According to the plot synopsis for the novel "The Stone," a young homosexual guy experiences Taipei's nightlife, complete with all of its thrills and heartbreaks, perils, and hopes.
The Story of the Stone, sometimes referred to as "The Dream of the Red Chamber," was one of the finest books in Chinese literature when it was published about 1760. Gao E painstakingly edited and finished Cao Xueqin's majestic saga's fifth chapter, "The Dreamer Awakens," decades later.
The Story of the Stone has several references to or hints at the issue of the difference between what is true and what is untrue. The first volume in a five-volume series on the illustrious Chinese Jia family is titled "The Story of the Stone."
The major storyline chronicles the development of the love triangle between the three main characters—cousins Bao-yu, Dai-yu, and Bao-chai—as they grow up.
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If the reference angle is 47° label the sides accordingly:
Answer:
side c = 10.72 = Opposite
side d = 14.66 = Hypotenuse
Side 10 = Adjacent side
Explanation:
The given sides are given from the triangle;
Adjacent = 10
Angle of elevation = 47degrees
Required
Opposite = c
Hypotenuse = d
Using the SOH CAH TOA identity;
Tan theta = opposite/adjacent
Tan 47 = c/10
c = 10tan47
c = 10(1.0724)
c = 10.72
hence side c = 10.72 = Opposite
Similarly;
Cos theta = adjacent/Hypotenuse
Cos 47 = 10/d
d = 10/Cos47
d = 10/0.6819
d = 14.66
Hence Side d = 14.66 = Hypotenuse
Side C: Adjacent
Side D: Hypotenuse
Side length of 10 units: Opposite
6) A new home is bought for $254,000, and home values appreciate by 1.5% each year. If you wantto sell your home in 8 years, how much will your house be worth? Round to the nearest hundredth.
Step 1:
Write the formula worth of the house after 8 years.
[tex]\begin{gathered} \text{Amount = P(1 + r)}^t \\ P\text{ = Cost price of the house} \\ r\text{ = rate} \\ t\text{ = time} \end{gathered}[/tex]Step 2: Given data
P = $254000
r = 1.5% = 0.015
t = 8 years
Step 3: Substitute the values of P, r and t.
[tex]\begin{gathered} \text{Amount = 254000 }\times(1+0.015)^8 \\ =\text{ 254000 }\times1.015^8 \\ =\text{ 254000 }\times\text{ 1.126}492587 \\ =\text{ \$286,}129.12 \end{gathered}[/tex]Step 4: Final answer
The house worth
$286,129.12
y=-5x - 13,7x+2y=-23*Different / Different(-1,-8)(4.10)One PointAl PointsSame/ differentInfinite Solutions
1) Let's solve this Linear System of equations
y=-5x-13
x+2y=-23
2) Using the method of Substitution on the 2nd equation
x +2(-5x-13) = -23
x -10x -26= -23
-9x -26 =-23 Add 26 to both sides
9x=-23+26
9x = 3
x= 3/9
x= 1/3
y=-5(1/3) -13
y=-5/3 -13
y=-44/3
3) So there is one solution to that Linear System, different than those points (-1,-8) (4,10).
need help with this question Determine the points, if any, at which the graph R intersects the horizontal or oblique asymptote, if one exist.
The graph has a horizontal asymptote given by y = 0.
We can check that R(-3) = 0
Therefore, the graph of R intersects the horizontal asymptote at (-3,0)
Answer: A
6. Find (G + G) then subtract H from the result H = (2x^2 + 6x + 5) and G = (6x^2 + 3x + 5)
ANSWER
[tex]10x^2\text{ + 5}[/tex]EXPLANATION
We have that:
[tex]\begin{gathered} G=6x^2\text{ + 3x + 5} \\ \text{and} \\ H=2x^2\text{ + 6x + 5} \end{gathered}[/tex]Let us find G + G:
[tex]\begin{gathered} 6x^2\text{ + 3x + 5 + }6x^2\text{ + 3x + 5} \\ 6x^2+6x^2\text{ + 3x + 3x + 5 + 5 } \\ 12x^2\text{ + 6x + 10} \end{gathered}[/tex]Now, let us subtract H:
[tex]\begin{gathered} 12x^2+6x+10-(2x^2\text{ + 6x + 5)} \\ 12x^2+6x+10-2x^2\text{ - 6x - 5} \\ 12x^2-2x^2\text{ + 6x - 6x + 10 - 5} \\ \Rightarrow10x^2\text{ }+\text{ 5} \end{gathered}[/tex]That is the answer
can I get help please
we have the equation
y=-4x+4
step 1
Find the x-intercept (value of x when the value of y is zero)
so
For y=0
0=-4x+4
4x=4
x=4/4
x=1
x-intercept is (1,0)step 2
Find the y-intercept (value of y when the value of x is zero)
so
For x=0
y=-4(0)+4
y=4
y-intercept is (0,4)This diagram is used to prove the Pythagorean Theorem, and to show that the purple square - the green square = the red square
Question 13(Multiple Choice Worth 4 points)(06.04 MC)The function f(x) = 4x + 30 represents the length of a rectangle. The function g(x) = x - 1 represents the width of the rectangle. Use (f•g)(5) to determine the area of the rectangle.44650200
From the problem, the length of the rectangle is f(x) = 4x + 30 and the width is g(x) = x - 1.
To find the area, use (f · g)(5)
That will be :
[tex]\begin{gathered} (f\cdot g)(x)=(4x+30)(x-1) \\ (f\cdot g)(5)=(4\times5+30)(5-1) \\ (f\cdot g)(5)=50(4) \\ (f\cdot g)(5)=200 \end{gathered}[/tex]ANSWER :
The area is 200
Write 12.4% as a decimal and simplified fraction
Given the following question:
We are given 12.4%
[tex]undefined[/tex]a) CF for 21,72 and 62
The three numbers given in the question : 21 , 72 and 62 do not have any common factor.
What do you mean by common factor ?The common factors are those that are found in both lists
Example: Factors of 12 and 30
Factors of 12 are 1, 2, 3, 4, 6 and 12
Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30
Thus common factor = 1, 2, 3, 6
-------------------------------------------------------------------------------------------------------------
Given numbers : 21,72 and 62
Factors of 21 = 3 and 7
Factors of 72 = 2 and 3
Factors of 62 are 2 and 31
Thus these three numbers do not have any common factor.
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You told your friend that you could eat 7/8 of a large pizza. If you only ate 2/3 of what you said you could eat, what fraction of a large pizza did you eat?
The fraction of the large pizza that you were supposed to eat is 7/8. You could only eat 2/3 of 7/8. Thus, the fraction that you ate would be
(2/3) / (7/8)
If we flip 7/8 such that it becomes 8/7, the division sign would change to multiplication sign. Thus, we have
2/3 * 8/7
= 16/21
The fraction of the large pizza pizza that you ate is 16/21
uh hey can you help me with my hw if you help send me your snap and if you want I will send pics
The question says 900,000 /556040 x 190600
[tex]\begin{gathered} \frac{900,000}{556040}\text{ x 190600 } \\ \text{cancel the zero in the denominator and one zero above, then divide by 4 } \\ \frac{900000}{13901}\text{ x 47650} \\ \text{divide the dirst expression into decimal, that gives } \\ 64.74\text{ x 47650 = 3085029.85} \end{gathered}[/tex]Hence, 3085029.85 isthe solution to the question.
Answer: why
Step-by-step explanation: help me
The owner of the deli recorded the number of costumers who ordered each of four sandwiches avaliable. If the deli has 50 customers the first hour it is open, predict how many customers will order turkey andwiches?Ham: 160Cheese: 100Turkey: 180Veggie: 60
First, we want to find the probability of having a costumer who choose Turkey sanwich.
In order to find it, we calculate the ratio of turkey sandwiches over the total number of orders.
Turkey sandwiches: 180
Total number of orders: 160 + 100 + 180 + 60 = 500
Ratio = turkey / total
Ratio = 180 / 500 = 0.36
Then, the probability of having a costumer who choose Turkey sanwich is
P(T) = 0.36 = 36%
Secondly, in order to find the 36% of 50, we just multiply 0.36 by 50:
[tex]0.36\cdot50=18[/tex]Answer: in the first hour there will be 18 costumers that will order Turkey sanwichesWhat is the total cost of a $717 tablet computer that is on sale at 12% off of the local sales tax rate is 7%? The cost of the tablet is ? (Round to two decimal places as needed)
Given: The cost of a table as
[tex]\begin{gathered} Cost=717 \\ Discount=12\% \\ Sales-tax=7\% \end{gathered}[/tex]To Determine: The cost of the tablet
Solution
Let us first determine the discount
[tex]\begin{gathered} Discount=12\%\times717 \\ =0.12\times717 \\ =86.04 \end{gathered}[/tex]Then calculate the discounted price
[tex]Discount-price=717-86.04=630.96[/tex]We would also calculate the sales tax
[tex]\begin{gathered} sales-tax=7\%\times discount-price \\ =0.07\times630.96 \\ =37.86 \end{gathered}[/tex]The total price of the tablet would be
[tex]\begin{gathered} Total-cost=discount-price+sales-tax \\ =630.96+37.86 \\ =668.82 \end{gathered}[/tex]Hence, the cost of the tablet is $668.82
Nathan receives a lump sum inheritance of $55 000 and invests the money into a savings account with an annual interest rate of 7.5%, compounded quarterly.(a) Calculate the value of Nathan's investment after 5 years, rounding your answer to thenearest dollar. After m months, the amount in the savings account has increased to more than $70000.(b) Find the minimum value of m, where me N.Nathan is saving to purchase a property. The price of the property is $150 000. Nathan puts down a 15% deposit and takes out a loan for the remaining amount.(c) Write down the loan amount.The loan duration is for eight years, compounded monthly, with equal monthly payments of$1500 made by Nathan at the end of each month.(d) For this lonn, find(i) the amount of interest paid by Nathan over the life of the loan.(i) the annual interest rate of the loan, correct to two decimal places After 5 years of paying this locu, Nathan decides to pay the outstanding loan amount in onefinal payment. (e) Find the amount of the final payment after 5 years, rounding your answer to the nearestdollarif Find the amount Nathan saved by making this final payment after 5 years, roundingyour answer to the nearst dollar.
The Solution:
Given:
[tex]\begin{gathered} P=\text{ \$}55000 \\ r=7.5\text{ \% compounded quarterly}=\frac{7.5}{400}=0.01875 \\ t=5\text{ years}=5\times4=20\text{ periods} \end{gathered}[/tex]Required:
Find the value of the investment after 5 years.
The Formula:
[tex]V=P(1+\frac{r}{n})^{nt}[/tex]In this case,
[tex]\begin{gathered} V=Value\text{ of the investment}=? \\ P=\text{ \$55000} \\ r=0.075 \\ n=\text{ number of periods in a year}=4 \\ t=5\text{ years} \end{gathered}[/tex]Substitute:
[tex]V=55000(1+\frac{0.075}{4})^{(5\times4)}[/tex][tex]V=55000(1+0.01875)^{20}=55000(1.01875)^{20}[/tex][tex]V=79747.1414\approx\text{ \$}79747.14[/tex]Answer:
(a) $79,747.14
Find the number of months it will take the account to increase to more than $70,000
Solve for n in the equation below:
[tex]55000(1.01875)^n>70000[/tex][tex]\begin{gathered} (1.01875)^n>\frac{70000}{55000} \\ \\ (1.01875)^n>\frac{14}{11} \end{gathered}[/tex][tex]ln(1.01875)^n>ln(\frac{14}{11})[/tex][tex]n=\frac{ln(\frac{14}{11})}{ln(1.01875)}>12.982\approx13\text{ months}[/tex]Answer:
13 months or more
50 points help (show ur work)
Answer all of them
Answer:
5. $40
6. 500 students
7. 60 books
8. 63 pages
Step-by-step explanation:
Question 5Given:
Aiden spent $18 on souvenirs.$18 is 45% of the money he brought on the trip.Let x be the money Aiden brought on the trip.
Create equivalent ratios with the given information and defined variable, and solve for x:
[tex]\implies 18:45\%=x:100\%[/tex]
[tex]\implies 18:0.45=x:1[/tex]
[tex]\implies \dfrac{18}{0.45}=\dfrac{x}{1}[/tex]
[tex]\implies 18=0.45x[/tex]
[tex]\implies x=\dfrac{18}{0.45}[/tex]
[tex]\implies 40[/tex]
Therefore, Aiden brought $40 on the trip.
Question 6Given:
Angel received 300 votes.300 votes was 60% of all the votes.Let x be the number of students who voted in the election.
Create equivalent ratios with the given information and defined variable, and solve for x:
[tex]\implies 300:60\%=x:100\%[/tex]
[tex]\implies 300:0.6=x:1[/tex]
[tex]\implies \dfrac{300}{0.6}=\dfrac{x}{1}[/tex]
[tex]\implies 300=0.6x[/tex]
[tex]\implies x=\dfrac{300}{0.6}[/tex]
[tex]\implies x = 500[/tex]
Therefore, there were 500 students who voted in the election.
Question 7Given:
The students sold 80% of the books.The total number of books they sold is 48.Let x be the number of books in the sale.
Create equivalent ratios with the given information and defined variable, and solve for x:
[tex]\implies 80\%:48=100\%:x[/tex]
[tex]\implies 0.8:48=1:x[/tex]
[tex]\implies \dfrac{0.8}{48}=\dfrac{1}{x}[/tex]
[tex]\implies 0.8x=48[/tex]
[tex]\implies x=\dfrac{48}{0.8}[/tex]
[tex]\implies x=60[/tex]
Therefore, there were 60 books in the book sale.
Question 8Given:
Aiyana read 147 pages of the book.She completed 70% of the book.If she has completed 70% of the book, then she still has 30% left to read, as 100% - 70% = 30%.
Let x be the number of pages Aiyana still has to read.
Create equivalent ratios with the given information and defined variable, and solve for x:
[tex]\implies 70\%:147=30\%:x[/tex]
[tex]\implies 0.7:147=0.3:x[/tex]
[tex]\implies \dfrac{0.7}{147}=\dfrac{0.3}{x}[/tex]
[tex]\implies 0.7x=44.1[/tex]
[tex]\implies x=\dfrac{44.1}{0.7}[/tex]
[tex]\implies x=63[/tex]
Therefore, Aiyana still has 63 pages left to read.
find a rational number lying at one fourth of the way between 3/4 and 2/3 from the greater side
(with steps)
Answer:
13 / 20
Step-by-step explanation:
This question does not require an understanding of number theory.
NUMBER THEORY
A rational number is any real number that can be represented as a fraction or an integer. This group of numbers excludes imperfect squares or constants like pi.
THE MATH PART
We can use a bit of logic and algebra to do this.
(2/3) > (3/5)
This means we need to find a number relative to (2/3).
Calculate the distance between (2/3) and (3/5) by finding the least common multiple denominators. Two brackets placed together mean multiplication.The rational number is ( 13 / 20 ).
I could have probably made step 2 easier by subtracting ( 1 / 4 ) of ( 1 / 15 ) from ( 2 / 3 ).
Hello I need help with question 6! I will give you a great rating! Please help, I’m not sure how to do this. Also this is not a quiz this is practice
6.
cos a = adjacent side / hypotenuse
Replacing with the values given:
Cos 45 = 13 / y
y= 13/cos45
y= 13/ (1 /√2 )
Y= 13√2
For x apply the Pythagorean theorem
c^2 = a^2 + b^2
Where:
c= hypotenuse
a & b = the other 2 legs
(13 √2 )^2 = x^2 + 13^2
338 = x^2 + 169
338 - 169 = x^2
169 =x^2
√169 = x
x = 13
Ava has $14. She earns $8 each hour she spent babysitting. She now has $78. Write and solve an equation to find the number of hours Chloe spent babysitting
Answer:
8 hours.
Step-by-step explanation:
Hello there! Let's help you with your question here!
To always begin questions, let's start with what we know! So, we know that Ava has a total of $14 and that she earns $8 each hour she spends babysitting and now her new total is $78. Alright! So, what do we have here? Here, we're solving for how much money Ava will earn in total. When being asked to write and solve an equation, we always look for what's known as fixed value and a variable value. And what do this mean?
A fixed value is something that can't really be changed under any circumstances. In the question we have here, we are looking for a number that does not change at all and that would be $14. Why? Because no matter what the new total amount of money being made, she'll always start with $14.
A variable value is something that can be changed based on a quantity. In the question we have here, we are looking for a number that follows up with something that we are unsure of but necessary. In this case, that would be $8 each hour. The reason we use this is because we don't know how many hours Ava's going to work. It can be anything and the total amount of money she earns depends on how many hours she worked.
So, now that we have all of our information, we can start by creating a formula! Let y be the new total amount of money that Ava has and let x be how many hours Ava has spent babysitting. And that would be as such:
[tex]y=8x+14[/tex]
Now that we have our formula, we can now begin to solve. We are looking for how many hours Ava spent babysitting to get her new total value up to $78. We substitute y and then solve for x. It would be as such:
[tex]78=8x+14[/tex]
[tex]64=8x[/tex] - Subtracting 14 from both sides.
[tex]8=x[/tex] - Dividing both sides by 8 to isolate x.
Therefore, in order for Ava to get $78 in total, she would need to spend 8 hours of babysitting, if she started out with $14.
pls help
Does this graph
show a linear,
quadratic, or
exponential
function?
Answer:
exponential
Step-by-step explanation:
HELP QUICK PLEASE
all i need is 6,10,&12
In exercises 1-8, the table or graph represents a quadratic function. Write an equation of the function in standard form.
In exercises 9-12, write a quadratic function in standard form whose graph has the given characteristics.
Answer:
y= - 104/125 (x - 1/2 2) +1
Step-by-step explanation:
hope this helps
Graph a line with an undefined slope that goes through the point (-14,0)Identify the slope:And the Intercept:Write special equation of the line:
We need to first graph a line that goes through the point (-14, 0).
The chosen line passes through the point (-14,0) and (0, 28).
The slope of a line is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where m is the slope, (x1,y1) is the first point and (x2,y2) is the second point. Applying these points to the problem:
[tex]m=\frac{28-0}{-0-(-14)}=\frac{28}{14}=2[/tex]The slope of the line is 2.
The intercept of the line is the point at which it crosses the "y" axis. In this case this point is (0,28).
We can write the line in its slope-intercept form, since we already calculated those values. This form is given by:
[tex]y(x)=m\cdot x+b[/tex]Where "m" is the slope and "b" is the intercept, therefore the equation of the line is:
[tex]y(x)=2\cdot x+28[/tex]help
subtracting integers
1. 9 - 13 =
2. 10 - (-20) =
3.36 - (-11) =
4.-15 - (-16) =
5.-8 - 30 =
A golf ball is dropped out of an airplane. The downward velocity of the ball at various times is given in the table below. What is the slope of the line that fits this data?
Let:
[tex]\begin{gathered} (x1,y1)=(1,21.8) \\ (x2,y2)=(2.2,33.56) \\ \text{Slope}=m=\frac{y2-y1}{x2-x1}=\frac{33.56-21.8}{2.2-1}=\frac{11.76}{1.2}=9.8 \end{gathered}[/tex]Write and solve an equation to find the unknown side length x (in inches).
Perimeter =24.2 in.
An equation is
=24.2.
The unknown side length is
inches.
The value of side length x is equal 6.05 in
Perimeter of a SquareThe perimeter of a square is given as the sum of the total sides in the square or 4 multiplied by the side length of the square since they all have equal sides.
Mathematically, this can be written as
[tex]P = 4 *L\\P = 4l\\[/tex]
L = side lengthIn this given question, the side length is equal to x and the perimeter of the square is given as 24.2in.
Let's substitute the values
[tex]P = 4L\\24.2 = 4L\\but l = x\\24.2 = 4x\\x = 6.05in[/tex]
The side length of the square is equal to 6.05in
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complete question
Write and solve an equation to find the unknown side length x (in inches).
Perimeter =24.2 in. assuming the figure is a square
help meeee pleasee!!!
thank youu
Answer:
Domain: A, [1, 7]
Range: [-4, 2]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Main street, Broad Street, and Park Street all intersect to form a right triangle. If broad Street is 75 yards ling and Park is 100 yards long, how long must Main Street be?
Option (D) is the correct answer.
Given:
The length of broad street is 75 yards.
The length of park street is 100 yards.
The objective is to find the length of the main street.
The length of the main street can be calculated using Pythagorean theorem.
[tex]\begin{gathered} \text{Park}^2=Main^2+Broad^2 \\ \text{Main}^2=Park^2-Broad^2 \\ \text{Main}^2=100^2-75^2 \\ \text{Main}^2=10000-5625 \\ \text{Main}^2=4375 \\ \text{Mai}n=\sqrt[]{4375} \\ \text{Main}^{}=66.144\text{ yards} \end{gathered}[/tex]Thus, the length of the Main street is 66.144 yards.
Hence, option (D) is the correct answer.
1 2/5 and a percent nnnnnn
Answer:
what does that even mean
Step-by-step explanation:
Graph the given equation by evaluating integer values of x from −2 to 2 and plotting the resulting points.y=−2x+3
Explanation
to evaluate a function replace the x place
so
[tex]y=-2x+3[/tex]Step 1
a) when x=-2
replace
[tex]\begin{gathered} y=-2x+3 \\ y=-2(-2)+3 \\ y=4+3 \\ y=7 \\ \end{gathered}[/tex]so
[tex]P1(-2,7)[/tex]b) when x= -1
[tex]\begin{gathered} y=-2x+3 \\ y=-2(-1)+3 \\ y=2+3 \\ y=5 \\ \end{gathered}[/tex]so
[tex]P2(-1,5)[/tex]c) when x= 0
[tex]\begin{gathered} y=-2x+3 \\ y=-2(0)+3 \\ y=0+3 \\ y=3 \\ \end{gathered}[/tex]so
[tex]P3(0,3)[/tex]d)when x= 1
[tex]\begin{gathered} y=-2x+3 \\ y=-2(1)+3 \\ y=-2+3 \\ y=1 \\ \end{gathered}[/tex]so
[tex]P4(1,1)[/tex]e) when x= 2
[tex]\begin{gathered} y=-2x+3 \\ y=-2(2)+3 \\ y=-4+3 \\ y=-1 \\ \end{gathered}[/tex]so
[tex]P4(2,-1)[/tex]Step 2
now, draw a line that connects the points, so
Write the point-slope form equation of the line that satisfies the given conditions. Also, rewrite the equation of the line such that it's in slope-intercept form.
f(3) = 18 and f(16) = -18
Equation of the line is y = [tex]\frac{-36x}{13}[/tex] + [tex]\frac{687}{13}[/tex].
Define slope intercept form.An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx+ c, where m denotes slope and c denotes the y-intercept. A line's equation written using a single point on the line and the line's slope is referred to as the point-slope form. The slope is the rise over run, or the ratio of the change in the y values over the change in the x values, and the point form is denoted as (x, y).
Given Data
f(3) = 18
f(16) = -18
Slope:
m = [tex]\frac{f(x_{2})-f(x_{1}) }{x_{2}-x_{1} }[/tex]
m = [tex]\frac{f(16)-f(3)}{16-3}[/tex]
m = [tex]\frac{-18-18}{13}[/tex]
m = [tex]\frac{-36}{13}[/tex]
Equation of the line in slope intercept form:
y - f(x₁) = m(x - x₁)
y - 3 = [tex]\frac{-36}{13}[/tex](x - 18)
y - 3 = [tex]\frac{-36x}{13}[/tex] + [tex]\frac{648}{13}[/tex]
y = [tex]\frac{-36x}{13}[/tex] + [tex]\frac{687}{13}[/tex]
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