1. The equation of the perpendicular line is: y = -x + 4
2. The equation of the parallel line is: y = -x + 4
What are the Equations of Parallel and Perpendicular Lines?The equations of two lines that are parallel to each other will have the slope (m), while the equations of two lines that are perpendicular to each other will have slope values that are negative reciprocals of each other.
The slope-intercept form for the equation of a line is, y = mx + b, where b is the y-intercept and m is the slope of the line.
1. The slope (m) of y = x - 4 is 1. The line that is perpendicular to y = x - 4 would have a slope (m) of -1.
Substitute (a, b) = (1, 3) and m = -1 into y - b = m(x - a):
y - 3 = -1(x - 1)
Rewrite in slope-intercept form:
y - 3 = -x + 1
y = -x + 1 + 3
y = -x + 4
2. The slope (m) of y = -x - 4 is -1. The line that is parallel to y = -x - 4 would have a slope (m) of -1.
Substitute (a, b) = (3, 1) and m = -1 into y - b = m(x - a):
y - 1 = -1(x - 3)
Rewrite in slope-intercept form:
y - 1 = -x + 3
y = -x + 3 + 1
y = -x + 4
Learn more about equation of parallel and perpendicular lines on:
https://brainly.com/question/7098341
#SPJ1
A T-shirt vendor
sells yellow shirts and
blue Shirts at a ratio of
1:4. What percent of the
Shirts are yellow?
The percentage of the T-shirt that are yellow will be 20%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A T-shirt vendor sells yellow shirts and blue Shirts at a ratio of 1: 4.
The ratio of the yellow T-shirt is given as,
Yellow ratio = 1 / (4 + 1)
Yellow ratio = 1 / 5
Then the percentage of the T-shirt that are yellow will be given as,
P = [1/5] x 100
P = 0.20 x 100
P = 20%
The percentage of the T-shirt that are yellow will be 20%.
More about the percentage link is given below.
https://brainly.com/question/8011401
#SPJ6
Please answer the question and help me pass
Answer:
10 *6= 60
60÷2=30
1÷2×b×h formula
answer- 30
if a study with a total sample size of 12 measures 7 successes, in how many different sequences could these successes have occurred?
The number of different sequences in which the 7 successes could have occurred is 792.
To calculate the number of different sequences, we can use the concept of permutations. Since we have a total sample size of 12 and 7 successes, we need to determine the number of ways these successes can be arranged within the sample.
The formula for permutations is given by nPr = n! / (n - r)!, where n is the total number of items and r is the number of items to be arranged.
In this case, we have n = 12 (total sample size) and r = 7 (number of successes). Plugging these values into the formula, we get:
12P7 = 12! / (12 - 7)!
= 12! / 5!
= (12 * 11 * 10 * 9 * 8) / (5 * 4 * 3 * 2 * 1)
= 792
Therefore, there are 792 different sequences in which these 7 successes could have occurred within the sample of size 12.
To learn more about Sampling
brainly.com/question/31890671
#SPJ11
pls help my mom will literally scream at me lol . thank you sm:)
Answer:
The amount Tobie invests in a bank, P = $25
The annual compound interest rate, i = 4%
a. The principal is amount invested in the bank, P = $25
The annual interest rate, i = 4%
b. The function that represents Tobie's account balance, A, after t years is given as follows;
\(A(t) = P \cdot (1 + i)^t\)
Where;
A(t) = The amount in the account after t years
P = The principal amount
i = The annual compound interest rate
t = The number of years
c. The values to place in the table are found as follows;
At t = 0, \(A(0) = 25 \times(1 + 0.04)^0\) = 25
At t = 10, \(A(10) = 25 \times(1 + 0.04)^{10}\) = 37
The given table is presented as follows;
\(\begin{array}{ccc}t&&A(t)\\0&&25\\10&&37\end{array}\)
Step-by-step explanation:
help me with this question please
Answer:
N+1
Step-by-step explanation:
It begins with = 2
then n+1=3
then n+2=4 and so on it is n+1
Katy buys 2 DVDs every 2 weeks.How many DVDs. Will she buy in 14 weeks?
Answer:
Step-by-step explanation:
If Katy buys 2 DVDs every 2 weeks, it the same as saying 1 DVD every week.
14 ÷ 2 = 7
2 × 7 = 14
1 × 14 = 14
Answer:21 dvds
Step-by-step explanation:
Set up a proportion in terms of DVDs to weeks and solve.
3/2 = x/14
(2)(x) = (3)(14)
2x = 42
x = 21
Therefore, Katy will buy 21 DVDs in 14 weeks.
brainliest pls?
16.) The population of Wolf County was 12,390 in 2000 and 13,090 in 2010. Assuming that population growth in this county is linear, find the following:
b.) When will the population reach 21,000 people?
c.) When did the first settlers arrive in Wolf County?
Input and outputRule: the output is t-3Input t: 17, 20, 22, 24Output r: ?
The output is given by:r= t-3
For the inputs,
t=17
The output is
r=17-3=14
For the input, t=20
The output is:
r=20-3=17
For the input, t=22
The output is
r=22-3=19.
For the input, t=24
The output is
r=24-3=21
When solving this system by elimination, which variable is the most convenient to eliminate,
x or y?
2x + y = 7
3/2 x - y = 7/2
Answer:
Y is the appropriate variable and the most easiest and convenient to eliminate
name 2x + y = 7 as equation i
and 3/2 x - y = 7/2 as equation ii
then add equation i and ii together
(3/2 + 2) x + y - y = (7 + 7/2)
(7/2) x = (21/2)
x = 3
then put in x = 3 in equation i
4 + y = 7
x = 7 - 4
x = 3
Therefore x = 3 and y = 3
round these numbers to the nearest 1000
8453
Mary’s yard is a mess. She needs to hire someone to prune her trees and shrubs. A landscaping service she calls quotes her a price of $15 consultation fee plus $8 an hour for the actual work. Mary’s neighbor has offered to help her out. She doesn’t charge a consultation fee, but does charge $10 an hour for her work. Who do you think Mary should hire for a 3-hour job? When, if at all, would it be more economical to hire the other service. (Set up and solve a system of equations to answer this question.) a. Mary should hire her neighbor; if there was more than 7.5 hours of work she should hire the landscaping service. b. Mary should hire her neighbor; if there was more than 4.2 hours of work she should hire the landscaping service. c. Mary should hire the landscaping service; if there was more than 7.5 hours of work she should hire her neighbor. d. Mary should hire the landscaping service; if there was more than 4.2 hours of work she should hire her neighbor.
Answer:
I think it's C
Step-by-step explanation:
Maey should hire a landscaping service and if ther is more than 7.5h she could hire her neighbour
Answer:
Please mark me brainliest and I hoped this helped!
She should ask her neighbor to help her.
Step-by-step explanation:
We can use equations to help us figure out this answer.
8x + 15 = y
10x = y
If she has a 3 hour job, we can use 3 instead of x.
8(3) + 15 = y
24 + 15 = y
30 = y for the landscaping service
10(3) = y
30 = y for a neighbors help
It will cost her 9 dollars less, so she should go with the neighbor.
intermediate models of integration are different from the enemies and allies models because
Intermediate models of integration differ from the enemies and allies models due to their approach in fostering collaboration and cooperation between different entities while maintaining a certain degree of autonomy and independence.
Intermediate models of integration, in contrast to enemies and allies models, aim to establish a framework where entities can work together while retaining their individual identities and interests. These models recognize that complete integration or isolation may not be the most optimal or feasible approaches. Instead, they emphasize the importance of collaboration and cooperation between different entities, such as organizations or countries, while respecting their autonomy.
In intermediate models of integration, entities seek to identify shared goals and interests, leading to mutually beneficial outcomes. They acknowledge the value of diversity and differences in perspectives, considering them as assets rather than obstacles. This approach encourages open communication, negotiation, and compromise to bridge gaps and find common ground. Rather than viewing other entities as adversaries or allies, the emphasis is on building relationships based on trust, transparency, and shared values.
Intermediate models of integration often involve the establishment of frameworks, agreements, or platforms that facilitate collaboration while allowing for flexibility and adaptation to changing circumstances. These models promote inclusivity, recognizing that integration can be a complex process that requires active participation from all involved entities. By combining the strengths and resources of different entities, intermediate models of integration strive to achieve collective progress and shared prosperity while acknowledging the importance of maintaining individual identities and interests.
To learn more about integration refer:
https://brainly.com/question/31744185
#SPJ11
It takes your equipment 3 minutes to travel 264 feet. what speed is the equipment traveling?
Answer:
To determine the speed, we can use the formula:
speed = distance / time
where distance is measured in feet and time is measured in minutes.
In this case, the distance is 264 feet and the time is 3 minutes. Plugging these values into the formula, we get:
speed = 264 feet / 3 minutes
simplifying, we get:
speed = 88 feet/minute
Therefore, the equipment is traveling at a speed of 88 feet per minute.
A rectangle formed by a 30cm wire , if the length of the rectangle was twice its width , then what is the area of the rectangle ?
A.15 B. 150
C. 300 D. 50
Answer:
Step-by-step explanation:
D
Adelynn and Kiyomi went to the bakery and bought some packages of cookies. Adelynn bought 270 cookies. Kiyomi bought 4 more packages than Adelynn and had 630 cookies. How many cookies are in one package
Answer:
90 Cookies
Step-by-step explanation:
If a person places their phone number on the do-not-call registry, how many years does it stay on the list before it is eligible again for cold calling
When an individual places their phone number on the Do Not Call (DNC) Registry, it remains there permanently, and telemarketers are prohibited from making unsolicited calls to that number until the individual requests to be removed from the list.
When an individual places their phone number on the Do Not Call (DNC) Registry, it remains there permanently, and telemarketers are prohibited from making unsolicited calls to that number until the individual requests to be removed from the list. This list is managed by the Federal Trade Commission (FTC), which enforces the Telephone Consumer Protection Act (TCPA) in the United States. If someone's phone number is on the DNC registry, the registry rules apply indefinitely. This means that even if the individual's phone number is still listed after a period of time, telemarketers are prohibited from calling that number. If the individual wishes to receive telemarketing calls again, they must remove their phone number from the list by dialing the DNC registry's phone number, which is 1-888-382-1222. The process of removing a phone number from the list is a simple one. Dial the number on your phone, and then follow the instructions that the voice prompt gives you. Furthermore, it is important to know that calls from organizations that you have given permission to call you are still allowed even if your number is on the DNC registry.
To know more about telemarketers visit: https://brainly.com/question/32807591
#SPJ11
Answer ASAP. :) Thank you!
Answer:
c = 55
Step-by-step explanation:
I would solve this by cross multiplying, but some teachers don't appreciate you skipping a step like that. Instead:
\(\frac{5}{2} =\frac{c}{22}\)
First, multiply both sides by 2:
\(5=\frac{2c}{22}\)
Then, multiply both sides by 22:
\(2c=110\)
Now, just solve for c by dividing both sides by 2:
\(c=55\)
Answer:
C = 55
Step-by-step explanation:
To figure out c you must first isolate c so there shouldn't be any other numbers or signs (addition, subtraction, division, and multiplication) on the same side of the equal sign as variable C.
The inverse of dividing 22 is multiplying 22 on both sides of the equation.
You would get 22/1 * 5/2 = C. 22 * 5 is 110 and 1 * 2 is still 2 so 110/2 = C.
Enter 110/2 into the calculator and you would get C = 55
Bryans gocket team is purchasing jersys. The company charges $250 for the onetime set-up fee and $23 for each printed jersey which expression repressents the total cost of x number for the team
Given:
The company charges $250 for the onetime set-up fee and $23 for each printed jersey.
To find:
The expression that represents the total cost of x number for the team.
Solution:
We have,
Fixed charges = $250
Additional charges = $23 per printed jersey
Let x be the number of printed jersey. Then,
Additional charges = $23x
Total chargers = Fixed charges + Additional charges
= $(250 + 23x)
Therefore, the expression for the total charges is $(250 + 23x).
Help me with these please
Answer:
1. Sound
Step-by-step explanation:
Sorry if wrong :> Hope i helped! Have a awesome day!!! You're a great hooman ^_^ Please mark brainliest !! I know the first one and only the first one ><
Find a vector equation with parameter t for the line of intersection of the planes x y z=2 and x z=0.
The vector equation with parameter t for the line of intersection of the planes x + y + z = 2 and x + z = 0 is r(t) = <0, 2, 0> - t<1, -1, 0>.
To find a vector equation with parameter t for the line of intersection of the planes x + y + z = 2 and x + z = 0, we can solve the system of equations formed by the planes.
First, let's solve for y in terms of x and z from the equation x + y + z = 2. Rearranging the equation, we have y = 2 - x - z.
Now, substitute this expression for y in the equation x + z = 0. We have x + (2 - x - z) + z = 2, which simplifies to 2 - z = 2.
Solving for z, we find z = 0.
Substituting z = 0 into the equation x + z = 0, we have x = 0.
Now that we have the values of x, y, and z, we can form a vector equation for the line of intersection as follows:
r(t) = = <0, 2 - x - z, 0> = <0, 2, 0> - t<1, -1, 0>.
Learn more about vector equation
https://brainly.com/question/31044363
#SPJ11
V + Iwh
I = 32, w = 14, and h = 7
V = ___
Options:
A: 53
B: 3,136
C: 448
Please show your work
Equation V + Iwh , I = 32, w = 14, and h = 7, V = -3,136. The correct answer is B.
To solve for V in the equation V + Iwh, we can plug in the given values of I, w, and h, and then isolate V on one side of the equation. Here are the steps:
1. V + Iwh = V + (32)(14)(7)
2. V + 3,136 = V + 3,136
3. Subtract 3,136 from both sides of the equation: V = -3,136
The correct answer is option B: 3,136. Here is the solution in HTML format:
To solve for V in the equation V + Iwh, we can plug in the given values of I, w, and h, and then isolate V on one side of the equation. Here are the steps:
V + Iwh = V + (32)(14)(7)
V + 3,136 = V + 3,136
Subtract 3,136 from both sides of the equation: V = -3,136
The correct answer is option B: 3,136.
Read more equation:
brainly.com/question/13763238
#SPJ11
Find the rectangular coordinates of the point(s) of intersection of the polar curves r = 5 sin(theta) and r = 5 cos(theta)|. a) (0, 0)| and (5, 5)| b) (0, 0)| and (5/2, 5/2)| c) (0, 0)| and (5/4, 5/4)| d) (1, 1)| and (5/4, 5/4)| e) (0, 0)| and (-5/2, -5/2)|
The coordinates of the first point of intersection in rectangular form are (x, y) = ((5/2), (5/2)).
To find the points of intersection between the polar curves r = 5 sin(θ) and r = 5 cos(θ), we need to equate the two equations and solve for θ. Let's start by setting the two equations equal to each other:
5 sin(θ) = 5 cos(θ)
Dividing both sides by 5 gives:
sin(θ) = cos(θ)
Now, we can use the trigonometric identity sin(θ) = cos(90° - θ). Replacing cos(θ) with sin(90° - θ), the equation becomes:
sin(θ) = sin(90° - θ)
Since the sine function is equal to itself for any angle plus multiples of 360°, we can write:
θ = 90° - θ + 360° x n
Here, n represents any integer value. Solving for θ, we get:
2θ = 90° + 360° x n
Dividing both sides by 2, we have:
θ = 45° + 180° x n
Now, let's substitute this value of θ back into the original equation r = 5 sin(θ) (or r = 5 cos(θ)) to find the corresponding r-values.
For θ = 45°:
r = 5 sin(45°) = 5 cos(45°)
Using the values of sine and cosine for 45°, we get:
r = 5 x √(2)/2 = 5 x √(2)/2
Simplifying further, we have:
r = (5/2) x √(2)
Therefore, the coordinates of the first point of intersection are (r, θ) = ((5/2) x √(2), 45°).
Now, let's consider the value of θ for n = 1:
θ = 45° + 180° x 1 = 45° + 180° = 225°
For θ = 225°:
r = 5 sin(225°) = 5 cos(225°)
Using the values of sine and cosine for 225°, we get:
r = 5 x (-√(2)/2) = -5 x √(2)/2
Simplifying further, we have:
r = (-5/2) x √(2)
Therefore, the coordinates of the second point of intersection are (r, θ) = ((-5/2) x √(2), 225°).
To convert these polar coordinates into rectangular coordinates, we can use the formulas:
x = r x cos(θ) y = r x sin(θ)
For the first point of intersection, (r, θ) = ((5/2) x √(2), 45°):
x = ((5/2) x √(2)) x cos(45°) = (5/2) x √(2) x √(2)/2 = (5/2) y = ((5/2) x √(2)) x sin(45°) = (5/2) x √(2) x √(2)/2 = (5/2)
Hence the correct option is (b).
To know more about rectangular coordinates here
https://brainly.com/question/31904915
#SPJ4
Juan organizes the stamps in his collection by country and by the decade in which they were issued. the prices he paid for them at a stamp shop were: brazil and france, cents each, peru cents each, and spain cents each. (brazil and peru are south american countries and france and spain are in europe.)how many of his european stamps were issued in the
The number of European stamps issued in the 1990s is equal to * 0.9 = stamps.
Let's assume Juan has the same number of stamps from Brazil and France, and that the stamps from Peru and Spain are of equal numbers.
The total number of European stamps Juan has is equal to the number of stamps from France and Spain, which is 2N, where N is the number of stamps from each country.
The number of stamps from France and Spain issued in the 1990s is equal to N * (90% of the total number of stamps)
Therefore, the number of stamps from France and Spain issued in the 1990s is equal to N * 0.9.
Using the given information, we can calculate N:
N = (Brazil + France) / (Cents + Cents)
N = (Cents + Cents) / (Cents + Cents)
N = Cents / Cents
Therefore, the number of European stamps issued in the 1990s is equal to * 0.9 = stamps.
Learn more about numbers here:
https://brainly.com/question/17429689
#SPJ4
Rewrite 4/6 and 1/3 as a unite rate
Answer: B
Step-by-step explanation: Hope this helps :)
A runner is running a 10 km race. It takes her 17.5 minutes to reach the 2.5 km mark. at that rate, how long would it take her to run the whole race?
Answer:
time = 70 minutes
A plant that floats on the surface of rural bodies of water is known as duckweed. The initial mass of a population of duckweed is 500g The mass of the population triples every Ͷͷ hours and can be represented by the function m(t)= 500x3^t/45 where (t) is time in hours. Determine how many hours it would take for the duckweed to grow to a mass triple the original size.
Therefore , the solution of the given problem of function comes out to be the duckweed to grow a mass triple the original size will be 45 hours.
Explain function.The mathematics curriculum involves examining numbers, the equation the environment we live in, structures, and both actual and hypothetical locations. A function is a variable representation of the relationship between the quantities of intake and the corresponding outputs for each. Simply explained, a function is a collection of inputs that, when combined, provide unique outputs for each input.
Here,
Given :
mass of a population of duckweed is 500g
=> function m(t)= 500x³^t/45
So,
=> t = 45 hours
Since it is given that the mass of the population of the duckweed triples every 45 hours
it is clear that the time taken for the duckweed to grow a mass triple the original size will be 45 hours .
Therefore , the solution of the given problem of function comes out to be the duckweed to grow a mass triple the original size will be 45 hours.
To know more about function visit:
https://brainly.com/question/28193995
#SPJ4
graph the inequalities
2y+8x<4
5x+20 is greater than or equal to -10y
The graph to the inequality is added as an attachment
How to determine the graph to the inequalityFrom the question, we have the following parameters that can be used in our computation:
2y+8x<4
5x+20 is greater than or equal to -10y
Express properly
2y+8x<4
5x+20 > -10y
Next, we make a plot of the system to determine the solution
The shaded area in the plot represent the solution to the inequality
In this case, the shaded area has a coordinate of (1.143, -2.571)
Hence, the solution is (1.143, -2.571)
Read more about inequality at
https://brainly.com/question/25275758
#SPJ1
What is “b” in the following quadratic equation:
4x^2-3x-11=0
Answer:
The value of b in the quadratic equation is -3
Step-by-step explanation:
4x²-3x-11=0
a = 4
b = -3
c = -11
(5 pts) A quadratic function f is given by f(x) = ax2 + bx + c where a is not 0. Select all
the statements that must be true about the graph of f.
a.
The y-intercept of the graph is at (0,c).
b.
The graph has an x-intercept at (c,0).
C.
When a < 0 the graph is open downward.
d.
The graph has two x-intercepts.
e.
If b = 0, then the vertex is on the y-axis.
Answers:
a) True. Plug in x = 0 and it leads to y = c. Therefore, the point (0,c) is on the parabola.b) False. Plug in y = 0 and apply the quadratic formula. One x intercept may sometimes be x = c, but it could easily be other values as well. Or perhaps you may not get any real number solutions at all. See part d) below.c) True. If a < 0, then the leading coefficient is negative. Overall, both endpoints will tend toward negative infinity to produce a parabola that opens downward.d) False. The quadratic may have one x intercept or it may not have any x intercepts at all. It depends on what the discriminant d = b^2 - 4ac is equal to. If d < 0, then we have no x intercepts. If d = 0, then we have exactly 1 x intercept. If d > 0, then we have two different x intercepts.e) True. The vertex's x coordinate is -b/(2a). If b = 0, then the x coordinate of the vertex is 0. The vertical line x = 0 is directly on top of the y axis.If the value of a is less than zero then the parabola is open downward. Then the correct option is C.
What is a quadratic equation?It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
A quadratic function f is given by f(x) = ax2 + bx + c where a is not 0.
a. The y-intercept of the graph is at (0,c). This is incorrect.
b. The graph has an x-intercept at (c,0). This is incorrect.
c. When a < 0 the graph is open downward. This is correct.
d. The graph has two x-intercepts. This is incorrect.
e. If b = 0, then the vertex is on the y-axis. This is incorrect.
More about the quadratic equation link is given below.
https://brainly.com/question/2263981
A rectangle has one corner in quadrant 1 on the graph of y=9-x^2 another at the origin a third on the positive y-axis and the fourth on the positive x-axis
The maximum area is, A = 10.392
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
y = 9-x²
first, Area = x × y
Area = x(9-x²)
Now,
the Domain: (0, 3)
Also, differentiating
A' = 0
9 - 3x² = 0
x²= 9/3
x =±3
So, the maximum area is
A= 1.732 x 6
A = 10.392
Learn more about equation here:
https://brainly.com/question/10413253
#SPJ1