Which equation represents a line that passes through the two points in thetable?хy3166A. y-6=3/5(x-6)B. y+1=5/3(x+3)C. y+6=3/5(x+6)D. y-1=5/3(x-3)
Answers
To obtain the equation of the line that passes through these points, you can first obtain the slope of the line, using the formula
\(\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1),(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}\)And then use the point-slope formula
\(y-y_1=m(x-x_1)\)So, in this case, you have
\(\begin{gathered} (x_1,y_1)=(3,1) \\ (x_2,y_2)=(6,6) \end{gathered}\)\(\begin{gathered} m=\frac{6-1}{6-3} \\ m=\frac{5}{3} \end{gathered}\)Now using the point-slope formula
\(\begin{gathered} y-y_1=m(x-x_1) \\ y-1=\frac{5}{3}(x-3) \end{gathered}\)Therefore, the correct answer is D.
\(y-1=\frac{5}{3}(x-3)\)Related Questions
A sample of a radioactive isotope had an initial mass of 650 mg in the year 2003 and decays exponentially over time. A measurement in the year 2005 found that the sample's mass had decayed to 490 mg. What would be the expected mass of the sample in the year 2007, to the nearest whole number?
Answers
Answer:
330 mg
Step-by-step explanation:
at the start of the year 2003 the starting mass is (650) mg
2 years have passed and the mass now is (490) mg
the subtraction of these will let us know how many MG decayed
650 - 490 = 160 mg
so in 2 years 160 mg decayed, how about in one year?
160/ 2 = 80 mg per year
we started at 2003 and we need the end result in 2007 which is
2007- 2003 = 4 years
4 multiplied by 80 = 320 mg decayed in 4 years
by subtracting it from 650 we will get the result
650 - 320 = 330 mg!
Last year, a gardening store ordered 530,570 potted plants. This year, they ordered 424,456 potted plants. What is the percent of decrease in the number of potted plants ordered annually?
Answers
Answer:
last year = 530570
this year = 424456
decreased plants = 530570-424456 = 106114
decreased percent = 106114÷530570×100%
= 20%
therefore 20% is the decrease precent in the number of potted plants ordered anually
The NWBC found that 16.5% of women-owned businesses did not provide any employee benefits. What sample size could be 99% confident that the estimated (sample) proportion is within 6 percentage points of the true population proportion?
Answers
A sample size of 329 would be required to be 99% confident that the estimated proportion of women-owned businesses not providing employee benefits is within 6 percentage points of the true population proportion.
To calculate the required sample size, we can use the formula:
n = (\(z^2\) * p * q) /\(e^2\)
where n is the sample size, z is the z-score corresponding to the desired level of confidence (in this case, 2.576 for 99% confidence), p is the estimated population proportion (0.165, based on the NWBC's finding), q is 1-p, and e is the maximum error we want to tolerate (in this case, 0.06 or 6 percentage points).
Substituting the values, we get:
n = (2.576^2 * 0.165 * 0.835) / \(0.06^2\)
Solving for n, we get:
n ≈ 329
Therefore, a sample size of 329 would be required to be 99% confident that the estimated proportion of women-owned businesses not providing employee benefits is within 6 percentage points of the true population proportion. Note that this assumes a simple random sample and that the population size is much larger than the sample size, so the finite population correction is not needed.
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s the Administrator for Cloud Computing, you have created a custom object that is the detail object in a master-detail relationship with Account. What is TRUE about the OWD setting for the custom object
Answers
In the scenario where a custom object is the detail object in a master-detail relationship with Account, the Organization-Wide Default (OWD) setting for the custom object would be controlled by the OWD setting of the master object, which is Account.
In Salesforce, the Organization-Wide Default (OWD) setting determines the default level of access for records of an object within an organization. When a custom object is set as the detail object in a master-detail relationship with Account, the OWD setting for the custom object will be controlled by the OWD setting of the master object, which is Account in this case.
The OWD setting for Account will dictate the level of access for the related records of the custom object. For example, if the OWD setting for Account is set to "Private," the related records of the custom object will also inherit the "Private" access level. This means that only users with appropriate sharing interest, such as those assigned to Account roles or sharing rules, will have access to the related records of the custom object.
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What is TRUE about the Organization-Wide Default (OWD) setting for the custom object in a master-detail relationship with Account?
As the balloon inflates at 20 cubic inches per second, the diameter and radius are changing. let's focus on the moment when the radius is 12 inches. share your answer with correct units.
Answers
At the moment when the radius is 12 inches, the balloon is inflating at a rate of 20 cubic inches per second.
To determine the rate at which the radius is changing, we can use the formula for the volume of a sphere, which is given by \(V = \left(\frac{4}{3}\right)\pi r^3\), where V is the volume and r is the radius.
Taking the derivative of both sides with respect to time t, we get \(\frac{dV}{dt} = 4\pi r^2\left(\frac{dr}{dt}\right)\), where \(\frac{dV}{dt}\) represents the rate of change of volume with respect to time and \(\frac{dr}{dt}\) represents the rate of change of radius with respect to time.
Given that \(\frac{dV}{dt} = 20\) cubic inches per second, we can substitute this value into the equation and solve for \(\frac{dr}{dt}\) when r = 12 inches:
\(20 = 4\pi (12)^2 \left(\frac{dr}{dt}\right)\)
Simplifying the equation:
\(20 = 576\pi \left(\frac{dr}{dt}\right)\)
Dividing both sides by 576π:
\(\left(\frac{dr}{dt}\right) = \frac{20}{576\pi}\)
Therefore, the rate at which the radius is changing when the radius is 12 inches is approximately \(\frac{20}{576\pi}\) inches per second.
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help pleaseeeeeeeeeee
Answers
the answer is the last 2. the 3rd one are both equal to -72 and the last one they both equals to 0.75.
Select all the correct answers. Which equations represent functions? 2x + 3y = 10 4x = 16 2x − 3 = 14 3y = 18 14.6 = 2x
Answers
The equation that represent a function is 2x + 3y = 10.
How to know an equation that represent a function?A function relates each element of a set with exactly one element of another set (possibly the same set).
A function relates input and output.
Linear equations are function. Linear equation can be represented in slope intercept form as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation that represent a function is 2x + 3y = 10.
Hence,
4x = 162x − 3 = 143y = 1814.6 = 2xare just relation not a function.
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Quadrilateral MNPQ is shown on the grid below.
What is the area, in square units, of the quadrilateral?
A) 182 square units
B) 4550 square units
C) 9100 square units
D) 91 square units
Answers
Answer:
42 square units
Step-by-step explanation:
Find the diagram attached
Area of the diagram = Area of the triangle + Area of rectangle
Area of rectangle = Length * Width
Area of rectangle = 3 * 6
Area of rectangle = 18 square units
Area of triangle = 1/2 * base * height
Get the base of the tringle using the pythagoras theorem;
b^2 = 10^2-6^2
b^2 = 100 - 36
b^2 = 64
b = 8units
height = 6 units
Area of the triangle = 1/2 * 8 * 6
Area of the triangle = 48/2
Area of the triangle = 24 square units
Area of the figure = 18+24
Area of the figure = 42 square units
how to solve part ii and iii
Answers
(i) Given that
\(\tan^{-1}(x) + \tan^{-1}(y) + \tan^{-1}(xy) = \dfrac{7\pi}{12}\)
when \(x=1\) this reduces to
\(\tan^{-1}(1) + 2 \tan^{-1}(y) = \dfrac{7\pi}{12}\)
\(\dfrac\pi4 + 2 \tan^{-1}(y) = \dfrac{7\pi}{12}\)
\(2 \tan^{-1}(y) = \dfrac\pi3\)
\(\tan^{-1}(y) = \dfrac\pi6\)
\(\tan\left(\tan^{-1}(y)\right) = \tan\left(\dfrac\pi6\right)\)
\(\implies \boxed{y = \dfrac1{\sqrt3}}\)
(ii) Differentiate \(\tan^{-1}(xy)\) implicitly with respect to \(x\). By the chain and product rules,
\(\dfrac d{dx} \tan^{-1}(xy) = \dfrac1{1+(xy)^2} \times \dfrac d{dx}xy = \boxed{\dfrac{y + x\frac{dy}{dx}}{1 + x^2y^2}}\)
(iii) Differentiating both sides of the given equation leads to
\(\dfrac1{1+x^2} + \dfrac1{1+y^2} \dfrac{dy}{dx} + \dfrac{y + x\frac{dy}{dx}}{1+x^2y^2} = 0\)
where we use the result from (ii) for the derivative of \(\tan^{-1}(xy)\).
Solve for \(\frac{dy}{dx}\) :
\(\dfrac1{1+x^2} + \left(\dfrac1{1+y^2} + \dfrac x{1+x^2y^2}\right) \dfrac{dy}{dx} + \dfrac y{1+x^2y^2} = 0\)
\(\left(\dfrac1{1+y^2} + \dfrac x{1+x^2y^2}\right) \dfrac{dy}{dx} = -\left(\dfrac1{1+x^2} + \dfrac y{1+x^2y^2}\right)\)
\(\dfrac{1+x^2y^2 + x(1+y^2)}{(1+y^2)(1+x^2y^2)} \dfrac{dy}{dx} = - \dfrac{1+x^2y^2 + y(1+x^2)}{(1+x^2)(1+x^2y^2)}\)
\(\implies \dfrac{dy}{dx} = - \dfrac{(1 + x^2y^2 + y + x^2y) (1 + y^2) (1 + x^2y^2)}{(1 + x^2y^2 + x + xy^2) (1+x^2) (1+x^2y^2)}\)
\(\implies \dfrac{dy}{dx} = -\dfrac{(1 + x^2y^2 + y + x^2y) (1 + y^2)}{(1 + x^2y^2 + x + xy^2) (1+x^2)}\)
From part (i), we have \(x=1\) and \(y=\frac1{\sqrt3}\), and substituting these leads to
\(\dfrac{dy}{dx} = -\dfrac{\left(1 + \frac13 + \frac1{\sqrt3} + \frac1{\sqrt3}\right) \left(1 + \frac13\right)}{\left(1 + \frac13 + 1 + \frac13\right) \left(1 + 1\right)}\)
\(\dfrac{dy}{dx} = -\dfrac{\left(\frac43 + \frac2{\sqrt3}\right) \times \frac43}{\frac83 \times 2}\)
\(\dfrac{dy}{dx} = -\dfrac13 - \dfrac1{2\sqrt3}\)
as required.
A local restaurant is premiering two new dishes in one night. From the customers who went to the restaurant that night, 71% chose to eat Dish A, and the other 29% chose to eat Dish B. Of those that chose Dish A, 65% enjoyed it. Of those that chose Dish B, 19% enjoyed it. Calculate the joint probability that a randomly selected customer chose Dish A and enjoyed it. Specify your answer to at least 3 decimals. (Hint: creating a probability tree may help) number (rtol=0, atol=0.001)
Answers
The joint probability that a randomly selected customer chose Dish A and enjoyed it can be calculated using the given information. The calculated probability is 0.464.
To calculate the joint probability, we can use the concept of conditional probability. Let's denote the events as follows:
A: Customer chooses Dish A
B: Customer enjoys the chosen dish
We are given the following probabilities:
P(A) = 0.71 (71% chose Dish A)
P(B|A) = 0.65 (65% enjoyed Dish A)
To calculate the joint probability, we multiply the probability of choosing Dish A by the probability of enjoying it:
P(A and B) = P(A) * P(B|A)
Substituting the values, we have:
P(A and B) = 0.71 * 0.65 = 0.4615
Rounding to three decimal places, the joint probability is approximately 0.464.
Therefore, the joint probability that a randomly selected customer chose Dish A and enjoyed it is 0.464 or approximately 0.464.
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Ndidi rides y km at 10 km/hr, then walks 0.5y km at 3 km/hr. She is away from. home less than 4hours. Find the range of values of y
Answers
Ndidi rides y km at 10 km/hr, then walks 0.5y km at 3 km/hr. She is away from. home less than 4hours.Range of the values of Y is =24/7
Let's call the total time spent riding and walking t hours. We know that t is less than 4 hours, so:
t = time spent riding + time spent walking < 4 hours
The time spent riding is given by y / 10 km/hr and the time spent walking is given by 0.5y / 3 km/hr. So, we can write the inequality as:
t = y / 10 + 0.5y / 3 < 4
Expanding and simplifying the expression on the left side gives:
7/6y < 4 * 6/7
Multiplying both sides by 6/7 gives:
y < 4 * 6/7 * 6/7 = 24/7
So, the range of values of y is 0 < y < 24/7 km. This means that Ndidi rode less than 24/7 km, but more than 0 km.
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Combine the like terms
2g + 15 + 3g + g + g- 18
Answers
Answer:
7g - 3
Step-by-step explanation:
2g + 15 + 3g + g + g - 18
2g + 3g + g + g + 15 - 18
7g - 3
Josie needs to rent a car from SureRide Car Rentals. The cost of renting a car iS a
one-time fee of $80 plus $0.75 per mile. Write and graph an equation to represent
pay tO rent a car a from SureRide.
the cost which Josie must
Answers
Answer: y = 0.75x + 80
Step-by-step explanation:
let x = 1 mile
y = 0.75x + 80
On Monday it rained for 3 hours and 20 minutes. The total rainfall amount in that time was 4 inches. What was the average rate of rainfall per hour?
Answers
Answer:
\(1\frac{1}{5}\)
~~~~~~~~~~~
4 ÷ 3\(\frac{1}{3}\)
4 ÷ \(\frac{10}{3}\)
4* \(\frac{3}{10}\)
\(\frac{12}{10}\)
\(1\frac{1}{5}\)
Step-by-step explanation:
Which set of ordered pairs does not represent a function?
○ {(0, -4), (8,5), (−5, 6), (6,5)}
○ {(0, -1), (-4, 0), (-2, -1), (7,-7)}
○ {(0, 3), (-3, 6), (-7,3), (9,-5)}
O {(8,-2), (-2, -3), (6, 6), (-2,-6)}
Answers
Is the second side “LK and HI” or the other way around?
Answers
Answer:
They aare both the same
Step-by-step explanation:
Theresa Mitsoto invested $3,500 in a 3-year CD that paid 6.5% annual interest. She cashed out the CD at the end of two years with an early withdrawal penalty of 3 months simple interest. What penalty did Theresa pay?
Answers
Answer:
$56.875
Step-by-step explanation:
Given that :
Amount invested = principal, p = 3500
Interest rate, r = 6.5% = 0.065
Penalty on withdrawal = 3 month simple interest
Simple interest = principal * rate * time
Time = 3 months = 3/12 = 0.25 years
Hence,
Simple interest = 3500 * 0.065 * 0.25
Simple interest = $56.875
Hence, penalty paid = $56.875
its not the right answer
Answers
R is the midpoint of ST. R has coordinates (4, -3) and S has coordinates (-1, 2). Find the coordinates of T.
Answers
Answer:
(1.5,2.5) I think
Step-by-step explanation:
I put it into demos
Suppose a company wants to introduce a new machine that will produce a marginal annual savings in dollars given by S '(x)= 175 - x^2, where x is the number of years of operation of the machine, while producing marginal annual costs in dollars of C'(x) = x^2 +11x. a. To maximize its net savings, for how many years should the company use this new machine? b. What are the net savings during the first year of use of the machine? c. What are the net savings over the period determined in part a?
Answers
a) To maximize its net savings, the company should use the new machine for 7 years. b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar). c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).
Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.
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Write the equation in standard form using integers
(no fractions or decimals): y= -2/3 x-1
Answers
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
\(y=-\cfrac{2}{3}x-1\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y)=3\left( -\cfrac{2}{3}x-1 \right)} \\\\\\ 3y=-2x-3\implies {\Large \begin{array}{llll} 2x+3y=-3 \end{array}}\)
(5y+3)(4y+9)=66 What is the value of y
Answers
Answer:
y = 39/20
Step-by-step explanation:
(20y + 27 = 66
20y = -27 + 66
20y =39
y = 39/20
how do I do this properly
Find the slope of the line that passes through (37, 7) and (-23, 100).
Answers
Answer:
the slope is -1.55
Step-by-step explanation:
(y2 -y1) / (x2 -x1)
A net force of 125 N is applied to a certain object. As a result, the object accelerates with an acceleration of 24.0 m/s2. The mass of the object is 144 kg.
Answers
The net force acting on the object is 3456 N, the objective with an acceleration.
The net force applied to an object is equal to the product of its mass and acceleration, according to Newton's second law of motion. Mathematically, this can be represented as:
Fnet = ma
Where Fnet is the net force, m is the mass, and a is the acceleration. In your scenario, the net force applied to the object is 125 N, and its acceleration is 24.0 m/s2. Therefore, we can rearrange the formula and solve for the mass of the object as follows:
m = Fnet / a
m = 125 N / 24.0 m/s2
m = 5.21 kg
However, this answer does not match the given mass of the object, which is 144 kg. This suggests that there may be an error in one of the values provided. Assuming the mass of the object is actually 144 kg, we can use the same formula to solve for the net force acting on it as follows:
Fnet = ma
Fnet = 144 kg * 24.0 m/s2
Fnet = 3456 N
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The mass of an object with net force value = 125 Newton and acceleration of 24.0 m/s² is equals to the 5.208 kg. So, option(c) is right one.
The force formula is derived by Newton's second law of motion. The basic formula force applied on object is F = ma, which implies that net force is equals to product of mass and acceleration of an object. We have an object with the following information, Net applied force on object, F = 125 N
Acceleration of an object, a = 24.0 m/s²
We have to determine mass of object. Using the above force formula, F = M× a
where M --> mass in kilograms
a --> Acceleration in m/s²
F --> net force in Newton
Substitute all known values in above formula, 125 N = M × 24.0 m/s²
=> M = = \(\frac{125}{24}\)
=> M = 5.208 kg
Hence, required value is 5.208 kg.
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Complete question:
A net force of 125 N is applied to a certain object. As a result, the object accelerates with an acceleration of 24.0 m/s^2. The mass of the object is ?
a) 144 kg
b) 236 kg
c) 5.208 kg
d) 459 kg
A store sells new video games for $55 each. Used video games sell for $12 each. Jacob is buying 3 new video games and x used video games. Which equation can be used to find y, the total price Jacob must pay in dollars?
A. y = 12x+55
B. y =12x+165
C. y = 165x + 12
D. y = 165x+12
Please help I need to pass 7th grade if I don't I'ma be in HUGE trouble
Answers
Answer:
D y=165x+12
Step-by-step explanation:
Answer:
D. y = 165x+12
Step-by-step explanation:
Draw two polygons that are similar but could be mistaken for not being similar. Explain why they are similar.
Answers
Answer:
they could possibly have the same number of vertices
A picture 10 feet long is to be centered on a wall that is 15 feet long, How much space is there from
the edge of the wall to the picture?
Answers
Answer:
2.5
Step-by-step explanation:
15-10=5
5/2=2.5
This triangle has one side that lies on an extended line segment.
Based on this triangle, what statement about x is true?
Responses
x = 33 because 180−147=33
x, = 33 because , 180 minus 147 equals 33
x = 62 because 147−85=62 and 85 + 62 = 147
x, = 62 because , 147 minus 85 equals 62, and 85 + 62 = 147
x = 95 because 180−85=95 and 85 + 95 = 180
x, = 95 because , 180 minus 85 equals 95, and 85 + 95 = 180
x = 118 because 180 − 147 + 85 = 33 + 85 = 118
Answers
In a triangle one side that lies on an extended line segment, statement about x is true, x = 62 because 147−85=62 and 85 + 62 = 147. So Option B is correct
What is a triangle?In mathematics, the triangle is a type of polygon which has three sides and three vertices. the sum of all the interior angles of the triangle is 180°
Given that,
A triangle, which has one interior angle 85° and one exterior angle 147°
Another exterior angle x = ?
It is already known that,
Sum of complementary angles are 180
So,
⇒ Y + 147 = 180
⇒ Y = 180 - 147
⇒ Y = 33
sum of all the interior angles of the triangle is 180°
X + Y + 85 = 180
X = 180 - 85 - 33
X = 62
Hence, the value of x is 62
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Find X? 40 Points :)
Answers
Answer:
x = 2 sqrt(7)
Step-by-step explanation:
since the right triangles are similar
hyp leg
------ = ---------
leg part
(6+8) x
--------- = ----------
x 2
Using cross products
x^2 = (6+8) *2
x^2 = 28
Take the square root of each side
x = sqrt(28)
x = sqrt(4) sqrt(7)
x = 2 sqrt(7)
Answer:
x= 69420
Step-by-step explanation:
bc it can be
Suppose that a researcher is interested in estimating the mean systolic blood pressure, μ, of executives of major corporations. He plans to use the blood pressures of a random sample of executives of major corporations to estimate μ. Assuming that the standard deviation of the population of systolic blood pressures of executives of major corporations is 24 mm Hg, what is the minimum sample size needed for the researcher to be 95% confident that his estimate is within 3 mm Hg of μ?Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).
Answers
In order to find the sample size, we can use the following formula that relates the population and sample standard deviations:
\(\sigma_{\bar{x}}=z\frac{\sigma}{\sqrt{n}}\)For a confidence interval of 95%, we have z = 1.96.
Then, using the values of the standard deviations, we have:
\(\begin{gathered} 3=1.96\frac{24}{\sqrt{n}}\\ \\ 3=\frac{47.04}{\sqrt{n}}\\ \\ \sqrt{n}=11.76\\ \\ n=138.3 \end{gathered}\)Rounding to the next whole number, we have a sample size of 139.