The measure of an angle is 9 more than twice its complement. Find the measure of each angle. Which equation below accurately translates the sentence and could be used to find the measure of each angle? 2x + 9 = 90 - x x + 9 = 2(x - 90) x = 9 + 2(90 - x) 2x = (x - 90) + 9
Answers
Answer:
1) Find the measure of each angle.
The measure of each angle = 63° and 27°
2) Which equation below accurately translates the sentence and could be used to find the measure of each angle?
a) 2x + 9 = 90 - x
Step-by-step explanation:
1) Find the measure of each angle.
Two Angles are Complementary when they add up to 90 degrees (a Right Angle)
Mathematically this is represented as:
x° + y° = 90°
From the above question, we are told that:
The measure of an angle is 9 more than twice its complement.
Let the complement of an angle be represented by x
And its measure of an angle be represented by y
Hence,
y = 2× x+ 9
y =(2x + 9)°
x° + y° = 90°
Substitute 2y + 9 for x
x + 2x + 9 = 90
Collect like terms
x + 2x = 90 - 9
3x = 81
Divide both sides by 3
3x/3 = 81/3
x = 27°
We find y(measure of the angle)
x + y = 90
27 + y = 90
y = 90 - 27
y = 63°
Therefore, the measure of each angle is given as:
Measure of an angle = 63°
Complement of an angle = 27°
2) Which equation below accurately translates the sentence and could be used to find the measure of each angle?
a)2x + 9 = 90 - x
b) x + 9 = 2(x - 90)
c) x = 9 + 2(90 - x)
d) 2x = (x - 90) + 9
Option a) is the correct option
Related Questions
Numerical pruun
a. Convert the following.
i) 2.4 millimetres into metre
i
Answers
2.4 millimetres into meter is 0.0024.
Answer:
0.0024 meters
Step-by-step explanation:
Using conversion.
Hope this helps!
xoxo,
cafeology
Helpppp I have no idea what to do
Answers
Answer:
Step-by-step explanation:
All I am saying its not 1 or 3
Charles buys 10 drinks and 3 sandwiches for $34. Isabel buys 5 drinks and 4
sandwiches for $37. They want to determine the cost of each item.
Write a system of linear equations to model the problem. Let d equal the cost
of each drink and let s equal the cost of each sandwich. Solve the system
algebraically. How much does each item cost?
Answers
Graph y = 2x and y= 2x
What x-values are solutions to the system?
Answers
Answer:
Wait u gave the same equation twice, do u mind checking back to it?
Step-by-step explanation:
Can someone help me with this math homework please!
Answers
Answer:
The rock hits the ground between 2 seconds and 2.5 seconds after it is dropped
Step-by-step explanation:
The given table is presented as follows;
\(\begin{array}{ccl}t&h(t)&Description\\0&20&Initial \ height\\0.5&18.8&Rock \ in \ downward \ motion\\1&15.1&\\1.5&9&\\2&0.4&The \ height \ just \ before \ the \ rock \ hits \ the \ ground \\2.5&-10.6&The \ calculated \ height \ after\ the \ rock \ hits \ the \ ground \\3&-24.1&Calculated \ height \ after\ the \ rock \ hits \ the \ ground\end{array}\)
Therefore, the rock hits the ground between t = 2 seconds and t = 2.5 seconds after it is dropped.
Determine whether the following are linear transformations and justify your answer: (a) L:Rn×n→Rn×n defined by L(A)=CA+AC, where C is a fixed n×n matrix. (b) L:P2→P3 defined by L(p(x))=p(x)+xp(x)+x2p′(x). (c) L:C[0,1]→R1 defined by L(f)=∣f(0)∣
Answers
All the three A-L:Rn×n→Rn×n defined by L(A)=CA+AC, (b) L:P2→P3 defined by L(p(x))=p(x)+xp(x)+x2p′(x). (c) L:C[0,1]→R1 defined by L(f)=∣f(0)∣ are linear transformation.
(a) Yes, L is a linear transformation. To prove this, we need to show that L satisfies two conditions: 1) L(u+v) = L(u) + L(v) for any u, v in Rⁿⁿ and 2) L(cu) = cL(u) for any scalar c and u in Rⁿⁿ.
To prove the first condition, we have:
L(u+v) = C(u+v) + (u+v)C = Cu + Cv + uC + vC = (Cu+uC) + (Cv+vC) = L(u) + L(v)
To prove the second condition, we have:
L(cu) = C(cu) + (cu)C = cCu + c(uC) = c(Cu+uC) = cL(u)
Therefore, L satisfies both conditions and is a linear transformation.
(b) Yes, L is a linear transformation. To prove this, we need to show that L satisfies the two conditions mentioned above.
For the first condition, let p(x) and q(x) be any two polynomials in P₂. Then, we have:
L(p(x) + q(x)) = (p(x) + q(x)) + x(p(x) + q(x)) + x²(p'(x) + q'(x))
= p(x) + x p(x) + x²p'(x) + q(x) + x q(x) + x²q'(x) = L(p(x)) + L(q(x))
For the second condition, let c be any scalar and p(x) be any polynomial in P₂. Then, we have:
L(c p(x)) = c p(x) + x c p(x) + x² c p'(x) = c L(p(x))
Therefore, L satisfies both conditions and is a linear transformation.
(c) Yes, L is a linear transformation. To prove this, we need to show that L satisfies the two conditions mentioned above.
For the first condition, let f(x) and g(x) be any two functions in C[0,1]. Then, we have:
L(f(x) + g(x)) = |f(0) + g(0)| = |f(0)| + |g(0)| = L(f(x)) + L(g(x))
For the second condition, let c be any scalar and f(x) be any function in C[0,1]. Then, we have:
L(c f(x)) = |c f(0)| = |c| |f(0)| = |c| L(f(x))
Therefore, L satisfies both conditions and is a linear transformation.
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5. Write an equation that models exponential decay.
Answers
Answer:
Step-by-step explanation:
y = ab^x where 0<b<1 for exponential decay
an example would be y = 3(1/7)^x
Suppose you are choosing a letter at random from the word DISCRETE and your friend chooses a letter at random from the word ALGEBRA . What is the probability that you choose the same letter
Answers
For a randomly selecting one letters from each words, DISCRETE and ALGEBRA, the probability that you choose the same letter is equals to the \( \frac{1}{28}.\).
When we divide the number of events by the possible number of outcomes. It will give the Probability. The value of probability lies between 0 and 1. We have two Words one is DISCRETE and ALGEBRA. One letter is randomly selected from each words. Total numbers of letters in word DISCRETE = 8
Total numbers of letters in word ALGEBRA = 7
We have to determine the probability to choose the same letter. Now, number of same letters in both of the words = 1 ( E)
So, the number of ways to selecting the 'E' letter from DISCRETE word = 2
The number of ways to selecting the 'E' letter from ALGEBRA word = 1
Probability that letter E selected from ALGEBRA word, P( A)\( = \frac{1}{7}\).
Probability that letter E selected from DISCRETE word, P( D) = \( = \frac{2}{8} = \frac{1}{4} \). So, probability that you choose the same letter from both words = P(A) × P(B)
\( = \frac{1}{7} \times \frac{1}{4}\)
\( = \frac{1}{28}\)
Hence, required value is \( \frac{1}{28} \).
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Please help! I really need to get the answer correct
Answers
Answer:
x + 9y²
Step-by-step explanation:
A prime polynomial is simply an irreducible polynomial.
x + 9y² is a prime polynomial
First, we test the options.
x + 9y²
The above function cannot be reduced further.
Hence, x + 9y² is a prime polynomial
3m + 9n
Factor out 3
3 (m + 3n)
3m + 9n is not a prime because it can be factored as 3 (m + 3n)
8x^7 - 9x + 12x²
Factor out x
x(8x^6 - 9 + 12x)
8x^7 - 9x + 12x² is not a prime because it can be factored as x(8x^6 - 9 + 12x)
Hence, x + 9y² is a prime polynomial
CAN SOMEONE MAKE SENSE OUT OF THIS. please i need explaining!!! Shawn's square living room needs new flooring. He needs 196 square feet of flooring to cover the living room. What are the dimensions of Shawn's living room? Since Shawn's living room is in the shape of a square, we know that the length of each side is exactly the same. If we let s represent the length of the room, we can write an equation using the area of a square formula (A = s2). A=s•s=s2=196 Using the definition of square root: s2 = 196 s = ±√196 s = ±14 But since we are talking about the dimensions of Shawn's living room, the only real solution to this problem is 14 feet (because a solution of -14 feet would not be possible).
Answers
Step-by-step explanation:
Shawn's living room is a square, so all four sides are the same length. Area of a square is A = s², and we know the area is 196 ft². If substitute this for A:
196 ft² = s²
Take square root of both sides:
s = √(196 ft²)
s = ±14 ft
Since measurements of lengths can't be negative, s must be +14 ft. So Shawn's living room is 14 ft x 14 ft.
Answer:
14 ft x 14 ft.
Step-by-step explanation:
A dog runs 18.4 meters down a sidewalk in 8.90 seconds. It then turns around and runs back the other way a distance 12.8 meters in 4.25 seconds. a. What is its average speed for the first part if its motion? b. What is its average speed for the second part if its motion? c. What is its average speed for the entire trip? d. What is the magnitude of its average velocity for the entire trip?
Answers
a. The average speed for the first part ≈ 2.067 meters per second.
b. The average speed for the second part ≈ 3.011 meters per second.
c. The average speed for the entire trip ≈ 2.374 meters per second.
d. The magnitude of the average velocity for the entire trip ≈ 0.425 meters per second.
To solve this problem, we'll use the formulas for average speed and average velocity.
a. Average speed for the first part:
Average speed is calculated by dividing the total distance traveled by the total time taken.
In this case, the dog runs 18.4 meters in 8.90 seconds, so the average speed for the first part is:
Average speed = distance / time
Average speed = 18.4 meters / 8.90 seconds
Average speed ≈ 2.067 meters per second
b. Average speed for the second part:
Similarly, for the second part of the motion, the dog runs 12.8 meters in 4.25 seconds.
The average speed for the second part is:
Average speed = distance / time
Average speed = 12.8 meters / 4.25 seconds
Average speed ≈ 3.011 meters per second
c. Average speed for the entire trip:
To calculate the average speed for the entire trip, we need to consider the total distance and total time taken for both parts of the motion.
The total distance is the sum of the distances traveled in each part, and the total time is the sum of the times taken in each part.
Total distance = 18.4 meters + 12.8 meters = 31.2 meters
Total time = 8.90 seconds + 4.25 seconds = 13.15 seconds
Average speed = total distance / total time
Average speed = 31.2 meters / 13.15 seconds
Average speed ≈ 2.374 meters per second
d. Average velocity for the entire trip:
Average velocity takes into account both the magnitude and direction of the motion.
Since the dog runs in opposite directions for the two parts, its displacement for the entire trip is the difference between the two distances traveled.
The magnitude of average velocity is calculated by dividing the displacement by the total time taken.
Displacement = distance traveled in the first part - distance traveled in the second part
Displacement = 18.4 meters - 12.8 meters = 5.6 meters
Average velocity = displacement / total time
Average velocity = 5.6 meters / 13.15 seconds
Average velocity ≈ 0.425 meters per second
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In each of the cases that follow, the magnitude of a vector is given along with the counterclockwise angle it makes with the +x axis. Us trigonometry to find the x and y components of the vector. Also, sketch each vector approximately to scale to see if your calculated answers seem reasonable.
A) 50.0 N at 60 degrees.
B) 75 m/s at 5pi/6 rad
c)254 lb at 325 degrees
d)69 km at 1.1pi rad
Answers
The vector would point upwards and to the left, at an angle of 70 degrees from the -x axis. Sketching the vectors approximately to scale would confirm the directions and magnitudes of the components.
A) To find the x component, we use cosine of the angle: x = 50.0 N * cos(60 degrees) = 25 N. To find the y component, we use sine of the angle: y = 50.0 N * sin(60 degrees) = 43.3 N. The vector would point upwards and to the right, at an angle of 60 degrees from the +x axis.
B) To find the x component, we use cosine of the angle: x = 75 m/s * cos(5pi/6 rad) = -37.5 m/s. To find the y component, we use sine of the angle: y = 75 m/s * sin(5pi/6 rad) = 64.95 m/s. The vector would point downwards and to the left, at an angle of 150 degrees from the +x axis.
C) To find the x component, we use cosine of the angle: x = 254 lb * cos(325 degrees) = -206.5 lb. To find the y component, we use sine of the angle: y = 254 lb * sin(325 degrees) = -129.6 lb. The vector would point downwards and to the left, at an angle of 35 degrees from the -x axis.
D) To find the x component, we use cosine of the angle: x = 69 km * cos(1.1pi rad) = -22.87 km. To find the y component, we use sine of the angle: y = 69 km * sin(1.1pi rad) = 66.62 km. The vector would point upwards and to the left, at an angle of 70 degrees from the -x axis.
Sketching the vectors approximately to scale would confirm the directions and magnitudes of the components.
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A 23-ft ladder is leaning against a building. If the base of the ladder is 6 ft from the base of the building, what is the angle of elevation of the ladder? (Round your answer to one decimal place.) How high does the ladder reach on the building?
Answers
The angle of elevation of the ladder is approximately 78.7 degrees. The ladder reaches approximately 22.2 ft high on the building.
To find the angle of elevation of the ladder, we can use trigonometry. The angle of elevation is the angle between the ladder and the ground.
Given:
Length of the ladder (hypotenuse) = 23 ft
Distance of the base of the ladder from the base of the building (adjacent side) = 6 ft
To find the angle of elevation (θ), we can use the inverse tangent function (arctan) with the ratio of the opposite side to the adjacent side:
\(\theta = tan^{-1}(opposite/adjacent)\)
In this case, the opposite side is the height the ladder reaches on the building.
Using the Pythagorean theorem, we can find the height (opposite side):
\(Height^2 = Length of the ladder^2 - Distance of the base^2\\Height^2 = 23^2 - 6^2\\Height^2 = 529 - 36\\Height^2 = 493\\Height = \sqrt{493}\)
Now, we can calculate the angle of elevation:
\(\theta = tan^{-1}(opposite/adjacent)\\\theta = tan^{-1}(\sqrt{493} / 6)\)
Calculating this value, we find:
θ ≈ 78.7 degrees (rounded to one decimal place)
Therefore, the angle of elevation of the ladder is approximately 78.7 degrees.
To find how high the ladder reaches on the building, we substitute the calculated value of the height:
Height = \(\sqrt{493}\)
Height ≈ 22.2 ft (rounded to one decimal place)
Therefore, the ladder reaches approximately 22.2 ft high on the building.
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25% of__Is 10.
Help me!!!!!!!!!
Answers
Answer:
40
Step-by-step explanation:
40 divided by 1/4 = 10
25% = 1/4
Answer:
40
Step-by-step explanation:
We Know
25% of x is 10
Find x
We Take
10 x 4 = 40
So, 25% of 40 is 10
A cube has edge length 3 inches.
Find the surface area?
Answers
Answer:
54 sq inches
Step-by-step explanation:
all cubes have six sides, and each side has a surface area of 3*3, so:
6*(3*3)
The surface area of the cube with an edge length of 3 inches is 54 square inches.
What is a cube?It is a polygon having six faces.
The volume of a cube is side³.
We have,
The surface area of a cube is given by the formula:
SA = 6s²
where s is the length of one of the cube's edges.
In this case,
s = 3 inches, so we can substitute it into the formula and simplify:
SA = 6(3 inches)²
SA = 6(9 square inches)
SA = 54 square inches
Therefore,
The surface area of the cube with an edge length of 3 inches is 54 square inches.
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I need this answered
Answers
Someone help me on this one
Answers
Answer: Times 5
Step-by-step explanation:
Find the key characteristics from the graph. Please find the
•domain
•range
•Rel. max
•Rel. Min
•End behavior
•Inc. intervals
•Dec intervals
•Zeros.
Answers
Domain: All Real Numbers
Range: All Real Numbers
Rel. Max: None
Rel. Min: None
End Behavior: Asymptotic to the x-axis
Inc. Intervals: All Real Numbers
Dec. Intervals: All Real Numbers
Zeros: None
What is Asymptotic ?Asymptotic is a mathematical term that describes the behavior of a function when the input values approach infinity. It is used to describe the limiting behavior of a sequence or a function without having to calculate all the terms of the sequence or function. Asymptotic behavior is mainly used for analyzing algorithms and determining the complexity of a problem.
Asymptotic analysis can provide insights into the behavior of a system and is an important tool for understanding the behavior of algorithms.
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Domain: All Real Numbers, Range: All Real Numbers, Rel. Max: None, Rel. Min: None, End Behavior: Asymptotic to the x-axis, Inc. Intervals: All Real Numbers, Dec. Intervals: All Real Numbers, Zeros: None
What is Asymptotic?Asymptotic is a mathematical term that describes the behavior of a function when the input values approach infinity. It is used to describe the limiting behavior of a sequence or a function without having to calculate all the terms of the sequence or function. Asymptotic behavior is mainly used for analyzing algorithms and determining the complexity of a problem.
Asymptotic analysis can provide insights into the behavior of a system and is an important tool for understanding the behavior of algorithms.
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2.4
Practice B
In Exercises 1-3, match the inequality with its graph.
Answers
1. B
2. C
3. A
N/A
N/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/AN/A
Answers
Answer:
why is there an N not paired up with A at the beginning, and an A without an N at the end? oh my gosh dude pair them up theyre lonely
Step-by-step explanation:
A bleach and water solution with a 2:3 ratio means: A 1/3 part bleach and 2/3 part water B 2 cups of bleach and 3 cups of water C 3 cups of bleach and 2 cups of water
Answers
The correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.
A bleach and water solution with a 2:3 ratio means that for every 2 parts of bleach, there should be 3 parts of water. This ratio is typically expressed in terms of volume or quantity.
To understand this ratio, let's break it down using different units:
A. 1/3 part bleach and 2/3 part water:
If we consider 1/3 part bleach, it means that for every 1 unit of bleach, there should be 2 units of water. However, this does not match the given 2:3 ratio.
B. 2 cups of bleach and 3 cups of water:
If we consider cups as the unit of measurement, this means that for every 2 cups of bleach, there should be 3 cups of water. This matches the given 2:3 ratio, making it a valid interpretation.
C. 3 cups of bleach and 2 cups of water:
If we consider cups as the unit of measurement, this means that for every 3 cups of bleach, there should be 2 cups of water. However, this interpretation does not match the given 2:3 ratio.
Based on the given options, the correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.
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find the exact value of cos(A+B) given that sin(A)=-1/2, with angle A in quadrant 4, and sin(B)=1/4, with angle B in quadrant 2
Answers
Answer:
cos(A + B) = \(\frac{-3\sqrt{5}+1}{8}\)
Step-by-step explanation:
Let us revise some rule of trigonometry
sin²(x) + cos²(x) = 1cos(x + y) = cos(x) cos(y) - sin(x) sin(y)The sign of the trigonometry functions in the four quadrants
In the 1st quadrant: sin(x) and cos(x) are positive valuesIn the 2nd quadrant: sin(x) is positive value, cos(x) is negative valueIn the 3rd quadrant: sin(x) and cos(x) are negative valuesIn the 4th quadrant: sin(x) is negative value, cos(x) is positive valueIn the given question
→ Angle A is in the 4th quadrant
∵ sin(A) = -1/2
→ Use the 1st rule above to find cos(A)
∵ (-1/2)² + cos²(A) = 1
∴ 1/4 + cos²(A) = 1
→ Subtract 1/4 from both sides
∴ cos²(A) = 3/4
→ Take square root for both sides
∴ cos(A) = ±√(3/4)
→ In the 4th quadrant cos is a positive value
∴ cos(A) = (√3)/2
→ Angle B is in the 2nd quadrant
∵ sin(B) = 1/4
→ Use the 1st rule above to find cos(B)
∵ (1/4)² + cos²(B) = 1
∴ 1/16 + cos²(B) = 1
→ Subtract 1/16 from both sides
∴ cos²(B) = 15/16
→ Take square root for both sides
∴ cos(B) = ±√(15/16)
→ In the 2nd quadrant cos is a negative value
∴ cos(B) = (-√15)/4
Let us find the exact value of cos(A + B)
→ By using the 2nd rule above
∵ cos(A + B) = cos(A) cos(B) - sin(A) sin(B)
∴ cos(A + B) = \((\frac{\sqrt{3}}{2})(-\frac{\sqrt{15}}{4})-(-\frac{1}{2})(\frac{1}{4}) =-\frac{3\sqrt{5}}{8}+\frac{1}{8}\)
∴ cos(A + B) = \(\frac{-3\sqrt{5}+1}{8}\)
Point N is on line segment \overline{MO} MO . Given MO=3x-10,MO=3x−10, NO=x,NO=x, and MN=8,MN=8, determine the numerical length of \overline{MO}. MO
Answers
Answer:
17
Step-by-step explanation:
The value of the line segment MO will be 17 units.
What is a line segment?A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.
Given that the length of the line segment Mo = 3x - 10, and N is the point on the line MO and Mn = 8, and NO = x.
The value of the line segment MO will be calculated as below:-
MO = MN + NO
3x - 10 = 8 + x
3x - x = 8 + 10
2x = 18
x = 18 / 2
x = 9
The value of the segment MO will be:-
MO = 3x - 10
MO = ( 3 x 9 ) - 10
MO = ( 27 ) - 10
MO = 17
Therefore, the value of the line segment MO will be 17 units.
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Add.
(6x³ + 3x² − 2) + (x³ - 5x² − 3)
Express the answer in standard form. (Please and thank you)
Answers
Answer:
\(\\\sf7x^3 - 2x^2 - 5\)
Step-by-step explanation:
\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)
Remove parenthesis.
6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3
Rearrange:
6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3
Combine like terms to get:
7x^3 - 2x^2 - 5----------------------------------------
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Answer:
7x³ - 2x² - 5
Step-by-step explanation:
(6x³ + 3x² - 2) + (x³ - 5x² - 3)
Remove the round brackets.
= 6x³ + 3x² - 2 + x³ - 5x² - 3
Put like terms together.
= 6x³ + x³ + 3x² - 5x² - 2 - 3
Do the operations.
= 7x³ - 2x² - 5
____________
hope this helps!
Which of the following is not a subset of {1, 2, 3}?
{0}
{1, 2, 3}
Ø
Answers
Answer:
{0}
Step-by-step explanation:
{0} is not because 0 is not an element of set {1, 2, 3}
The null set is a subset of every set, so Ø is.
A set is a subset of itself.
The graph shows the movement of a car from point A to point D, there are two slant line AB and CD.
(1) Calculate the speed of the car during the first 10 seconds.
(2) For how long did the car stop.
(3) What is the average speed of the car for the whole journey.
(4) Why the line BC is flat not slant.
Answers
Answer:
The answer is below
Step-by-step explanation:
a) The speed of the car during the first 10 seconds is equal to the slope of the line AB. The line AB passes through (0, 0) and (10, 200)
slope = (200 - 0)/(10 - 0) = 20 m/s
The speed of the car during the first 10 seconds is 20 m/s
b) The time for the car to move from point A to point D = 60 seconds
c) Distance from point A to B = 200 m, distance from C to D = 500 - 200 = 300 m, distance from B to C = 20 m/s * 20 s = 400 m
Total distance from A to D = 200 + 400 + 300 = 900 m
Average speed = total distance / total time = 900 m / 60 seconds = 15 m/s
d) line BC is flat because the car moves at a constant speed from point B to point C. That is the speed does not change.
Select the following plant adaptations for the terrestrial environment that are correctly listed by their function. Stomata allow for gas exchange between the plant and the atmosphere. Tracheids protect against desiccation. Stomata transport water around plant body. Tracheids transport water and minerals around the plant body.
Answers
The correct plant adaptations for the terrestrial environment that are listed by their function are, "stomata, which allow for gas exchange between the plant and the atmosphere; and tracheids, which transport water and minerals around the plant body".
Plants have evolved a variety of adaptations to survive in the terrestrial environment. Two key adaptations are stomata and tracheid. Stomata are small pores found on the surface of leaves, stems, and other plant parts that allow for gas exchange between the plant and the atmosphere. Specifically, stomata enable the plant to take in carbon dioxide (CO2) from the air and release oxygen (O2) and water vapor (H2O) back into the atmosphere through the process of photosynthesis. This is important for plant growth and survival, as photosynthesis is the primary way that plants produce the food they need to grow and reproduce.
Tracheid's, on the other hand, are specialized cells found in the xylem tissue of vascular plants that transport water and minerals from the roots to the rest of the plant body. The walls of tracheids are thickened and reinforced with lignin, which helps protect them against desiccation and other environmental stresses. This is important for plant survival in the terrestrial environment, where water can be scarce and conditions can be harsh.
In summary, stomata and tracheids are two important plant adaptations for the terrestrial environment. Stomata allow for gas exchange between the plant and the atmosphere, while tracheids transport water and minerals around the plant body. By enabling these key functions, stomata and tracheids help plants survive and thrive in a variety of terrestrial environments
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how would one go about solving this graph?
Answers
Mass= Density x volume
Volume= mass/density
Density = Mass / Volume, so you could use that information to solve for each value in the graph.
2. Mass = Density * Volume = 8.07 * 1.04 = 8.59 g
3. Volume = Mass / Density = 8.26 / 8.10 = 1.02 mL
4. Density = Mass / Volume = 7.91 / 0.99 = 7.99 g/mL
5. Mass = Density * Volume = 8.05 * 0.98 = 7.89 g
6. Volume = Mass / Density = 8.53 / 8.05 = 1.06 mL
How do you find f inverse?
Answers
Inverse of function is written by using notation f⁻¹
What is inverse of function?The function that can be reversed into another function is termed as inverse function. It is also called anti function. There are different types of inverse function such as inverse trigonometric function, inverse rational function, inverse log function and so on.
We can determine an inverse function by interchanging the elements that present in the given expressions.
How do we find f inverse?Inverse of the function f is denoted by notation f⁻¹
let, we have given a function, f(x) = 8x + 9
now, we need to find the inverse of the above function.
in the first step we write the function using y and set equal to x
x = 8y +9
in the next step, we arrange to make the y subject,
x - 9 = 8y
8y = x - 9
y = (x - 9)/ 8
use the notation f⁻¹ = (x - 9)/ 8
this is the inverse of function f.
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Write a linear function f with the given values f(0) = 2, f(3) = -1
Answers
The linear function f with the given values f(0) = 2, f(3) = -1 is f(x) = -x + 2.
What is Linear Function?
A straight line on the coordinate plane is represented by a linear function.
The linear function formulas are:
y = mx + b (slope-intercept form)y−y1 = m(x−x1) (point-slope form)Ax + By = C (standard form)xa+yb = 1 (intercept form)Here, we have
The given functions are f(0)=2 and f(3) = -1
For f(0) = 2
Coordinate: (0,2)
y-intercept, c: 2
For f(3) = -1
Coordinate: (3,-1)
gradient or slope, m when x₁ = 0, y₁ = 2, x₂ = 3, y₂ = -1
=( y₂-y₁)/(x₂-x₁)
= ( -1 -2)/(3 - 0)
= -3/3
= -1
The linear equation is in the slope-intercept form, y=mx+c
f(x) = -x+2, where -1 is the slope and 2 is the y-intercept.
Hence, The linear function f with the given values f(0) = 2, f(3) = -1 is f(x) = -x + 2.
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