The length of segment OP, which represents the distance from the origin to point P on the unit circle, is always equal to 1.
To determine the length of segment OP on the unit circle, we need to use trigonometry. Let's break down the problem step by step:
Definition: The unit circle is a circle with a radius of 1 centered at the origin (0, 0) in the Cartesian coordinate system.
Initial Ray: The initial ray is a line segment that starts from the origin (0, 0) and extends to a point on the unit circle. It forms an angle with the positive x-axis.
Rotation: We are rotating the initial ray counterclockwise by θ degrees. This means we are essentially finding a new point on the unit circle based on the angle θ.
Trigonometric Functions: The trigonometric functions sine (sin) and cosine (cos) are particularly useful for calculating the coordinates of points on the unit circle.
sin(θ) gives the y-coordinate of a point on the unit circle.
cos(θ) gives the x-coordinate of a point on the unit circle.
Coordinates of Point P: Since we are rotating the initial ray counterclockwise by θ degrees, the coordinates of point P on the unit circle can be obtained as follows:
x-coordinate of P: cos(θ)
y-coordinate of P: sin(θ)
Distance from the Origin (Length of Segment OP):
Using the coordinates of point P, we can calculate the distance between the origin (0, 0) and point P using the distance formula.
The distance formula states that for two points (x1, y1) and (x2, y2), the distance between them is given by:
d = √((x2 - x1)² + (y2 - y1)²)
In this case, point P has coordinates (cos(θ), sin(θ)), and the origin is (0, 0). Thus, the distance (length of segment OP) is:
d = √((cos(θ) - 0)² + (sin(θ) - 0)²)
= √(cos²(θ) + sin²(θ))
= √(1) [Using the trigonometric identity: sin²(θ) + cos²(θ) = 1]
= 1
Therefore, the length of segment OP, which represents the distance from the origin to point P on the unit circle, is always equal to 1.
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the bus comes at 8:05. It takes me 31 minutes to get to the bus stop. What time should I leave to catch the bus?
You should leave at 7:34 to catch the bus that comes at 8:05.
We have,
To catch the bus that arrives at 8:05, you should leave with enough time to reach the bus stop 31 minutes before the bus's arrival time.
To catch the bus that arrives at 8:05, you need to be at the bus stop before the bus arrives. Since it takes you 31 minutes to get to the bus stop, you should leave your starting point early enough to allow for that travel time.
By subtracting 31 minutes from the bus's arrival time of 8:05, you determine the time at which you should depart.
In this case, subtracting 31 minutes gives you 7:34, meaning you should leave at 7:34.
To calculate the departure time, subtract 31 minutes from the bus's arrival time:
= 8:05 - 31 minutes
= 7:34
Thus,
You should leave at 7:34 to catch the bus that comes at 8:05.
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I will give brainliest out please help me answer the unsolved ones
For the given triangles:
(1) x = 5.4
(2) x = √23
(3) θ = 25.84 degree
(4) x = 9.5
(5) n = 41
(1) In the given triangle,
One angle = 16 degree
Perpendicular = x
Hypotenuse = 20
Since we know that
Sinθ = opposite side of θ/hypotenuse
Therefore,
⇒ sin 16 = x/20
⇒ 0.27 = x/20
⇒ x = 5.4
(2) In the given triangle,
Hypotenuse = 12 km
Base = 11 km
perpendicular = x
We know that the Pythagoras theorem for a right angled triangle:
⇒ (Hypotenuse)²= (Perpendicular)² + (Base)²
⇒ (12)²= (x)² + (11)²
⇒ 144 = (x)² + 121
⇒ x² = 23
Taking square root both sides we get,
Hence,
⇒ x = √23
(3) In the given,
Base = 20
Perpendicular = 42
We know that the Pythagoras theorem for a right angled triangle:
⇒ (Hypotenuse)²= (Perpendicular)² + (Base)²
⇒ (Hypotenuse)² = (42)² + (20)²
⇒ (Hypotenuse)² = 2164
Taking square root both sides,
⇒ (Hypotenuse) = 46.51
⇒ cosθ = Adjacent/hypotenuse
= 42/46.51
= 0.90
Taking inverse of cosθ,
⇒ θ = 25.84 degree
(4) In the given triangle,
One angle = 30 degree
Base = x
Hypotenuse = 11
Since we know that
cosθ = Adjacent/hypotenuse
Therefore,
⇒ cos 30 = x/11
⇒ √3/2 = x/11
⇒ x = 9.5
(4) In the given triangle,
Base = 40
Perpendicular = 9
Hypotenuse = n
We know that the Pythagoras theorem for a right angled triangle:
⇒ (Hypotenuse)²= (Perpendicular)² + (Base)²
⇒ n² = 9² + 40²
⇒ n² = 81 + 1600
⇒ n² = 1681
⇒ n = 41
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Question 7
A cylinder with a circular base is sliced through the center
vertically, perpendicular to the base. The cross section
that results would be which shape?
A
B
с
O D
circle
oval
rectangle
triangle
The cross section will be of rectangle in shape .
Given,
A cylinder with a circular base is sliced through the center vertically, perpendicular to the base.
Now,
A vertical cross section is a cross section in which the intersecting plane is perpendicular to the base of the solid.
If the intersecting plane is perpendicular to the base of cylinder then the shape obtained will be of rectangular in nature .
Therefore, vertical cross section of a cylinder is a rectangle.
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Could someone explain how to solve this?
Answer:
Step-by-step explanation:
Given f(x) = log2 (x+2), complete the table of values for the function -f(x) - 3. Show your work.
Answer:
Step-by-step explanation:
find the volume of this cylinder use 3 pi . 7cm 2cm
The volume of the cylinder is 98π cubic centimeters.
To find the volume of a cylinder, we use the formula:
Volume = π × [tex]r^2[/tex] × h
Given:
Radius (r) = 7 cm
Height (h) = 2 cm
Substituting the values into the formula, we have:
Volume = π × (7 [tex]cm)^2[/tex] × 2 cm
Calculating the values inside the parentheses:
Volume = π × 49 [tex]cm^2[/tex] × 2 cm
Multiplying the values:
Volume = 98π [tex]cm^3[/tex]
Therefore, the volume of the cylinder is 98π cubic centimeters.
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Find Tan A and Tan B. write each answer as a fraction and as a decimal rounded into four places.
TanA value is 22/3 and TanB is 3/2 from the given triangle ABC.
We have to find the values of Tan A and TanB.
We know that tan function is a ratio of opposite side and adjacent side.
To find TanA, we have to take opposite side of vertex A has opposite side.
TanA=18/27
TanA=2/3
Now let us find TanB , which is 27/18
TanB =3/2
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PLEASE HURRY! When you know the volume of a prism and some dimensions, you can solve for a(n) ____________ dimension.
When you know the volume of a prism and some dimensions, you can solve for an unknown dimension.
How to solve for unknown dimension ?When armed with knowledge about the volume of a prism alongside certain known dimensions, the possibility emerges to determine an elusive dimension within the prism. By leveraging the given information, the missing dimension can be unearthed, unraveling the intricacies of the prism's complete set of measurements.
This calculation empowers us to gain a comprehensive understanding of the geometric structure, further enriching our grasp of its spatial characteristics. The interplay between the volume and the known dimensions acts as a gateway to unlocking the enigma of the unknown dimension.
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what three costs contribute to the total cost of a mortage?
Answer:
The three costs that contribute to the total cost of a mortgage are the down payment, mortgage tax and monthly interest.
Step-by-step explanation:
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Select the correct answer.
If u =(1+i√3) and v=(1-i√3), what is uv?
Ο Α. 1
OB. -4
OC. 0
OD. 4
Reset
Next
If u =(1+i√3) and v=(1-i√3), product uv is: D. 4.
What is product uv?To find the product of u and v let us simply multiply them together:
u = 1 + i√3
v = 1 - i√3
uv = (1 + i√3)(1 - i√3)
Using the difference of squares formula (a² - b² = (a + b)(a - b)) we can simplify the expression:
uv = (1 + i√3)(1 - i√3)
uv= 1² - (i√3)²
uv= 1 - (-3)
uv= 1 + 3
uv= 4
Therefore the product uv is equal to 4.
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A company was hired to build a tunnel through a mountain. The company started at the south end of the mountain and completed only five hundred eighty five feet of the required seven thousand, six hundred five feet before going bankrupt. A different company was hired to complete the job, but th
ey decided to use two crews. Crew A would start where the other company left off at the southern end, while Crew B would start at the northern end and dig towards the other crew. Crew A was able to dig fifty eight feet of the tunnel per week. Crew B, which was larger, was able to dig fifty nine feet of the tunnel per week.
Let's denote crew A's work per week as A and crew B's work per week as B.
We are given that A = 58 ft per week and B = 59 ft per week.
We have to calculate how many weeks it will take both crews to complete the tunnel.
585 feet have already been dug from the south end. So, the total tunnel length that needs to be dug is 7605 - 585 = 7020.
Now, let's assume that both the crews continue to work at their respective rate of A = 58 ft/week and B = 59 ft/week.
Therefore, total tunnel length that needs to be dug in weeks = (7020 ft) / (A + B)
= (7020 ft) / (58 ft/week + 59 ft/week)
= 120.20 weeks
Hence, it will take a total of 120.20 weeks for both crews to complete the tunnel.
Graph the line. y=3x-8
By connecting these points with a straight line, we can graph the line y = 3x - 8.
The line should have a positive slope, rising from left to right.
To graph the line y = 3x - 8, we can use the slope-intercept form of a linear equation, which is y = mx + b. In this equation, m represents the slope of the line, and b represents the y-intercept.
Comparing the given equation with the slope-intercept form, we can see that the slope, m, is 3, and the y-intercept, b, is -8.
To plot the graph, we'll start by plotting the y-intercept, which is the point (0, -8)T.
his point represents where the line intersects the y-axis.
Next, we can use the slope to find additional points on the line. The slope of 3 means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 3.
Starting from the y-intercept (0, -8), we can move 1 unit to the right and 3 units up to reach the next point (1, -5).
We can continue this pattern to plot more points.
Using this information, we can plot multiple points and then connect them to form the line:
Point 1: (0, -8)
Point 2: (1, -5)
Point 3: (2, -2)
Point 4: (-1, -11)
Point 5: (-2, -14)
By connecting these points with a straight line, we can graph the line y = 3x - 8.
The line should have a positive slope, rising from left to right.
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a sine function has an amplitude of 6, a period of pi, and a phase shift of pi/4 . what is the y intercept of the function?
y intercept will be 0,-6 .
Given,
Amplitude = 6
Time period = pi
Phase shift = pi/4
In trigonometry, the sine function can be defined as the ratio of the length of the opposite side(perpendicular) to that of the hypotenuse in a right-angled triangle.
The sine function is used to find the unknown angle or sides of a right angled triangle.
Mathematically,
sinФ = p/h
Now ,
Let us assume the phase shift to be on right side.
So the graph will be at negative y axis.
Thus the points will be 0 , -6 .
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How many tiles can fit in a rectangular floor with length 14 ft and width 6 ft if the square tiles has an edge of 3/4 ft. Show your work
A 3-quart jug of water costs $3.48. What is the price per cup?
The calculated value of the price per cup is $1.16
How to calculate the price per cup?From the question, we have the following parameters that can be used in our computation:
A 3-quart jug of water costs $3.48
The price per cup is calculated as
Unit rate = Total cost/Size of the cup
Substitute the known values in the above equation, so, we have the following representation
Unit rate = 3.48/3
Evaluate
Unit rate = 1.16
Hence, the price per cup is $1.16
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How many roots do the functions have in common f(x)=x^2+x-6
To find the common roots between two functions, we need to find the roots (or solutions) of each function individually and then identify the shared solutions.
For the function f(x) = x^2 + x - 6, we can find the roots by setting the function equal to zero and solving for x:
x^2 + x - 6 = 0
To factorize this quadratic equation, we need to find two numbers that multiply to -6 and add up to 1 (the coefficient of x). The numbers that satisfy these conditions are 3 and -2:
(x + 3)(x - 2) = 0
Setting each factor equal to zero:
x + 3 = 0 or x - 2 = 0
Solving for x in each equation:
x = -3 or x = 2
Therefore, the function f(x) = x^2 + x - 6 has two roots: x = -3 and x = 2.
To find the common roots between this function and another function, we would need to know the second function. If you provide the second function, I can help determine if there are any shared roots.
2. In a complete paragraph, pick a scenario where concepts from this course would be used - it could be in you
or working in a business, etc.
Choose at least 2-3 concepts to include, explain your scenario, how these concepts apply, and provide a wa
Use the following format:
Topic Sentence: 1 concise sentence describing a scenario where concepts from this course could be used.
Supporting Detail: 1-2 sentences explaining how 1 concept from the class can be applied to the scenario.
Worked Example: Show a worked example for the concept described above.
Supporting Detail: 1-2 sentences explaining how 1 concept from the class can be applied to the scenario.
Worked Example: Show a worked example for the concept described above.
Conclusion: 1-2 sentences describing how applying the concepts in this course to a real-life situation helps
Write your response using your own words and do not use any other sources outside of this course
Topic Sentence: In a business setting, concepts from this course can be applied when optimizing customer service operations and improving customer satisfaction.
The Supporting DetailsSupporting Detail: One concept from the course that can be applied is the use of queuing theory to manage customer wait times and reduce service bottlenecks. By analyzing arrival rates, service rates, and queue lengths, businesses can optimize staffing levels and allocate resources efficiently.
Worked Example: One practical application of queuing theory is in call centers. With the aid of this theory, the center can analyze the number of customer service reps required in different periods of the day. The objective is to keep waiting times at their lowest and deliver timely service to customers.
Supporting Detail: Another concept that can be applied is the concept of customer lifetime value (CLV). By understanding CLV, businesses can identify their most valuable customers, prioritize their needs, and tailor personalized marketing strategies to enhance customer retention.
Worked Example: An e-commerce business may use information on customer buying patterns, typical order amounts, and the rate of customer loss to determine the overall lifetime value of a customer. By utilizing this data, the organization has the opportunity to execute tailored loyalty initiatives and customized suggestions, ultimately enhancing customer contentment and optimizing overall revenue for the long haul.
Conclusion:
The application of course concepts in a business environment can result in better customer service, shorter wait times, higher customer approval, and increased customer allegiance, thereby fueling the expansion and profitability of a business.
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4x Which reason is NOT typically used in a proof?
A
4x B
D
definition of supplementary angles
substitution property
C two angles being congruent
parallel fines
The reason that is NOT typically used in a proof is two angles being congruent. Option C.
Among the options A, B, C, and D, the reason that is NOT typically used in a proof is option C: two angles being congruent.
Congruence is a fundamental concept in geometry that refers to the equality of shape and size. When two angles are congruent, it means they have the same measure. While congruence is an important concept used in geometric proofs, it is typically not used as a standalone reason in a proof.
In geometric proofs, various properties, theorems, and postulates are used to establish relationships and make deductions. Let's briefly discuss the other options:
A. Definition of supplementary angles: This is a valid reason that is commonly used in proofs involving supplementary angles. The definition states that if the sum of two angles is 180 degrees, they are considered supplementary.
B. Substitution property: The substitution property is a logical property used in algebraic proofs. It allows us to replace one expression with another expression that is equal to it. This property is often employed when simplifying equations or substituting known values.
D. Parallel lines: The concept of parallel lines is frequently utilized in geometric proofs, particularly in proving angles and angle relationships. Properties such as alternate interior angles, corresponding angles, and vertical angles are established based on the parallel lines. Option C is correct.
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What is the balance after 4 years on $2000 at 4%
The balance after 4 years on $2000 at 4% is equal to $2320.
How to calculate the simple interest and future value?In Mathematics, simple interest can be calculated by using this formula:
S.I = PRT or S.I = A - P
Where:
S.I represents the simple interest.P is the principal or starting amount.R is the interest rate.A is the future value.T represents the time measured in years.Substituting the given parameters into the simple interest formula, we have;
S.I = 2000 × 4/100 × 4
S.I = 2000 × 0.04 × 4
S.I = $320.
Next, we would calculate the future value as follows;
Future value, A = S.I + P
Future value, A = $320 + $2000
Future value, A = $2320.
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What is the circumference of the circle if the radius is 10 cm?
The circumference of the circle is 62.8cm.
The Circumference of the circle is given by the formula,
Circumference = 2*[tex]\pi[/tex]*r cm.........equation 1
Given, r = 10cm
On substituting the radius value in equation 1
Circumference = 2*[tex]\pi[/tex]*10
Circumference = 62.8 cm
Therefore, the circumference of the circle is 62.8cm.
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Find the equation of a parabola with focus (3, 4) and directrix y = 1.
The equation of the parabola with focus (3, 4) and directrix y = 1 is [tex]x^2 - 6x - 12y + 57 = 0.[/tex]
To find the equation of a parabola with a given focus and directrix, we can use the standard form of the equation of a parabola:
[tex]4p(y - k) = (x - h)^2[/tex]
where (h, k) represents the coordinates of the vertex, and p is the distance between the vertex and the focus or directrix.
In this case, the focus is given as (3, 4), which means the vertex of the parabola will also be located at (3, 4).
The directrix is given as y = 1.
First, let's find the value of p, which is the distance between the vertex and the focus (or the vertex and the directrix). In this case, p will be the distance between the vertex (3, 4) and the directrix y = 1.
Since the directrix is a horizontal line, the distance between the vertex and the directrix is the vertical distance, which is |4 - 1| = 3.
Now that we have the value of p, we can substitute it into the equation:
[tex]4p(y - k) = (x - h)^2[/tex]
Plugging in the values (h, k) = (3, 4) and p = 3, we get:
[tex]4(3)(y - 4) = (x - 3)^2[/tex]
Simplifying further:
[tex]12(y - 4) = (x - 3)^2[/tex]
Expanding the equation:
[tex]12y - 48 = x^2 - 6x + 9[/tex]
Bringing all terms to one side:
[tex]x^2 - 6x - 12y + 57 = 0[/tex]
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which two transformations are applied to pentagon ABCDE to create A''B''C''D''E''
The two transformations applied to pentagon ABCDE to create A''B''C''D''E'' are rotation and reflection.
To determine the two transformations applied to pentagon ABCDE to create A''B''C''D''E'', we need more specific information about the transformations or the corresponding points.
Transformations can include translations, rotations, reflections, dilations, or combinations of these.
Without knowing the specific transformations applied or having additional information, it is challenging to provide an accurate answer.
However, I can briefly explain some common transformations that could potentially be applied to a pentagon:
Translation: A translation involves moving the entire figure in a specific direction without changing its shape or orientation.
This transformation can be described by shifting the points of the pentagon horizontally or vertically.
Rotation: A rotation involves rotating the pentagon about a fixed point. The point of rotation could be inside or outside the pentagon, and the angle of rotation would determine the final position of the points.
Reflection: A reflection involves flipping the pentagon across a line, called the line of reflection.
Each point of the pentagon would be reflected across the line, resulting in a mirrored image.
Dilation: A dilation involves scaling the size of the pentagon by a certain factor.
This transformation can result in an enlarged or reduced version of the original pentagon.
Without specific details or information about the corresponding points in A''B''C''D''E'', it is not possible to determine the exact transformations applied.
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Need the correct answers for this. Can you help me?
The length of PQ is 3√5 and its slope is -2
The length of SR is 3√5 and its slope is -2
The length of SP is 5√2 and its slope is -7
The length of RQ is 5√2 and its slope is -1
So PQ ≅ SR and SP ≅ RQ. By the Perpendicular Bisector theorem, adjacent sides are perpendicular. By the selection of side, ∠PSR, ∠SRQ, ∠RQP and ∠QPS are right angles. So, the quadrilateral is a rectangle.
Understanding QuadrilateralTo find the lengths and slopes of the sides of the quadrilateral PQRS, we apply the distance formula:
D = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
and the slope formula:
m = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
1. Length PQ:
Using the distance formula, the length PQ can be calculated as follows:
PQ = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
= √((3 - 0)² + (-4 - 2)²)
= √(3² + (-6)²)
= √(9 + 36)
= √45
= 3√5
2. Length SR:
Using the distance formula, the length SR can be calculated as follows:
SR = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
= √((1 - (-2))² + (-5 - 1)²)
= √((1 + 2)² + (-6)²)
= √(3² + 36)
= √(9 + 36)
= √45
= 3√5
3. Length SP:
Using the distance formula, the length SP can be calculated as follows:
SP = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
= √((1 - 0)² + (-5 - 2)²)
= √(1² + (-7)²)
= √(1 + 49)
= √50
= 5√2
4. Length RQ:
Using the distance formula, the length RQ can be calculated as follows:
RQ = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
= √((-2 - 3)² + (1 - (-4))²)
= √((-2 - 3)² + (1 + 4)²)
= √((-5)² + 5²)
= √(25 + 25)
= √50
= 5√2
Now, let's calculate the slopes of the sides:
1. Slope PQ:
The slope of PQ can be calculated using the slope formula:
m = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
= (-4 - 2) / (3 - 0)
= -6 / 3
= -2
2. Slope SR:
The slope of SR can be calculated using the slope formula:
m = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
= (-5 - 1) / (1 - (-2))
= -6 / 3
= -2
3. Slope SP:
The slope of SP can be calculated using the slope formula:
m =[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
= (-5 - 2) / (1 - 0)
= -7 / 1
= -7
4. Slope RQ:
The slope of RQ can be calculated using the slope formula:
m = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
= (1 - (-4)) / (-2 - 3)
= 5 / (-5)
= -1
Therefore, the lengths and slopes of the sides of the quadrilateral PQRS are:
Length PQ: 3√5
Length SR: 3√5
Length SP: 5√2
Length RQ: 5√2
Slope PQ: -2
Slope SR: -2
Slope SP: -7
Slope RQ: -1
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please help. Identify which of the following is NOT equivalent to a^1/4?
Answer:
D
Step-by-step explanation:
A. a^1/8 x a^1/8 = a^2/8 = a^1/4
B. a^3/4 / a^1/2 = a^3/4 / a^2/4 = a^1/4
C. (a^1/8)^2 = a^2/8 = a^1/4
D. √a = a^1/2
Linear equations graph
Step-by-step explanation:
PLot two pioints....connect the points
Use the y -intercept given y = -1 when x = 0 Plot that
when y = 0 x = 1/2 plot that
draw line through these points :
Answer:
Step-by-step explanation:
These shapes are similar.
Find X.
5
X
5
30
24
30
The value of x is 4.
To determine the value of x, we can use the concept of similarity between shapes.
Similar shapes have corresponding sides that are proportional to each other.
Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:
5/x = 30/24
To solve for x, we can cross-multiply:
30 · x = 5 · 24
30x = 120
Dividing both sides of the equation by 30:
x = 120 / 30
x = 4
Therefore, the value of x is 4.
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En uno de los corrales de la granja de mi abuela hay gallinas y conejos. Aún cuando todos se mueven, logré contar 40 cabezas y 106 patas.
a) Explica cuáles son las incógnitas del problema.
b) Escribe una ecuación que represente el número de animales que hay en el corral.
c) Escribe una ecuación que represente el número total de patas.
d) ¿cuántos conejos y cuántas gallinas hay en el corral?
There are 27 chickens and 13 Rabbits in the pen on your grandmother's farm, based on the given information of 40 heads and 106 legs.
a) The unknowns in the problem are the number of chickens and rabbits in the pen. We don't know the exact quantities of each animal, which is what we need to determine.
b) Let's denote the number of chickens as "C" and the number of rabbits as "R." To represent the total number of animals in the pen, we can write the equation: C + R = total number of animals.
c) The total number of legs can be represented by the equation: 2C + 4R = total number of legs. This equation accounts for the fact that chickens have two legs, while rabbits have four.
d) To find the solution, we can use the given information: 40 heads and 106 legs. Since each animal has one head, the total number of animals is equal to the total number of heads, which is 40.
Using the equation C + R = 40, we can solve for one variable in terms of the other. For example, if we solve for C, we get C = 40 - R.
Substituting this value of C into the equation 2C + 4R = 106, we can solve for R:
2(40 - R) + 4R = 106
80 - 2R + 4R = 106
2R = 26
R = 13
Therefore, there are 13 rabbits in the pen.
To find the number of chickens, we can substitute the value of R into the equation C = 40 - R:
C = 40 - 13
C = 27
Hence, there are 27 chickens in the pen.
In conclusion, there are 27 chickens and 13 rabbits in the pen on your grandmother's farm, based on the given information of 40 heads and 106 legs.
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Which value of a would make the expression 5
13÷4a
equivalent to a whole number?
5
7
9
11
A value of a that would make the expression 5 1/3 ÷ 4/a equivalent to a whole number include the following: C. 9.
How to determine the value of that would make the expression equivalent to a whole number?In order to use the given expressions to determine the value of a (a-value) that makes the expression equivalent to a whole number, we would have to substitute the values of a (a-value or domain) into each of the expressions and then evaluate as follows;
First of all, we would re-write the mixed fraction as an improper fraction and then evaluate the given expression;
16/3 ÷ 4/a
16/3 × a/4
When a = 5, we have the following:
16/3 × a/4
16/3 × 5/4 = 20/3 (not a whole number).
When a = 7, we have the following:
16/3 × a/4
16/3 × 7/4 = 28/3 (not a whole number).
When a = 5, we have the following:
16/3 × a/4
16/3 × 9/4 = 36/3
36/3 = 12 (a whole number).
When a = 11, we have the following:
16/3 × a/4
16/3 × 11/4 = 44/3 (not a whole number).
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Complete Question:
Which value of a would make the expression 5 1/3 ÷ 4/a equivalent to a whole number?
5
7
9
11
Which scenarto could be modeled by the graph of the function A) & 10041.002)4
A
An ant colony that has an initial population ef 100 increases by 0.296 per year.
An ant colony that has an Infal population of 100 increases at a constant rate of 0.2 per year.
An ant colony that has an intal population of 100 decreases by 0.2% per year
D
An ant colony that has an Infial population of 100 decreases at a constant rate of 0.2 per year.
The function A(x) = 100 + 4x describes the scenario of an ant colony that starts with an initial population of 100 and experiences a constant rate of increase of 4 ants per year.
We have,
The function A(x) = 100 + 4x represents a linear relationship between the variable x (representing time in this case) and the variable A(x) (representing the population of the ant colony).
The term 100 in the function represents the initial population of the ant colony.
It indicates that at the starting point (x = 0), the population is 100.
The term 4x in the function represents the rate at which the population increases over time. Since the coefficient of x is positive (4), it indicates that the population is increasing.
For every unit increase in x (in this case, for every year that passes), the population increases by 4.
Therefore,
The function A(x) = 100 + 4x describes the scenario of an ant colony that starts with an initial population of 100 and experiences a constant rate of increase of 4 ants per year.
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Please Help!! Solve For X
The value of x in the given figure is 8.
In the given figure there are two lines which are parallel.
We have to find the value of x.
In the straight line the sum of angles is 180 degrees.
8x+1+115=180
8x+116=180
Subtract 116 from both sides:
8x=180-116
8x=64
Divide both sides by 8:
x=64/8
x=8
Hence, the value of x in the given figure is 8.
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