Find an equation of the line perpendicular to 9x-8y=10 that passes through the point (0,0). If possible, write the equation in slope-intercept form.
Answers
If we have two perpendicular lines of slopes m₁ and m₂, then we have the following equation:
\(m_1\cdot m_2=-1\ldots(1)\)From the problem, we have the line with equation 9x - 8y = 10. The slope-intercept form of this line is:
\(\begin{gathered} 9x-8y=10 \\ 8y=9x-10 \\ \Rightarrow y=\frac{9}{8}x-\frac{5}{4} \end{gathered}\)Then, the slope of this line is:
\(m_1=\frac{9}{8}\)Using (1), we can find the slope of any perpendicular line to this line. Then:
\(\begin{gathered} \frac{9}{8}\cdot m_2=-1 \\ \Rightarrow m_2=-\frac{8}{9} \end{gathered}\)Additionally, we know that this line passes through the point (0, 0), so the point-slope form of the perpendicular line is:
\(y-0=-\frac{8}{9}(x-0)\)And the corresponding slope-intercept form is:
\(y=-\frac{8}{9}x\)Related Questions
The length of a rectangle exceeds its width by
3 inches, and the area is 108 square inches.
What are the length and width of the
rectangle?
Answers
l=36in
width = 12in
there's ur answer
16) Total asset turnover is used to evaluate: A. The efficiency of management's use of assets to generate sales. B. The necessity for asset replacement. C. The number of times operating assets were sold during the year. D. The cash flows used to acquire assets. E. The relation between asset cost and book value.
Answers
Answer:
A. The efficiency of management's use of assets to generate sales.
Step-by-step explanation:
The total asset turnover is calculated by dividing the sales to the assets. It measures the ability for a company so that in efficient way it would generate the sales.
By using the assets of the company, the company is able to generate the sales that could help the company for achieving the goals and objectives
Therefore according to the given situation, the a option is correct
The circuifference of a circular garden is 138.16 feet. What is the radius of the garden? Use 3.14 for it and do not round your
Answers
The circumference of a circle is given as:
\(C=\pi D\)where D is the diameter. Plugging the value given and solving for D we have:
\(\begin{gathered} 138.16=(3.14)D \\ D=\frac{138.16}{3.14} \\ D=44 \end{gathered}\)Now, the radius is twice the diameter, that means that:
\(r=\frac{D}{2}=\frac{44}{2}=22\)Therefore the radius is 22 ft.
Explain your answer to the question in the picture with steps please, thank you.
Answers
Part (a)
Answer: Constant of proportionality = 5/8
Reason:
The general template equation is y = kx where k is the constant of proportionality. It is the slope of the line.
The direct proportion line must pass through the origin. In other words, the y intercept must be zero.
=====================================
Part (b)
Answer: Not Proportional
Reason:
The y intercept isn't zero.
Plug x = 0 into the equation to find y = 1 is the y intercept. This graph does not pass through the origin.
At a charity fundraiser, some guests will be randomly selected to receive a gift. The probability of receiving a gift is 5 over 18. Find the odds in favor of receiving a gift.
Answers
Odds in favor of receiving a gift = 5/13
Explanation:The probability of receiving a gift, P(R) = 5/18
Probability of not receiving a gift, P(nR) = 1 - 5/18 = 13/18
The odds in favor of receiving a gift is calculated below:
\(Odds(R)=\frac{P(R)}{P(nR)}\)Therefore:
\(\begin{gathered} Odds(R)=\frac{5}{18}\div\frac{13}{18} \\ \\ Odds(R)=\frac{5}{18}\times\frac{18}{13} \\ \\ Odds(R)=\frac{5}{13} \end{gathered}\)Odds in favor of receiving a gift = 5/13
Ammariah has finished 17/20 of her homework. How much more does she have to complete.
A.15/100
B.6/10
C.3/10
D.6/20
EXPLAIN
Answers
Answer: A 15/100
Step-by-step explanation:
1. Convert 17/20 into percents
2. You get 85% Which is how much of her homework she has completed
3. To find what she has left subtract 85 from 100
4. You get 15 or 15/100 or 15% more of the test she hasn’t completed and needs to complete
y=4x+6slope: 4y-int: (0,6)why after graphing y-int, is the second point on the line given a slope of 4/1? shouldn't it be 4,0?
Answers
The given line is,
\(y=4x+6\)Here, the slope is, 4 and y intecept is 6.
For x = 4, we have,
\(y=4\times4+6=16+6=22\)Therefore, the two points on the graph is, (0, 6) and (4, 22).
Now, for y = 1, we have,
\(\begin{gathered} 1=4x+6 \\ 4x=-5 \\ x=-\frac{5}{4} \end{gathered}\)There are 40 students eating lunch in the cafeteria. of the students ordered chicken nuggets and the rest of the students are eating nachos. How many students are eating nachos? A 16 B 24 C 40 D 80
Answers
Answer:
what number is right before "of the students ordered chicken nuggets and the rest of the students are eating nachos." you cant answer the question otherwise.
Step-by-step explanation:
PLEASE HELPPPP
________ have had the greatest influence on Russian culture.
Turks
Europeans
Serbs
Slavs
Answers
Answer:
The Byzantine Empire, so I would say the Turks
Step-by-step explanation:
Slavs have had the greatest influence on Russian culture.
What is culture?A population's collective ways of life, including its institutions, beliefs, and artistic expressions, are collectively referred to as its culture. A society's whole way of life has been referred to as its culture. It encompasses manners, dress, language, religion, rituals, and artistic standards as a result.
Russia’s unique and vibrant culture developed, as did the country itself, from a complicated interplay of native Slavic cultural material and borrowings from a wide variety of foreign cultures. In the Kievan period (c. 10th–13th century), the borrowings were primarily from Eastern Orthodox Byzantine culture.
Although many traces of the Slavic culture that existed in the territories of Kievan Rus survived beyond its Christianization (which occurred, according to The Russian Primary Chronicle, in 988), the cultural system that organized the lives of the early Slavs is far from being understood.
therefore, We can say that the greatest influence on Russian culture is because of Slavs.
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A film distribution manager calculates that 9% of the films released are flops. If the manager is correct, what is the probability that the proportion of flops in a sample of 701 released films would be greater than 7%? Round your answer to four decimal places. Please show how to enter short hand in calculator.
Answers
Answer:
The probability that the proportion of flops in a sample of 701 released films would differ from the population proportion by greater than 7% is 0.00001
Step-by-step explanation:
We are given;
Probability that the films released are flops = 9% = 0.09
Sample size = 701
Formula for standard deviation is;
σ = √(p(1 - p)/n)
σ = √(0.09(1 - 0.09)/701)
σ = √0.0001168331
σ = 0.0108
We want to find the probability that the proportion of flops in a sample of 701 released films would be greater than 7%.
Thus, it means x - μ = 7% = 0.07
Z-score formula here is;
z = (x - μ)/σ
z = 0.07/0.0108
z = 6.4815
From online p-value from z-score calculator attached using; z = 6.4815, Nominal significance level = 0.05, two tailed distribution, we have;
P-value = 0.00001
Y (4)
+4y ′′
+4y=0 A general solution with x as the independent variable is y(x)=
Answers
Answer:
Step-by-step explanation:
We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.
For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,
y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0
(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.
Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get
yp″=a1+2a2x....yp‴=2a2+3a3x+....
Substituting the general solution into the non-homogeneous equation, we get
a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)
So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:
a(n+1)=Y(n-2)/n^2
From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.
HELP PLEASE DUE IN 10 MIN
Answers
The correct statement regarding the measure of variability used to represent the data is given as follows:
The IQR of 10 is the most accurate to use, as the data is skewed.
How to obtain the interquartile range?The interquartile range of a data-set is given by the difference of the third quartile by the first quartile of the data-set.
It is the measure of variability to be used when a data-set contains outliers, or is skewed, as is the case for this problem.
The charity received 18 donations, hence the quartiles are given as follows:
First quartile: 0.25 x 18 = 4.5th element = median of 10 and 15 = 12.5.Third quartile: 0.75 x 18 = 13.5th element = median of 20 and 25 = 22.5.Hence the IQR is given as follows:
IQR = 22.5 - 12.5
IQR = 10.
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In a pre algebra class containing 43 students, there are 4 freshman, 35 sophomores, and 4 juniors. what fraction of the class are sophomores
Answers
The fraction of the class that is sophomores is \(35/43\).
The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.
Number of sophomores = 35
Total number of students = 43
Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)
Fraction of sophomores \(= 35 / 43\)
Therefore, the fraction of the class that are sophomores is = \(35/43\).
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After drawing a square on the board, Mr. Hinkle asked his class to identify the shape. Timothy stated that Mr. Hinkle had drawn a rhombus. Which of the following statements is true?
Answers
The graph f(x)=x^5 is transformed to form a new function, g(x). Which set of transformations takes f(c) to g(x) in the correct order?
- translation 2 units to right,vertical stretch by a factor 1/3, translation 1 unit up
-translation 2 units to the right, vertical stretch by a factor of 3, translation 1 unit up
-translation 2 units to the right,translation 1 unit up,vertical stretch by a factor of 1/3
-translation 2 units to the right,translation 1 unit up,vertical stretch by a factor of 3
Answers
Answer:
Translation 2 units to the right
Vertical stretch by a factor of 3
Translation 1 unit up
Step-by-step explanation:
Correct on plato :}
How do I graph the function f(x) = 1/2(2)^x
Answers
Answer:
y=0
Step-by-step explanation:
School is out ladies and Gentlemen hope y’all have a great summer!
Answers
Hey there!
I hope you have a great one too :)
In City A, 4,099 of 5,289 residents, have reliable high-speed internet access. In City B, 15,798 of 20,868 residents have reliable high-speed internet access. In which town are residents more likely to have reliable high-speed internet access?
Answers
Answer:
4,099 and 5,011
Step-by-step explanation:
Describe the shape of the distribution shown in the dot plot.
The dot plot displays the golf scores from a golf tournament.
140
132
134
136
138
golf score (strokes)
A. Uniform
B. Bimodal
C. Left-Skewed
D. Right-Skewed
E. Symmetrical
F. Bell-shaped
Answers
Answer:
The answer is C. Left-Skewed
what type of charge does a proton in an atom hold
Answers
The slope of a curve at each point (x,y) is given by 4x - 1. Which one of the following is an equation fo curve if it passes through the point (-2,3)? A) y = 4x^2 - x - 15 B) y = 2x^2 - x C)y=2r^2-r+7 D) y= 2x^2-1-7
Answers
The following is an equation fo curve if it passes through the point (-2,3) is y=2 x^2-x-7.
What is Slope?
A graph is a set of vertices—points—and edges—the lines connecting those vertices in discrete mathematics. Graphs come in a variety of forms, including connected and disconnected graphs, bipartite graphs, weighted graphs, directed and undirected graphs, and simple graphs.
Slope of the carne at (x, y) is 4 x-1
Let the curve is: y=2 x^2-x-7
\($$\begin{gathered}\text { Slope: } \frac{d y}{d x}=\frac{d}{d x}\left[2 x^2-x-7\right] \\\frac{d y}{d x}=4 x-1\end{gathered}$$\)
And passes Iowa's the point (-2,3).
\($$\begin{aligned}& y=2 x^2-x-7 \\& 3=2(-2)^2-(-2)-7 \\& 3=8+2-7 \\& 3=10-7 \\& 3=3\end{aligned}$$\)
Satisfied.
y=2 x^2-x-7
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Some softball players hit a softball. Amalia hit the softball 36 inches. Nick hit the softball 6 feet. Lila hit the softball 108 inches. Pablo hit the softball 2 yards. Which two players hit the softball the same distance?
Answers
Answer: Nick and Pablo
Step-by-step explanation:
6 feet and 2 yards are the same distance because each yard is 3 feet
Answer:
6 feet 2 yards
Step-by-step explanation:
2. Given: y varies inversely with x.
If y=-24 when x =36, what is the value of x
when y = 45?
Answers
Using inverse variation, the value of x = -19.2
What is inverse variation?Inverse variation is when a quantity varies inversely as the other.
Given: y varies inversely with x.
If y=-24 when x =36, what is the value of x when y = 45.
To splve this, we proceed as follows
Since y varies inversely with x, we have that
y ∝ 1/x
y = k/x where k = constant of proportionality
So, making k subject of the formula, we have that
k = yx
Now, If y=-24 when x =36, we have that
k = - 24 × 36
= -864
So, substituting k into y, we have that
y = k/x
= -864/x
So, to find the value of x when y = 45, making x subject of the formula, we have that
x = -864/y
So, substituting y into the equation, we have that
x = -864/y
= -864/45
= -19.2
So, the value of x = -19.2
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-1000 2/3 is not real fraction. True or false
Answers
True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.
The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.
In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.
To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.
It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.
In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.
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What formula would be used to find the future value?
Return on balance 7.00%
Monthly rate of return 0.583%
Monthly payment -$200
Number of payments 120
Answers
Step-by-step explanation:
To calculate the future value of an investment with a given return on balance, monthly rate of return, monthly payment, and number of payments, you can use the formula for the future value of an annuity:
Future Value = P * [(1 + r)^n - 1] / r
Where:
P = Monthly payment
r = Monthly rate of return
n = Number of payments
In this case, using the given values:
P = -$200 (assuming the negative sign represents an outgoing payment)
r = 0.583% (0.00583 as a decimal)
n = 120
The formula becomes:
Future Value = -$200 * [(1 + 0.00583)^120 - 1] / 0.00583
Note that the negative sign indicates that you are making payments rather than receiving them. The future value will represent the accumulated balance after 120 months of making monthly payments.
Please note that this calculation assumes the monthly rate of return remains constant throughout the entire period, and the monthly payments are made at the end of each month.
I hope I helped
Desperate Need Of Help
Answers
The domain and range of the graph above in interval notation include the following:
Domain = [-6, 3]
Range = [-3, 3]
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.
In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [-6, 3] or -6 ≤ x < 3.
Range = [-3, 3] or -3 < y < 3
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Determine the area of the composite figure.
Answers
Answer:
113 \(m^{2}\)
Step-by-step explanation:
top rectangle = l x w = 6 x 13 = 78
lower rectangle width = 13-8=5. so a = l x w. 7 5 = 35
78+35= 113
Answer:
113 will be the correct answers
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answers
Step-by-step explanation:
take the reference of the above picture
hope that helps
through: (1, 3), perp. to y = x + 5
Answers
Answer:
y = 3x + 2
Step-by-step explanation:
Convert the equation to slope intercept form to get y = –1/3x + 2. The old slope is –1/3 and the new slope is 3. Perpendicular slopes must be opposite reciprocals of each other: m1 * m2 = –1
With the new slope, use the slope intercept form and the point to calculate the intercept: y = mx + b or 5 = 3(1) + b, so b = 2
So y = 3x + 2
Joyce works at Fortunato's Furniture. She is paid on commission. She receives 10% of her first $1,200 in sales and 15% of the balance of her sales. Last week she earned $950. What was the value of the furniture she sold? show your work.
Answers
The total value of the furniture sold by Joyce last week is A = $ 6,733.33
Given data ,
Let's call the value of the furniture Joyce sold "x".
She receives 10% commission on the first $1,200 of sales, which is $120:
Commission on first $1,200 = 0.1 * 1200 = 120
The remaining sales that she earns commission on is the difference between the total value of the furniture sold and the first $1,200:
Remaining sales = x - 1200
She earns 15% commission on the remaining sales, which is 0.15 times the remaining sales:
Commission on remaining sales = 0.15 * (x - 1200)
Her total earnings from commission last week was $950. So we can write an equation:
Commission on first $1,200 + Commission on remaining sales = $950
Substituting the expressions we found for the two commissions, we get:
120 + 0.15(x - 1200) = 950
120 + 0.15x - 180 = 950
On simplifying the equation , we get
0.15x - 60 = 950
0.15x = 1010
x = 6,733.33
Hence , the value of the furniture Joyce sold last week was $6,733.33
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