Therefore , the solution of the given problem of equation comes out to be the equation of the parabola in standard form is x² - 10x - 12y + 13 = 0
Define equation.In arithmetic equations, the identical figure (=) is used to denote the equivalence of two assertions. It is demonstrated that mathematical methods, which have acted as manifestations of reality, can be used to assess a variety of numerical factors. The equal sign actually splits the number 12 into two separate pieces, despite the fact that the result is y + 6 = 12.
Here,
The distance between the focus and vertex is the same as the distance between the vertex and directrix, which is |-4 - (-1)| = 3. This distance is also equal to the absolute value of the coefficient "a" in the equation of the parabola.
Therefore, the equation of the parabola in vertex form is:
(x - 5)² = 4p(y + 1)
where "p" is the distance between the vertex and the focus, which is 3. Substituting this value into the equation gives:
(x - 5)² = 4(3)(y + 1)
Simplifying:
(x - 5)² = 12y + 12
Expanding the left side:
x² - 10x + 25 = 12y + 12
Moving all the terms to one side:
x² - 10x - 12y + 13 = 0
So the equation of the parabola in standard form is:
x^2 - 10x - 12y + 13 = 0
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When a plant or animal dies, it stops acquiring carbon-14 from the atmosphere. The amount y (in grams) of carbon-14 in the body of an organism after
t years is-y = a(0. 5)*/3730, where a is the initial amount grams). What percent of the carbon-14 is released each year? Round your answer to the
nearest hlindredth
At 0.0175% of the carbon-14 is released each year, rounded to the nearest hundredth.
The amount of carbon-14 released each year can be represented as the rate of change of the amount of carbon-14 in the body of an organism with respect to time.
Carbon-14, the longest-lived radioactive isotope of carbon, whose decay allows the accurate dating of archaeological artifacts. The carbon-14 nucleus has six protons and eight neutrons, for an atomic mass of 14.[tex]\frac{d(y)}{dt}=\frac{-y}{tau}[/tex]Where
d(y)/dt represents the rate of change of the amount of carbon-14 in the body. y represents the amount of carbon-14 in the body, and tau (τ) represents the half-life of carbon-14 (5730 years).To find the percent of the carbon-14 that is released each year, we can divide the rate of change by the initial amount of carbon-14 and multiply by 100 to express it as a percentage:
⇒percent released/year =[tex]=100*\frac{ d(y)}{dt}[/tex]/a
[tex]=\frac{-100*y}{a* tau}[/tex] = [tex]-100 * (0.5)^(t / tau) / tau[/tex]
At t = tau, the percent released/year will be[tex]-100 * (0.5)^\frac{(1) }{tau}[/tex],
which is approximately -0.0175 per year.
So,
Therefore, each year approximately 0.0175 percent of the carbon-14 is released, rounded to the nearest hundredth.
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ayudaa
la tarea es sobre intercalos numéricos en la recta numérica
x=2xER/2_>x<7(
Los intervalos numéricos para la recta numérica en el punto x=2, con 2>x<7, son: (2,7) e (2,∞).
Esto significa que los valores de x pueden oscilar entre 2 y 7, o bien entre 2 y el infinito.
Por ejemplo, el intervalo numérico (2,7) incluiría todos los números entre 2 y 7, incluyendo 2 y 7, pero excluyendo los números menores que 2 y mayores que 7. El intervalo numérico (2, ∞) significa que todos los números mayores que 2 están incluidos, mientras que los números menores que 2 no están incluidos.
Versión en inglés:
The numerical intervals for the number line at the point x=2, with 2>x<7, are: (2,7) and (2,∞).
This means that the values of x can range from 2 to 7, or from 2 to infinity.
For example, the numerical interval (2,7) would include all numbers between 2 and 7, including 2 and 7, but excluding numbers less than 2 and greater than 7. The numerical interval (2, ∞) means that all numbers greater than 2 are included, while numbers less than 2 are not included.
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-6(n-1)<3or2(n+1)>0 solve and then put on a number line pls
Answer: To solve the inequality, we start by isolating the variable n:
-6(n-1) < 3
-6n + 6 < 3
-6n < -3
n > 1/2
And for the other inequality:
2(n+1) > 0
2n + 2 > 0
2n > -2
n > -1
Now, we can plot these solutions on a number line:
[-----1/2-----][-------------n > 1/2----------------]
[-----n > -1-----][-------------]
So, the solution set for the inequality is n > -1 and n > 1/2, which means that n belongs to the interval (1/2, +∞).
Step-by-step explanation:
please help im not sure what it means
The slope of the linear function in this problem is given as follows:
m = -4.
How to calculate the slope?The slope of a linear function represents the rate of change of the linear function, hence it is calculated as the change in y divided by the change in x, taking two points.
From the graph of the function, when x increases from 0 to 3, y decays from 5 to -7, hence the slope is calculated as follows:
m =(-7 -5)/3
m = -4.
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FIST PERSON GETS THIS ANSWER RIGHT GET BRAINIEST!!!!!!!!!!
Answer: To happen before
Step-by-step explanation:
5. what rate (in mm/yr ) is the north american plate moving relative to the boundary? round your answer to 2 significant figures.
The major plate motion rates range from less than 10 mm/y to more than 100 mm/y. The fastest plate is the Pacific Plate, followed by the Australian and Nazca Plates. The North American Plate is one of the slowest, with average rates ranging from around 1 cm/y in the south to nearly 4 cm/y in the north.
Plates move as rigid bodies, it may appear surprising that the North American Plate can move at different rates in different locations. Plates move in a rotational fashion, as explained. For example, the North American Plate rotates counter-clockwise, while the Eurasian Plate rotates clockwise.
There are three types of plate boundaries: divergent, convergent, and transform (moving side by side). Before we discuss processes at plate boundaries, it is critical to note that there are no gaps between plates.
The plates are made up of crust and the lithospheric part of the mantle, and despite moving in different directions all the time, there is never a significant amount of space between them.
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a triangle with a vetex (-3, 5) is translated up 6 units. what are the coordinates of this vertex after it is translated?
Step-by-step explanation:
It is translated up 6 units, with the y value is vertical (up and down). The y value is 5, (x, y). Because it only moves up you would keep the x value, -3, and add 6 to the y value. So 5+6=11
The new coordinates are now (-3,5)
Hope this helps :)
Casey buys a bracelet. She pays for the bracelet and pays
$
0.72
$0.72dollar sign, 0, point, 72 in sales tax. The sales tax rate is
6
%
6%6, percent.
What is the original price of the bracelet, before tax?
Answer: The original price of the bracelet before tax can be found using the following formula:
original price = (total price) / (1 + sales tax rate as decimal)
In this case, the total price is 0.72 dollars, and the sales tax rate as a decimal is 0.06. Plugging these values into the formula, we get:
original price = 0.72 / (1 + 0.06)
original price = 0.72 / 1.06
Step-by-step explanation:
3/4 (1/6x + 16) = 3/7 (35/8 - 21)
Answer:
x=-153
Step-by-step explanation
3/4(1/6x) + 3/4(16) = 3/7(35/8)-3/7(21)
1/8x+12=15/8-9
8(1/8x+12=15/8-9)
1x+96=15-72
1x+96=-57
x=-153
the diameter of a manufactured widget is normally distributed with a mean of 65 and a standard deviation of 9. what is the probability a widget sampled at random will be less than or equal to 56? use excel and carry your answer to at least five decimal places.
Considering all the given information, the probability of a widget being less than or equal to 56 is approximately 0.1587
The formula for converting a value to a standard score, also known as a z-score, is:
z = (x - μ) / σ
Where x is the value of interest, μ is the mean, and σ is the standard deviation.
To find the probability of a widget being less than or equal to 56, we first find the corresponding z-score:
z = (56 - 65) / 9 = -1
We can then use the cumulative distribution function (CDF) of the standard normal distribution to find the probability of a z-score being less than or equal to -1:
P(z ≤ -1) = 0.1587
So the probability of a widget being less than or equal to 56 is approximately 0.1587, or 15.87%.
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A quantity with an initial value of 8500 grows exponentially at a rate such that the quantity doubles every 9 years. What is the value of the quantity after 23 years, to the nearest hundredth?
Answer: We can use the formula for exponential growth to find the value of the quantity after 23 years:
Q(t) = 8500 * 2^(t/9)
Where Q(t) is the value of the quantity after t years, and t/9 is the number of doublings that have occurred.
Substituting t = 23 into the formula:
Q(23) = 8500 * 2^(23/9) = 8500 * 2^2.56 = 8500 * 12.90 = 109350
So, after 23 years, the quantity has a value of approximately 109,350, rounded to the nearest hundredth.
Step-by-step explanation:
Why in arithmetic sequence does the graph of Tn vs n need to be a straight line
Answer:
It's because the graph of arithmetic sequence forms a set of discrete points lying on a straight line.
In a direct variation, y=16 when x=2. Write a direct variation equation that shows the relationship between x and y.
A direct variation equation that shows the relationship between x and y is,
y = 8x.
What is proportional relationship?A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.
Given:
In a direct variation, y=16 when x=2.
The proportional relationship between x and y:
y ∝ x.
y = kx, where k is constant.
When x = 2,
16/2 = k
k = 8.
Therefore, the relationship is y = 8x.
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Please help me solve: 10(s+9)+3
Answer:
[tex]\huge\boxed{\sf 10s + 93}[/tex]
Step-by-step explanation:
Given expression:= 10 (s + 9) + 3
Distribute 10 to s and 9= 10s + 90 + 3
Add 90 and 3= 10s + 93[tex]\rule[225]{225}{2}[/tex]
Answer:
Step-by-step explanation:
10(s + 9) +3
10s + 90 + 3
10s + 90 +3
10s + 93
Solution 10s + 93
Lin is shopping for a couch with her dad and hears him ask the salesperson, "How much is your commission?" The salesperson says that her commission is 5 1/2% of the selling price. (Hint: 5 1/2% is what decimal number?)
In linear equation, the store will get $468.72 from the sale of the couch.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
a.
Commission can be referred to as the reward given by the company on goods for the employee to sell products in order to make more sales and more money.
Commission is calculated as follows:
Total commission = Total Sales * Commission Percentage
Given
Total Sales = $495
Commission Percentage = 5½%
Substitute in, the above values
Total Commission = $496 * 5½%
Total Commission = $496 * 5.5%
Total Commission = $496 * 0.055
Total Commission = $27.28
Hence, the total commission is calculated as $27.28
b. The amount remitted to the store is calculated as
Amount = Total Sales - Total Commission
Where Total Sales = $496
Total Commission = $27.28
Amount = $496 - $27.28
Amount = $468.72
Hence, the store will get $468.72 from the sale of the couch.
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The complete question is -
Lin is shopping for a couch with her dad and heard him ask the salesperson “how much is your commission?” The salesperson says that her commission is 5½% of the selling price.
A.How much commission will the salesperson earn by selling a couch for $495?
B.How much money will the store get from the sale of the couch?
Answer:
a. The total commission is $27.28
b. The store will get $468.72 from the sale of the couch
Please help me with this
Answer:
40 to 60 is the answer of this question
The diagram shows the floor plan of Jill's dining room.
Jill is going to cover the floor with wooden floorboards.
1.5m
Diagram NOT
accurately drown
The floorboards are sold in packs. One pack of floorboards will cover 2.25 m²
Work out how many packs Jill needs.
You must show all your working.
Answer:
7 packs of floorboards
Step-by-step explanation:
total area of floor= (4.5×2)+(2×3)
= 9+6
= 15m2
15÷2.25= 6.6666666
~7 packs (rounded up to the nearest whole no.)
what is the common denominator for 2/5,2/4,2/3?????
Answer:
60
good luck!
A professor biked to work this morning. He made the 6-mile trip to the university in 49 minutes. After a day of teaching and meeting with students, he took the same route back. This time, the trip took 58 minutes. What was his average speed for the whole trip?
Write your answer as a whole number or as a decimal rounded to the nearest tenth.
The average speed of whole trip was 6.7 mile per hour.
What is the average speed?Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t, where S is the average speed, d is the total distance, and t is the total time, is used to determine average speed.
Given that, the total distance =6+6=12 miles and total time
=58+49= 107 minutes
So, number of hours = 107/60
= 1.8 hours
Now, the average speed = 12/1.8
= 6.7 mile per hour
Therefore, the average speed is 6.7 mile per hour.
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please answer all these for crown and separate them from each other ty ill give u a crown
The values of x for the different diagrams are given below.
What are parallel lines?Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.
Given:
There are four diagrams.
Diagram 1:
By the alternate exterior angles,
8x + 19 = 139
8x = 120
x = 15
Diagram 2:
By the corresponding angles,
17x - 45 = 108
17x = 153
x = 9
Diagram 3:
By the alternate interior angles,
7x -1 = 13x - 43
6x = 42
x = 7
Diagram 4:
By the consecutive interior angles,
8x + 19 = 139
8x = 120
x = 15
Hence, the solutions for all the values are given above.
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The medal Zena won for athletics consists of silver and brass in the ratio 3:5. If the medal has a mass of 200g, calculate the mass of the silver.
Answer: mass of silver is 75g
Step-by-step explanation:
what is 16/21 as a decmil round to the nerste huderned
Answer:
0.7619047619≈0.76
Step-by-step explanation:
an activity has an optimistic time of 15 days, a most likely time of 18 days, and a pessimistic time of 27 days. what is the expected time?
The expected time (also known as the expected value or the mean) Is approximately 12.5 days.
The expected time for an activity is the average time it is likely to take, taking into account its optimistic, most likely, and pessimistic estimates. The three-point estimate formula is used to calculate the expected time by weighting the most likely estimate four times as much as the optimistic and pessimistic estimates. In this case, the optimistic time is 15 days, the most likely time is 18 days, and the pessimistic time is 27 days. By plugging these values into the formula, the expected time is calculated to be 12.5 days. This means that, on average, the activity is likely to take 12.5 days to complete.
The expected time (also known as the expected value or the mean) can be calculated using the three-point estimate formula, which is:
Expected time = (Optimistic time + 4 * Most likely time + Pessimistic time) / 6
Plugging in the values, we get:
Expected time = (15 + 4 * 18 + 27) / 6 = (75) / 6 = 12.5
So the expected time for this activity is 12.5 days.
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please please please help!
Answer:
I only
Step-by-step explanation:
any point and its coordinates is an ordered pair of (x, y).
in other words, we get the x value used for the function and the resulting y value.
if the equation is true for such a pair, then the point is on the line. if it is false, then not.
y = (-5/4)x + 5
(4, 0)
0 = (-5/4)×4 + 5 = -5 + 5 = 0
true.
(0, 5)
5 = (-5/4)×0 + 5 = 0 + 5 = 5
true.
y + 5 = (-5/4)(x - 4)
(4, 0)
0 + 5 = (-5/4)(4 - 4)
5 = (-5/4)×0 = 0
false.
so, II is not containing (4, 0).
therefore, only I is contains both points.
trevor wants to know the volume of the box shown so he can determine if it is large enough to hold his gardening supplies. What is the) volume of the box?
(The length is 1 1/2 and the widths are 1 1/6 and 1 /14)
Answer:
Step-by-step explanation:
The formula of volume is length x width x height.
please help with this i need the answer pleas answer and do not just talk
Answer:
Below
Step-by-step explanation:
a) DIRECT variation y = k x
10 = k (4)
10/4 = k = 2.5
y = 2.5 x
b) y = 2.5 x
y = 2.5 (10) = 25
i need help
schoology
Answer: 37 degrees
Hope this helps :)
Step-by-step explanation:
(The box in the corner tells you this is a right angle)
A right angle is 90 degrees
90 - 53 = 37
Answer:
37 degrees
Step-by-step explanation:
Angle a is equivalent to 37 degrees because the picture signifies a right angle; all right angles are equal to 90 degrees. The equation to solve this would be: 53+x=90, you would solve this by subtracting 90-53=x; x=37
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In 2010, the population of a city was 87,000. From 2010 to 2015, the population grew by 7.7%. From 2015 to 2020, it fell by 4.5%. To the nearest 100 people, what was the population in 2020?
Answer:
The population of the city in 2020 was 89,500 to the nearest 100 people.
Step-by-step explanation:
The original population in 2010 is 100%.
If the population is increased by 7.7% from 2010 to 2015, the total percentage in 2015 is 107.7% of the population in 2010.
Convert this to a decimal and multiply by the original population of 87,000 to find the population of the city in 2015.
[tex]\begin{aligned}\implies \sf 107.7\%\;of\;87000&=\sf 1.077 \times 87000\\&=\sf 93699\end{aligned}[/tex]
Therefore, the population of the city in 2015 was 93,699.
The population in 2015 is 100%.
If the population is decreased by 4.5% from 2015 to 2020, the total percentage in 2020 is 95.5% of the population in 2015.
Convert this to a decimal and multiply by the population in 2015 to find the population of the city in 2020.
[tex]\begin{aligned}\implies \sf 95.5\%\;of\;93699&=\sf 0.955 \times 93699\\&=\sf89482.545 \end{aligned}[/tex]
Therefore, the population of the city in 2020 was 89,500 to the nearest 100 people.
A skier moves 100.0 m horizontally, and then travels another 35.0 m uphill at an angle of 35.0º above the horizontal. What is the skier's displacement from his starting point? (Use the graphical method to answer and include your scale on the graph paper.) Give both the magnitude and the angle in your answer.
The skier's displacement from his starting point is 127.179 m and makes an angle of 33.78°.
What is the law of cosine?The law of cosines, commonly referred to as the cosine rule or the cosine formula, in trigonometry essentially connects the length of the triangle to the cosines of one of its angles. It claims that we can determine the length of the third side of a triangle if we know the length of the first two sides and the angle between them.
Given A skier moves 100.0 m horizontally, and then travels another 35.0 m uphill at an angle of 35.0º
base distance = 100 m
We will utilize the cosine rule to determine the magnitude of displacement because the triangle formed by the starting point, where he begins to ascend, and the ending point does not have a 90-degree angle. Cosine law requires a triangle with two sides and an angle between them, both of which are present.
a² = b² + c² - 2.b.ccos(α)
here a is the length of the third side,
b = base = 100m
c = 35 m
and α = 180 - 35 = 135°
so a² = b² + c² - 2.b.ccos(α)
a² = 100² + 35² - 2(100)(35)cos(135)
a² = 10000 + 1225 + 4949.74
a² = 16174.74
a = 127.179 m
and the angle between sides 100m and 127.179 m is given by
cosβ = (a² + c² - b²)/2a.c
cosβ = (127.179² + 35² - 100²)/2(127.179)(35)
cosβ = 0.831
β = cos⁻¹(0.831)
β = 33.78°
Hence displacement from the starting point is 127.179 m and forms an angle of 33.78°.
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ryan earns for each small dog he walks and for each large dog he walks. today he walked dogs and made a total of . how many small dogs did ryan walk? ryan walked blank small dogs.
According to the given data, Ryan walked 12 small dogs.
Let x be the number of small dogs that Ryan walked.
The number of large dogs that Ryan walked would then be y = 4 - x.
Using the information given, we can set up the following equation:
x * 2 + (4 - x) * 5 = 40
Expanding and solving for x, we get:
2x + 4 - 5x = 40
-3x = 36
x = 12
So, Ryan walked 12 small dogs.
In this problem, we used a system of equations to solve for the unknown variable, x, which represents the number of small dogs that Ryan walked. By substituting this value back into the equation for the number of large dogs, we were able to confirm that Ryan walked 4 - x = 4 - 12 = 4 large dogs.
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