A binomial is a polynomial expression which contains exactly two terms. A binomial can be considered as a sum or difference between two or more monomials. Examples of binomials are:
– 5x+3, 6a^4 + 17x.
Trinomial:-A trinomial is an expression which is composed of exactly three terms. A Examples of trinomial expressions are:
– 8a^4+2x+7, 4x^2 + 9x + 7.
Now,
Given polynomials are 2x ^ 2 - 2, 3x - 9, - 3i ^ 2 - 6i + 9.
As the number of terms in first two polynomials is 2, they are binomial.
and the number of terms in third polynomial is 3, it is trinomial.
hence,
Given polynomials are Binomial and Trinomial.
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How many square feet of outdoor carpet will we need for this hole?
The area of carpet that will be needed for the hole is 6 square feet
What is area off a rectangle?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
The hole has a rectangular shape.
Therefore the area of the hole =l×w
length = 3ft
width = 2ft
area of the hole = 3×2 = 6 squared feet
therefore the area of the carpet that will be needed for the hole is 6 square feet
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write a function g(x) that transforms the function f(x)=4 square root x +1 such that f(x) is horizontally stretched by a factor of 5, reflected across the x-axis, then translated down 5.
Answer:
[tex]g(x)=-4\sqrt{\dfrac{x}{5}}-6[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=4\sqrt{x}+1[/tex]
1. Horizontal stretch
[tex]f\left(\dfrac{1}{a}x\right) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $a$}.[/tex]
Therefore, if f(x) is horizontally stretched by a factor of 5:
[tex]\implies f\left(\dfrac{1}{5}x\right)=4\sqrt{\dfrac{x}{5}}+1[/tex]
2. Reflection across the x-axis
[tex]-f(x)\implies f(x) \: \textsf{reflected in the $x$-axis}.[/tex]
Therefore, if f(x/5) is reflected in the x-axis:
[tex]\begin{aligned}\implies -f\left(\dfrac{1}{5}x\right)&=-\left(4\sqrt{\dfrac{x}{5}}+1\right)\\\\&=-4\sqrt{\dfrac{x}{5}}-1 \end{aligned}[/tex]
3. Translation
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]
Therefore, if -f(x/5) is translated 5 units down:
[tex]\begin{aligned}\implies -f\left(\dfrac{1}{5}x\right)-5&=-4\sqrt{\dfrac{x}{5}}-1 -5\\\\&=-4\sqrt{\dfrac{x}{5}}-6\end{aligned}[/tex]
Therefore:
[tex]g(x)=-4\sqrt{\dfrac{x}{5}}-6[/tex]
Assuming that there are 95 million workers in the labor force in 2030 and 55 million retirees drawing Social Security, how many workers will be paying in per retiree at that time? Round to 2 decimal places.
However, the recent 2022 Social Security Trustees report finds that in 2034, retirees will start receiving a reduced benefit if Congress doesn't fix funding issues for the social program. In other words, Social Security will exist after 2034, but retirees will only receive 77% of their full benefit starting then.
What is Social Security?Social Security has provided financial protection for our nation's people for over 80 years. Chances are, you either receive Social Security benefits or know someone who does. With retirement, disability, and survivors benefits, Social Security is one of the most successful anti-poverty programs in our nation's history.We are passionate about supporting our customers by delivering financial support, providing superior customer service, and ensuring the safety and security of your information — helping you secure today and tomorrow.Social Security is committed to helping maintain the basic well-being and protection of the people we serve. We pay benefits to about 64 million people including retirees, children, widows, and widowers. From birth, to marriage, and into retirement, we are there to provide support throughout life's journey.To learn more about Social Security refer to:
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The curved surface area of a cylindrical lampshade is 3520cm₂ . if the height is 40cm calculate its radius (Take π = 3.142) PLS HELP
Answer:
Step-by-step explanation:
S= 2πrh
<=> 3520= 2x3.142xrx40
=> r ≈ 14
The radius of the cylindrical lampshade is approximately 13.98 cm.
The formula for the curved surface area of a cylinder is 2πrL, where r is the radius, L is the height and π is pi. Given that the curved surface area of a cylindrical lampshade is 3520 cm² and the height is 40cm.
We know that:
2πrL = 3520cm²
So we can solve for the radius by dividing both sides by 2πL:
r = 3520cm² / (2π * 40cm)
Substituting the value of pi we have
r = 3520cm² / (6.284 * 40cm) = 3520cm² / 251.36cm = 13.98cm
The radius of the cylindrical lampshade is approximately 13.98 cm.
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Simplificar -3+{4-2[6-3+4(5-7)]+3
Answer:
14
Step-by-step explanation:
Para simplificar esta expresión, debemos seguir el orden de las operaciones, también conocido como PEMDAS: paréntesis, exponentes, multiplicación y división (de izquierda a derecha), y suma y resta (de izquierda a derecha).
1. Comience por simplificar la expresión dentro de los paréntesis.
4-2[6-3+4(5-7)]
4-2[6-3+4(-2)]
4-2[6-3-8]
4-2[-5]
4+10 = 14
2. Ahora sustituya el valor simplificado dentro de los paréntesis en la expresión original:
-3+{14}+3
3. Ahora podemos sumar y restar de izquierda a derecha.
-3+14+3 = 14
Entonces, la expresión simplificada es 14.
Rachel bought and downloaded 6 songs on Friday and 8 more songs on Saturday.
Each song costs 2 dollars. Which expression represents the amount of money that
Rachel payed?
Answer:
Rachel bought 6 songs on Friday and 8 more songs on Saturday. The total number of songs she bought is 6+8 = 14
Rachel paid $2 for each song, the amount of money Rachel payed for all the songs is 14*2 = $28
Therefore, the expression that represents the amount of money that Rachel payed is "14*2 = $28" or simply "28"
- C
Given that sin(x)+cos(x)=2/5, compute the following.
sin^3(x)+cos^3(x)
PLEASE HELP URGENT
The computation of sin^3(x) + cos^3(x) is mathematically given as (2/5)(1 - sin(x)cos(x))
What is trigonometry?Generally, The study of the connections between the lengths of the sides of triangles and the angles of those triangles is the subject of the mathematical discipline known as trigonometry.
Applications of geometry to astronomical research gave rise to the discipline in the Hellenistic civilization during the third century B.C.
To compute sin^3(x) + cos^3(x), we can use the identity:
sin^3(x) + cos^3(x) = (sin(x) + cos(x))(sin^2(x) - sin(x)cos(x) + cos^2(x))
We know that sin(x) + cos(x) = 2/5, so we can substitute this into the above equation: sin^3(x) + cos^3(x) = (2/5)(sin^2(x) - sin(x)cos(x) + cos^2(x))
We also know that sin^2(x) + cos^2(x) = 1, so we can substitute this into the above equation:
sin^3(x) + cos^3(x) = (2/5)(1 - sin(x)cos(x))
Then we can simplify the above equation:
sin^3(x) + cos^3(x) = (2/5)(1 - sin(x)cos(x))
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Alton shoveled snow on 5/6 of his driveway before lunch. Then he shoveled 2/7 of it after lunch. How much more of his driveway did Alton shovel before lunch than after lunch?
The required difference is equal to 25x/42
What is a fraction in math?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Given here: Alton shoveled snow on 5/6 of his driveway before lunch. Then he shoveled 2/7 of it after lunch.
Let the total snow quantity be x then we have
Before lunch as = 5/6×x
=5x/6
After lunch = 5x/6 × 2/7
=5x/21
∴ Difference = 5x/6 - 5x/21
=35x-10x / 42
= 25x/42
Hence, The required difference is equal to 25x/42
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For how many years would $1,000 need to be invested at a 1% annual Interest rate to have an invest-
ment with a Future Value of $2,000?
Answer:
To find out how many years it would take to double an initial investment with a 1% annual interest rate, you can use the rule of 72. The rule of 72 states that you can divide 72 by the annual interest rate to find out how many years it would take to double an investment.
In this case, you would divide 72 by 1 to get 72 years. Therefore, it would take 72 years for an investment of $1,000 at a 1% annual interest rate to have a future value of $2,000.
ES = ___ units
Round your answer to the nearest tenth.
ES = 10.63 units
How to find the length of the line ?The length of the line segment connecting any two points represents the distance between them. There is just one line that connects the two places. Therefore, by measuring the length of the line segment that connects the two sites, the distance between them may be determined.
When given a straight line on a graph, you can find the length of this line by using the Distance Between Two Points Formula. This formula uses the vertices of the beginning and ending points of a straight line to find the length of the line, which is the distance between the two points.
The Distance Between Two Points Formula is:
= √(( x₂ – x₁ )² + ( y₂ – y₁) ²)
The vertices of the line ES are E ( -3, -4 ) and S ( 4, 4 ).
The distance is:
= √(( 4 – (-3) )² + ( 4 ( - 4 )) ²)
= 10. 63 units
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Terrence deposited $5,520 in a bank account that earned simple interest at an interest rate of 6%. How much interest, in dollars, was earned in 7 years? (Round your answer to the nearest cent.)
Answer:
$5520×6÷100×7=2318.40
One aircraft has a capacity of 64 more seats than a second
aircraft. A third aircraft has 152 seats less than twice the seating
capacity of the second aircraft. If their total number of seats is
1900, find the number of seats for each aircraft.
Using the provided conditions and values, This is solved with the concept of word problem, The answer is first, second and third aircrafts have 576,512 and 864 seats.
What is word problem?A word problem in mathematics is a problem that is written in natural language (i.e., words) rather than in mathematical notation. It presents a real-world scenario that requires the use of mathematical concepts and skills to solve. Word problems often involve finding unknown quantities based on given information, and they can be challenging because they require students to understand the problem and translate it into mathematical equations or formulas. They are often used in primary and secondary education to help students apply their math skills to real-world situations and develop critical thinking skills.
What do you mean by mathematical expression?A mathematical expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that represents a mathematical statement or equation. Mathematical expressions can be evaluated to find a numerical value. They can also be simplified by applying the order of operations (PEMDAS) to combine like terms or to remove unnecessary parentheses. Additionally, mathematical expressions can also be used to represent the relationship between different variables.
Let x be the number of seats on the second aircraft. Then, the first aircraft has x+64 seats and the third aircraft has 2x-152 seats.
We know that the total number of seats for all three aircraft is 1900, so we can set up the following equation:
x + (x+64) + (2x-152) = 1900
Solving this equation gives us x = 512, which means the second aircraft has 512 seats. We can then use this information to find the number of seats for the other two aircraft:
First aircraft: 512 + 64 = 576 seats
Third aircraft: 2(512) - 152 = 864 seats.
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I need help on this question please and thank you
The missing angle x of the interior angles of the quadrilateral is; x = 40°
How to find the angles in a quadrilateral?The sum of interior angles of a quadrilateral is 360°. Now, we are given the interior angles of this quadrilateral as;
(2x + 20)°
2x°
2x°
(2x + 20)°
Thus;
(2x + 20)° + (2x + 20)° + 2x° + 2x° = 360°
8x + 40 = 360
8x = 360 - 40
8x = 320
x = 320/8
x = 40°
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Hi please help me with this project I really need help I!!!!
6. The measure of angle BEC is 48°
7. The measure of angle 1 is 41°
8. The value of x is 12
The measure of angle UST is 36°
6. The angles AEB and BEC form a straight line whose angle measure is 180°.
So that,
∠AEB + ∠BEC = 180°
132° + ∠BEC = 180°
∠BEC = 180° - 132°
∠BEC = 48°
7. The angles 1 and 5 form a right angle whose measure is 90°.
So that,
∠5 + ∠1 = 90°
49° + ∠1 = 90°
∠1 = 90° - 49°
∠1 = 41°
8. The angles RSU and UST form a right angle whose measure is 90°.
∠RSU + ∠UST = 90°
(5x - 6)° + (2x + 12)° = 90°
(7x + 6)° = 90°
7x° = (90 - 6)°
7x° = 84°
x = 12
∠UST = (2x + 12)°
∠UST = (2(12) + 12)°
∠UST = (24 + 12)°
∠UST = 36°
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please answer a, b and c please! tysm
a) The increasing line y = 2x is plotted on the graph given at the end of the answer.
b) The horizontal line y = 3 is plotted on the graph given at the end of the answer.
c) The point of intersection of the two graphs is given as follows: (1.5, 3).
How to plot the graph of the functions?The increasing line is given as follows:
y = 2x.
Hence we plot a few points of coordinate (x,y), from the numeric values of the function, and connect them through a line.
The numeric values of the function are given as follows:
x = -2: y = 2(-2) = -4.x = -1: y = 2(-1) = -2.x = 0: y = 2(0) = 0.x = 1: y = 2(1) = 2.x = 2: y = 2(2) = 4.x = 3: y = 2(3) = 6.The horizontal line is given as follows:
y = 3.
Meaning that a single horizontal line through y = 3 is traced, for which we are going to use the same domain as the increasing line.
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Carter has a collection of 200 coins. How many coins represent 25% of his collection?
1. On June 10, Bertha Wooten deposited $8,241.78 in a
that pays 5.5% interest compounded
savings account daily. How much interest will the money earn in 31 days?
Answer:
To calculate the interest earned on an investment, we can use the formula:
A = P(1 + r)^t
Where A is the amount in the account after time t, P is the initial principal or deposit, r is the interest rate, and t is the time in years.
In this case, the initial deposit is $8,241.78, the interest rate is 5.5% (or 0.055 as a decimal), and the time is 31 days.
Since the interest is compounded daily, we need to calculate the number of compounding periods for 31 days, which is 31 days.
Therefore, the formula becomes:
A = 8241.78(1+0.055)^31
To calculate the interest earned, we will subtract the initial deposit from the final amount in the account
Interest = A - P
So the interest earned in 31 days will be:
$8241.78 * (1+ 0.055)^31 - $8241.78 = $35094.06
its math's question pleases help me to solve
The domain of the composite function f(g(x)) is equal to (x - 2)/(4 + 4x).
What is composite functionA function is composite when the co- domain of the first mapping is the domain of the second mapping
We shall evaluate the domain of the function f(g(x)) as follows:
f(g(x)) = 1 ÷ 12/[(x - 2) + 4]
f(g(x)) = 1 ÷ [12 + 4(x - 2)]/(x - 2) {simplify the denominator to a single fraction}
f(g(x)) = 1 ÷ (12 + 4x - 8)/(x - 2) {open bracket for 4(x - 2)}
f(g(x)) = 1 ÷ (4 + 4x)/(x - 2) {simply like terms}
f(g(x)) = 1 × (x - 2)/(4 + 4x) {changing division to multiplication}
f(g(x)) = (x - 2)/(4 + 4x)
Therefore, the result (x - 2)/(4 + 4x) is the domain of the composite function f(g(x)).
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Can someone help me with this word problem? The answer is supposed to be 3 in. but I don't know how to get there.
The border should be 6 inches wide.
What is area?The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.
Given that, A picture is to be put on a poster board that is 18 in. by 22 in. there is to be an even amount of poster board around the picture, the area of the picture is 192 in.²
Let the marginal space left is x in
Therefore,
(18-x)(22-x) = 192
396 -18x - 22x + x² = 192
x² - 40x + 204 = 0
Factorizing the expression, we get,
x = 34 or x = 6
(Note :- Neglecting 34 because 34 is grater than the dimensions given)
Therefore, the marginal space is 6 inches.
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An amount of money is deposited in an account that pays 8% annual interest that is compounded 4 times per year.
How long will it take for the amount to triple? (round to 3 decimal places)
How long will is take for the amount to triple if the interest is compounded continuously? (round to three decimal places)
let's take it from the basic one dolla!! So how long for one dolla to turn into 3?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 3\\ P=\textit{original amount deposited}\dotfill &\$1\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &4\\ t=years \end{cases}[/tex]
[tex]3 = 1\left(1+\frac{0.08}{4}\right)^{4\cdot t} \implies 3=1.02^{4t}\implies \log(3)=\log(1.02^{4t}) \\\\\\ \log(3)=t\log(1.02^{4})\implies \cfrac{\log(3)}{\log(1.02^{4})}=t\implies \stackrel{years}{13.870\approx t} \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 3\\ P=\textit{original amount deposited}\dotfill & \$1\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years \end{cases} \\\\\\ 3 = 1e^{0.08\cdot t} \implies \log_e(3)=\log_e(e^{0.08t})\implies \log_e(3)=0.08t \\\\\\ \ln(3)=0.08t\implies \cfrac{\ln(3)}{0.08}=t\implies \stackrel{years}{13.733\approx t}[/tex]
celestine invested 1500000 simple interest at a rate of 5% per annum which amounted to 2000000. how long will it take in this investment.
The required it would take 6 years for the amount to be 2000000.
What is simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.
here,
Celestine invested 1500000 simple interest at a rate of 5% per annum which amounted to 2000000.
Amount = 20,000,00
Principal = 15,000,00
Rate = 5% = 0.05
Time = n years
Amount = Principal [1 + rate×time]
20,000,00 = 15,000,00 [1 + 0.05×n]
n = 6.6 years
Thus, the required, it would take 6 years for the amount to be 2000000.
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7) Yesterday, Cindy re-posted a meme on social media and tagged 3 of her friends. Today, each
of her 3 friends re-posts the meme and tags 3 of their friends. This pattern of re-posting and
tagging 3 friends continues for several days. How many people have re-posted the meme
after 8 days? (Hint: If this is geometric, you should write a formula to help answer the
question)
The people that have posted the meme after 8 days using the exponential equation y=t^3 will be 512.
What are Exponential Equations?
An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable. For example, 3^x = 81, 5^x - 3 = 625, 62^y - 7 = 121, etc are some examples of exponential equations. We may come across the use of exponential equations when we are solving the problems of algebra, compound interest, exponential growth, exponential decay, etc.
Now,
To find number of people who have re-posted
we need to make a exponential equation
Here, As cindy tags meme to 3 people in starting and they also tag 3 people in subsequent days, then equation will be y=t^3 where t=no of days.
No of people after 8 days,
y=8^3
y=512 (no of people after 8 days)
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This is an example of geometric growth, So after 8 days 6561 people will have re-posted the meme.
What is geometric growth and explanation of above answer? Geometric growth is a type of exponential growth where a quantity increases at a fixed rate multiplied by itself over time. It is represented by a geometric sequence, where each term is the previous term multiplied by a constant factor. It is commonly used to model population growth, compound interest, and viral spread of information.where each day the number of people who have re-posted the meme is multiplied by 3. The formula to calculate the total number of people who have re-posted the meme after 8 days is 3^8 = 6561 peopleTo learn more about geometric growth refer:
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Each row in the table shows how a picture was enlarged or reduced.
Drag each copy to its correct place in the table.
In the late afternoon, Tessa is standing next to an old maple tree in her backyard. Tessa's shadow is 2' 3" long, and the maple tree's shadow is 18' long. Tessa is 5' 8" tall.
How tall is the maple tree?
15ft
Step-by-step explanation:
bc I said so..............
Hi, can any of you help me with this circle question?
Answer:
We can use the formula for the area of a circle and the information provided to find the approximate area of the circle.
The formula for the area of a circle is A = πr², where r is the radius of the circle.
We know that the distance from the center of the circle to the chord AB is 6 and the length of the chord AB is 10.
We can use the Pythagorean theorem to find the radius of the circle.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
So, we can use this theorem to find the radius of the circle as follows:
r² = (length of the chord /2)² + (distance of the chord to the center)²
r² = (10/2)² + 6²
r² = 25 + 36
r² = 61
r ≈ 7.8
Now that we know the radius of the circle, we can use the formula for the area of a circle to find the area of the circle:
A = πr²
A ≈ π (7.8)²
A ≈ 191.8
The approximate area of the circle is 192 square units.
Which statements are always true regarding the diagram? Select three options.
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
Answer:
Step-by-step explanation:
m∠5 + m∠3 = m∠4 is always true, because in a triangle, the sum of all the angles is always 180°.m∠3 + m∠4 + m∠5 = 180° is always true, because in a triangle, the sum of all the angles is always 180°.m∠5 + m∠6 =180° is not always true, since it depends on the specific diagram and the measure of m∠6.
use logical equivalence theorem to verify the logical equivalence below
p ∨ q → r ≡ (p → r) ∧ (q → r)
By logical equivalence theorem, we find that composite proposition p ∨ q → r is equivalent to composite proposition (p → r) → (q → r).
How to demonstrate a logical equivalence by means of theorems
Propositions are structures that contains a truth value, and can be, but not exclusively, a sentence. Propositions can be simple or composite, that is, a combination of simple propostions and operators.
In this problem we must determine that a given composite proposition is equivalent to another composite proposition by means of logical equivalence theorem. First, write the complete proposition:
p ∨ q → r
Second, use a conditional formula:
¬ (p ∨ q) ∨ r
Third, apply the DeMorgan's theorem:
(¬ p ∧ ¬ q) ∨ r
Fourth, use distributive property:
(¬ p ∨ r) ∧ (¬ q ∨ r)
Fifth, use conditional formula once again:
(p → r) → (q → r)
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D The point-slope form of the equation of a straight line is y + 3 = −2/7 (x − 5) . What is the general form of the equation?
Answer:
Step-by-step explanation:
The general form of the equation for the line described by the point-slope form y + 3 = −2/7 (x − 5) is y = -2/7x + 19/7.
