The graph of the line will be a straight line that slopes downward from left to right, intersecting the x-axis at -3 and the y-axis at 3.To find the x-intercept and y-intercept of the line −5x + 5y = 15, we can set either x or y to zero and solve for the other variable.
For the x-intercept, we set y = 0:
−5x + 5(0) = 15
−5x = 15
x = -3
So the x-intercept is -3.For the y-intercept, we set x = 0:
−5(0) + 5y = 15
5y = 15
y = 3
Therefore, the y-intercept is 3.
Now let's plot these intercepts on a graph. The x-intercept is at -3 on the x-axis, and the y-intercept is at 3 on the y-axis. We can connect these two points to draw the line.
By connecting the x-intercept (-3) and the y-intercept (3) on the graph, we obtain a straight line that represents the equation −5x + 5y = 15.
Note that the line passes through the points (-3, 0) and (0, 3).
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Enter values to write the function that matches the graph shown.
Answer:
The roots of this function are at -4 and -1.
f(x) = (2x + 8)(-2x - 2)
= (2x + 8)(-2x + (-2))
help me Find the base angles of the figure below.
A) 130°
B) 65°
C) 25°
D) 50°
Answer:
C) 25°
Step-by-step explanation:
You want the base angles in an isosceles triangle with vertex angle 130°.
Base anglesThe base angles of an isosceles triangle are congruent. If each is represented by 'b', then the sum of angles in the triangle is ...
2b +130° = 180°
2b = 50° . . . . . . . . subtract 130°
b = 25° . . . . . . . divide by 2
The base angles of the triangle are 25°, choice C.
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2 questions please answer both parts
A)Find the perimeter of the plot land
B) Find the area of the plot land without the building and parking lot.
The perimeter of the plot land is 78.49 units and the area of the plot land without the building and parking lot is 210 square units
Finding the perimeter of the plot landFrom the graph, the vertices of the land are
A = (0, 20), B = (25, 19), C = (20, 2) and D = (5, 0)
Calculate the distance between adjacent vertices
So, we have
AB = √[(0 - 25)² + (20 - 19)²] = 25.02
BC = √[(20 - 25)² + (2 - 19)²] = 17.72
DC = √[(20 - 5)² + (2 - 0)²] = 15.13
AD = √[(0 - 5)² + (20 - 0)²] = 20.62
The perimeter of the plot land is
P = 25.02 + 17.72 + 15.13 + 20.62
P = 78.49 units
Finding the area of the plot landThis is calculated as
Area = Plot land - Building - Parking lot
Using the vertices, we have
Area = 1/2 * |0 * 19 + 25 * 2 + 20 * 0 + 5 * 20 - (20 * 25 + 19 * 20 + 2 * 5 + 0 * 0)| - [1/2 *(15 - 7 + 17 - 7) * (15 - 10)] - [(18 - 10) * (10 - 5)]
This gives
Area = 295 - 45 - 40
So, we have
Area = 210
Hence, the area is 210 square units
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What is the probability either event will occur?
The probability that either event will occur is given as follows:
P(A or B) = 0.82 = 82%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The total number of events in this problem is given as follows:
23 + 18 + 9 = 50.
The events are given as follows:
A = 23.B = 18.Hence the number of desired outcomes is given as follows:
23 + 18 = 41.
And the probability is of:
p = 41/50 = 0.82 = 82%.
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What conclusion can be determined from the dot plot below?
The number of observations is 10.
The median of the data set is 10.
The mean of the data set is 15.
The range of the data set is 12.
The conclusion can be determined from the dot plot is
The median of the data set is 10.
1. The number of observations is 10:
There are total 15 observations.
2. The median of the data set is 10.
From the dot plot the data is
9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 12
Thus, the median is 10.
3. Mean = Sum of observation / Total Number of observation
Mean = (9+9+9+9+9+10+10+10+10+10+10+11+11+11+12) /15
Mean= 150/15=10
Thus, the Mean is 10.
4. Range = 12 - 9
Range = 3.
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At a certain intersection, the light for eastbound traffic is red for 15 seconds, yellow for 5 seconds, and green for 30 seconds. What is the probability that the light is red? Using the binomial distribution, what is the probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red light?
The Probability that exactly three out of the next eight eastbound cars that arrive randomly at the light will be stopped by a red light is approximately 0.268.
The probability that the light is red is given by the ratio of the time the light is red to the total cycle time:
P(red) = 15 / (15 + 5 + 30) = 0.375
Using the binomial distribution, the probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red light is:
P(X = 3) = (8 choose 3) * (0.375)^3 * (0.625)^5
where (8 choose 3) is the binomial coefficient, which represents the number of ways to choose 3 cars out of 8. Evaluating this expression gives:
P(X = 3) = (8 choose 3) * (0.375)^3 * (0.625)^5
= (8! / (3! * 5!)) * (0.375)^3 * (0.625)^5
= 56 * 0.052734375 * 0.1787109375
≈ 0.268
Therefore, the probability that exactly three out of the next eight eastbound cars that arrive randomly at the light will be stopped by a red light is approximately 0.268.
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Factoring Polynomials Formative
QUESTION 1
Solve the following by factoring:
y³ - 6y² = 0
[tex]y^3 - 6y^2 = 0\\y^2(y-6)=0\\y^2=0 \vee y-6=0\\y=0 \vee y=6[/tex]
I WILL GIVE THE BRAINLIEST 69 POINTS
Step-by-step explanation:
the answer is 3
the answer is 3
Answer:
3
Step-by-step explanation:
explanation
f(x) =2x + 1 and g(x) = [tex]x^{2}[/tex]- 7
Thus, we have:
(g/f ) (x) = g(x) / f(x) = [tex]x^{2}[/tex]-7 ÷ 2x ÷ [tex]x^{2}[/tex] + 1
Question 11 of 30
Suppose that a regression line for some data transformed with logarithms
predicts that when x equals 3, log(y) will equal 2.725. What does the
regression line predict y will equal when x equals 3? Round your answer to the
nearest whole number.
A. 22,577
OB. 531
OC. 20
OD. 27
SUBMIT
The regression line predict y will equal 531 when x equals 3
How to solve the regression linelog(y) = 2.725
To undo the logarithm, we can use the exponential function:
y = 10^(2.725)
Using a calculator, we find:
y ≈ 530.8
We have to approximate this to 531
Rounding to the nearest whole number, the regression line predicts that y will equal 531 when x equals 3.
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Type the correct answer in each box. If necessary, use / for the fraction bar(s).
A shaded right triangle uppercase C uppercase A uppercase B with side uppercase C uppercase A equals lowercase b, side uppercase A uppercase B equals lowercase c, and side uppercase C uppercase B equals lowercase a. Right angle is at uppercase A.
In this triangle, the product of sin B and tan C is , and the product of sin C and tan B is .
The product of sin B and tan C is c/a.
The product of sin C and tan B is b/a.
Given is a right triangle, ABC, we need to find the product of sin B and tan C and the product of sin C and tan B,
So, we know,
Sine = Opposite ÷ Hypotenuse.
Cosine = Adjacent ÷ Hypotenuse.
Tangent = Opposite ÷ Adjacent.
Therefore,
Sin B = b/a
Tan C = c/b
Sin B x Tan C = b/a x c/b = c/a
And,
Sin C = c/a
Tan B = b/c
Sin C x Tan B = c/a x b/c = b/a
Hence the products are c/a and b/a.
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The complete is attached.
a) (i) 830 + 50 gives the same answer as x + 100
Work out the value of x.
X =
(ii) What is the value of 830 + 50?
A coach can take 50 people.
(iii) How many coaches would be needed to transport 830 people?
b) Jayne needs to hire 13 coaches.
Each coach costs £450 to hire.
Work out the total cost of hiring 13 coaches. £
Total marks: 6
The value of x is 780 and 830 + 50 equals 880
The number of coaches is 17 and the total cost is £5850
Calculating the value of x.From the question, we have the following parameters that can be used in our computation:
830 + 50 gives the same answer as x + 100
This means that
830 + 50 = x + 100
So, we have
x = 830 + 50 - 100
Evaluate
x = 780
Also, we have
830 + 50 = 880
So, the value of x is 780 and 830 + 50 equals 880
Calculating the number of coachesHere, we have
People = 830
People per coach = 50
So, we have
Coaches = 830/50
Evaluate
Coaches = 16.6
Approximate
Coaches = 17
The total cost of hiring 13 coaches is
Cost = 450 * 13
Evaluate
Cost = 5850
Hence, the number of coaches is 17 and the total cost is £5850
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Mr brainiac has found the Treasure Chest help him to get the code to open the chest the last digit is the half of 18 the sum of the two middle digit is 10 the third of and the fourth digit is the same the first digit is double the second digit what's the answer
A contradiction in the given clues and it is not possible to find a valid code with the given information.
The code to open the treasure chest can be determined using a few simple steps.
Firstly, we know that the last digit is half of 18, which is 9.
This means that the code ends with the number 9.
Next, we are given the information that the sum of the two middle digits is 10.
This tells us that the two middle digits must be 4 and 6, as they add up to 10.
Thirdly, we know that the third and fourth digits are the same.
Since we already know that the last digit is 9, this means that the third digit must also be 9.
Finally, we are told that the first digit is double the second digit.
Since we know that the second digit is 4, we can determine that the first digit must be 8.
Therefore, the code to open the treasure chest is 8469.
Mr Brainiac can now use this code to unlock the chest and discover the treasures inside.
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please help asap i’m stuck
Answer:
10%
Step-by-step explanation:
P(reading paper 'given' that they are <40)
= P(reading paper AND < 40) / P(< 40)
= (4/80) / (40/80)
= 4/40
=1/10
=0.1
=10%
The rule is y = |x| sketch the graphs for y+x and y = -x
Where the rules is is y = |x| the graph for y+x and y = -x will become the graph for y+x and y = x. Because x has to become an absolute (positive) value.
What is a graph?In discrete mathematics, and more particularly in graph theory, a graph is a structure consisting of a set of objects, some of which are "related" in some way.
Distances between locations are often measured using the absolute value function. The absolute value function can also be used to address applied issues such as ranges of feasible values.
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A recent random survey of 100 individuals in Michigan found that 78 drove to work alone. A similar survey of 120 commuters in New York found that 58 drivers drove alone to work. Find the 95% confidence interval for the difference in proportions
The 95% confidence interval for the difference in proportions is approximately 0.0957 to 0.4977.
To find the 95% confidence interval for the difference in proportions between Michigan and New York commuters who drove alone to work, we can use the formula:
CI = (p1 - p2) ± Z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))
Where:
p1 and p2 are the proportions of Michigan and New York commuters who drove alone to work, respectively.
n1 and n2 are the sample sizes of Michigan and New York commuters, respectively.
Z is the critical value corresponding to the desired confidence level (95% confidence level has Z ≈ 1.96).
Given:
Michigan: p1 = 78/100 = 0.78, n1 = 100
New York: p2 = 58/120 = 0.4833, n2 = 120
Plugging in the values:
CI = (0.78 - 0.4833) ± 1.96 * sqrt((0.78 * (1 - 0.78) / 100) + (0.4833 * (1 - 0.4833) / 120))
CI = 0.2967 ± 1.96 * sqrt(0.006456 + 0.004074)
CI = 0.2967 ± 1.96 * sqrt(0.01053)
CI ≈ 0.2967 ± 1.96 * 0.1026
CI ≈ 0.2967 ± 0.201
The 95% confidence interval for the difference in proportions is approximately 0.0957 to 0.4977.
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Which of the word problems exemplify a linear function?
A. Angie's swimming classes required $50 enrollment fee and $10 safeguard
insurance cost each month.
B. Ken's car value depreciates by about 20% in the first year and then at estimated
15% each year following the first year.
C. A candy manufacturing business began its venture with 1,200 packets of candy
varieties. Then, 3,600 and 10,800 packets on the 2nd and 3rd days respectively.
D. The area of a triangular yard that has a right angle.
The word problem that exemplifies a linear function is
- Angie's swimming classes required a $50 enrollment fee and a $10 safeguard insurance cost each month.
Option A is the correct answer.
We have,
A linear function is a mathematical model that represents a relationship between two variables that is a straight line.
In this problem,
The cost of Angie's swimming classes is a linear function of the number of months.
The enrollment fee of $50 is a fixed cost that does not depend on the number of months, and the safeguard insurance cost of $10 per month is a variable cost that increases linearly with the number of months.
Thus,
The word problem that exemplifies a linear function is
- Angie's swimming classes required a $50 enrollment fee and a $10 safeguard insurance cost each month.
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(Worth 100 Brainly points)After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the
rainbow is the shape of a parabola.
The equation for this parabola is y=-x² + 36
1.Create a table of atleast 4 values of the function that includes two points of intersection between the airplane and the rainbow
2.What is the domain and range of the rainbow? Explain what the domain and range represent.Do all of the values make sense in the situation. Why or why not.
3.what are the x and y intercepts of the rainbow. Explain what each intercept represents.
1) Equation for the parabola y = - x² + 36.
2) A drone is in the distance, flying upward in a straight line. It intersects the rainbow at two points. Choose the points where your drone intersects the parabola and create a table of at least four values for the function.
The points of intersection will be: (0,36) and (4, 20)
Table of values for a linear function and the parabola
x linear function parabola y = - x² + 36
0 36 (0)² + 36 = 36
1 32 - (1)² + 36 = 35
2 28 - (2)² + 36 = 32
3 24 -3² + 36 = 27
4 20 -4² + 36 = 20
It is a linear function because the rate of change is constant: for each increase of 1 unit in x, there is a decrease of 4 units in y: ⇒ slope = - 4
Remember to include the two points of intersection in your table. Analyze the two functions; they are there (0,36) and (4, 20)
Answer the following reflection questions in complete sentences. What is the domain and range of the rainbow?
Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not? What are the x- and y-intercepts of the rainbow? Explain what each intercept represents.
The domain is all the real values of x between - 6 and 6: - 6 ≤ x ≤ 6
The range is all the values between 0 and 36: 0 ≤ y ≤ 36
The domain represents the horizontal distance between the extremes of the rainbow at the ground.
The range represents: the altitude of the rainbow from the ground (y = 0). The height is at x = 0, y = 36.
The x-intercepts are - 6 and 6, that is the opening of the rainbow at the ground level.
The y-intercept is when x = 0, it is y = 36, and is the height of the rainbow.
Is the linear function you created positive or negative? Explain. What are the solutions or solution to the system of equations created? Explain what it or they represent.
The linear function is positive and decreasing. It is positive because it goes above the x-axis, this is y ≥ 0.
The solutions were already signaled: (0,6) and (4, 20). They are the points at which the drone intercepts the rainbow.
The following figure is made of 1 rectangle and 2 triangles find the area of each part of the figure and the whole figure
The area of the rectangle is 32 square units, the area of each triangle is 6 square units, and the Total area is 44 square units.
1. The rectangle, which has a length of 8 units and a width of 4 units.
2. The two triangles, which are identical and have a base of 4 units and a height of 3 units.
To find the area of the rectangle, we can use the formula:
Area = Length x Width
Area = 8 x 4 = 32 square units
To find the area of each triangle, we can use the formula:
Area = 1/2 x Base x Height
Area = 1/2 x 4 x 3 = 6 square units
So, the total area of both triangles is:
Total area = 6 + 6 = 12 square units
Now, to find the total area of the figure, we can add the areas of the rectangle and the two triangles:
Total area = Area of rectangle + Total area of triangles
Total area = 32 + 12 = 44 square units
Therefore, the area of the rectangle is 32 square units, the area of each triangle is 6 square units, and the total area is 44 square units.
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Two friends visited a taffy shop. Jon bought 4 kilograms of strawberry taffy and 1 kilogram of banana taffy for $23. Next, Charlotte bought 5 kilograms of strawberry taffy and 2 kilograms of banana taffy for $34. How much does the candy cost?
A kilogram of strawberry taffy costs $____, and a kilogram of banana taffy costs $____.
A kilogram of strawberry taffy costs $4, and a kilogram of banana taffy costs $7.
Let us assume
the price of 1 kg strawberry taffy = $x
And the price of 1kg banana taffy = $y
Then according to given information
the expression for Jon be,
4x + y = 23 ....(i)
the expression for Charlotte be,
5x + 2y = 34 ...(ii)
Now use elimination method
2x(i) - (ii) we get,
3x = 12
x = 4
Plug it into (i) we get
y = 7
Hence, costs are:
1 kg strawberry taffy = $4
1kg banana taffy = $7
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Find the length of the hypotenuse of the right triangle.
Answer:
The length of the hypotenuse is 100.
Step-by-step explanation:
To find the length of the hypotenuse, we use the following formula:
c=[tex]\sqrt{a^2+b^2}[/tex]
c=[tex]\sqrt{28^2+96^2}[/tex]
c=[tex]\sqrt{10,000}[/tex]
c=100
Therefore, the length of the hypotenuse is 100.
Practice A shuttle space suit, including the life support system, weighs about 310 pounds. The break in the y-axis represents the values from 0-300. What does each ordered pair on the line represent? 2. Write an equation to represent the relationship shown in the graph. 3. Is this a proportional relationship? Justify your answer. 4. In this problem situation, do all the points on the line make sense? Explain your reasoning. 5. Determine the weight of an astronaut without the shuttle suit given that the astronaut's weight while wearing the shuttle suit. a. 480 lb b. 467 lb c. 520 lb Weight of Astronaut With Suit (pounds)
Step-by-step explanation:
Each ordered pair on the line represents the weight of an astronaut with the shuttle space suit, given in pounds, and the total weight of the shuttle space suit and life support system, also given in pounds.
Let x represent the weight of the astronaut without the shuttle suit, and let y represent the weight of the astronaut with the shuttle suit and life support system. Then the equation for the relationship shown in the graph is: y = x + 310.
No, this is not a proportional relationship because the slope of the line is not constant. In a proportional relationship, the ratio of y to x would always be the same, but in this case, the ratio changes depending on the value of x.
No, not all the points on the line make sense in the context of the problem situation. For example, the point (0, 310) would represent an astronaut with no weight without the shuttle suit, which is not physically possible. Also, the point (480, 790) would represent an astronaut with a weight of 480 pounds without the suit, which is also not physically possible. Therefore, we need to restrict the domain of the equation to make sense in the context of the problem situation.
To determine the weight of an astronaut without the shuttle suit, we need to solve the equation y = x + 310 for x, given that y = 480. Substituting y = 480 into the equation, we get: 480 = x + 310. Solving for x, we get: x = 170. Therefore, the weight of the astronaut without the shuttle suit is 170 pounds.
receiving a direct hit will take 15% of your health score if your health score is 24 and you receive a direct hit what will be your health score after the hit
Answer: 20.4
Step-by-step explanation:
Find the volume of the sphere show ur work it’s
Answer:
904.78 [tex]in^{3}[/tex]
Step-by-step explanation:
The volume formula for a sphere is the following:
[tex]v=\frac{4}{3} \pi r^{3}[/tex]
[tex]d = 2r[/tex]
Replace with values and the answer is 904.78
you are given f(x) = x + 3 and g(x) = 2x + 1
find g[g(-3)
find f[g(x)]
find g[f(x)]
Answer:
Step-by-step explanation:
f(x) = x + 3
g(x) = 2x + 1
g(g(-3)) = g(-5) = -9
f(g(x) = f(2x + 1) = 2x + 1 + 3 = 2x + 4
g(f(x) = g(x + 3) = 2(x + 3) + 1 = 2x + 7
X<= -5 or x >= 3 which answer represents the inequality in interval notation
The inequality x ≤ -5 or x ≥ 3 in interval notations is (-∞, -5] ∪ [3, ∞)
Inequality is the relationship between two expressions or values that are not equal to each other
The inequality x ≤ -5 or x ≥ 3 represents the solution set of all real numbers less than or equal to -5 or greater than or equal to 3.
The interval notation of the given inequality is (-∞, -5] ∪ [3, ∞)
The closed brace means the number is included and open bracket doesnot includes a number
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Calculator
Pyramid ABCDE is a square pyramid.
What is the lateral area of pyramid ABCDE?
URGENT
The lateral area of the pyramid is 512√3 in.
What is area?Area is the region bounded by plane shape.
To calculate the area of the pyramid, we use the formula below
Formula:
A = 8aL.................................... Equation 1Where:
A = Area of the pyramida = Length of the square baseL = Slight height of the PyramidFrom the question,
Given:
a = 16 inL = 8sin60° = 4√3 inSubstitute these value into equation 1
A = (8×16×4√3)A = 512√3 inHence, the right option is D. 512√3 in.
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please help me with my geometry i cant fail this class or i’ll have to move out of my parents house :(
The length of the arcs are calculated to the nearest hundredth as:
12. 14.03 meters 13. 6.91 meters
How to Find the Length of an Arc?The formula used to find the length of a an arc is: length of arc = ∅/360 * 2πr, where ∅ is the central angle measure and r is the radius of the circle.
Length of arc XW:
∅ = m<XZW = 180 - 113
∅ = 67 degrees
r = 24/2 = 12 meters
Plug in the values:
length of arc XW = 67/360 * 2 * π * 12 ≈ 14.03 meters
Length of arc XW:
∅ = m<YVU = 180 - 67 - 80
∅ = 33 degrees
r = 24/2 = 12 meters
Plug in the values:
length of arc YVU = 33/360 * 2 * π * 12 ≈ 6.91 meters
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 write a quadratic function that is three units write four units down and five times narrower then y=x squared
Answer:
y = 5(x - 3)^2 - 4 + c
Step-by-step explanation:
The standard form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants. To shift the graph three units to the right and four units down, we can modify the constant term c and the linear term bx:
y = a(x - 3)^2 - 4 + c
To make it five times narrower, we can modify the coefficient of the squared term a:
y = (1/5)a(x - 3)^2 - 4 + c
Since we want the shape to be the same as y = x^2, we can set a = 5:
y = 5(x - 3)^2 - 4 + c
The value of c will depend on the specific context of the problem or graph.
5.2 Given that cos 20° = p Without using a calculator, write EACH of the following in terms p: 5.2.1 5.2.2 5.2.3 cos 200° sin(-70°) sin 10°
The trigonometric ratio in terms p are
cos 200 = -p
- sin 70 = -p.
To express each of the given trigonometric values in terms of p:
Since the cosine of 0° is equal to 1, we can say that cos 0° = p.
cos 200°: Using the identity
cos(180° + θ) = -cos(θ), we can rewrite
cos 200° = -cos(180° + 20°).
Since cos 20° = p, we can express cos 200° as -p.
sin(-70°): Using the identity
sin(-θ) = -sin(θ), we can rewrite
sin(-70°) as -sin(70°)
=- sin (90- 20)
= - cos 20
= -p
sin 10°: Since sin 10° is not related to p, we cannot express sin 10° in terms of p.
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Help as soon as possible please!!
The coordinates of the triangle A'B'C' after rotating triangle ABC 90 degrees clockwise are A'(3, 6), B'(3, 2), and C'(7, 4).
To rotate the points of a triangle 90 degrees clockwise, we can use the following formula for a 2D rotation:
x' = x cos(θ) + y sin(θ)
y' = -x sin(θ) + y cos(θ)
Let's apply this formula to each point of the triangle ABC:
For point A(-6, 3):
x' = -6 cos(90°) + 3 sin(90°) = -6 (0) + 3(1) = 3
y' = -(-6) sin(90°) + 3 cos(90°) = 6 (1) + 3 (0) = 6
So, point A' is (3, 6).
For point B(-2, 3):
x' = -2 cos(90°) + 3 sin(90°) = -2 .0 + 3. 1 = 3
y' = -(-2) sin(90°) + 3 cos(90°) = 2 .1 + 3 .0 = 2
So, point B' is (3, 2).
For point C(-4, 7):
x' = -4 cos(90°) + 7 sin(90°) = -4 .0 + 7 . 1 = 7
y' = -(-4) sin(90°) + 7 cos(90°) = 4.1 + 7 .0 = 4
So, point C' is (7, 4).
Therefore, the coordinates of the triangle A'B'C' after rotating triangle ABC 90 degrees clockwise are A'(3, 6), B'(3, 2), and C'(7, 4).
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