PLEASE HELP PLEASE ASAP PLEASE HELP
What are the coordinates of each point after the quadrilateral RSTU is rotated 90 degrees about the origin?
Answers
The coordinates of each point after the quadrilateral RSTU is rotated 90 degrees about the origin are;
M = (1, 2)
N = (2, 4)
P = (4, 5)
Q = (3, 3)
What are the coordinates of each point?The coordinates of the quadrilateral RSTU is
R = (1, -2)
S =(2, -4)
T = (4, -5)
U = (3, -3)
When the quadrilateral RSTU is rotated 90 degrees about the origin, it forms the quadrilateral MNPQ which has the coordinates
M = (1, 2)
N = (2, 4)
P = (4, 5)
Q = (3, 3)
Read more on coordinates:
https://brainly.com/question/11337174
#SPJ1
Related Questions
On jeopardy during the month of September the champions Won a total of $694563 assuming that there were 22 jeopardy shows in September what was the average amount won each day by the champions
Answers
Answer:
To find the average amount won each day by the champions, we need to divide the total amount won by the number of days:
Average amount won each day = Total amount won / Number of days
Total amount won = $694,563
Number of days = 22
Average amount won each day = $694,563 / 22 = $31,611.95 (rounded to the nearest cent)
Therefore, the average amount won each day by the champions on Jeopardy in September was approximately $31,611.95.
Step-by-step explanation:
g(x)=-4x^2+36/x+3 What key features does f(x), shown in the graph, share with g(x), shown in the equation? Select three options.
Answers
The graph's function g(x) has a single x-intercept, a y intercept, a vertical asymptote, an oblique asymptote, and both.
Describe Asymptotes?Asymptotes are points along a line that a curve approaches but never touches. The term "asymptote" refers to the point at which a function's graph converges. Asymptotes are often not necessary when graphing functions.
There are three distinct asymptotes.
Asymptote horizontal (HA) - Given that it is horizontal, its equation has the form y = k. The horizontal asymptote is the point at which the function f(x) tends to zero.
As it is a vertical line, the vertical asymptote's equation has the form x = k. When the denominator of a rational function approaches towards 0, vertical asymptotes are defined.
The equation for the slanting asymptote (also known as the oblique asymptote) is y = mx + b since the line is inclined.
given the information,
Let's write the function as g. (x)
The value of g (x) is right now.
g (x) = ( -4x² + 36) / (x + 3)
We gain by simple.
g (x) = -4x² - 4×9) / (x + 3)
We gain more after additional simplification.
g (x) = -4 (x + 3) (x - 3) / (x + 3)
g (x) = -4x + 12
There is now a vertical asymptote for the function at (0, 12)
There is a horizontal asymptote for the function at (3, 0)
The function is so resolved.
To know more about asymptotes, visit:
https://brainly.com/question/27871406
#SPJ1
The complete question is:
G(x)=-4x^2+36/x+3
What key features does f(x), shown in the graph, share
with g(x), shown in the equation? Select three options.
at least one x-intercept
at least one y-intercept
Dan oblique asymptote
O a vertical asymptote
the domain of x
Answer:
Step-by-step explanation:
For problems 7-12, consider the sets below, and indicate if each statement is true or false.
A = {1, 2, 3, 4, 5} B = {1, 3, 5} C = {4, 6} U = {numbers from 0 to 10}
7. 3 ∊ B 8. 5 ∊ C 9. B ⊂ A 10. C ⊂ A 11. C ⊂ B 12. C ⊂ U
Using the sets from above, and treating U as the Universal set, find each of the following:
13. A ⋃ B 14. A ⋃ C 15. A ⋂ C 16. B ⋂ C 17. A c 18. B c
Answers
The correct statements are 7. 3 ∈ B, 9. B ⊂ A, 12. C ⊂ U
13. A ⋃ B = {1, 2, 3, 4, 5, } 14. A ⋃ C = { 1, 2, 3, 4, 5, 6}
15. A ⋂ C = { 4 } 16. B ⋂ C = { }
17. [tex]A^{c}[/tex] = {6, 7, 8, 9, 10} 18. [tex]B^{c}[/tex] = {0, 2, 4, 6, 7, 8, 9, 10}
What are sets:
In mathematics, a set is a collection of distinct objects, which are called its elements or members. These objects can be anything - numbers, letters, people, animals, or other sets.
Sets are typically denoted using curly braces, and the elements of the set are listed inside the braces, separated by commas.
Here we have
A = {1, 2, 3, 4, 5} B = {1, 3, 5} C = {4, 6} and U = {numbers from 0 to 10}
=> U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }
i. Indicate if each statement is true or false.
7. 3 ∈ B which means 3 belongs to set B
Since, set B = {1, 3, 5}
=> ∴ 3 ∈ B is true
8. 5 ∈ C which means 5 belongs to set C
The set C = {4, 6}
=> 5 ∈ C is false
9. B ⊂ A which means B is a subset of A and elements of B are belongs to set A.
Since elements of B are lies in set A
=> B ⊂ A is true
10. C ⊂ A which means C is a subset of A
Since all the elements of C are not lie in set A
=> C ⊂ A is false
11. C ⊂ B which means C is a subset of B
Since all the elements of C are not lie in set B
=> C ⊂ B is false
12. C ⊂ U which means C is a subset of U
Since all the elements of C are lies in U
=> C ⊂ U is true
13. A ⋃ B = {1, 2, 3, 4, 5} ∪ {1, 3, 5} = {1, 2, 3, 4, 5, }
14. A ⋃ C = {1, 2, 3, 4, 5} ∪ {4, 6} = { 1, 2, 3, 4, 5, 6}
15. A ⋂ C = {1, 2, 3, 4, 5} ⋂ {4, 6} = { 4 }
16. B ⋂ C = {1, 3, 5} ⋂ {4, 6} = { }
17. [tex]A^{c}[/tex] = The elements in the universal set but not in A = {6, 7, 8, 9, 10}
18. [tex]B^{c}[/tex] = The elements in universal set but not in B = {0, 2, 4, 6, 7, 8, 9, 10}
Therefore,
The correct statements are 7. 3 ∈ B, 9. B ⊂ A, 12. C ⊂ U
13. A ⋃ B = {1, 2, 3, 4, 5, } 14. A ⋃ C = { 1, 2, 3, 4, 5, 6}
15. A ⋂ C = { 4 } 16. B ⋂ C = { }
17. [tex]A^{c}[/tex] = {6, 7, 8, 9, 10} 18. [tex]B^{c}[/tex] = {0, 2, 4, 6, 7, 8, 9, 10}
Learn more about Subsets at
brainly.com/question/28666324
#SPJ1
Which expression represents the prime factorization of 192?
A. 2 x 2 x 2 x 2 x 12
B. 2 x 2 x 2 x 2 x 2 x 3
C. 3 x 2 x 2 x 2 x 2 x 2 x 2
D. 2 x 2 x 2 x 2 x 2 x 3 x 3
Answers
The expression represents the prime factorization of 192 is 2×2×2×2×2×2×3. Therefore, option C is the correct answer.
What is factorization?The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.
The given number is 192.
The prime factorization is process of writing the given number into product of prime numbers.
Here, 192= 2×2×2×2×2×2×3
Therefore, option C is the correct answer.
To learn more about the factorization visit:
https://brainly.com/question/26923098.
#SPJ1
The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume 360 days in a year.
P = $370, r = 2%, t = 2 years
Answers
Step-by-step explanation:
Using the formula for simple interest:
Simple Interest = P * r * t
where P is the principal, r is the rate of interest, and t is the time in years.
Substituting the given values:
Simple Interest = $370 * 0.02 * 2 = $14.80
Therefore, the simple interest owed for the use of the money is $14.80.
Kira works mowing lawns and babysitting. She earns $9.20 an hour for mowing and $7.50 an hour for babysitting. How much will she earn for 6 hours of mowing and 1 hour of babysitting?
Answers
Answer:
$62.70
Step-by-step explanation:
of means "x"
and means "+"
6 hours of mowing and 1 hour of babysitting
(6 hours of mowing) + ( 1 hour of babysitting)
6 hours of mowing
6 hours x mowing
6x9.20 = answer 1
1 hour of babysitting
1 hour x babysitting
1 x 7.50 = answer 2
add both answers together to get final answer
find x, show proofs
Answers
The side x of the similar triangle is 12.7 units.
How to find the side of a triangle?The triangles are similar triangle.
Two triangles are said to be similar when they have two corresponding angles congruent and the sides proportional.
Therefore, using the proportion
37- 5 / x = x / 5
Evaluate the difference of 37 and 5
32 / x = x / 5
Cross multiply the equation
x × x = 32 × 5
So, we have
x² = 160
Take the square root of both sides
x = √160
Evaluate the square roots
x = 12.6491106407
Hence, the value of x is x = 12.7 units (when approximated)
learn more on triangle here:
https://brainly.com/question/2773823
#SPJ1
7. A pot of water is heated to 200°F. The table shows typical temperature readings for the pot. The room temperature is 70°F.
After 5 minutes the pot of water is 164°F. How long will it take the water to cool to 150°F? Round to the nearest minute.
A. About 4 min
B. About 3 min
C. About 8 min
D. About 6 min
Answers
The amount of time it would take the water to cool to 150°F is: C. About 8 min.
How to find an equation of the line of best fit for the data?In this scenario, the time would be plotted on the x-axis of the scatter plot while the temperature would be plotted on the y-axis of the scatter plot.
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the time and temperature, an exponential equation for the line of best fit is given by:
[tex]y = 192e^{-0.028x}[/tex]
When temperature y = 150°F, the value of x (in minutes) can be calculated as follows:
[tex]150 = 192e^{-0.028x}[/tex]
ln(150/192) = -0.028x
x = -0.24686007793/0.028
x = 8 mins.
Read more on scatter plot here: brainly.com/question/28605735
#SPJ1
PLEASE HELP !!!! IM SO CONFUSED
Answers
For your question just change domain x=-4,-2,0,2,4 to the function y=-1/2x to find y and graph.
The question is present in the image
Answers
The value of variables are,
a = 0
c = 7
d = 2
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ [tex]\frac{32x^{4} y^{3} z^{- 6} }{(4x^{2} y^{-2} z^{-2})^2 } = \frac{Ax^ay^c}{z^d}[/tex]
Now, We can simplify as;
⇒ [tex]\frac{32x^{4} y^{3} z^{- 6} }{(4x^{2} y^{-2} z^{-2})^2 } = \frac{Ax^ay^c}{z^d}[/tex]
⇒ [tex]\frac{32x^{4} y^{3} z^{- 6} }{(16x^{4} y^{-4} z^{-4}) } = \frac{Ax^ay^c}{z^d}[/tex]
⇒ [tex]\frac{2x^0y^7}{z^2} = \frac{Ax^ay^c}{z^d}[/tex]
By comparing, we get;
a = 0
c = 7
d = 2
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
You write 6 3/10 pages of a report in 2 1/3 hours. What is the average number of pages you write per hour?
Answers
the answer is 2 5/14
Answer:
Step-by-step explanation:
To find the average number of pages written per hour, we need to divide the total number of pages written by the total time taken:
Total pages written = 6 3/10 = 63/10
Total time taken = 2 1/3 = 7/3
Average pages written per hour = Total pages written / Total time taken
= (63/10) / (7/3)
= (63/10) x (3/7)
= 9/2
Therefore, the average number of pages written per hour is 9/2, which is equal to 4.5 pages per hour.
To help pay for culinary school, Keiko borrowed money from her credit union.
She took out a personal, amortized loan for $50,000, at an interest rate of 5.5%, with monthly payments for a term of 10 years.
For each part, do not round any intermediate computations and round your final answers to the nearest cent.
If necessary, refer to the list of financial formulas.
(a) Find Keiko's monthly payment.
$0
(b) If Keiko pays the monthly payment each month for the full term,
find her total amount to repay the loan.
$0
(c) If Keiko pays the monthly payment each month for the full term,
find the total amount of interest she will pay.
$0
X
Answers
If to help pay for culinary school, Keiko borrowed money from her credit union:
a. Keiko's monthly payment is $542.63.
b. The total amount to repay the loan is $65,115.60
c. The total amount of interest she will pay is $15,115.60
What is the monthly payment?(a) To find Keiko's monthly payment, we can use the formula for calculating the monthly payment for an amortized loan:
P = (r * A) / (1 - (1 + r)^(-n))
Where:
P =Monthly payment
A= loan amount
r = Monthly interest rate
n = Total number of payment
Plugging in the values for Keiko's loan, we get:
P = $50,000
r = 0.055 / 12 = 0.00458
n = 10 * 12 = 120
P = (0.055/12 * $50,000) / (1 - (1 + 0.055/12)^(-120)) = $542.63
(b) If Keiko pays the monthly payment each month for the full term, the total amount she will repay the loan will be:
Total amount = Monthly payment * Total number of payments
= $542.63* 120 = $65,115.60
(c) If Keiko pays the monthly payment each month for the full term, the total amount of interest she will pay will be:
Total interest = Total amount - Loan amount
=$65,115.60 - $50,000 = $15,115.60
So, Keiko will pay a total of $15,115.60 in interest over the 10-year term of the loan.
Learn more about monthly payment here:https://brainly.com/question/2151013
#SPJ1
ANWSER QUICK
After a couple of years, you’ve decided to sell your house. You originally bought it for $250,000 and spent an additional $10,000 in renovations, Your realtor thinks you can sell it for $290,000.
Answers
The profit to be made by selling the house for $290000 is $30000
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
You originally bought it for $250,000 and spent an additional $10,000 in renovations, Hence:
Total money spent = $250000 + $10000 = $260000
The realtor thinks you can sell it for $290,000. Therefore:
Profit = $290000 - $260000 = $30000
The profit to be made by selling the house is $30000
Find more on equation at: https://brainly.com/question/2972832
#SPJ1
Which expression represents the distance between Q and R
Answers
Answer:
Translation
Step-by-step explanation:
Translation
Evaluate the given expression:
Answers
In answering the question above, the solution is The answer is s 4 = 632 expressions as a result.
what is expression ?In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.
Let's start by condensing the expression included within the summation:
[tex]2(3^n - 1) = 2*3^n - 2[/tex]
We may now enter the following expression in the original equation:
[tex]s_4[/tex] = 4 * ∑[tex](k=1[/tex]to [tex]4) 2(3^k - 1)[/tex]
[tex]s_4 = 4 * [2(3^1 - 1) + 2(3^2 - 1) + 2(3^3 - 1) + 2(3^4 - 1)]\\s_4 = 4 * [2(3^1 + 3^2 + 3^3 + 3^4) - 8]\\s_4 = 4 * [2(3^1 + 3^2 + 3^3 + 3^4) - 2^3]\\s_4 = 4 * [2(80) - 8]\\s_4 = 632[/tex]
The answer is s 4 = 632 as a result.
To know more about expressions visit :-
https://brainly.com/question/14083225
#SPJ1
Kevin put a deposit of 10% on his new car. The deposit was $4000, so how much does he still owe?
Answers
Answer:
3600
Step-by-step explanation:
Based on the given conditions, formulate: 4000 x ( 1 - 10\% )
Calculate the sum or difference:4000 x 0.9
Calculate the product or quotient:3600
get the result: 3600
Answer: 3600
-3 + ___= -1.9
What is in the missing blank
Answers
Answer:
1.1
Step-by-step explanation:
-3+1.9 =-1.1
-3+1.1=-1.9
Answer:
-3 + 1.1 = -1.9
Step-by-step explanation:
Let us assume that,
→ Missing number = m
Now we have to,
→ Find the required value of m.
Forming the equation,
→ -3 + m = -1.9
Then the value of m will be,
→ -3 + m = -1.9
→ m - 3 = -1.9
→ m = -1.9 + 3
→ [ m = 1.1 ]
Hence, the value of m is 1.1.
5x ^ 2 y^ prime prime +23xy^ prime +16.2y=0
Answers
Answer:
Step-by-step explanation:
5
What is the future value of a 10-year investment of $1200 at an APR of 7% compounded monthly?
Round to nearest cent
Answers
The future value of a 10-year investment of $1200 at an APR of 7% compounded monthly is $2366.84
what is compound interest ?
Compound interest is the interest earned on an initial deposit or investment, plus all the interest that has accumulated on it over time. It is interest calculated on both the principal amount and any interest earned from previous periods, which is added to the principal amount at the end of each compounding period.
[tex]FV = P * (1 + r/n)^{n*t}[/tex]
Where:
FV = Future Value
P = Principal or initial investment
r = Annual interest rate
n = Number of times interest is compounded per year
t = Time in years
According to the question:
In this case:
P = $1200
r = 7% = 0.07
n = 12 (compounded monthly)
t = 10
Plugging these values into the formula, we get:
[tex]FV = P * (1 + r/n)^{n*t}[/tex]
[tex]FV = 1200 * (1 + 0.07/12)^{12*10}[/tex]
[tex]FV = 1200 * (1.00583333)^{120}[/tex]
[tex]FV = 1200 * 1.97236812[/tex]
[tex]FV = 2366.84[/tex]
Therefore, the future value of a 10-year investment of $1200 at an APR of 7% compounded monthly is $2366.84 (rounded to the nearest cent).
To know more about compound interest visit:
https://brainly.com/question/20406888
#SPJ1
Pls Help! Will give brainliest!
Write the following linear equation in function notation. y = 2x + 5
(A.) f = 2x + 5
(B.) f(x) = 2x + 5
(C.) It is already written in function notation.
(D.) f(y) = 2x+ 5
Answers
The given expression is already written in function notation.
Solving linear equationFunction notation is a way of representing a mathematical relationship between two variables, where one variable (usually denoted as x) is the input and the other variable (usually denoted as y) is the output. In this case, y is a function of x, which means that the value of y depends on the value of x.
To write the linear equation y = 2x + 5 in function notation, we replace y with f(x) to get:
f(x) = 2x + 5
This means that f(x) is a function of x, where the output f(x) is equal to 2 times the input x plus 5. The variable f(x) represents the value of y for a given value of x.
Learn more on linear equation here: https://brainly.com/question/2030026
#SPJ1
ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST FOR ANSWER
Answers
I think it is C. but i am a little rusty
A shop employs one man and one woman as shop assistants. The man works for 10 hours per day and the woman for 8 hours per day, and their wages per hour are in the ratio 7:5 If the woman receives $24 per day, find the man's daily wage.
Answers
The man's daily wage is given as follows:
$42.
How to obtain the man's daily wage?The man's daily wage is obtained applying the proportions in the context of the problem.
Their wages per hour are in the ratio 7:5, hence the man's hourly wage is 7/5 of the woman's hourly wage, hence:
7/5 x 24/8 = 7/5 x 3 = 21/5 = $4.2 per hour.
The man works 10 hours a day, hence the daily wage is given as follows:
10 x 4.2 = $42.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Mica is going to buy a computer for $2,000. He
can finance it at the store for 14% interest for
2 years, or he can use his credit card at 21%
interest for 1 year.
1. Find the monthly payment for each option.
Answer in the box.
2. Find the total repayment for each option.
Answer in the box.
Answers
Answer: To find the monthly payment for each option, we can use the following formula:
Monthly Payment = Total Cost * (Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))
For the option to finance at the store for 2 years at 14% interest:
Total Cost = $2,000
Monthly Interest Rate = 14% / 12 = 0.011667
Number of Months = 2 years x 12 months/year = 24 months
Substituting these values into the formula, we get:
Monthly Payment = $2,000 * 0.011667 / (1 - (1 + 0.011667)^(-24)) = $95.13
Therefore, the monthly payment for financing at the store for 2 years at 14% interest is $95.13.
For the option to use his credit card at 21% interest for 1 year:
Total Cost = $2,000
Monthly Interest Rate = 21% / 12 = 0.0175
Number of Months = 1 year x 12 months/year = 12 months
Substituting these values into the formula, we get:
Monthly Payment = $2,000 * 0.0175 / (1 - (1 + 0.0175)^(-12)) = $185.44
Therefore, the monthly payment for using his credit card at 21% interest for 1 year is $185.44.
To find the total repayment for each option, we can multiply the monthly payment by the number of months:
For the option to finance at the store for 2 years at 14% interest:
Total Repayment = $95.13/month x 24 months = $2,283.12
Therefore, the total repayment for financing at the store for 2 years at 14% interest is $2,283.12.
For the option to use his credit card at 21% interest for 1 year:
Total Repayment = $185.44/month x 12 months = $2,225.28
Therefore, the total repayment for using his credit card at 21% interest for 1 year is $2,225.28.
Step-by-step explanation:
PLEASE HELPP!!!! DUE IN 2 HOURSSSS!!!!!!
5) Solve.
The altitude leg of a right triangle has a length of √32 cm. Its hypotenuse measures 9 cm.
How long is its base leg?
(A). b = 5cm
(B). b = 9cm
(C). b = 6cm
(D). b = 7cm
Answers
Answer:B
Step-by-step explanation:
Answer: D : 7cm
Step-by-step explanation:
Select which option is most appropriate for describing the number line below.
Answers
Answer:
Answer D is correct
Step-by-step explanation:
Quantitative data can be ___
O discrete
O continuous
O discrete or continuous
O none of the above
Answers
Answers:
Quantitative data can be discrete or continuous
Step-by-step explanation:The Qualitative data are also called categorical or attribute data deals with characteristics and descriptors that can't be easily measured but can be observed subjectively. We can say that smells tastes textures attractiveness and color are all examples of qualitative data. We can see that qualitative data are not numerical.for example, dimensions such as height, width, and length, temperature and humidity, prices, area and volume. The Discrete data is a count that cannot be made more precise. Continuous data could be divided and reduced to finer and finer levels.Solve for the following....
[tex]\boxed{\tt 4x-(9-3x)=8x-1}[/tex]
Answers
Answer:
-8
Step-by-step explanation:
4x - 9 + 3x = 8x - 1
7x - 9 = 8x - 1
7x = 8x + 8
x = -8
Therefore, the solution to the equation 4x - (9 - 3x) = 8x - 1 is x = -8.
Given:-
[tex] \sf \: 4x - ( 9 - 3x ) = 8x - 1[/tex][tex] \: [/tex]
Solution:-
[tex] \sf \: 4x - ( 9 - 3x ) = 8x - 1[/tex][tex] \: [/tex]
[tex] \sf \: 4x - 9 + 3x = 8x - 1[/tex][tex] \: [/tex]
[tex] \sf \: 4x + 3x - 9 = 8x - 1[/tex][tex] \: [/tex]
[tex] \sf \: 7x - 9 = 8x - 1[/tex][tex] \: [/tex]
[tex] \sf \: 7x - 8x = -1 + 9[/tex][tex] \: [/tex]
[tex] \sf \: -1x = 8[/tex][tex] \: [/tex]
[tex] \sf \: x = \cancel \frac{8}{ - 1} [/tex][tex] \: [/tex]
[tex] \underline{ \sf \color{lightgreen} \: x = -8 \: }[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━
hope it helps! :)
The sum of two numbers is 37. If one of the numbers is greater by 1 than the two times the other, find the numbers.
Answers
According to the problem, the sum of the two numbers is 37. Therefore, we can write an equation:
x + (2x+1) = 37
Simplifying the left side of the equation:
3x + 1 = 37
Subtracting 1 from both sides:
3x = 36
Dividing both sides by 3:
x = 12
So the smaller number is 12. To find the larger number, we can use the equation we derived earlier:
2x+1 = 2(12) + 1 = 25
Therefore, the two numbers are 12 and 25.
(100 POINTS) Use the function f(x) to answer the questions.
f(x) = −16x2 + 60x + 16
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
Answers
a. The x-intercepts are 1/4 and 4. b. The vertex of the graph of f(x) is (1.875, 56), and it represents a maximum point on the graph.
What is axis of symmetry?The object's form is symmetrical because of the axis of symmetry, which is a straight line. On each of its sides, the axis of symmetry produces a perfect reflection. It could be lateral, vertical, or horizontal. The two sides of an object are the same if we fold and unfold it along the axis of symmetry. Various forms have various symmetry lines. There are four lines of symmetry in a square, two lines in a rectangle, infinite lines in a circle, and no lines of symmetry in a parallelogram. There are n axes of symmetry in a regular polygon with n sides.
We know that,
To find the x-intercepts, we set f(x) equal to 0 and solve for x:
-16x² + 60x + 16 = 0
4x² - 15x - 4 = 0
4x² - 16x + x - 4 = 0
4x (x - 4) - 1(x - 4) = 0
(4x - 1) (x - 4) = 0
x = 1/4
x = 4
The x-intercepts are 1/4 and 4.
The vertex of the graph of f(x) can be found using the formula x = -b/2a
x = -60 / (2(-16)) = 1.875
To establish whether the vertex is a maximum or minimum, we examine the shape of the coefficient of the x square term, which is negative (-16). This signifies that the graph expands down and the vertex is a maximum.
Hence, the vertex of the graph of f(x) is (1.875, 56), and it represents a maximum point on the graph.
Learn more about symmetry here:
https://brainly.com/question/1597409
#SPJ1
the quotient of 7 and the sum of 8 and m
Answers
Answer: :)
n
_
8
I used n as the unknown number
Step-by-step explanation:
The quotient is the result of division between two numbers.
The quotient of a number (I used n) and 8 would be n 8