To enlarge the photo proportionally so that it is as wide as the computer screen, we need to find the scaling factor. The scaling factor is the ratio of the width of the computer screen to the width of the photo:
Scaling factor = 1024 ÷ 640 = 1.6
We can then use this scaling factor to find the new dimensions of the photo:
New width = 640 × 1.6 = 1024 pixels
New height = 300 × 1.6 = 480 pixels
Therefore, the new dimensions of the photo are 1024 × 480 pixels.
2a. We cannot enlarge the photo proportionally so that it is as tall as the computer screen because the aspect ratio of the photo is different from the aspect ratio of the computer screen. The aspect ratio of the photo is 640 ÷ 300 ≈ 2.13, while the aspect ratio of the computer screen is 1024 ÷ 768 ≈ 1.33. This means that if we enlarge the height of the photo to match the height of the computer screen, the width of the photo will be too wide to fit on the screen.
b. We cannot correct the difficulty in (a) by scaling the width of the photo by a factor of 1024 ÷ 640 and the height by a factor of 768 ÷ 300 because this would change the aspect ratio of the photo. The aspect ratio of the photo would become 1024 ÷ (640 × 1024 ÷ 640) ≈ 1.6, which is the same as the aspect ratio of the computer screen. However, the height of the photo would be scaled by a factor of 768 ÷ 300 ≈ 2.56, which would make the photo too tall to fit on the screen.
To enlarge the photo proportionally, we need to scale it up by the same factor in both dimensions. Since we want to scale it so that its width matches the width of the screen, we can find the scaling factor by dividing the screen width by the photo width:
scaling factor = screen width / photo width = 1024 / 640 = 1.6
Now we can use this scaling factor to find the new height of the photo:
new height = photo height x scaling factor = 300 x 1.6 = 480 pixels
Therefore, after the photo is scaled up proportionally, its measurements are 1024 x 480 pixels.
2a. We can't enlarge the photo proportionally so that it is as tall as the computer screen because its aspect ratio (the ratio of its width to its height) is different from the aspect ratio of the screen. The photo's aspect ratio is 640/300 = 2.13, while the screen's aspect ratio is 1024/768 = 1.33. Enlarging the photo so that its height matches the screen's height would require stretching the photo vertically, which would distort the image.
2b. Scaling the width of the photo by a factor of 1024/640 and the height by a factor of 768/300 would not correct the difficulty in part (a) because it would not change the aspect ratio of the photo. The aspect ratio of the photo would still be 2.13, which is different from the aspect ratio of the screen. The photo would still need to be stretched vertically to match the screen's height, which would distort the image.
Which of the following explains why this inequality is true?
7 3/8 × 4/5 < 7 3/8
Answer:
Step-by-step explanation:
To compare these two values, we first need to convert the mixed number 7 3/8 to an improper fraction. To do so, we multiply the whole number (7) by the denominator of the fraction (8), then add the numerator (3), and put the result over the denominator:
7 3/8 = (7 x 8 + 3) / 8 = 59/8
Now we can rewrite the inequality as:
(59/8) × (4/5) < 59/8
To simplify the left-hand side of the inequality, we multiply the numerators and denominators:
(59/8) × (4/5) = (59 × 4) / (8 × 5) = 236/40 = 59/10
So the inequality becomes:
59/10 < 59/8
To compare these fractions, we need to find a common denominator. The least common multiple of 8 and 10 is 40, so we can convert both fractions to have a denominator of 40:
59/10 = (59 x 4) / (10 x 4) = 236/40
59/8 = (59 x 5) / (8 x 5) = 295/40
Now we can see that 236/40 < 295/40, which means that:
59/10 < 59/8
Therefore, the inequality 7 3/8 × 4/5 < 7 3/8 is true.
how to do 0.002 / 2000
Answer:
Step-by-step explanation:
If the given expression is multiplied by 36
, which expression is NOT equivalent?
Responses
A (32
)(38
)( 3 2 )( 3 8 )
B 910
9 10
C 310
3 10
D (35
)(35
)
Answer:
The correct answer is (C) 310.
Multiplying the given expression by 36 gives:
(32)(38) + (35)(35) - (33)(37)
= 1216 + 1225 - 1221
= 1220
So the equivalent expression is 1220.
Option (C) 310 is not equivalent to 1220.
Please help with trigonometry
14.4 is the value of x in triangle .
What is known as a triangle?
Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point. 180 degrees is the sum of the triangle's three angles.
Triangular shapes have three vertices, three angles, and three sides. 180 degrees is the sum of a triangle's three interior angles. The length of a triangle's two longest sides added together exceeds the length of its third side.
17² = 9² + X²
289 = 81 + x²
289 - 81 = x²
208 = x²
x = √208
= 14.4
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PLEASE IM BEGGING HELP PLEASE!!!!!
Answer:
C
Step-by-step explanation:
a) Find the value of 8 1/3 b) Find the value of 8 2/3 c) Find the value of 16 3/4
Answer:
a) 27. b) 27.3333 c) 40.75
f(25) = 80 , find the value of f(2022) and give proper method and the final answer
The value of f(2020) is 39/100.
Given function is,
f(25) = 80
And f(xy) = f(x)/y² .....(i)
Since
f(25) = 80
Then we define function as
f(x) = x + 55 .....(ii)
Now we can write 2020 = 101 x 20
So f(2020) = f(101x20) = f(101)/20² from (i)
= (101 + 55)/400 from(ii)
= 156/400
= 39/100
Hence, f(2020) = 39/100
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According to Bureau of Labor Statistics26.0% of the total part-time workforce in the USwas between the ages of 25 and 34 during a recent monthA random sample of 90 part-time employees was selected during this quarter. Using the normal approximation to the binomial distribution, what is the probability that fewer than 18 people from this sample were between the ages of 25 and 342 (round standard deviation to 4 decimal places)
The probability that fewer than 18 people from this sample were between the ages of 25 and 34 is 0.1089 (or 10.89%).
Using the normal approximation to the binomial distribution, the mean (μ) of the sample is:
μ = np = 90 x 0.26 = 23.4
The standard deviation (σ) of the sample is:
σ = √(np(1-p)) = √(90 x 0.26 x 0.74) = 4.37 (rounded to 4 decimal places)
To find the probability that fewer than 18 people from this sample were between the ages of 25 and 34, we need to calculate the z-score:
z = (x - μ) ÷ σ = (18 - 23.4) ÷ 4.37 = -1.24
Using a standard normal table or calculator, we find that the probability of a z-score less than -1.24 is 0.1089.
0.1089 = 10.89%
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Trigonometry homework help
The distance between the installations is given as follows:
126.42 miles.
What is the law of cosines?The Law of Cosines is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is also known as the Cosine Rule.
The Law of Cosines states that for any triangle with sides a, b, and c and angle B opposite to side b, the following equation holds true:
b^2 = a^2 + c^2 - 2ac cos(B)
The parameters for this problem are given as follows:
a = 143, c = 70, B = 62.1º.
Hence the distance b is obtained as follows:
b² = 143² + 70² - 2 x 143 x 70 x cosine of 62.1 degrees
b² = 15981.
[tex]b = \sqrt{15981}[/tex]
b = 126.42 miles.
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Pls, HELP!!
Law of Cosines
Solve for c. Round your final answer to the nearest tenth
The length of c in the triangle is 4.2 units.
How to find the side of a triangle?The side of a triangle can be found using cosine law as follows:
Hence,
c² = a² + b² - 2ab cos C
where
a, b and c are the side lengthC is angle opposite to side cTherefore,
c² = 7² + 8² - 2(7)(8) cos 32°
c² = 49 + 64 - 112 cos 32°
c² = 113 - 112(0.84804809615)
c² = 113 - 94.9813867695
c² = 18.019
square root both sides of the equation
c = √18.019
c = 4.24487926801
c = 4.2 units
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Simplify the polynomial expression. (x+7)^2
Answer:
x²+14x+49
Step-by-step explanation:
(a+b)²=a²+2ab+b²
(x+7)²=x²+2×7×x+7²=x²+14x+49
During a game, a spinner landed on several different colors. During a game, a spinner landed on several different colors.
Considering this data, how many of the next 13 spins should you expect to land on purple?
First, we need to find the experimental probability (probability using the provided data) of landing on purple.
Experimental probability of purple = # of purple / total #
Experimental probability of purple = 2 / 26 = 1 / 13 (simplified)
Next, we need to consider the probability in the context of 13 spins, as per the question. Our experimental probability tells us that 1 out of every 13 spins will be purple. Therefore, we can expect 1 of the next 13 spins to land on purple.
Answer: 1 spin
Hope this helps!
A research study indicated a negative linear relationship between two variables: the number of hours per week spent exercising (exercise time) and the number of seconds it takes to run one lap around a track (running time). Computer output from the study is shown below.
A figure of a computer output is shown. At the top is a table with two rows. The first row reads variable, N, mean, S E mean, and standard deviation. The second row reads running time, 11, 74.81, 2.21, and 7.33. Below this is a second table with three columns labeled predictor, coefficient, and S E coefficient. The first row reads constant, 88.01, and 0.49. The second row reads exercise time, negative 2.20, and 0.07. At the bottom it reads S equals 0.76 and R squared equals 99 percent.
Assuming that all conditions for inference are met, which of the following is an appropriate test statistic for testing the null hypothesis that the slope of the population regression line equals 0 ?
Answer:
The appropriate test statistic for testing the null hypothesis that the slope of the population regression line equals 0 is the t-statistic.
The t-statistic for testing the slope coefficient is calculated as follows:
t = (b1 - 0) / SE(b1)
where b1 is the estimated slope coefficient, and SE(b1) is the standard error of the estimated slope coefficient.
From the computer output, we see that the estimated slope coefficient for exercise time is -2.20, and the standard error of the estimated slope coefficient is 0.07.
Therefore, the t-statistic is:
t = (-2.20 - 0) / 0.07 = -31.43
This t-statistic follows a t-distribution with n-2 degrees of freedom, where n is the sample size. The sample size is not given in the output, so we cannot determine the exact degrees of freedom.
Mrs. Davis had 6 bowls of flour for a group project. The line plot below shows the fraction of a cup of flour that was left in each bowl after the project.
By summing all the fractions that was left, we have 3 cups of flour left. The correct option is (B).
Understanding Simple Line PlotThe "x" represents the quantity while the fractions represents the value.
To get the cups of flour left, we first multiply the number of "x" with the fraction and then add the resulting fractions together.
Cups left = 1 (1/8) + 1(3/8) + 2(1/2) + 2(3/4)
= 1/8 + 3/8 + 1 + 3/2
Find the LCM
= [tex]\frac{1 + 3 + 8 + 12}{8}[/tex]
= 24/8
Cups left = 3 cups
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does a number being squared with x and being negative make it so it has to be multiplied by 2 like the first number in the third part of the question? I'm unsure where it came from
Squaring a number implies increasing it by itself. In case the number being squared is negative, the result will continuously be positive. Increasing a number by 2 implies multiplying it, which is not linked to squaring a number.
What is the number about?To square a number, one must raise it to the power of two, that is different from carrying out its multiplication with itself. One way of squaring a value is shown by taking the number 3 and raising it to the power of 2.
3² = 3 x 3 = 9
By the same way , if we raise -2 to the power of 2, the result will be a positive value of four.
Raising numbers to the power of two is a frequent mathematical procedure use in numerous academic fields such as algebra, geometry, physics, and statistics.
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Let u = - 3i + 2j, v = 3i - 3j and w = - 3j
Find the specified scalar or vector.
5u(3v - 4w)
If u = - 3i + 2i, v = 2i - 2j and w = - 4j, 5u(3v - 4w) is a scalar quantity with a value of 440.
To evaluate the expression 5u(3v - 4w), we need to first perform the scalar multiplication and then the vector subtraction. We can start by computing the scalar multiplication of 3v - 4w:
3v - 4w = 3(2i - 2j) - 4(-4j) = 6i + 14j
Next, we can perform the scalar multiplication of u and the vector 6i + 14j:
5u(3v - 4w) = 5(-3i + 2j)(6i + 14j)
Expanding the product, we get:
5(-18i² + 36ij + 42ij - 28j²)
Since i² = j² = -1, we can simplify this expression as:
5(18 + 70) = 440
Therefore, 5u(3v - 4w) is a scalar quantity with a value of 440.
The key concept used in this problem is the distributive property of scalar multiplication over vector addition and subtraction. This property allows us to simplify expressions that involve scalar multiplication and vector operations by distributing the scalar to each component of the vector.
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Please help! Daniel incorrectly solved the equations shown. Explain what he did wrong in each solution and then solve both equations correctly.
25x^2-16=9
√(25x^2 )-√16=√9
5x-4=±3
5x=±7
x=±7/5
z^3-2=6
z^3=8
∛(z^3 )=∛8
z=±2
Daniel incorrectly applied the square root to both terms on the left side of the equation and he forgot to take into account the possibility of multiple roots when solving for the cube root of z³.
Let's first look at the first equation that Daniel solved incorrectly:
25x²-16=9
Daniel's solution:
√(25x² )-√16=√9
5x-4=±3
5x=±7
x=±7/5
What Daniel did wrong here is that he incorrectly applied the square root to both terms on the left side of the equation.
Instead, he should have simplified the left side first, using the fact that √(a²) = |a|, before applying the square root. So the correct solution is:
25x²-16=9
25x²=25
x²=1
x=±1
Now let's look at the second equation that Daniel solved incorrectly:
z³-2=6
Daniel's solution:
z³=8
∛(z^3 )=∛8
z=±2
What Daniel did wrong here is that he forgot to take into account the possibility of multiple roots when solving for the cube root of z³.
In fact, z³ = 8 has three roots: z = 2, z = -1 + i√3, and z = -1 - i√3. So the correct solution is:
z³-2=6
z³=8
z=2
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The stemplot below represents the number of bite-size snacks grabbed by 32 students in an activity for a statistics class.
A stemplot titled Number of Snacks has values 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 23, 23, 27, 29, 29, 29, 32, 32, 34, 38, 42.
Which of the following best describes the shape of this distribution?
skewed to the left
bimodal symmetric
skewed to the right
unimodal symmetric
Answer: The stemplot shows that the distribution is unimodal and skewed to the right.
The stem values (tens digits) are:
1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4
The leaf values (ones digits) are:
5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 7, 9, 9, 9, 2, 2, 4, 8, 2
The data is unimodal because there is one clear peak in the distribution. The data is skewed to the right because the long tail of the distribution extends to the right, with a few large values pulling the mean to the right.
Therefore, the best description of the shape of this distribution is skewed to the right.
divide to 7 digits after the decimal point. Do not round your answer 3.1 divided by 6
The value of 3.1 divided by 6 leaving 7 digits after the decimal point without rounding is 0.5166666
Evaluating the quotient expressionFrom the question, we have the following parameters that can be used in our computation:
3.1 divided by 6
When represented as an expression, we have
3.1 divided by 6 = 3.1/6
The above expression can be calculated using a calculator
Using a calculator, we have
3.1/6 = 0.51666666666
This means that
3.1 divided by 6 = 0.51666666666
Leaving 7 digits after the decimal point without rounding, we have
3.1 divided by 6 = 0.5166666
Hence, the value of 3.1 divided by 6 is 0.5166666
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-(4-8) + (-3-7)−(−1+6) + (−2+5) =
Step by step
Answer:
Step-by-step explanation:
-4+8-3-7+1-6-2+5
4-10-5+3
-6-2
-8
Step-by-step explanation:
the negative sign changes to a positive sign so
( -12)+ (-10) -(-7)+(-7)
= -22
A motorist travelled from Town A to Town B. After travelling for 1 1/2 hours , he passed
a cyclist travelling at an average speed of 45 Km/h in the opposite direction.
when the motorist reached Town B 2 h later, the cyclist was 30 km away from Town A.
a) Find the average speed of the motorist.
b) Find the distance between Town A and Town B.
Answer:
the formula: Speed = Distance / Time.
Let's break down the problem into two parts:
a) Find the average speed of the motorist.
Let's assume the average speed of the motorist is "v" km/h.
The distance the motorist traveled in 1 1/2 hours is given by: Distance = Speed × Time = v × (3/2) km.
The distance the cyclist traveled in 1 1/2 hours (opposite direction) is given by: Distance = Speed × Time = 45 × (3/2) km.
Since they passed each other, the sum of their distances should be equal to the distance between Town A and Town B.
So, we can set up the equation: v × (3/2) + 45 × (3/2) = Distance between Town A and Town B.
b) Find the distance between Town A and Town B.
When the motorist reached Town B 2 hours later, the cyclist was 30 km away from Town A.
We can set up the equation: Distance between Town A and Town B = v × 2 + 30.
Now, let's solve the equations:
v × (3/2) + 45 × (3/2) = v × 2 + 30.
Simplifying the equation, we have: (3v + 135)/2 = 2v + 30.
Multiplying both sides of the equation by 2 to eliminate the fraction, we get: 3v + 135 = 4v + 60.
Subtracting 3v from both sides of the equation, we have: v = 75.
Therefore, the average speed of the motorist is 75 km/h.
To find the distance between Town A and Town B, we substitute the value of v into the equation:
Distance between Town A and Town B = v × 2 + 30 = 75 × 2 + 30 = 150 + 30 = 180 km.
Therefore, the distance between Town A and Town B is 180 km.
Find an angle in each quadrant with a common reference angle with 285°, from 0°≤θ<360
The four angles, one in each quadrant, with a common reference angle of with 285° are: 15°, 165°, 195°, 345°
Understanding QuadrantA common reference angle is an angle that is shared by multiple angles in different quadrants when measured from the x-axis. The reference angle for an angle measured in degrees can be found by subtracting the nearest multiple of 90 degrees that is less than the angle.
For the angle 285°, the nearest multiple of 90 degrees that is less than it is 270°. Therefore, the reference angle for 285° is 285° - 270° = 15°.
Using this reference angle, we can find an angle in each quadrant with a common reference angle with 285° as follows:
First Quadrant: An angle in the first quadrant with a reference angle of 15° is 15° itself.Second Quadrant: An angle in the second quadrant with a reference angle of 15° can be found by subtracting the reference angle from 180°. Therefore, an angle in the second quadrant with a common reference angle with 285° is 180° - 15° = 165°.Third Quadrant: An angle in the third quadrant with a reference angle of 15° can be found by subtracting the reference angle from 180° and then adding 180°. Therefore, an angle in the third quadrant with a common reference angle with 285° is 180° + 15° = 195°.Fourth Quadrant: An angle in the fourth quadrant with a reference angle of 15° can be found by subtracting the reference angle from 360°. Therefore, an angle in the fourth quadrant with a common reference angle with 285° is 360° - 15° = 345°.Learn more about quadrant here:
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need help with this geometry problem
The shaded area of the circle is around 65.44 square meters in size.
How to find area?To find the area of the shaded region, subtract the area of sector FGH from the area of sector FEGH.
The area of sector FEGH is:
A1 = (1/2) r² θ₁
where r = radius of the larger circle and θ₁ = angle subtended by the arc EH.
Since EH = 30 m and the radius of the larger circle = 18 m (half of 10 + 8):
θ₁ = (EH arc length) / r = 30/18π radians
So,
A₁ = (1/2) (18)² (30/18π) = 270/π m²
The area of sector FGH is:
A₂ = (1/2) r² θ₂
where θ₂ = angle subtended by the arc GH.
Since GH is 8 m and the radius of the larger circle is 18 m:
θ2 = (GH arc length) / r = 8/18π radians
So,
A₂ = (1/2) (18)² (8/18π) = 64/π m²
Therefore, the area of the shaded region is:
A = A₁ - A₂ = (270/π) - (64/π) = 206/π ≈ 65.44 m²
Hence, the area of the shaded region is approximately 65.44 square meters.
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What is the slope intercept form of the equation y-5=-1/4(x-12)
Each of the following people bought a watch that costs 300. Which of the following people will pay the most for their purchase
The individual that will be paying the most for their purchase is: B.edgar paid with a credit card and paid the minimum payment each month
Which individual will pay the most?The individual that will pay the most according to the data provided is Edgar. Edgar's payment is spread out to the longest length of time. So, he will have to pay the added dues for extending his payment.
Usually, the person who pays cash pays the least amount while the person who pays in installments is charged for additional time spent in making the payment.
Complete Question:
Each of the following people bought a watch that costs $300. Which of the following people will pay the most for their purchase A.Sarah paid cash B.edgar paid with a credit card and paid the minimum payment each month C.susan paid with a credit card and paid the minimum payment plus 30 each month D. Sean paid with a credit card and paid the full balance the first of the month
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on the first day of training Zari runs 2 miles north, the 4 miles east and then back home via shortest route. Taye runs 2 miles west then 4 miles south, and then back home again via the shortest route. a. draw their routes on the coordinate plane above, use a straightedge for accuracy. b. create a proof that demonstrates that the two triangles formed by their routes are congruent. proof needs three pairs of congruent properties of the triangles followed by a triangle congruency statement. show if congruent by ASA, SAS, or SSS.
By ASA (Angle-Side-Angle) congruence, triangle ABC is congruent to triangle DEF.
Instructions to draw the routes:
Draw the x-axis and y-axis to create a coordinate plane.
Mark the starting point of Zari's run as (0,0) on the coordinate plane.
From (0,0), move 2 units north to reach (0,2).
From (0,2), move 4 units east to reach (4,2).
From (4,2), move directly back to the starting point (0,0) using the shortest route.
Mark the starting point of Taye's run as (0,0) on the coordinate plane.
From (0,0), move 2 units west to reach (-2,0).
From (-2,0), move 4 units south to reach (-2,-4).
From (-2,-4), move directly back to the starting point (0,0) using the shortest route.
Instructions to prove that the two triangles are congruent using ASA:
Label the vertices of Zari's triangle as A (0,0), B (4,2), and C (0,0).
Label the vertices of Taye's triangle as D (0,0), E (-2,-4), and F (0,0).
Show that angle A and angle D are congruent because they are both right angles (90 degrees).
Show that segment AB and segment DE are congruent because they both have a length of 4 units.
Show that segment AC and segment DF are congruent because they both have a length of 2 units.
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College Level Trig Question Any help will do!!
The value of x in the equation y = 9 sec(2x) at [0, π/4) ∪ (π/4, π/2] is x = 1/2[sec₋¹(y/9)]
Calculating the values of xFrom the question, we have the following parameters that can be used in our computation:
y = 9 sec(2x)
The interval of x is also given as
[0, π/4) ∪ (π/4, π/2]
This means that the values of x is from 0 to π/2, however, the function is undefined at x = π/4 i.e. there is a hole at x = π/4
Next, we set the equation to y
So, we have
9 sec(2x) = y
Divide both sides by 9
sec(2x) = y/9
Take the arc sec of both sides of the equation
2x = sec₋¹(y/9)
Divide both sides by 9
x = 1/2[sec₋¹(y/9)]
Hence, the value of x is x = 1/2[sec₋¹(y/9)]
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PLS HELP ME WITH THIS QUESTION PLS
PLS SHOW YOUR WORKING OUT
p = 3, q = 41, and r = 2, and we can write:
[tex]Sn = 3(gt^2 - t) + 41(gt - t).[/tex]
What is an arithmetic series?According to the given information we are given that the first term of an arithmetic series is (21 + 1), which simplifies to 22. We are also given that the common difference of the series is 3. Therefore, the second term of the series is 22 + 3 = 25, the third term is 22 + 2(3) = 28, and so on.
To find the nth term of this arithmetic series, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where an is the nth term, a1 is the first term, n is the number of terms, and d is a common difference. We are given that the nth term is (141-5), so we can set up an equation and solve for n:
(141-5) = 22 + (n - 1)3
136 = 22 + 3n - 3
117 = 3n
n = 39
Therefore, there are 39 terms in the arithmetic series.
To find the sum of the first n terms of an arithmetic series, we can use the formula:
Sn = n/2(a1 + an)
where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term. We know that a1 = 22, an = (141-5), and n = 39, so we can substitute these values into the formula:
S39 = 39/2(22 + (141-5))
S39 = 19(136)
S39 = 2584
Therefore, the sum of the first 39 terms of the series is 2584.
Now, we need to write the sum of the first n terms of the series as p(gt - 1), where p, q, and r are integers.
We know that the common difference is 3, so we can write the nth term as:
an = a1 + (n - 1)d
an = 22 + (n - 1)3
an = 3n + 19
Substituting this into the formula for the sum of the first n terms, we get:
Sn = n/2(a1 + an)
Sn = n/2(22 + 3n + 19)
Sn = n/2(3n + 41)
[tex]Sn = 3/2 n^2 + 41/2 n[/tex]
Therefore, p = 3, q = 41, and r = 2, and we can write:
[tex]Sn = 3(gt^2 - t) + 41(gt - t).[/tex]
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This circle is centered at the origin, and the length of its radius is 5. What is the equation of the circle? A. x2 + y2 = 52 B. x2 + y2 = 5 C. (x - 5)2 + (y - 5)2 = 25 D.
Answer:A
Step-by-step explanation:
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Therefore , the solution of the given problem of parallel lines comes out to be parallel lines stay parallel option C is correct.
What applications do parallel lines have?A parallelogram in Euclidean geometry is essentially a straightforward hexagon with two different groups & equal distances. When both sets of sides evenly share a horizontal path, a particular type of quadrilateral known as a parallelogram is created. There are four distinct types of parallelograms, three of them being incompatible. The four distinct forms are slightly parallelograms, rectangular shapes, squares, and parallelograms.
Here,
C. It is untrue that a line may be translated into two parallel lines.
A line can be translated into another line that runs parallel to the first line, but not into two parallel lines.
Every point on the line is rigidly transformed by a translation, which moves all of the points along the line uniformly and in one direction.
After a translation, parallel lines stay parallel.
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