y = 2
Step-by-step explanation:To determine the equation of the line that passes through (10,2) and (-3,2), we need to determine the slope of the line. Then substitute the slope and any given point in point slope form to obtain the equation of the line.
Finding the Slope of the line:[tex]\implies \text{Slope} = \dfrac{\text{Rise}}{\text{Run}} = \dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
[tex]\implies \text{Slope} = \dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
Substitute the coordinates of the given points:
[tex]\implies \text{Slope} = \dfrac{2 - 2}{-3 - 10 }[/tex]
Simplify the equation to determine the slope:
[tex]\implies \text{Slope} = \dfrac{0}{-3 - 10 }[/tex]
∴ 0 divided by ANY number is ALWAYS 0.
[tex]\implies \text{Slope} =0[/tex]
Finding the equation of the line:Point slope form formula: y - y₁ = m(x - x₁)
x₁ and y₁ are the coordinates of any given point.m is the slopeSubstitute the values in the point slope form:
[tex]\implies \text{Equation of line:} \ y - y_{1} = m(x - x_{1} )[/tex]
[tex]\implies \text{Equation of line:} \ y - 2 = 0(x - 10)[/tex]
Simplify the equation to determine the equation of the line:
∴ Any number multiplied by 0 is 0.
[tex]\implies \text{Equation of line:} \ y - 2 = 0[/tex]
[tex]\implies \text{Equation of line:} \ y = 0 + 2[/tex]
[tex]\implies \text{Equation of line:} \ y = 2[/tex]
Thus, the equation of the line is y = 2.
1. The Rock has an 88-gallon fish tank. When it needs to be cleaned, it can be drained at a rate of 6 gallons per minute. Handwritten. Show all work. Complete sentence for each question. (a) Assuming the tank was full, write a function in the form y=mx + b that represents the amount of water in the tank, Y, after X minutes. You will need to know the initial value and the rate of change. (b) How long has the tank been draining for if it has 34 gallons left?
Using linear function concepts, it is found that:
a) The function is y = 88 - 6x.
b) The tank has been draining it for 9 minutes.
What is a linear function?
A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Item a:
The full volume of the tank is of 88 gallons, hence the y-intercept is of b = 88.The volume can be drained at a rate of 6 gallons per minute, hence the slope is of m = -6.Thus, the equation is given by:
y = 88 - 6x.
Item b:
This is x for which y = 34, hence:
y = 88 - 6x
34 = 88 - 6x
6x = 54
x = 9.
The tank has been draining it for 9 minutes.
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The amount of water in the tank is given by y = -6x + 88, it would take 9 minutes for the water to remain 34 gallons.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let y represent the amount of water after x minutes.
The Rock has an 88-gallon fish tank which can be drained at a rate of 6 gallons per minute. Hence:
m = -6, b = 88
y = -6x + 88
For 34 gallons:
34 = -6x + 88
x = 9
The amount of water in the tank is given by y = -6x + 88, it would take 9 minutes for the water to remain 34 gallons.
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12. Make a box-and-whisker plot of the data. (1 point)
20, 23, 28, 14, 13, 24, 18, 11
O
10 12 14 16 18 20 22 24 26 28 30
10 12 14 16 18 20 22 24 26 28 30
O
.
.
10 12 14 16 18 20 22 24 26 28 30
.
10 12 14 16 18 20 22 24 26 28 30
The box-and-whisker plot of the data, showing the five-number summary, is shown in the image atatched below.
What is the Box-and-whisker Plot?The box-and-whisker plot is a plot that displays the minimum, maximum, median, lower and upper quartile of a data, which is termed as the five-number summary of a data.
Given the data, 20, 23, 28, 14, 13, 24, 18, 11, find the five-number summary:
Minimum - 11Lower Quartile - 13.5Median - 19Upper Qaurtile - 23.5Maximum - 28Therefore, the box-and-whisker plot of the data, showing the five-number summary, is shown in the image atatched below.
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Sharon wants to buy a shirt that costs $25. The sales tax is 5%. How much is the sales tax? What is her total cost for the shirt?
Answer:
Price before Taxes: $ 25.00
+ Sales Tax (5%):$ 1.25
Total Price with Tax:$ 26.25
for charles the great please help
Answer:
119
Step-by-step explanation:
23 plus 64 plus 32
I think I just did this question
A 16-pound force is applied to a 36-inch input arm. The resultant output torque is
A. 4 pound feet
B. 12 pound feet
C. 48 pound feet
D. 64 pound feet
So
Torque
[tex]\\ \rm\Rrightarrow \tau=3(16)[/tex]
[tex]\\ \rm\Rrightarrow \tau=48lbs\:ft[/tex]
10 ft
12 ft
15 ft
surface area:
volume :
Answer:
Step-by-step explanation:
Not enough information given in your question to provide an answer.
A store is having a Black Friday sale where all electronics are 20% off. Jessica also has a one-time use
coupon for 15% off. If Jessica received both discounts and paid $108.80 for a pair of headphones, what was
the original price of the headphones?
WILL GIVE BRAINLIEST
Step-by-step explanation:
20+15=35%
to find the original price all we have to do is use the formula-
original price = sale price / (1 - percent off/100)
original price = 108.80 / (1 - 35/100)
original price = 167.3846...
original price = 167.38
hope this helps you :D
Help please! I need help!!!!
Evita is solving the system of equations shown using the elimination method. first equation: 3x + 8y = 20 second equation: 5x – 2y = 4 - What operation will eliminate one of the variables?
A. multiply the first equation by 2
B. multiply the first equation by 4
C. multiply the second equation by 2
D. multiply the second equation by 4
Answer:
D. multiply the second equation by 4
Step-by-step explanation:
3x + 8y = 20 __ equation 1
5x – 2y = 4 ___ equation 2
multiply the second equation by 4
3x + 8y = 20 __ equation 1
20x – 8y = 16 ___ equation 2
============
23x = 36
x = 36/23
y = (4-5x)/-2
y = (4-5(36/23))/-2
y = 44/23
what is the digit 9 in this number 195,487
Answer: Is in the 10 thousands place 4
Step-by-step explanation: 100,000 90,000 400 80 7
Answer:
In this case the number 9 would be located in the tens of thousands.
---
Thank you so much for participate in the community of Brainly.com
I hope help you :)
Kind regards, Antonio.
The original price of a phone was reduced by $200.
If p = the phone's original price in dollars, which algebraic expression
represents the reduced price?
A. p- 200
B. 200 + p
C. 2002
D. 200-P
Given f(x) = 10/x^2- 7x-30
which of the following is true?
(see attached image, it’s not A)
Answer: f(x) is positive for all x<10
Proof of validity is shown below.
(-5, -1), 6
Write an equation of a circle with the given center & radius
Step-by-step explanation:
The equation of a circle with the given center and radius.
center = (-5,-1) and radius is 6
x²-y²-10x-2y-6=0.
What is the equation of circle?
The equation of the circle is the equation which is used to represent the circle in the algebraic equation form with the value of center point in the coordinate plane and measure of radius.
The standard form of the equation of the circle can be given as,
Here (h,k) is the center of the circle and (r) is the radius of the circle.
The equation of a circle with the given center and radius. center (-5,-1) and radius 6 has to be written. Use the above equation,
Thus, the equation of a circle with the given center and radius.
center (-5,-1) and radius is 6
x²-y²-10x-2y-6=0.
Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.2 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 12 minutes with each customer. (a) Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. (Round your answers to four decimal places. Report time in hours.)
The operating characteristics of the customer waiting line shows that the average service rate per hour is 5 customers per hour.
How to compute the operating characteristics?The average service rate per hour will be:
= 60/12 = 5
The average number of customers waiting will be:
= (2.2)²/5(5 - 2.2)
= 4.84/14
= 0.3457
The average number of customers in the system will be:
= 0.3457 + 2.2/5
= 0.7857
The average time that a customer spends waiting in the system will be:
= 0.3457/2.2
= 0.1571
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There are 5 dogs playing at the dog park. Tyrone has 4 biscuits to share equally among the dogs. Tyrone wants to know how many dog biscuits each dog will get.
21 = r -5
=
HOW DO WE SLOVE THIS
Answer:
R = 26.
Step-by-step explanation:
The way to solve this is to add 5 to both sides.
r=4.2
It may show subtraction but it is division, 21÷5=4.2
Luke’s has seven coins. He can make 11p with two of his coins. He can make 11p with three of his coins. He can make 11p with four of his coins. What are the seven coin that Luke’s has?
Answer:
1p 2p 2p 2p 5p 5p 10p
Step-by-step explanation:
Available coins that are less than 11p: 1p 2p 5p 10p
11p with two coins ⇒ 1p + 10p only
11p with three coins ⇒ 1p + 5p + 5p only
11p with three coins ⇒ 2p + 2p + 2p + 5p only
Therefore, the seven coins that Luke has are:
1p 2p 2p 2p 5p 5p 10p
Two science classes got to go to an amusement park. Counting the students and the chaperones, there were 54 people that went to the park, for a total cost of $367.50. Adult tickets cost $8.00 and student tickets cost $6.50.
Answer:
43 students and 11 chaperones
Step-by-step explanation:
Let a = number of chaperones or adults
Let s = number of students
1) We could set up two equations and solve them simultaneously using the substitution or the elimination method.
s + a = 54
8a + 6.50s = 367.50
I choose the substitution method.
2) Solve for s or y. I choose s.
a = 54 - s
8(54 - s) + 6.50s = 367.50
--------------------------------------
432 - 8s + 6.50s = 367.50
432 - 1.50s = 367.50
-1.50s = 367.50 - 432
-1.50s = -64.50
s = [tex]\frac{-64.50}{-1.50}[/tex]
s = 43
3) Substitute the result into one of the two equations above. I choose the first one.
43 + a = 54
a = 54 - 43
a = 11
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
Read explanation.
Step-by-step explanation:
The dilation is by a sf (of 6)
This means that to find P'Q', you do 3*6 which is 18
To find N'Q, you do 9*6 which is 54.
how many solutions does this system of equations have?
x-4y= -20
x-4y = -8
Answer:
Infinitely many
Step-by-step explanation:
Same slope, DIfferent Y-intercept
Find the area of the figure
Answer:
its 60
Step-by-step explanation:
because 10 time 6 equals 60
Tell if the slope is positive, negative, zero, or no slope. UNDEFINED
Answer:
Zero Slope
Step-by-step explanation:
A Negative Slope is going down on the graph and it is negative M (y=mx+b)
A Positive Slope has is going up on the Graph and it is a positive M (y=mx+b)
(Imagine a Mountain)
Zero Slope is where there is only one y value and infinite x values
Undefined is where there is one x value and infinite y values
This is what the questions/answers say for #16-19 or last picture if you can't read it, please answer all questions
16. The number of hours of sunlight in a particular location S(t) can be modeled by the function S of t equals 12 plus 2 times the sine of the quantity 2 times pi over 365 times t end quantity comma where t is the number of days after January 1st. (That is, t = 0 means January 1st.) After how many days will there be 12 hours of sunlight for the first time during the year?
365 over 4 days
365 over 2 days
1095 over 4 days
1095 over 2 days
17. A student was asked to prove the trigonometric identity tangent of one half times x plus cotangent of one half times x equals 2 times cosecant x period Which of the following could be the first step in proving the identity?
the quantity 1 minus cosine x end quantity over sine x plus sin x over the quantity 1 minus cosine x end quantity equals 2 times cosecant x
sine x over the quantity 1 plus cosine x end quantity plus the quantity 1 plus cosine x end quantity over sine x equals 2 times cosecant x
the quantity 1 minus cosine x end quantity over sine x plus the quantity 1 minus cosine x end quantity over sine x equals 2 times cosecant x
I only
II only
I and II only
I, II, and III
18. Based on the graph of the trigonometric functions f (θ) = 4sin θ + 1 and g (θ) = cos 2θ, at what value(s) on the interval [0, 2π) does f (θ) = g (θ)?
0, π
pi over 2 comma 5 times pi over 2
5 times pi over 4 comma 7 times pi over 4
pi over 4 comma 3 times pi over 4 comma 5 times pi over 4 comma 7 times pi over 4
19. Which of the following shows a graph of a tangent function in the form y = atan(bx − c) + d, such that b = 2?
Problem 9 (#16)
In order to figure out when the amount of sunlight becomes 12 hours for the first time, we need to have [tex]S(t)=12[/tex] and solve the function for [tex]t[/tex]:
[tex]\displaystyle S(t)=12+2\sin\biggr(\frac{2\pi}{365}t\biggr)\\\\12=12+2\sin\biggr(\frac{2\pi}{365}t\biggr)\\\\0=2\sin\biggr(\frac{2\pi}{365}t\biggr)\\ \\0=\sin\biggr(\frac{2\pi}{365}t\biggr)\\\\\pi=\frac{2\pi}{365}t\\\\365\pi=2\pi t\\\\\frac{365}{2}=t[/tex]
Thus, B is the correct answer
Problem 10 (#17)
Recall the half-angle identity [tex]\displaystyle \tan\frac{x}{2}=\frac{1-\cos x}{\sin x}=\frac{\sin x}{1+\cos x}[/tex]Hence, [tex]\displaystyle \cot\frac{1}{2}x=\frac{1}{\tan\frac{1}{2}x }=\frac{\sin x}{1-\cos x}=\frac{1+\cos x}{\sin x}[/tex]So, you could techincally say that the first two options work as each function has their respective identities true for each option.
Thus, I and II is the correct answer
Problem 11 (#18)
[tex]f(\theta)=g(\theta)\\\\4\sin\theta+1=\cos2\theta\\\\4\sin\theta+1=1-2\sin^2x\\\\2\sin^2\theta+4\sin\theta=0\\\\2\sin\theta\bigr(\sin\theta+2)=0[/tex]
[tex]\displaystyle 2\sin\theta=0\\\\\sin\theta=0\\\\\theta=\{0,\pi\}[/tex]
[tex]\sin\theta+2=0\\\\\sin\theta=-2[/tex]
The solution is indeterminate since -2 does not fall in the range of [tex][-1,1][/tex].
Thus, A is the correct answer
Problem 12 (#19)
Recall that the period of a tangent function [tex]y=a\tan(bx-c)+d[/tex] is [tex]\frac{\pi}{|b|}[/tex]. Hence, if [tex]b=2[/tex], then the period of the tangent function is [tex]\frac{\pi}{2}[/tex]. Since I can't see the graphs, you need to identify which graph has a period of [tex]\frac{\pi}{2}[/tex] (meaning the distance between two vertical asymptotes is pi/2), or post this problem again with the graphs.
3. Select all expressions equivalent to x-5.
Copied for free from openurresources.org
Select all that apply:
A. x+(-5)
OB. X-(-5)
nc. -5+x
OD. -5-x
DE. 5-X
OF. -5-(-x)
OG. 5+x
Submit Answer
The fraction strip shown below is shaded to represent dam fraction which fraction strip is shaded to represent a fraction equal to the fraction strip shown above
Answer:shade 2 strips out of 4 to get fraction strip equivalent to Mandy's fraction strip
Step-by-step explanation:
Please help :(
A data set has a median of 12, an upper quartile of 15, a lower quartile of 10, a minimum of 4, and a maximum of 20. Which statement is true of the box plot of this data set?
The box will go from 10 to 12.
A line dividing the box will be at 12.
The left whisker will go from 4 to 15.
The right whisker will go from 12 to 20.
Give explanation for brainliest.
And thanks for all the follows!
Given:
A data set has a median of 12, an upper quartile of 15, a lower quartile of 10, a minimum of 4, and a maximum of 20.
To find:
The correct statement for the box plot.
Solution:
Lower quartile is 10 and upper quartile is 15, so the box will go from 10 to 15.
Median of the data set is 12, so a line dividing the box will be at 12.
Minimum value is 4 and lower quartile is 10, so the left whisker will go from 4 to 10.
Upper quartile is 15 and maximum value is 20, so the right whisker will go from 15 to 20.
Therefore, the correct option is B.
-HEAVEN
help me please aaaaaaaaaaaaaaaaaaaaaaa
Answer: 162
Step-by-step explanation:
C D
5
What is the slope of the equation Y =
7
-42
0-7
7
4
54
05
Answer:
The answer is:
[tex] \frac{5}{4} [/tex]
Step-by-step explanation:
Because In the equation y=mx+b, m is always the slope.
Which of the following is a solution of y-x>-3?
(2,6)
(2,-1)
(6,2)
Answer:
Step-by-step explanation:
Answer= (2,6)
">" means greater than..
y-x >-3 so in this case you would plug in y= 6, and x=2
6-2=4 and 4 is greater than -3. :)
The other answers give negative numbers of -3, and -4 which aren't greater than -3.
solve tan(x)(tanx+1)=0
Answer: [tex]x=n\pi , \frac{3\pi }{4} +n\pi[/tex]
Step-by-step explanation:
Since we have a product here, either term can be zero. We can individually set each term equal to zero:
[tex]tan(x)=0[/tex]
[tex]tan(x)+1=0[/tex]
Beginning with the first term. It is saying "tangent of what gives zero". Well, tangent of zero gives zero. The value pi also gives zero:
[tex]tan(0)=0[/tex]
[tex]tan(\pi )=0[/tex]
We can generalize this by saying 'x' is equal to pi multiplied by an integer 'n', where 'n' is 0, 1, 2, 3...
[tex]x=n\pi[/tex]
Moving on to the second term, lets subtract that 1 to the other side to get:
[tex]tan(x)=-1[/tex]
Tangent of what gives -1? That would be 3pi/4. Tangent is the ratio of sine and cosine. So, you can essentially think of tangent as the slope of the line on a unit circle. Refer to the figure below. Another location along the unit circle where we get -1 is at 7pi/4, which is just 3pi/4 shifted by 180 degrees. Therefore, we can generalize this solution by adding 'npi' to 3pi/4 to get:
[tex]x=3\pi /4+n\pi[/tex]
where 'n' is 0, 1, 2, 3...
Marlon has 2 gallons. how many cups of juice does he have?
Answer: Marlon would have 32 cups of juice
Step-by-step explanation:
Since there are 16 cups in one gallon, you simply multiply 16 by 2, to get your answer of 32 cups.