The equation of the line in the slope-intercept form will be y = (-2/3)x - 2.
Given that:
Points, (-3, -4) and (6, -10)
The equation of the line in slope-intercept form is written as,
y = mx + b
The slope of the line is calculated as,
m = (y2 - y1) / (x2 - x1)
m = (-10 - (-4)) / (6 - (-3))
m = -6 / 9
m = -2/3
Now, to find the y-intercept, we can use the point-slope form of a line:
y - y1 = m(x - x1)
y - (-4) = (-2/3)(x - (-3))
y = (-2/3)x - 2
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Point K is located at ( 1 , 2 ) on the following coordinate plane. A square that has a perimeter of 20 units will be drawn so that K is one vertex of the square. Which three ordered pairs could represent the location of another vertex of the square? Select the three correct answers.
Three ordered pairs that could represent the location of another vertex of the square are (7, 2), (-5, 2), (1, 8).
To find the possible locations of the other vertices of the square, we need to determine the distance from point K to any other vertex of the square. Since the perimeter of the square is 20 units, each side of the square has a length of 20/4 = 5 units.
One way to find the other vertices is to draw a circle with center at K and radius 5 units, and then look for points on the circle that have integer coordinates. Alternatively, we can use the distance formula to calculate the distance from K to another point (x, y), which must be 5 units, and then solve for y in terms of x.
Using the distance formula, we get:
[tex]\sqrt{(x-1)^{2} +(y-1)^{2} }[/tex] = 5
Simplifying and squaring both sides, we get:
(x-1)^2 + (y-2)^2 = 25
Expanding the left side and simplifying, we get:
[tex]x^{2}[/tex] - 2x + [tex]y^{2}[/tex] - 4y + 20 = 0
Completing the square for x and y, we get:
[tex](x-1)^{2}[/tex] + [tex](y-1)^{2}[/tex] = [tex]6^{2}[/tex]
This is the equation of a circle with center at (1, 2) and radius 6 units. Any point on this circle that has integer coordinates could be a vertex of the square, since it will be exactly 5 units away from K.
Using this method, we can find several possible locations of the other vertices of the square. Three of them are:
(7, 2), (-5, 2), (1, 8)
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someone pls help me asapppp
Answer:
[tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] : a₁ = 7
Step-by-step explanation:
a recursive formula allows a term in the sequence to be found from the preceding term.
the sequence here has a common ratio between consecutive terms
[tex]\frac{21}{7}[/tex] = [tex]\frac{63}{21}[/tex] = 3
thus to find a term in the sequence multiply the previous term by 3, that is
[tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] : first term a₁ = 7
Use a net to find the surface area of the prism.
A. 426 m2
B. 213 m2
C. 306 m2
D. 336 m2
The surface area of the rectangular prism in this problem is given as follows:
A. 426 m².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas. -> net method.
By the net method, the prism is divided as follows:
Two rectangles of dimensions 5 m and 12 m.Two rectangles of dimensions 5 m and 9 m.Two rectangles of dimensions 12 m and 9 m.Hence the surface area of the prism is given as follows:
S = 2(5 x 12 + 5 x 9 + 12 x 9)
S = 426 m².
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Which measure should Raul use to find how much the distance that the ball travels during each hit varies, on average, from the mean distance?
We can see here that the measure that Raul should use to find the distance that the ball travels during each hit varies, on average, from the mean distance is the measure of variability known as standard deviation.
What is mean?The mean, commonly referred to as the arithmetic mean or average, is a statistic that depicts the usual or centre value of a dataset. It is determined by adding up all of the dataset's values, then dividing by all of the values.
We can see here that standard deviation actually refers to the statistical measure that represents the amount of dispersion or variability in a dataset.
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Amir travelled from Town A to Town B. He travelled 1/5 of the journey in the first two hours and 1/3 of the remaining journey in the next one hour. He then took another 2 h to cover 136 km to reach Town B. What was his average speed for the whole journey?
Amir's average speed for the whole journey was 51 km/h.
We have,
Let the total distance between Town A and Town B be D.
According to the problem,
Amir traveled 1/5 of the journey in the first two hours, which means he covered a distance of D/5 in 2 hours.
The remaining distance is 4D/5.
He then traveled 1/3 of the remaining journey in the next one hour, which means he covered a distance.
= (1/3) × (4D/5)
= 4D/15 in the next hour.
Therefore, the remaining distance.
= 4D/5 - 4D/15
= 8D/15.
It took him another 2 hours to cover the remaining distance of 136 km, so we have:
8D/15 = 136 km
Solving for D.
D = (136 km)×(15/8)
= 255 km
Therefore,
The total distance between Town A and Town B is 255 km.
The total time Amir took for the journey is 2 + 1 + 2 = 5 hours.
His average speed for the whole journey.
= Total distance ÷ Total time
= 255 km ÷ 5 hours
= 51 km/h
Therefore,
Amir's average speed for the whole journey was 51 km/h.
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18. AB =
A
8
Los
D
B
1
Answer: the area of the triangle is 150 cm².
Step-by-step explanation:
To solve this problem, we need to use the formula for the area of a triangle:
Area = (1/2) x base x height
From the diagram, we can see that the base of the triangle is 20 cm and the height is 15 cm. Plugging these values into the formula, we get:
Area = (1/2) x 20 cm x 15 cm
Area = 150 cm²
Therefore, the area of the triangle is 150 cm².
Name the characteristics a shape has to have to be defined as the following
quadriatera
Triangle
square
Answer:
A quadrilateral is a shape that has four straight sides and four angles.
A triangle is a shape that has three straight sides and three angles.
A square is a special type of quadrilateral that has four straight sides of equal length and four right angles.
Spinning a coin, unlike tossing it, may not give heads and tails equal probabilities. I spun a penny 300 times and got 134 heads. We wish to find how significant is this evidence against equal probabilities.
What is the sample proportion of heads?
0.444
Incorrect Round to 3 places.
Heads do not make up half of the sample. Is this sample evidence that the probabilities of heads and tails are different?
Take p to be the probability of getting heads in a spin of a penny. Which hypotheses do we want to test?
H0: p = 0.5
H0: p > 0.5
H0: p = 0.5
H0: p ≠ 0.5
H0: p ≠ 0.5
H0: p = 0.5
H0: p = 0.5
H0: p < 0.5
Incorrect
Compute the z test statistic.
z =
0.444
Incorrect Round to 2 places.
The resulting z-test statistic is 0.44, indicating that the evidence is not significant enough to reject the null hypothesis that the probability of heads is equal to 0.5.
The problem we are trying to solve is to determine if the sample proportion of heads obtained from spinning a penny 300 times (134 heads) is significant evidence against equal probabilities of heads and tails. To do this, we will be testing the null hypothesis H0: p = 0.5, which states that the probability of getting heads is equal to 0.5.
We can calculate the z-test statistic using the formula z = (sample proportion - hypothesized proportion) / (standard error). In this case, the z-test statistic is z = (0.444 - 0.5) / (√(0.5 * 0.5 / 300)) = -0.86. This means that the sample proportion of heads is 0.86 standard errors away from the hypothesized proportion of 0.5.
Therefore, the resulting z-test statistic is 0.44, indicating that the evidence is not significant enough to reject the null hypothesis that the probability of heads is equal to 0.5.
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Express sin
�
L as a fraction in simplest terms.
Answer:
3/5
Step-by-step explanation:
opposite/hypotenuse
21/35
Simplify by dividing by 7 on the numerator and denominator
3/5
Which of the following points are on the line given by the equation y = x? Check all that apply. A. (3, 6) B. (4, 2) C. (3, 15) D. (-2, 1) E. (2, 1) F. (-2, -1)
Answer:
The points that are on the line given by the equation y = x are:
A. (3, 3)
B. (2, 2)
D. (-1, -1)
E. (1, 1)
To check if a point is on the line, you can substitute its coordinates into the equation and see if the equation is true. For example, for point (3, 6), we have:
y = x
6 = 3
This is not true, so the point (3, 6) is not on the line. Repeat this process for each point to determine which points are on the line.
6. Find the components of the vector V with initial point P(-4,5) and terminal point
Q(-2,7).
(i) < -2,-2>
(iv) <-6, 12>
(ii) < 8,35 >
(iii) <2, 5/7>
(v) <2,2>
(vi) not listed
Answer:
Okay, let's break this down step-by-step:
The initial point is P(-4, 5)
The terminal point is Q(-2, 7)
To find the components of the vector V, we need to determine:
The change in x-coordinate = -4 - (-2) = -2
The change in y-coordinate = 5 - 7 = -2
So the vector components are:
<change in x-coordinate, change in y-coordinate>
= <-2, -2>
Therefore, the answer is choice (i): < -2,-2>
The other choices do not represent the correct changes between the given points P and Q.
Step-by-step explanation:
Select the correct answer.
If the temperature outside is 86°F, the heat index can be found using the equation y = 0.004x²-0.1243x 84.028. This equation is also the curve of
best fit for the values in the table. In the equation, x represents the relative humidity and y represents the heat index.
Relative Humidity
Heat
If the temperature outside is 86°F and the relative humidity is 55%, the heat index is: C. 89°F.
How to determine the equation of line of best fit?In this scenario, the relative humidity would be plotted on the x-axis (x-coordinate) of the scatter plot while the heat index would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
From the scatter plot which models the relationship between the x-values and y-values, a quadratic equation for the line of best fit when the temperature outside is 86°F, is given by:
y = 0.004x²- 0.1243x + 84.028
when x = 55%, the heat index can be calculated as follows;
y = 0.004(55)²- 0.1243(55) + 84.028
y = 89.2915 ≈ 89°F
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ing Angles
If m/DBC = 47°, then
m
A
B
47°
D
Enter
D
Answer:
<ABC + <CBD =180⁰
<ABC =180⁰ - <CBD
<ABC =180⁰ - 47⁰
<ABC =133⁰
Convert the rectangular coordinates (5,−5√3) to polar form. Let r>0 and 0≤θ<2π.
Enter your answer by filling in the boxes. Enter coordinates as simplifed fractions or radicals in simplest form.
( , )
Answer:
(10, 5π/3)
Step-by-step explanation:
To convert rectangular coordinates (5, -5√3) to polar form, we can use the following formulas:
r = √(x^2 + y^2)
θ = arctan(y/x)
Substituting the given values, we get:
r = √(5^2 + (-5√3)^2) = √(25 + 75) = √100 = 10
θ = arctan((-5√3)/5) = arctan(-√3) = -π/3
Note that the value of θ is in the fourth quadrant, which corresponds to a negative angle. However, we need to express the angle θ in the range 0 ≤ θ < 2π. To do this, we can add 2π to the angle if it is negative:
θ = -π/3 + 2π = (5π/3)
Therefore, the rectangular coordinates (5, -5√3) in polar form are (10, 5π/3).
A spherically shaped hot air balloon has a
diameter of about 27 meters when fully inflated.
What is the volume of the hot air balloon when it
is fully inflated?
Answer: 7725.5775
Step-by-step explanation:
d=27
r=d/2=27/2=13.5
the volume of the spherical balloon= 3.14*r^3
= 3.14*(13.5)^3
= 7725.5775
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6
Professor Snozz wrote a new book, Pi to
Ten Million Places. He earns 8% of total
sales dollars as a royalty. If 300 copies
of his book are sold at $29.50 each, how
much does Professor Snozz make?
If professor Snozz earns 8% of "total-sales", then the amount that the professor make on selling of 300 copies is $708.
In order to find out how much Professor Snozz makes, we first calculate the "total-sales" revenue of the 300 copies of the book;
⇒ Total sales revenue = (number of copies sold) × (price per copy),
⇒ Total sales revenue = 300 × $29.50,
⇒ Total sales revenue = $8850;
Next, we calculate amount of royalty that Professor Snozz earns, which is 8% of the total sales revenue;
So, Royalty = 8% of "Total sales revenue";
⇒ Royalty = 0.08 × $8850,
⇒ Royalty = $708;
Therefore, Professor Snozz earns $708 as a royalty for selling 300 copies of his book.
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Find the missing point of the following rectangle. (1, 8) (0, 8) (2, 8) (3, 7)
The missing point of the rectangle is determined as (3, 8).
What is a rectangle?A rectangle is a four-sided flat shape in which the opposite sides are equal in length and parallel to each other, and all four angles are right angle.
The area of a rectangle is equal to the length multiplied by the width, and the perimeter is equal to the sum of the lengths of all four sides.
Since each angle of a rectangle must be 90 degrees, the length of each opposite side must be equal.
the missing side must be parallel to point (0, 8) and perpendicular to point (3, 7).
the side must be (3, 8)
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The number of seeds found in a sample of 7 different oranges were: 3, 3, 4, 5, 7, 8, and 12. What is the range of the number of seeds in the sample of oranges? Answer options with 4 options A. 5 B. 6 C. 7 D. 9
Answer:
The range of the number of seeds in the sample of oranges is 9.
Write a recursive formula for
Answer:
[tex]a(1) = 144[/tex]
[tex]a(n) = 144{( - \frac{1}{6} )}^{n - 1} [/tex]
[tex]a(n) = - \frac{1}{6} a(n - 1)[/tex]
Solve for the missing side. Round to the nearest tenth.
Answer:
x ≈ 6.5
Step-by-step explanation:
using the tangent ratio in the right triangle
tan25° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{14}[/tex] ( multiply both sides by 14 )
14 × tan25° = x , then
x ≈ 6.5 ( to the nearest tenth )
Hello, I hope you are having a great day so far, I was wondering if someone ca (seriously) help me and not play around. I really need an Answer asap as soon as possible
PLEASE HELP (I NEED AN ANSWER QUICK!)
Answer:
the corresponding sides are proportional
Please help 100 points
Answer:
SA = 48 cm²
Step-by-step explanation:
the surface area (SA) is the sum of the areas of the 5 faces.
1 square and 4 congruent triangles form the pyramid
area of square = 4 × 4 = 16 cm²
area of triangle = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 4 and h = 4
area = [tex]\frac{1}{2}[/tex] × 4 × 4 = 2 × 4 = 8 cm²
area of 4 triangles = 4 × 8 = 32 cm²
SA = 16 + 32 = 48 cm²
what is the answer to 7/8 x 6
Answer:
5.25
Step-by-step explanation:
7 divide 8 = 0.875
0.875 × 6 = 5.25
14. During 2006, a swimming lesson at a particular school lasted 45 minutes.
(a) In 2007, the lesson time will be 50 minutes.
Find the increase in the lesson time from 2006 to 2007 as a percentage of the lesson time in 2006.
(b) The lesson time in 2007 will be 25% more than it was in 2005. Find how long the lesson lasted in 2005.
(c) At present, James takes 240 seconds to swim 100 metres. In a year's time, he would have improved his swimming time by 25%. Calculate the time he will take to swim 100 metres in a year's time.
m (d) Robert, at present, also takes 240 seconds to swim 100 metres. In a year's time, he would have increased his swimming speed by 25%. Calculate the time he will take to swim 100 metres in a year's time.
(e) Who will be the faster swimmer, James or Robert, in a year's time?
(a) The lesson time in 2007 is 11.1% more than the lesson time in 2006.
(b) The lesson lasted 40 minutes in 2005.
(c) James will take 180 seconds to swim 100 meters in a year's time.
(d) Robert will also take 180 seconds to swim 100 meters in a year's time.
(e) James and Robert will swim equally which means that their speed will be same and they will be complete at same time.
(a) The increase in lesson time from 2006 to 2007 is:
Increase = 50 - 45 = 5 minutes
The percentage increase is:
Percentage increase = (5 / 45) x 100% = 11.1%
Therefore, the lesson time in 2007 is 11.1% more than the lesson time in 2006.
(b) Let x be the lesson time in 2005. The lesson time in 2007 is 25% more than it was in 2005, so:
1.25x = 50
Solving for x, we get:
x = 40
Therefore, the lesson lasted 40 minutes in 2005.
(c) James currently takes 240 seconds to swim 100 meters. If he improves his time by 25%, his new time will be:
New time = 240 - (0.25 x 240) = 180 seconds
Therefore, he will take 180 seconds to swim 100 meters in a year's time.
(d) Robert currently takes 240 seconds to swim 100 meters. If he increases his speed by 25%, his new time will be:
New time = 240 - (0.25 x 240) = 180 seconds
Therefore, he will also take 180 seconds to swim 100 meters in a year's time.
(e) Both James and Robert will take the same time to swim 100 meters in a year's time, so they will be equally fast.
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Jaime is setting up his tent. He is using two nylon ropes to pull the tent taut and stabilize it at each end. If the tent is 6.5 feet tall, and Jaime stakes the ropes into the ground 4 feet from the center of the tent, what is the total length of nylon rope he will use, to the nearest tenth of a foot? Show all of your work by writing out the steps you used to solve the problem or by using the drawing features in the space provided.
The total length of the nylon rope that Jamie will use would be 15.3 feet of nylon rope.
How to find the total length ?Within this scenario specifically, one side of the right-angled triangle comprises the height of the tent (standing at 6.5-feet), and the other forms as the measure from the center of the tent to where Jaime stakes the ropes stretching outwards in another direction (with a calculated measure of 4-feet). Subsequently, we will refer to the extent of the nylon rope as R.
The Pythagorean theorem formula is:
R ² = 6.5 ² + 4 ²
R ² = 42. ²25 + 16
R ² = 58.25
R = 7. 63 ft
There are two ropes so the length would be :
= 7. 63 + 7. 63
= 15. 3 ft
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[tex](x+7)x^{2} -(x-3)x^{2} =(x+35)x^{2} -(x+34)x^{2}[/tex]
The equation (x+7)x^2 -(x-3)x^2 =(x+35)x^2 -(x+34)x^2 has no solution for x
Evaluating the equationFrom the question, we have the following parameters that can be used in our computation:
(x+7)x^2 -(x-3)x^2 =(x+35)x^2 -(x+34)x^2
Divide through the equation by x^2
so, we have the following representation
(x+7) -(x-3) = (x+35) -(x+34)
When the brackets are removed and the like terms are evaluated, we have
2x + 10 = 2x - 1
Evaluate the like terms again
So, we have
10 = -1
The above equation is false
Hence, the equation has no solution for x
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An office building worth $1 million when completed in 2010 is being depreciated linearly over 25 years. What was the book value of the building in 2013? What will it be in 2019? (Assume the scrap value is $0
Answer:
2013 - $880,000
2019 - $640,000
Step-by-step explanation:
The office building is being depreciated linearly over 25 years, which means the annual depreciation rate is:
Depreciation rate = (Cost - Scrap value) / Useful life = ($1,000,000 - $0) / 25 = $40,000 per year
To find the book value of the building in 2013, we need to determine how many years have elapsed since 2010. Since 2013 is three years after 2010, the building has been depreciated for three years. Therefore, the book value in 2013 is:
Book value in 2013 = Cost - Depreciation = $1,000,000 - ($40,000/year x 3 years) = $880,000
To find the book value of the building in 2019, we need to determine how many years have elapsed since 2010. Since 2019 is nine years after 2010, the building has been depreciated for nine years. Therefore, the book value in 2019 is:
Book value in 2019 = Cost - Depreciation = $1,000,000 - ($40,000/year x 9 years) = $640,000
Therefore, the book value of the building was $880,000 in 2013 and will be $640,000 in 2019.
hey guys, im b-o-r-e-d in class... what should i do?
Answer:
Do whatever you want, but paying attention would really help you.
Step-by-step explanation:
If you find yourself bored in class, consider the following options to make the most of your time and stay engaged:
1. Actively participate: Ask questions, contribute to discussions, and try to engage with the material. Active participation can make the class more interesting and help you retain the information better.
2. Take notes: Focus on taking detailed notes, even if you think you understand the material. This will help you stay engaged and make it easier to review the content later.
3. Find connections: Try to relate the class material to your interests or real-world applications. This can make the content more engaging and relevant.
4. Set learning goals: Set specific learning objectives for each class, and try to achieve them during the session. This can help you stay focused and motivated.
5. Practice active listening: Pay attention to the teacher and try to understand the main points they are making. This can help you stay focused and better comprehend the material.
6. Break down the material: Divide the content into smaller chunks and focus on understanding each part. This can make the material more manageable and engaging.
7. Speak with your teacher: If you're consistently bored in class, consider discussing your concerns with your teacher. They may be able to offer suggestions or modify their teaching approach to better suit your learning style.
Remember, it's essential to stay engaged in class to maximize your learning experience and make the most of your education.
Answer:
watch RUN BTS EPISODE simple
What happens to the mode of the data set shown below if the number 6 is added? A The mode will change to two numbers. B The mode will increase by 4. C The mode will change to one number. D The mode will increase by 2.
Adding the number 6 to the given dataset did not affect the mode, as the number 19 still appeared the most frequently in the new dataset. (option c).
Now, if we add the number 6 to this dataset, we need to determine how this will affect the mode. We can start by looking at the number 19, which was the original mode. If the number 19 still appears the most frequently in the dataset after the addition of the number 6, then the mode will remain 19. However, if another number appears more frequently than 19 after the addition of 6, then the mode will change.
In this case, the number 6 does not appear anywhere in the original dataset, so it cannot be the mode. Therefore, the mode can either remain as 19 or change to a new number, depending on whether any other number appears more frequently than 19 after the addition of 6.
To determine if the mode changes, we need to calculate the frequency of each number in the new dataset. After adding 6, the dataset becomes:
18 24 19
19 18 20
26 25 19
6
From this dataset, we can see that the number 19 still appears twice, while all other numbers appear only once. Therefore, the mode of the new dataset is still 19, and the answer to your question is (C) "The mode will change to one number."
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Complete Question:
What happens to the mode of the data set shown below if the number 6 is added?
18 24 19
19 18 20
26 25 19
A The mode will change to two numbers.
B The mode will increase by 4.
C The mode will change to one number.
D The mode will increase by 2.
What is the component form of the vector whose tail is the point (−1,5), and whose head is the point (8,−6)?
The vector in component form whose tail is the point (−1,5), and whose head is the point (8,−6) is (-9, 11)
What is a vector?A vector is a physical quabntity thet has both magnitude and direction.
To find the component form of the vector whose tail is the point (−1,5), and whose head is the point (8,−6), we proceed as folows
Since we have the points (-1, 5) and (8, -6) and we want the head to be at (8, -6),
Let A = (8, -6) and B = (-1, 5)
So, AB = B - A
= (-1, 5) - (8, -6)
= (-1 - 8), (5 - (-6))
= (-9, 5 + 6)
= (-9, 11)
So, the vector in component form is (-9, 11)
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