You need to know the direction of the line and at least one point on it in order to parametrize a line. x is 5 + 4.0t ,y is 0 + 4.0t
How is a line segment with two points parametrized?You need to know the direction of the line and at least one point on it in order to parametrize a line. You can determine the direction of the line if you know two of its points. Point-slope form → y - y₁ = m (x - x₁)Slope-intercept form → y = mx+bStandard form → ax + by = cWe must locate two vectors parallel to the plane, as well as a point on the plane, in order to discover a parametrization. Finding a location aboard the aircraft is simple. Any number for x and y may be used to compute z using the plane equation. If x and y are set (5,0.5) to (0,4.0) equation (1)means that .x = 5 + 4.0t
y = 0 + 4.0t
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Reacting with water in an acidic solution at a particular temperature, compound A decomposes into compounds B and C according to the law of uninhibited decay. An initial amount of 0.40 M of compound A decomposes to 0.37 M in 30 minutes. How much of compound A will remain after 2 hours? How long will it take until 0.10 M of compound A remains? After 2 hours, the amount of compound A remaining will be ? M. (Do not round until the final answer. Then round to thenearest hundredth as needed.)
The answers to all parts are shown below.
The law of uninhibited decay is a first-order chemical reaction, which means that the rate of the reaction is proportional to the concentration of compound A.
The rate law can be written as:
rate = k[A]
where k is the rate constant and [A] is the concentration of compound A.
From the given data, we can use the following equation to determine the rate constant:
ln([A]t/[A]0) = -kt
where [A]t is the concentration of compound A at time t, [A]0 is the initial concentration of compound A, k is the rate constant, and t is the time.
Using the given data:
[A]t = 0.37 M
[A]0 = 0.40 M
t = 30 minutes = 0.5 hours
ln(0.37/0.40) = -k(0.5)
k = 0.0486 h⁻¹
(a) How much of compound A will remain after 2 hours?
Using the same equation and substituting the known values:
ln([A]t/[A]0) = -kt
ln([A]t/0.40) = -0.0486 x 2
[A]t/0.40 = e⁻(⁹⁷² /¹⁰⁰⁰⁰)
[A]t = 0.25 M
Therefore, after 2 hours, 0.25 M of compound A will remain.
(b) How long will it take until 0.10 M of compound A remains?
Substituting the known values into the equation again:
ln([A]t/[A]0) = -kt
ln(0.10/0.40) = -0.0486t
t = 4.26 hours
Therefore, it will take approximately 4.26 hours until 0.10 M of compound A remains.
(c) After 2 hours, the amount of compound A remaining will be 0.25 M.
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can u give an answer
Answer: 0
Step-by-step explanation:
Put 0 in the front box.
this is because you cant divide 11 apples equally into 6 people; 11 isn't a multiple of 6
Geometry problem (possible drop down answers are ellipse rectangle and circle) please help! Will give crown to first to give correct answer.
Answer:
ellipses
a pair of parallel straight
Step-by-step explanation:
Can someone please answer and provide an explanation for these problems?
62. The slope of the line is 1/8. the equation of line is y = 1/8x - 3/8
63. It has an infinite slope. The equation of line is x = 3
64. The slope of the line is -5. The slope of the new line is 1/5. The equation of line is y = 1/5x - 1
65. The slope of the line is 2/9. The slope of the new line is -9/2. The equation of line is y = -9/2x - 4
How do we identify the slope and equation of line?62) through: (3,0), parallel to y = 1/8x - 3. If a line is parallel to another, they have the same slope. Therefore the slope is 1/8.
For line equation⇒ (y - y1 = m(x - x1))
Substituting (3,0) and slope 1/8 gives us:
(y = mx + b) ⇒ y - 0 = 1/8 × (x - 3)
First, substitute the point and the slope into the equation: 0 = 1/8×3 + b
Then solve for b, the y-intercept: b = -3/8
⇒ y = 1/8x - 3/8
63) through: (3,-1), parallel to x = 0. A line parallel to x = 0 is a vertical line. A vertical line has the equation x = a, where a is the x-coordinate of any point on the line. A line through (3, -1) and parallel to x = 0 would simply be x = 3 or y = -1
64) through: (5, 0), perp. to y= -5x - 4. If a line is perpendicular to another, their slopes are negative reciprocals. The slope of y = -5x - 4 is -5, so the slope of the line we are looking for is -1/(-5) = 1/5
65) through: (-2, 5), perp. to y=2/9x - 1. perpendicular line to y = 2/9x - 1 has the slope that is the negative reciprocal of 2/9, which is -9/2. y = -9/2x - 4.
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The perimeter of a right triangle is equal to 4x + 3. If two sides of the triangle measure: x + 7 and x – 7, what is the measurement of the hypotenuse?
If two sides of the triangle measure: x + 7 and x – 7, the measurement of the hypotenuse is 2x + 3.
In a right triangle, the hypotenuse is the side opposite the right angle and it is the longest side. We can use the Pythagorean theorem to relate the sides of the right triangle:
a² + b² = c²
where a and b are the lengths of the legs of the triangle and c is the length of the hypotenuse.
We are given that the perimeter of the triangle is 4x + 3. The perimeter of a triangle is the sum of the lengths of its sides, so we can write:
a + b + c = 4x + 3
Substituting the given side lengths, we get:
(x + 7) + (x - 7) + c = 4x + 3
Simplifying, we get:
2x + c = 4x + 3 - 7 + 7
2x + c = 4x + 3
Solving for c, we get:
c = 2x + 3
We did not need to use the Pythagorean theorem in this problem, as we were only asked for the measurement of the hypotenuse in terms of x.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
4x = 100, so x = 25
The correct answer is C.
What is an equation of the line that passes through the point
(
8
,
7
)
(8,−7) and is parallel to the line
x+2y=18?
Find the volume of a rectangular prism with a length of 12 inches a width of 4.5 inches and a height of 3.6 inches
Answer:
194.4
Step-by-step explanation:
V=l*w*h
V=12*4.5*3.6
V=194.4
5. In AABC, ZA = 70°, ZB = 50°, and a = 15 cm. Solve ▲ABC.
In triangle ABC, side BC (a) is 15 cm, side AC (b) is 13.30 cm, and side AB (c) is 12.23 cm. Also angle A is 70°, B is 50°, and C is 60°
Understanding the Angles and Sides of TriangleUsing the Law of Sines and the fact that the sum of the angles in a triangle is 180 degrees.
The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. Using this, we can find the lengths of the other sides of triangle ABC.
Let's denote side AB as c, BC as a, side AC as b, and angle C as ∠C.
Using the Law of Sines, we have:
sin(∠A) / a = sin(∠B) / b
Substitute in the known values, we get:
sin(70°) / 15 = sin(50°) / b
Make b the subject of the formula:
b = (15 * sin(50°)) / sin(70°)
Using a calculator, we can find the value of b:
b = (15 * 0.766) / 0.9397
= 12.23 cm
Therefore side AC = b = 12.23 cm
Now, to find side AB (c), we can use the Law of Sines again:
sin(∠B) / b = sin(∠C) / c
But ∠C is unknown. To find ∠C, we apply the sum of angle in a triangle rule
∠A + ∠B + ∠C = 180
70 + 50 + ∠C = 180
∠C = 180 - 70 - 50
∠C = 60°
Substitute the values in the Sine rule equation
sin(50°) / 12.233 = sin(60) / c
Make c the subject of the formula
c = (12.233 * sin(60)) / sin(50°)
c = (12.233 * sin(60°)) / sin(50°)
= 13.30 cm
Therefore, the lengths of the sides of triangle ABC are:
Side AB = c = 12.23 cm
Side BC = a = 15 cm
Side AC = b = 13.30 cm
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Can anyone help me w tvis
The number of weeks that the puppies weigh the same amount will be A. 6 weeks.
The equation that has no solution is A. 13 - 7x = -7x + 13.
The option determined from the graph is B. The ordered pair (25, 6) is a solution to y = x + 40 and y = 3x + 15.
How to calculate the number of weeksPuppy A weighs 4 1/5 pounds at birth and gains 3/4 pound each week. Puppy B weighs 5 2/3pounds at birth and gains 1/2 pound each week.
After how many weeks will the puppies weigh the same amount will be calculated thus:
4 1/5 + 3/4x = 5 2/3 + 1/2x
4.2 + 0 75x = 5.67 + 0.5x
Collect the like terms
5.67 - 4.2 = 0.25x
Divide
x = 1.47 / 0.25
x = 6
Hence ,the number of weeks that the puppies weigh the same amount will be A. 6 weeks.
It should be noted that the equation that has no solution is A. 13 - 7x = -7x + 13. This is because the values gives 0 all through.
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Find the surface area of the prism. Round to the nearest tenth if necessary.
Regular pentagon base
B≈61.94 cm2
Base length=6cm
Lateral edge=5cm
A regular pentagonal prism is shown. The length of the side of the pentagon is six centimeters. The height of the prism is five centimeters.
The surface area of the prism is 248.88 cm²
What is surface area of prism?The area occupied by a three-dimensional object by its outer surface is called the surface area.
The surface area of a prism is expressed as;
SA = 2B + ph
where h is the height of the prism, B is the base area of the prism and P is the perimeter of the base.
Base area = 61.94 cm²
height = 5cm
perimeter = 5 × 5 = 25cm
SA = 2 × 61.94 + 25 × 5
SA = 123.88+ 125
SA = 248.88 cm²
Therefore the surface area of the prism is 258.88 cm²
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The EPA fuel economy estimates for automobiles models tested recently found them to be
normally distributed with a mean of 24.8 mpg and a standard deviation of 6.2 mpg. What is
the percentile rank of an automobile that has a fuel economy of 35 mpg?
90th Percentile
O 5th Percentile
O 95th Percentile
10th Percentile
Step-by-step explanation:
(35-24.8) / 6.2 = z-score of + 1.645 corresponding to .9495 =
~ 95th percentile
Simplify (3xy³ + 8x²y - 3xy) + (7xy³ - 9x²y + 6xy).
O4xy³ - x²y - 3xy
O4xy³ - x²y + 3xy
O 10xy³ + x²y - 3xy
O 10xy³x²y + 3xy
Answer: 10xy³ - x²y + 3xy
Step-by-step explanation:
To simplify the expression (3xy³ + 8x²y - 3xy) + (7xy³ - 9x²y + 6xy), we can combine like terms.
Adding the corresponding terms together, we have:
3xy³ + 7xy³ = 10xy³
8x²y - 9x²y = -x²y
-3xy + 6xy = 3xy
Combining these terms, the simplified expression becomes:
10xy³ - x²y + 3xy
Therefore, the correct option is:
O 10xy³ - x²y + 3xy
100 Points! Algebra question. Photo attached. Sketch the angle. Then find its reference angle. Show your calculations. Thank you!
The reference angle of 13π/8 is 3π/8 and the sketch of the angle is attached
How to sketch the angle and find the reference angleFrom the question, we have the following parameters that can be used in our computation:
Angle = 13π/8
Rewrite as
θ = 13π/8
The above angle is in the fourth quadrant
So, we subtract it from 2π to calculate the reference angle
Using the above as a guide, we have the following:
Reference angle = 2π - 13π/8
Evaluate the difference
Reference angle = 3π/8
Hence, the reference angle is 3π/8 and the sketch of the angle is added as an attachment
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What is the length of Arc LM? Use 3.14 as pi and round your answer to the nearest tenth. please show work, will mark brainliest.
To find the length of arc LM, we need to use the formula for the circumference of a circle:
C = 2πr
In this case, the arc LM is a portion of the circumference of the circle. To find the length of the arc, we need to determine the angle at the center of the circle that corresponds to the arc.
Looking at the image you provided, we can see that angle LOM is a right angle (90 degrees). The angle at the center of the circle, LOCM, is half of the right angle, which is 45 degrees.
To calculate the length of arc LM, we need to find the fraction of the total circumference represented by the central angle LOCM. The fraction is given by:
Fraction of circumference = Angle at center / 360 degrees
Fraction of circumference = 45 degrees / 360 degrees
Fraction of circumference = 1/8
Now, we can calculate the length of arc LM:
Length of arc LM = Fraction of circumference * Circumference
Length of arc LM = (1/8) * (2πr)
Since the radius (r) is not given in the image, we cannot calculate the exact length of arc LM. However, we can provide the formula for the length of arc LM in terms of the radius:
Length of arc LM = (1/8) * (2πr) = πr/4
So, the length of arc LM is πr/4, where r is the radius of the circle.
If you have the value of the radius, you can substitute it into the formula to find the specific length of arc LM.
Question 2 (Multiple Choice Worth 1 points)
(06.02 MC)
Simplify (3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab).
O-a³b-8ab2 + 10ab
O-a³b-8ab²
07a³b-8ab² + 10ab
The simplified expression of (3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab) is (b) -a³b - 8ab²
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
(3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab)
Open the bracket
So, we have
(3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab) = 3a³b - 4ab² + 5ab -4a³b - 4ab² - 5ab
Evaluate the like terms
So, we have
(3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab) = -a³b - 8ab²
Hence, the simplified expression is (b) -a³b - 8ab²
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10. Kipp constructed a pentagonal pyramid for his social studies report. The base had an area of 12 cm². It took 48 cubic centimeters of clay to make his model. Find the height of the pyramid.
We can use the formula for the volume of a pentagonal pyramid to solve this problem:
Volume = (1/3) × Base Area × Height
We know that the base area is 12 cm² and the volume is 48 cubic centimeters. We can substitute these values into the formula and solve for the height:
48 = (1/3) × 12 × Height
Multiplying both sides by 3 gives:
144 = 12 × Height
Dividing both sides by 12 gives:
Height = 12
Therefore, the height of the pentagonal pyramid is 12 centimeters.
radius of 18 feet and a central angle of 52° is shown below. Which of the following is the closest to the length of the arc from point C to point D?
The closest length to the arc from point C to point D is 16.34 ft (option c).
To find the length of the arc from point C to point D, we need to calculate the circumference of the circle and then find the fraction of the circumference represented by the central angle.
The circumference of a circle can be calculated using the formula:
Circumference = 2 × π × radius
Given the radius of 18 feet, the circumference is:
Circumference = 2 × π × 18 = 36π feet
To find the length of the arc, we need to find the fraction of the circumference represented by the central angle of 52°. The fraction is calculated by dividing the central angle by 360° and then multiplying it by the circumference.
Length of the arc = (Central angle / 360°) * Circumference
Length of the arc = (52° / 360°) × 36π
Length of the arc = (13/90) × 36π
Length of the arc = 468π / 90
Length of the arc ≈ 16.41 ft
Among the given options, the closest length to the arc from point C to point D is 16.34 ft (option c).
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I have not gone to school in a month for family reasons and I have to submit 39 math assignments before Friday HELP
Diego is correct as the number of groups result to 6/5 or 1 1/5.
We have to find the number of groups of 5/6 in 1.
So, we need to perform the division as
= 1/ (5/6)
= 1 x 6/5
= 6/5
= 1 1/5
Thus, Diego is correct as the number of groups result to 6/5 or 1 1/5.
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?? geometry question
The measure of angle BGF from the given parallel lines is 108°.
Given that, measure of angle BGF=4x+28 and the measure of angle EHD = 2x+32.
1) From the given figure, angle BGF and angle EHC are interior alternate angles.
Angle FHC and angle EGA are corresponding angles.
Angle FHC and angle EGA are exterior alternate angles.
2) angle BGF+angle EHD=180°
3) 4x+28+2x+32=180°
6x+60=180
6x=120
x=20
Angle BGF=4x+28=108 °
Angle EHD = 2x+32
= 112°
Angle FHD=180-112=68°
Angle EGB=180-108=72°
Therefore, the measure of angle BGF from the given parallel lines is 108°.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each sine or cosine value to its equivalent measure
The equivalent sine and cosine values are as follows:
cos(74°) = sin(16°)cos(57°) = sin(33°)sin(32°) = cos(58°)sin(43°) = cos(47°)What is the relationship between sine and cosine angles?The relationship between sine and cosine angles is:
sinθ = cos(90 - θ)
This equation is known as the complementary angle identity for sine and cosine. It states that the sine of an angle is equal to the cosine of its complementary angle (90 degrees minus the original angle).
For example, if we have an angle theta = 30 degrees, its complementary angle would be 90 - 30 = 60 degrees.
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Can someone answer this question
The options 2nd and 3rd are the monomials with degree 2.
Given are the expressions we need to find the monomials with degree 2.
So,
The general form of a monomial with degree 2 is:
ax²
The highest exponent of a polynomial's variable(s) in any of its terms is referred to as the polynomial's degree in mathematics.
It controls the polynomial's behavior and complexity.
A non-negative integer is used to represent the degree.
And,
A monomial is a mathematical expression consisting of a single term. It is composed of a coefficient multiplied by one or more variables raised to non-negative integer exponents.
Here, the monomials can be 2x² and x²
Hence the options 2nd and 3rd are the monomials with degree 2.
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Brenda types 15 words per minute. How long will it take her to type 750 words?
It will take Brenda 50 minutes to type 750 words at a rate of 15 words per minute.
To solve this problem, we can use the formula:
time = amount of work / rate
In this case, the amount of work is typing 750 words, and the rate is 15 words per minute. Substituting these values into the formula, we get:
time = 750 / 15 = 50 minutes
This calculation assumes that Brenda types at a constant rate of 15 words per minute. If her typing speed varies, the time it takes her to type 750 words may be different.
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you
cou
Recommendations
Florida's B.E.S.T. Standards: Grade 8 > GG.5 Make predictions 38C
thro
Skill plans
pieces of vanilla cake
You have prizes to reveall Go to
Passersby have taken 4 pieces of vanilla cake and 6 pieces of coconut cake from a
sample tray. Based on past data, of the next 30 samples taken, how many should you expect
to be pieces of vanilla cake?
Vid
Out of the following 30 samples, you may expect that about 12 will be portions of vanilla cake.
How to determine probability?To solve this problem, use the concept of probability and make a prediction based on the past data.
In this case, out of the 10 pieces of cake that have been taken, 4 are vanilla and 6 are coconut.
Therefore, the probability of selecting a piece of vanilla cake from the tray is 4/10, or 2/5.
To predict how many of the next 30 samples will be pieces of vanilla cake, multiply the probability of selecting a vanilla cake by the total number of samples:
(2/5) x 30 = 12
So expect that out of the next 30 samples taken, approximately 12 of them will be pieces of vanilla cake.
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A shirt manufacturer pays a worker $0.47 for each acceptable shirt inspected under the prescribed job description. If the worker had the following work record, find the gross earnings for the week: Monday, 250 shirts; Tuesday, 300 shirts; Wednesday, 178 shirts; Thursday, 326 shirts; Friday, 296 shirts
if you walked 3 blocks north and then 8 blocks west and then 10 blocks south how far are you from your starting point it each block is 2/10 of a mile?
You are approximately 3.4 miles from your starting point.
We have,
To solve this problem, we need to use the Pythagorean theorem, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse.
|\
8 | \
| \
|___\
3
We can see that the three blocks north and 10 blocks south cancel each other out, so we only need to consider the 8 blocks west.
Using the distance formula, we can find that the distance traveled west is:
8 blocks × 2/10 mile per block = 1.6 miles
Now we can use the Pythagorean theorem to find the distance from the starting point:
distance = √(3² + 1.6²)
distance ≈ 3.4 miles
Therefore,
You are approximately 3.4 miles from your starting point.
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Please help me answer this question ASAP!! It’s due tomorrow! Will mark as brainliest if explained very simply and correct.
Answer:
The answer is B:14
Step-by-step explanation:
When you simply multiply 5% by 14, you get 0.7. So you know that 5% of 14 is 7.
Britney is a volunteer at the Westside Library. She collects the books that come down the
chute from the outside drop-off and puts them on the library shelves. Of the books that have
come down the chute so far today, 41 have been fiction and 23 have been nonfiction.
Based on the data, estimate how many of the next 100 books that come down the chute will
be nonfiction.
Based on the given data, we can estimate that approximately 36 out of the next 100 books that come down the chute will be nonfiction.
To estimate the number of nonfiction books out of the next 100, we can use the ratio of nonfiction to the total number of books that came down the chute so far today.
The total number of books that came down the chute so far is:
41 (fiction) + 23 (nonfiction) = 64
The ratio of nonfiction books to the total number of books in library is:
[tex]23/64[/tex]
To estimate the number of nonfiction books out of the next 100, we can multiply the ratio by 100:
[tex](23/64)*100=35.9375[/tex]
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D. 17 °F 2. Franky earns $(100+ x) daily for five days, $(175 + 2x) for two days, and $(75 + 2x) for three days. If the average amount she earns is $80 per day, what is the median amount she earned?
The median total of amount Franky earned is A = $81.67 per day.
Given data ,
For the first five days: $(100 + x) per day
For the next two days: $(175 + 2x) per day
For the final three days: $(75 + 2x) per day
Now , the average amount she earns is $80 per day
So , Average earnings = Total earnings / Total number of days
Average earnings = [(100 + x) * 5 + (175 + 2x) * 2 + (75 + 2x) * 3] / 10
Simplifying the equation:
80 = [500 + 5x + 350 + 4x + 225 + 6x] / 10
Multiplying both sides by 10:
800 = 1075 + 15x
Subtracting 1075 from both sides:
15x = -275
Dividing both sides by 15:
x = -18.33
For the first five days: $(100 - 18.33) = $81.67 per day
For the next two days: $(175 + 2*(-18.33)) = $138.34 per day
For the final three days: $(75 + 2*(-18.33)) = $38.34 per day
Arranging the earnings in ascending order: $38.34, $38.34, $38.34, $81.67, $81.67, $81.67, $81.67, $138.34, $138.34
The median is the middle value when the earnings are arranged in ascending order. In this case, the middle value is $81.67
Hence , the median is $81.67
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Brendon finished an obstacle course in 22.5 minutes. Tobias finished the course 85 seconds after Brendon. How long did it take Tobias to finish?
Answer:
23.35 minutes
Step-by-step explanation:
Brendan finished in 22.5 minutes. Tobias finished 85 seconds after. Just add 85 seconds to 22.5 minutes. There are 100 second in 1 minute. Since Brendan is already at 22.5, there is only 0.5 left to get to 23. 0.5 in this case means 50 seconds. You do 85 - 50 = 35. Now, you are at 23 minutes. Add 35 seconds to that to get to 23.25 minutes.