Answers
Step-by-step explanation:
A. To find the equation of a line parallel to line f (y = 2) and passing through point P(-2, -1), we need to understand that parallel lines have the same slope. Since line f is a horizontal line with a slope of 0, the line we are looking for will also have a slope of 0. The equation for a horizontal line with the same y-intercept as point P is simply y = -1.
B. To find the equation of a line parallel to line g (y = 2x - 1) and passing through point P(-2, -1), we need to consider that parallel lines have the same slope. The slope of line g is 2. Using the point-slope form (y - y1 = m(x - x1)), where m is the slope and (x1, y1) is the given point P(-2, -1):
y - (-1) = 2(x - (-2))
y + 1 = 2(x + 2)
Now, we can convert this to slope-intercept form (y = mx + b):
y = 2x + 4 - 1
y = 2x + 3
C. To find the equation of a line perpendicular to line f (y = 2) and passing through point Q(3, -2), we need to know that perpendicular lines have slopes that are negative reciprocals of each other. Since line f is a horizontal line with a slope of 0, the line perpendicular to it will be a vertical line. The equation for a vertical line passing through point Q with the same x-coordinate is simply x = 3.
D. To find the equation of a line perpendicular to line g (y = 2x - 1) and passing through point Q(3, -2), we need to find the negative reciprocal of the slope of line g. The slope of line g is 2, so the negative reciprocal is -1/2. Using the point-slope form (y - y1 = m(x - x1)), where m is the new slope and (x1, y1) is the given point Q(3, -2):y - (-2) = -1/2(x - 3)
y + 2 = -1/2(x - 3)
Now, we can convert this to slope-intercept form (y = mx + b):
y = -1/2x + 3/2 - 2
y = -1/2x - 1/2
Related Questions
A roll of copper tubing is 50 ft. long. If gas range connectors must be 30 in. long, how many connectors can be cut from the roll of tubing? (Ignore cutting waste.)
Answers
50 ft. x 12 in./ft. = 600 in.
So, the roll of copper tubing is 600 inches long.
To find out how many 30-inch connectors can be cut from the tubing, we need to divide the length of the tubing by the length of each connector:
600 in. ÷ 30 in./connector = 20 connectors
Therefore, 20 connectors can be cut from the roll of tubing.
A creative writing competition accepts only
poems and stories.
In one year, the competition received 1000
entries.
750 of the entries were poems.
24% of the poems and 65 of the stories were
shortlisted for a prize.
a) Draw a frequency tree to show the
information above.
b) An entry is picked at random. What is the
probability that it is a poem that has not been
shortlisted?
Give your answer as a decimal.
c) A story is picked at random. What is the
probability that it has not been shortlisted?
Give your answer as a decimal.
Answers
Answer:
b) 0.57
c) 0.74
Step-by-step explanation:
part a:
frequency graph is attached with this answer (in png format).
part b:
let A be the event an entry is picked at random and the entry is a poem that has not been shortlisted.
P(A) = [tex]\dfrac{\text{number of poems not shortlisted}}{\text{total number of entries}}[/tex]
P(A) = [tex]\dfrac{570}{1000}[/tex] (see the frequency graph)
P(A) = 0.57
part c:
let B be the event a story is picked at random and the story has not been shortlisted.
P(B) = [tex]\dfrac{\text{number of stories not shortlisted}}{\text{total number of stories}}[/tex]
P(B) = [tex]\dfrac{185}{250}[/tex] (see the frequency graph)
P(B) = 0.74
Hopefully this answer helped you!!
Evaluating functions
Linear and quadratic or cubic
Answers
Answer:
f(3) = -39g(-6) = -28Step-by-step explanation:
You want f(3) and g(-6) when f(x) = -4x² -3 and g(x) = 5x +2.
Function evaluationTo find the value of the function for a particular value of the variable, put that value in place of the variable and do the arithmetic.
f(3) = -4(3²) -3 = -4(9) -3 = -36 -3
f(3) = -39
g(-6) = 5(-6) +2 = -30 +2
g(-6) = -28
__
Additional comment
Your calculator can help with the arithmetic.
The correlation coefficient is always a number between ____ and ___.
Answers
A correlation coefficient is consistently a number between 1 and - 1 .
The correlation coefficient is a factual measure that demonstrates the strength and heading of the straight connection between two factors. It goes from - 1 to 1, where - 1 addresses a completely bad correlation (i.e., as one variable expands, different declines), 0 addresses no correlation, and 1 addresses an entirely sure correlation (i.e., as one variable builds, the other likewise increments).
The indication of the correlation coefficient demonstrates the heading of the relationship, while the extent of the coefficient shows the strength of the relationship. A correlation coefficient of 0 shows no straight connection between the factors, while values nearer to - 1 or 1 demonstrate a more grounded direct relationship.
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Zain is using a protractor to measure an angle.
What is the measure of the angle?
Answers
The measure of the angle that Zane is using the protractor is a 113 degrees.
Degree is the unit of measure of an angle and is measured by using the geometric tool - a protractor. A degree is denoted by the symbol '°'. A circle completely rotates at a 360° and a degree is a part of that 360° rotation as it is divided into 360 equal parts.
Therefore, The measure of the angle that Zane is using the protractor is a 113 degrees.
multiply the y-value of each point by 1/2 and drag the blue point to its new location.
Answers
The function y = ∛x when transformed is added as an attachment
Transforming the functionFrom the question, we have the following parameters that can be used in our computation:
y = ∛x
When the y values are multiplied by 1/2 the rule is
(x, 1/2y)
To transform the function y = ∛x by the point (x, 1/2y), we can use the following steps:
Replace y with 1/2y in the original function: y = ∛x becomes 1/2y = ∛xSolve for y: multiply both sides by 2 to get y = 2∛xTherefore, the transformation by the point (x, 1/2y) is y = 2∛x
See attachment for the graph
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What are the perimeter and area of triangle XYZ ?
Answers
Answer:
B) P = 42; A = 84
Step-by-step explanation:
Perimeter:
You have two right triangles, so you need to find the third side length.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]5^{2}[/tex] + [tex]12^{2}[/tex] = [tex]c^{2}[/tex]
25 + 144 = [tex]c^{2}[/tex]
169 = [tex]c^{2}[/tex]
[tex]\sqrt{169}[/tex] = [tex]\sqrt{c^{2} }[/tex]
13 = c
The top right missing outside length is 13
We do the same thing to find the missing bottom outside.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]12^{2}[/tex] + [tex]9^{2}[/tex] = [tex]c^{2}[/tex]
144 + 81 = [tex]c^{2}[/tex]
225 = [tex]c^{2}[/tex]
[tex]\sqrt{225}[/tex] = [tex]\sqrt{c^{2} }[/tex]
15 = c
The perimeter of triangle xyz is 5 + 9 + 13 + 15 = 42 units
Area:
a = 1/2 bh
a= 1/2 (5 + 9) (12)
a = 1/2 (14)(12)
a = 84 [tex]units^{2}[/tex]
Helping in the name of Jesus.
Find the length of BC with work
Answers
Answer:
Step-by-step explanation:
add c with b and then add a multiply 30 and divide by 12
Does the long division process end or does it continue indefinitely?
Answers
Answer:
It depends, sometimes it continues with a pattern in the decimal places, sometimes it ends.
Step-by-step explanation:
How do the sulotions of the two inequalities differ are any sulotions the same x+5<8 and x+5>8 B x+5_< 8 and x+5_>8
Answers
Solution set for both inequalities is x ≤ 3 and x ≥ 3, which can be written as x = 3.
The two inequalities are: x + 5 < 8 and x + 5 > 8. The first inequality states that the sum of x and 5 is less than 8, while the second inequality states that the sum of x and 5 is greater than 8.
To solve the first inequality, we need to isolate x by subtracting 5 from both sides of the inequality: x < 3. This means that any value of x that is less than 3 will satisfy the inequality.
To solve the second inequality, we need to isolate x by subtracting 5 from both sides of the inequality: x > 3. This means that any value of x that is greater than 3 will satisfy the inequality.
The solutions of the two inequalities differ in terms of the values of x that satisfy each inequality. The first inequality has a solution set that consists of all values of x less than 3, while the second inequality has a solution set that consists of all values of x greater than 3. Therefore, the solutions of the two inequalities do not overlap.
The second set of inequalities are x + 5 ≤ 8 and x + 5 ≥ 8. The first inequality states that the sum of x and 5 is less than or equal to 8, while the second inequality states that the sum of x and 5 is greater than or equal to 8.
To solve the first inequality, we need to isolate x by subtracting 5 from both sides of the inequality: x ≤ 3. This means that any value of x that is less than or equal to 3 will satisfy the inequality.
To solve the second inequality, we need to isolate x by subtracting 5 from both sides of the inequality: x ≥ 3. This means that any value of x that is greater than or equal to 3 will satisfy the inequality.
The solutions of the two inequalities in this case do overlap. The common solution is x = 3, which satisfies both inequalities since it is both less than or equal to 8 and greater than or equal to 8. Therefore, the solution set for both inequalities is x ≤ 3 and x ≥ 3, which can be written as x = 3.
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In DEF, f= 960 inches, m/D=101° and mZE=27°. Find the length of e, to the
nearest 10th of an inch.
Answers
The length of the side e for the triangle ∆DEF is equal to 553.1 inches to the nearest tenth tenth of an inch using the sine rule.
What is the sine ruleThe sine rule is a relationship between the size of an angle in a triangle and the opposing side.
We shall first evaluate for the angle m∠F and then solve for the e using the sine rule as follows:
m∠F = 180° - (27 + 101) {sum of interior angles of a triangle}
m∠F = 52°
e/sin27 = 960/sin52
e = (960 × sin27)/sin52 {cross multiplication}
e = 553.0773
Therefore, the length of the side e for the triangle ∆DEF is equal to 553.1 inches to the nearest tenth tenth of an inch using the sine rule.
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how do you do this question, I can't seem to get the answer
Answers
Answer:
74π cm²
Step-by-step explanation:
You want to know the painted area of a cone 10 cm in diameter and 12 cm high that has an unpainted hole in the base that has a 4 cm radius.
Lateral areaThe area of the curved surface of the cone is found using the given formula. To use that formula, we need to know the slant height of the cone. The slant height is the hypotenuse of a right triangle that is 12 cm high and has a base of 5 cm:
l² = r² +h²
l = √(5² +12²) = √(25 +144) = √169
l = 13 . . . . cm
Then the lateral area is ...
LA = πrl = π(5 cm)(13 cm) = 65π cm²
Base areaThe painted area of the base is the difference between the areas of circles 5 cm in radius and 4 cm in radius:
A = π(r₁² - r₂²) = π((5 cm)² -(4 cm)²) = π(25 -16) cm² = 9π cm²
Total painted areaThe painted area is the sum of the areas of the curved surface and the donut base:
A = 65π cm² +9π cm² = 74π cm²
__
Additional comment
The radius of the base is half the diameter. If you slice the cone through its vertex and perpendicular to its base, the cross section is an isosceles triangle with height 12 cm and base 10 cm. The altitude of that triangle divides it into two congruent right triangles that have base 5 cm and height 12 cm.
You may recognize this as the {5, 12, 13} right triangle, which tells you the slant height is 13 cm. If not, you can use the Pythagorean theorem to find the slant height, as above.
I need somebodys help quickly please!
(look at the attachment it shows the math equation).
Answers
Answer:
First box is seven; second box is 16; third box is 14
Step-by-step explanation:
Since a square has all equal sides, we know that s+s+s+s or 4s=Perimeter.
SInce we are finding the area of a square, the equation would be s^2. 7 squared is 49, 16 squared is 256, and 14 squared is 196.
The figure below is dilated by a factor of 1/4 centered at the origin. Plot the resulting image.
Answers
Check the picture below.
The results of a survey show that the percent of adults in a certain town who want to change the name of the town is in the interval [0.38,0.41].
Answers
The point estimate for the percent who want to change the name of the town is 39.5%.
The poll's margin of error is 1. 5 %.
The town most likely will not change its name because the point estimate is less than half.
How to find the point estimate ?The point estimate for the percent who want to change the town's name is the midpoint of the interval [0.38, 0.41]. To find the midpoint, add the endpoints of the interval and divide by 2:
(0.38 + 0.41) / 2 = 0.79 / 2 = 0.395
So, the point estimate is 39.5%.
The margin of error is half the width of the interval. To find the width, subtract the lower endpoint from the upper endpoint and divide by 2:
(0.41 - 0.38) / 2 = 0.03 / 2 = 0.015
So, the margin of error is 1.5%.
Based on the given data, the town is most likely not going to change its name. The point estimate, 39.5%, is less than 50%, which indicates that less than half of the surveyed adults want to change the town's name. The margin of error (1.5%) is relatively small compared to the point estimate, which means that the true percentage is likely to be within 1.5% of the point estimate.
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the trees shadow is 36.2 feet long. The tree is 15 feet away from the edge of the lake. Cade is 6.2 feet tall and his shadow is 2.5 feet long, his shadow is measured at the exact time the trees shadow reaches the other side of the lake which is 15.6 feet long. What is the distance across the lake (water's edge to opposite side)
Answers
Answer:
24.3ft
Step-by-step explanation:
36.2ft - 15ft = 21.2ft
Cade height = 6.2 - 2.5 = 3.7
21.2 + 3.7 = 24.9ft
24.9ft - 15.6ft = 24.3ft
8x=-10y slope and y intercept
Answers
Answer:
To solve the equation 8x = -10y for the slope and y-intercept, we need to first rearrange it into the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To do this, we can divide both sides of the equation by -10, which gives us:
y = (-8/10)x
Simplifying further, we get:
y = (-4/5)x
Therefore, the slope of the line represented by this equation is -4/5. This means that for every increase of 1 in x, y decreases by 4/5.
To find the y-intercept, we can set x to 0 and solve for y:
y = (-4/5)(0)
y = 0
Thus, the y-intercept is 0.
In summary, the slope of the line represented by 8x = -10y is -4/5 and its y-intercept is 0.
Step-by-step explanation:
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Answer: x=5y/4
Step-by-step explanation:
8x=10y
Divide both sides by 8
8x/8 = 10y/8
8x divided by 8, will cancel out resulting in x.
So, your final answer will be x=5y/4
In how many ways can 8 distinguishable rooks be placed on an 8 × 8 chessboard so that none can capture any other, namely no row and no column contains more than one rook? For example, in a 2 × 2 chessboard, you can place 2 rooks labled 'a, and 'b' in 4 ways. There are 4 locations to place'a', and that location determines the location of b'.
Answers
There are 40,320 ways to place 8 distinguishable rooks on an 8 × 8 chessboard so that none can capture any other.
In order to place 8 distinguishable rooks on an 8 × 8 chessboard so that none can capture any other, we need to place one rook in each row and each column exactly once.
The first row can be filled in 8 ways, as there are 8 columns to choose from. The second row can be filled in 7 ways, as we cannot choose the column that has already been filled in the first row. Continuing in this way, we see that the number of ways to place 8 distinguishable rooks on an 8 × 8 chessboard is:
8! = 40,320
Therefore, there are 40,320 ways to place 8 distinguishable rooks on an 8 × 8 chessboard so that none can capture any other.
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What is the square root of 16?
Answers
Students in ms seiko's made a line plot of the number of books they read over the summer what two numbers of books read occur the least frequently enter your answers in the boxes in increasing order
Answers
The two numbers of books read that occur the least frequently are 7 and 15.
To determine which two numbers occur the least frequently, we need to count the number of tally marks for each number on the line plot. Based on the line plot, we can see that the number of tally marks for each number is as follows:
7: 1 tally mark
8: 2 tally marks
9: 3 tally marks
10: 4 tally marks
11: 2 tally marks
12: 4 tally marks
13: 3 tally marks
14: 2 tally marks
15: 1 tally mark
The two numbers that occur the least frequently are 7 and 15, as they each have only one tally mark.
Therefore, the answers to the question are: 7 in the first box and 15 in the second box.
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Students in ms seiko's made a line plot of the number of books they read over the summer.
books read
7 8 9 10 11 12 13 14 15
what two numbers of books read occur the least frequently enter your answers in the boxes in increasing order?
A submarine dives 240 meters below the surface of the water and then rises 65 meters.
Which integer describes the position of the submarine in relation to the surface of the
water?
A. -305 m
B. -175 m
C.175 m
D 305 m
Answers
Answer:
B
Step-by-step explanation:
-240 +65 = -175
(We use a -240 instead of 240 because it's below water.) :)
Adam calculates his annual salary (base pay and commission), y, using the model y = 0.28x + 38,000, where x represents his total sales for the year. What is the meaning of the y-intercept in the model?
A. The y-intercept represents Adam's base pay
B. The y-intercept represents the highest salary Adam can earn
C. The y-intercept represents Adam's total sales when he earned no commission
D. The y-intercept represents Adam's commission pay when he had zero total sales
the y-intercept represents Adam's commission pay when he had zero total sales
Answers
Answer: A
Step-by-step explanation:
The Y intercept is his base pay, because no matter what he is getting 38,000. So, his total salary will always start out at 38,000 then continue up with commission sales.
A poker hand consists of 5 cards from a standard deck of 52. How many hands will include all red cards or all black cards?
Answers
Answer:There are two cases to consider: a hand that consists of all red cards and a hand that consists of all black cards.
Case 1: All red cards
There are 26 red cards in a standard deck of 52 cards. To form a 5-card hand consisting of all red cards, we need to choose 5 cards from the 26 red cards. The number of ways to do this is:
C(26, 5) = (26!)/(5!21!) = 65,780
Case 2: All black cards
Similar to the first case, there are 26 black cards in a standard deck of 52 cards. To form a 5-card hand consisting of all black cards, we need to choose 5 cards from the 26 black cards. The number of ways to do this is:
C(26, 5) = (26!)/(5!21!) = 65,780
Therefore, the total number of hands that include all red cards or all black cards is the sum of the two cases:
65,780 + 65,780 = 131,560
So there are 131,560 hands that consist of either all red cards or all black cards.
Step-by-step explanation:
A student had 50 minutes of homework on Monday and 30 minutes of homework on Tuesday. What is the percent decrease in homework time from Monday to Tuesday?
Answers
If a student had 50 minutes of homework on Monday and 30 minutes of homework on Tuesday, then there was a 40% decrease in homework time from Monday to Tuesday.
To calculate the percent decrease in homework time from Monday to Tuesday, we need to find the difference between the two values and then divide that difference by the original value (Monday’s homework time). The difference between 50 minutes and 30 minutes is 20 minutes. Dividing this difference by the original value (50 minutes) gives us:
(20 / 50) x 100% = 40%
Therefore, there was a 40% decrease in homework time from Monday to Tuesday.
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we want to test if more than 6% of byu students are from texas. is the sampling distribution of p-hat approximately normal in this example? group of answer choices yes, because n > 30. no, because the sample distribution is not normal. no, because the sampling distribution of p-hat does not have a shape. yes, because np0 > 10 and n(1-p0) > 10.
Answers
Yes, because[tex]np0 > 10[/tex]and [tex]n(1-p0) > 10[/tex].
Thus, the sampling distribution of p-hat is approximately normal, given the conditions of [tex]np0 > 10 and n(1-p0) > 10.[/tex]
This is because the sampling distribution of p-hat follows the Central Limit Theorem, which states that when sample sizes are greater than 30,
the sampling distribution of the sample proportion will be approximately normal. The Central Limit Theorem is used in this example because the number of BYU students from Texas (n) is greater than 30, so the sample proportion (p-hat) is normally distributed.
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What is the surface area of this composite figure? The slant height of the cone is 3. The height of the cone is approximately 1.658. (It is all one figure. Watch for surfaces that are not needed in your formulas because they are not actually surfaces in this figure.)
150л units²
125л units³
100л units²
Answers
Answer:
125pi units cubed
Step-by-step explanation:
if a destination goal is created for a newsletter sign-up and a user completes the newsletter sign-up three times in three separate sessions, how many goal conversions will analytics count?3621
Answers
Analytics will count three goal conversions if a user completes the newsletter sign-up three times in three separate sessions.
When a goal is set up in analytics, it is assigned a unique ID. When a user completes the desired action that triggers the goal, the ID is recorded in the user's session data. Each time the user completes the action, a new session is created, and a new goal completion is recorded with a unique ID.
Therefore, if the user completes the newsletter sign-up three times in three separate sessions, analytics will count three goal conversions, each with a unique ID.
It's worth noting that while this behavior is typical for most analytics platforms, it's possible to configure goals in different ways, so the behavior may vary depending on the specific implementation. Therefore, it's important to consult the analytics documentation or work with a knowledgeable analyst to confirm the expected behavior.
Therefore, the correct answer is three goal conversions will be counted in analytics.
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Plssssss helppp
What do you think an appropriate domain for the mold area function A is? Explain your
reasoning
Answers
Assuming that the function A calculates the surface area of a mold, the appropriate domain for A would be a set of all possible molds, which can be represented by a set of positive real numbers.
It is important to note that the mold's geometry, size, and complexity will affect the calculation of its surface area. Therefore, the domain of the mold area function A should include all possible variations of mold shapes and sizes.
In practical applications, the domain of A may also be limited by the manufacturing capabilities or constraints, such as the maximum size or complexity of molds that can be produced. In such cases, the domain of A may need to be further restricted to reflect these limitations.
Overall, the appropriate domain for the mold area function A would depend on the specific context and application of the function.
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Please solve this equation
24+0. 44x=19+1. 69x
Answers
Given equation is: 24+ 0.44x = 19+ 1. 69x is x = 4.
Equation:
In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal. Solving an equation involving variables involves determining which values of the variables make the equation true. The variables for which the equation must be solved are also called unknowns, and the values of the unknowns that satisfy the equation are called solutions of the equation. There are two types of comparisons: identity comparisons and conditional comparisons. The identity is true for all values of the variable. A conditional comparison is only true for certain values of a variable.
According to the Question:
Given equation:
24+0. 44x = 19+ 1. 69x
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
24 - 19 = 1.69x - 0.44x
⇒ 5 = 1.25x
⇒ x = 5/1.25
⇒ x = 4
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Triangle RST was dilated by a scale factor of 3 to create triangle LMN. What is true about the special relationship between the trigonometric ratios of the two triangles? Choose ALL that apply.
A.
sin angle R = ST/RT
B.
sin angle L = 3(ST)/3(RT)
C.
sin angle R = 3(MN)/3(LM)
D.
sin angle L= MN/NL
Answers
The answers are sin angle R = ST/RT and sin angle L = 3(ST)/3(RT) Fοr the given questiοn trigοnοmetry.
Thus option A & B are correct.
What is trigοnοmetric ratiοs?Trigοnοmetric ratiοs are mathematical relatiοnships between the sides and angles οf a right triangle. The three main trigοnοmetric ratiοs are sine, cοsine, and tangent, abbreviated as sin, cοs, and tan.
The sine οf an angle is the ratiο οf the length οf the side οppοsite the angle tο the length οf the hypοtenuse. The cοsine οf an angle is the ratiο οf the length οf the adjacent side tο the length οf the hypοtenuse. The tangent οf an angle is the ratiο οf the length οf the οppοsite side tο the length οf the adjacent side. These ratiοs are useful in sοlving prοblems invοlving right triangles and have many applicatiοns in fields such as physics, engineering, and navigatiοn.
We knοw that when a triangle is dilated by a scale factοr οf k, all cοrrespοnding sides are multiplied by k, and all cοrrespοnding angles remain cοngruent.
Using this fact, we can determine the relatiοnships between the trigοnοmetric ratiοs οf the twο triangles:
A. Sin angle R = ST/RT is true fοr bοth triangles, as the sine οf an angle is defined as the ratiο οf the οppοsite side tο the hypοtenuse, which dοes nοt change when dilated.
B. Sin angle L = 3(ST)/3(RT)simplifies tο Sin angle L = ST/RT, which is true fοr bοth triangles (as shοwn in part A).
C. Sin angle R = 3(MN)/3(LM) simplifies tο sin angle R = MN/LM, which is nοt necessarily true. This is because the cοrrespοnding sides οf the triangles are nοt prοpοrtiοnal tο each οther.
D. Sin angle L = MN/NL is nοt necessarily true fοr the same reasοn as in part C.
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