Answer:
Step-by-step explanation:
Hello!
We want to know the area of the original circle - the now circle.
The original circle's diameter is 110 meters.
To figure out the area you use this formula: [tex]r^2*pi[/tex]
The diameter is 107 meters, so the equation is [tex]55^2[/tex][tex]*\pi[/tex].
The area is about 9503.3 meters.
The next area is the "now circle".
The now circle's diameter is 107 meters.
When you use this formula, you end up with [tex]53.5^2*\pi[/tex].
The area is about 8892 meters.
So it's just basic subtraction!
I'll let you figure out the rest.
:)
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
250πcm³
Step-by-step explanation:
Length of bigger = k X length of smaller (k is a constant)
Area of bigger = k² X area of smaller (k is a constant)
Volume of bigger = k³ X volume of smaller (k is a constant)
ratio of 3:5 means that there are 3 + 5 = 8 parts.
Length of bigger = k X length of smaller
5 = 3k
k = 5/3.
Volume of bigger = k³ X volume of smaller
= (5/3)³ 54π
= 250πcm³
If 5sinA=3 and cosA is smaller than 0 , with an aid of a diagram determine the value of 2tanAcosA
If 5sinA=3 and cosA is smaller than 0 , the value of 2tanAcosA is -6/5.
To determine the value of 2tanAcosA, we need to find the values of tanA and cosA first. We are given that 5sinA = 3 and cosA is smaller than 0.
Let's start by finding sinA. Since sinA = opposite/hypotenuse, we can set up a right triangle with the opposite side as 3 and the hypotenuse as 5. Using the Pythagorean theorem, we can find the adjacent side:
adjacent^2 = hypotenuse^2 - opposite^2
adjacent^2 = 5^2 - 3^2
adjacent^2 = 25 - 9
adjacent^2 = 16
adjacent = 4
Now we can find cosA using the adjacent side and hypotenuse:
cosA = adjacent/hypotenuse
cosA = 4/5
Since cosA is smaller than 0, it means that cosA is negative. Therefore, cosA = -4/5.
Next, we can find tanA using the given information. tanA = opposite/adjacent = 3/4.
Now, we can calculate the value of 2tanAcosA:
2tanAcosA = 2 * (3/4) * (-4/5) = -24/20 = -6/5
Therefore, the value of 2tanAcosA is -6/5.
To aid in visualizing the situation, it would be helpful to draw a right triangle with the appropriate side lengths based on the given values of sinA and cosA. The opposite side would be 3, the adjacent side would be 4, and the hypotenuse would be 5. Additionally, since cosA is negative, we can indicate the direction of the adjacent side to be in the negative x-axis direction. This diagram would provide a visual representation of the values and relationships involved in solving the problem.
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Pls help me!!!
Robin's teacher asked her to find a box that would hold some small
1 inch cubes that the kindergartners used for counting. Robin
found three boxes with the following dimensions: Box A: 4" x 6" x
8" Box B: 6" x 3" x 12" Box C: 6" x 6" x 4" Which box would be
able to hold all the cubes if Robin's teacher had 200 cubes?
To determine which box can hold all the cubes, we need to calculate the volume of each box and compare it to the volume occupied by the cubes.
The volume of a rectangular box is calculated by multiplying its length, width, and height.
Box A:
Volume = 4" x 6" x 8" = 192 cubic inches
Box B:
Volume = 6" x 3" x 12" = 216 cubic inches
Box C:
Volume = 6" x 6" x 4" = 144 cubic inches
Since the cubes have a side length of 1 inch, the volume occupied by 200 cubes would be:
Volume of cubes = 200 cubic inches
Comparing the volumes, we find that:
- Box A has a volume of 192 cubic inches, which is less than the volume of the cubes.
- Box B has a volume of 216 cubic inches, which is greater than the volume of the cubes.
- Box C has a volume of 144 cubic inches, which is less than the volume of the cubes.
Therefore, the box that would be able to hold all 200 cubes is Box B: 6" x 3" x 12".
Write the quadratic equation in standard form that corresponds to the graph shown below.
The Quadratic equation in standard form that corresponds to the given parabola is (x + 1)^2 = 12y.
The quadratic equation in standard form that corresponds to the graph of the parabola passing through the points (2, 0) and (-4, 0), we can use the vertex form of a parabola equation, which is (x - h)^2 = 4a(y - k). the vertex of the parabola. The vertex is the midpoint of the line segment connecting the two given points.
The x-coordinate of the vertex is the average of the x-coordinates of the two points:
(2 + (-4))/2 = -2/2 = -1
The y-coordinate of the vertex is the same as the y-coordinate of both given points:
y = 0
Therefore, the vertex of the parabola is (-1, 0).
Now, let's find the value of 'a', which represents the coefficient in front of the y-term. We know that the distance from the vertex to either of the given points is equal to 'a'. In this case, the distance from the vertex (-1, 0) to either (2, 0) or (-4, 0) is 3 units.
So, 'a' = 3.
Now, we can write the quadratic equation in standard form:
(x - h)^2 = 4a(y - k)
Plugging in the values we found:
(x - (-1))^2 = 4(3)(y - 0)
Simplifying:
(x + 1)^2 = 12y
Therefore, the quadratic equation in standard form that corresponds to the given parabola is (x + 1)^2 = 12y.
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I have a problem at 4'o clock on the given attachment picture please check it out
Answer:
4
Step-by-step explanation:
You want the product of terms (n+1)/n for integers n from 1 to 3.
ProductWhen there are only 3 terms, we can write out the product:
(1 +1)/1 × (2 +1)/2 × (3 +1)/3 = 2 × 3/2 × 4/3 = 4
The product is 4.
__
Additional comment
You will notice the first term has a denominator of 1. In each pair of terms, the numerator of a term cancels the denominator of the next term. This means the product of k terms will always be (k+1). For 3 terms, the product is 3+1 = 4.
Apparently, the answer in each case is the hour number.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The area of the parallelogram of triangle would be listed below as follows:
19A.) = 336mm²
19B.) = 416in²
How to calculate the area of the parallel of triangle?To calculate the area of the parallelogram of triangle, the formula for the area of the parallelogram should be used and it is given as follows:
Area of parallelogram = base×height
For A.)
Base = 18+10 = 28mm
height = 12mm
Area = 28×12 = 336mm²
For B.)
Base = 26in
Height = 16(using the sine rule)
Area = 26×16 = 416in²
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The perimeter of the rectangle below is 202 units. Find the value of x.
5x +3
4x - 1
amara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible combinations when rolling two number cubes. How many times should Tamara expect the sum of the two cubes be equal to if she rolls the two number cubes 180 times?
Tamara should expect the sum of the two cubes to be equal to 7 around 30 times when rolling the two number cubes 180 times.
To determine how many times Tamara should expect the sum of the two number cubes to be equal to a certain value, we need to analyze the chart and calculate the probabilities.
Let's examine the chart and count the number of times each sum occurs:
Sum: 2, Occurrences: 1
Sum: 3, Occurrences: 2
Sum: 4, Occurrences: 3
Sum: 5, Occurrences: 4
Sum: 6, Occurrences: 5
Sum: 7, Occurrences: 6
Sum: 8, Occurrences: 5
Sum: 9, Occurrences: 4
Sum: 10, Occurrences: 3
Sum: 11, Occurrences: 2
Sum: 12, Occurrences: 1
Now, let's calculate the probabilities of each sum occurring.
Since there are 36 possible combinations when rolling two number cubes, the probability of each sum is the number of occurrences divided by 36:
Probability of sum 2 = 1/36
Probability of sum 3 = 2/36
Probability of sum 4 = 3/36
Probability of sum 5 = 4/36
Probability of sum 6 = 5/36
Probability of sum 7 = 6/36
Probability of sum 8 = 5/36
Probability of sum 9 = 4/36
Probability of sum 10 = 3/36
Probability of sum 11 = 2/36
Probability of sum 12 = 1/36
To find out how many times Tamara should expect a certain sum when rolling the two number cubes 180 times, we can multiply the probability of that sum by 180.
For example, to find the expected number of times the sum is 7:
Expected occurrences of sum 7 = (6/36) [tex]\times[/tex] 180 = 30
Similarly, we can calculate the expected occurrences for all other sums.
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Yesterday, Lily withdrew $25 from her savings account to buy a birthday gift for her grandfather.
What integer represents the change in Lily's account balance?
The integer number that represents the change in Lily's account balance is given as follows:
-25.
What are integer numbers?Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.
For the balance of the bank account, we have that:
Deposits are represented by positive integers.Withdraws are represented by negative integers.Lily withdrew $25 from her savings account to buy a birthday gift for her grandfather, hence the integer number is given as follows:
-25.
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Find the measure of the each angle to the nearest degree. cos−11013
Simplifying a product involving square roots using distributi…
The simplified expression in the context of this problem is given as follows:
[tex]5\sqrt{5}(\sqrt{10} - 3) = 25\sqrt{2} - 15\sqrt{5}[/tex]
How to simplify the expression?The expression in the context of this problem is given as follows:
[tex]5\sqrt{5}(\sqrt{10} - 3)[/tex]
Applying the distributive property, we multiply the outer term by each of the inner terms, hence:
[tex]5\sqrt{50} - 15\sqrt{5}[/tex]
The number 50 can be written as follows:
50 = 2 x 25.
Hence the square root is simplified as follows:
[tex]\sqrt{50} = \sqrt{2 \times 25} = 5\sqrt{2}[/tex]
Hence the simplified expression is given as follows:
[tex]25\sqrt{2} - 15\sqrt{5}[/tex]
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The circle below has center D. Suppose that m BC = 42°. Find the following.
The measure of angle BDC is 42° and the measure of angle BAC is 21°.
Given that, the measure of arc BC of circle = 42°.
An arc of a circle is a section of the circumference of the circle between two radii. A central angle of a circle is an angle between two radii with the vertex at the centre. The central angle of an arc is the central angle subtended by the arc. The measure of an arc is the measure of its central angle.
From the given circle,
The measure of arc BC = Angle BDC = 42°
Here, Angle BDC = 2×Angle BAC
42° = 2×Angle BAC
Angle BAC = 21°
Therefore, the measure of angle BDC is 42° and the measure of angle BAC is 21°.
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Match the trigonometric expressions to their solutions.
cos [140°- (50° +30°)]
√3
tan 240°
-√6-√2
cos 150°
1
Reset
Next
sin 255
Hi,
cos[140˚- ( 50˚ + 30˚)] = 1/2
tan 240˚ = √3
cos 150˚ = -√3/2
sin 255˚ = -√6 - √2/4
Those above should be the correct ones
XD
The temperature is 12 celcius when the altitude is 3,000 meters above sea level.At a higher altitude the temperature reads 4 celcius.Was there an increase or decrease in the temperature?
Answer:
Decrease in temp.
Step-by-step explanation:
Here is the reason:
Initially, at an altitude of 3,000 meters above sea level, the temperature was 12 degrees Celsius. As the altitude increased, the temperature dropped to 4 degrees Celsius. Since the temperature decreased from 12 degrees Celsius to 4 degrees Celsius, there was a decrease in the temperature
What is the value of x? Round to the nearest thousandth.
Applying the tangent ratio, the value of x in the image, rounded to the nearest thousandth is: 15.824.
How to Find the Value of x Using the Tangent Ratio?The tangent ratio, commonly referred to as "tangent," is a trigonometric function that relates the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle. It is expressed as:
tan (∅) = opposite/adjacent
We have the following:
Reference angle (∅) = 53 degrees
Length of opposite side = 21
Length of adjacent side = x
Plug in the values:
tan 53 = 21/x
x * tan 53 = 21
x = 21 / tan 53
x = 15.824
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A cylinder has a radius of 4 millimeters. Its volume is 200.96 cubic millimeters. What is the height of the cylinder?
Answer:
3.999 millimeters.
Step-by-step explanation:
To find the height of the cylinder, we can use the formula for the volume of a cylinder:
V = πr²h
Given that the radius (r) of the cylinder is 4 millimeters and the volume (V) is 200.96 cubic millimeters, we can substitute these values into the formula and solve for the height (h).
200.96 = π(4²)h
200.96 = 16πh
To solve for h, we can divide both sides of the equation by 16π:
200.96 / (16π) = h
Using a calculator, we can calculate the approximate value of h:
h ≈ 200.96 / (16 × 3.14159)
h ≈ 3.999
Therefore, the height of the cylinder is approximately 3.999 millimeters.
There is an upcoming election for student council president at a high school. Candidate A must get over 50% of the vote against Candidate B to be elected. A poll was taken of a random sample of 80 students from the high school and 44 students said they would vote for Candidate A. Simulations were done with an assumption that the population is split 50-50 using a sample size of 80 to see how likely a sample of 80 would have 44 who preferred Candidate A. The results of 200 simulations are shown below. Create an interval containing the middle 95% of the data based on the data from the simulation, to the nearest hundredth, and state whether the observed proportion is within the margin of error of the simulation results.
The interval containing the middle 95% of the data based on the simulation results is approximately (0.35, 0.65), and the observed proportion of 0.55 falls within this interval, indicating that it is within the margin of error of the simulation results.
To create an interval containing the middle 95% of the data based on the simulation results, we can calculate the lower and upper bounds of the interval.
Let's analyze the simulation results and find the appropriate values.
Out of 200 simulations, we observe that the proportion of students who preferred Candidate A ranges from a minimum of 0.35 (35%) to a maximum of 0.65 (65%).
Since the simulations assume a 50-50 split, we can consider these values as the lower and upper bounds for the middle 95% of the data.
To find the range of the middle 95% of the data, we calculate the difference between the upper and lower bounds.
Upper bound: 0.65
Lower bound: 0.35
Range: 0.65 - 0.35 = 0.30
To find the interval containing the middle 95% of the data, we divide the range by 2 and add/subtract it from the midpoint.
The midpoint is the average of the upper and lower bounds.
Midpoint: (0.65 + 0.35) / 2 = 0.50
Range / 2: 0.30 / 2 = 0.15
Lower bound of the interval: 0.50 - 0.15 = 0.35
Upper bound of the interval: 0.50 + 0.15 = 0.65
Therefore, the interval containing the middle 95% of the data based on the simulation results is approximately (0.35, 0.65).
Now let's compare the observed proportion from the poll to this interval. The poll indicates that out of a random sample of 80 students, 44 students said they would vote for Candidate A.
To calculate the observed proportion, we divide the number of students who preferred Candidate A (44) by the sample size (80).
Observed proportion: 44/80 = 0.55
The observed proportion of 0.55 is within the margin of error of the simulation results.
It falls within the interval (0.35, 0.65), indicating that the observed proportion is consistent with the simulation and aligns with the assumption of a 50-50 split in the population.
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A pine cone is 60 feet above the ground when it falls from a tree. The height h (in feet) of the pine cone
above the ground can be modeled by h = -16t2+ 60, where t is the time (in seconds) since the pine
cone started to fall.
a. Solve the equation for t. Write your answer in simplest form.
t=
b. After how many seconds will the pine cone be 20 feet above the ground? Round your answer to the
nearest hundredth.
The pine cone is 20 feet above the ground after about ____
seconds.
The pine cone is 20 feet above the ground after about 1.58 seconds.
To solve the equation h = -16t² + 60 for t, we can rearrange the equation as follows:
-16t² + 60 = h
Subtract 60 from both sides:
-16t² = h - 60
Divide both sides by -16:
t² = (h - 60) / -16
Take the square root of both sides:
t = ±√((h - 60) / -16)
Since time cannot be negative in this context, we can ignore the negative square root:
t = √((h - 60) / -16)
We are given that the pine cone is 20 feet above the ground, so we substitute h = 20 into the equation:
t = √((20 - 60) / -16)
Simplifying:
t = √(-40 / -16) = √(2.5)
t = 1.58 seconds
Therefore, the pine cone is 20 feet above the ground after about 1.58 seconds.
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Find the area of the parallelogram in the coordinate plane.
A (7,5)
D(-9,-2)
Units
B(6,5)
C(4-2)
To find the area of a parallelogram in the coordinate plane, we need to determine the base and the height of the parallelogram.
Using the given coordinates, we can find the length of one side of the parallelogram as the distance between points A and B.
The length of AB = sqrt((6 - 7)^2 + (5 - 5)^2) = sqrt((-1)^2 + 0^2) = sqrt(1) = 1
The height of the parallelogram can be found as the distance between point D and the line passing through points A and B. We can use the formula for the distance between a point and a line to find the perpendicular distance.
The equation of the line passing through A and B can be found using the point-slope form:
y - 5 = (5 - 5)/(7 - 6) * (x - 7)
y - 5 = 0 * (x - 7)
y - 5 = 0
y = 5
The perpendicular distance from point D(-9, -2) to the line y = 5 is the difference in their y-coordinates:
Perpendicular distance = |-2 - 5| = 7
Now, we have the base length AB = 1 and the height = 7.
The area of the parallelogram is given by the formula: Area = base * height.
Area = 1 * 7 = 7 square units.
Check the picture below.
[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=1\\ b=13\\ h=7 \end{cases}\implies A=\cfrac{7(1+13)}{2}\implies A=49[/tex]
Ratio of surface area to volume of cylinder
The ratio of the surface area to the volume of a cylinder is (2rh + 2r²) / (r²h).
The formula for the surface area of a cylinder is:
Surface Area = 2πrh + 2πr²
Volume of Cylinder: The volume of a cylinder is given by the formula:
Volume = πr²h
Ratio of Surface Area to Volume:
Ratio = (2πrh + 2πr²) / (πr²h)
Simplifying the expression, we can cancel out the common factors of π and r:
Ratio = (2rh + 2r²) / (r²h)
So, the ratio of the surface area to the volume of a cylinder is (2rh + 2r²) / (r²h).
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Let z=f(u,v)=sinucosv
, u=4x2−5y
, v=3x−5y
,
and put g(x,y)=(u(x,y),v(x,y))
. The derivative matrix D(f∘g)(x,y)=
(
,
To find the derivative matrix of the composition of functions f∘g, we need to compute the partial derivatives of f with respect to u and v, and then evaluate them at the point (u(x, y), v(x, y)). Let's calculate the partial derivatives first:
∂f/∂u = cos(u)cos(v)
∂f/∂v = -sin(u)sin(v)
Now, let's substitute u = 4x^2 - 5y and v = 3x - 5y into the partial derivatives:
∂f/∂u = cos((4x^2 - 5y))cos((3x - 5y))
∂f/∂v = -sin((4x^2 - 5y))sin((3x - 5y))
The derivative matrix D(f∘g)(x, y) is a 1x2 matrix (a row vector) where each entry represents the partial derivative of f∘g with respect to x and y, respectively.
D(f∘g)(x, y) = (∂f/∂u ∂f/∂v) evaluated at (u(x, y), v(x, y))
D(f∘g)(x, y) = (cos((4x^2 - 5y))cos((3x - 5y)), -sin((4x^2 - 5y))sin((3x - 5y)))
please see the attached
The expression (r-s)(x) is 4x² - x + 5, (r.s)(x) is 4x³ - 20x² and value of (r-s)(-1) is 10.
To find the expression (r-s)(x), we subtract the function s(x) from the function r(x):
(r-s)(x) = r(x) - s(x)
Substituting the given functions, we have:
(r-s)(x) = 4x² - (x-5)
Simplifying further:
(r-s)(x) = 4x² - x + 5
To find the expression (r.s)(x), we multiply the functions r(x) and s(x):
(r.s)(x) = r(x) × s(x)
Substituting the given functions, we have:
(r.s)(x) = (4x²)×(x-5)
Expanding and simplifying:
(r.s)(x) = 4x³ - 20x²
Now, let's evaluate (r-s)(-1) by substituting x = -1 into the expression (r-s)(x):
(r-s)(-1) = 4(-1)² - (-1) + 5
(r-s)(-1) = 4 - (-1) + 5
(r-s)(-1) = 4 + 1 + 5
(r-s)(-1) = 10
Therefore, (r-s)(-1) equals 10.
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In need of help asap!
Answer:
Step-by-step explanation:
please what grade this if you answer i will help you
In this picture b, d, and f are midpoints. Ac=50 ce=60 and bd=35. What is fe
The length of FE is equal to 35 units.
What is the triangle midpoint theorem?In Mathematics and Geometry, the triangle midpoint theorem states that the line segment which connects the midpoints of two (2) sides of a triangle must be parallel to the third side, and it's congruent to one-half of the third side.
By applying the triangle midpoint theorem to the triangle, we have the following:
AE = 1/2(FE)
BD ≅ FE (midpoints of AC and CE)
BD = FE = 35 units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
The given picture with Midpoints B, D, and F, AC is 50 units, CE is 60 units, and BD is 35 units. The length of segment FE is determined to be 35 units.
In the given picture, let's label the points as A, B, C, D, E, and F. It is mentioned that points B, D, and F are midpoints.
Given information:
AC = 50
CE = 60
BD = 35
Since B, D, and F are midpoints, we know that BD is equal to half of AC and half of CE. Therefore, BD = AC/2 and BD = CE/2.
We are given that BD = 35, so we can set up the equations:
35 = AC/2 ...(Equation 1)
35 = CE/2 ...(Equation 2)
Let's solve Equation 1 for AC:
AC = 35 * 2
AC = 70
Similarly, solving Equation 2 for CE:
CE = 35 * 2
CE = 70
Now, let's consider triangle AFE. Since B and D are midpoints, we know that BD is parallel to FE, and FD is parallel to AE. Therefore, triangle AFE is similar to triangle ADC.
In similar triangles, corresponding sides are proportional. Hence, we can write the following ratios:
FE/AC = FD/AD
Substituting the known values, we get:
FE/70 = 35/AC
Cross-multiplying, we have:
FE * AC = 70 * 35
Since we know AC is 70, we can solve for FE:
FE = (70 * 35) / 70
FE = 35
Therefore, the length of FE is 35 units.
the given information, in the given picture with midpoints B, D, and F, AC is 50 units, CE is 60 units, and BD is 35 units. The length of segment FE is determined to be 35 units.
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Match the system of equations with the number of solutions.
y = 6z+8
y = 6x-4
y = 3x + 2
y + 3x = -7
4z - 2y = 10
2z-y = 5
4z + y = 8
y=-2z+8
No Solution
Answer:
Step-by-step explanation:
The system of equations with no solution is:
y + 3x = -7
4z - 2y = 10
The system of equations with exactly one solution is:
y = 6z+8
y = 6x-4
y = 3x + 2
2z-y = 5
y=-2z+8
The system of equations with infinitely many solutions is:
4z + y = 8
100 Points! Geometry question. Photo attached. Find the measure. Please show as much work as possible. Thank you!
Answer:
The answer would lie within 31 degrees of MP and also as in PM.
Answer:
central m arc MP=118°
Step-by-step explanation:
here
central m arc MN=2* inscribed m arc MN=2*31=62°
again
central m arc MN+ central m arc MP=180° being linear pair
substituting value
62°+central m arc MP=180°
central m arc MP=180°-62°
central m arc MP=118°
6. Prove that linear functions grow by equal differences over equal intervals.
Part I. This is the graph of. Use the graph to show that equal intervals of x-values have equal differences
of y-values.
a) Think about an interval on the x-axis starting with p and ending with p + k. What is the difference
between the x-values? What is the difference between the y-values for these x-values? Complete the
tables using.
The linear function equation, y = m·x + c, indicates;
6. The growth in the y-values over each unit x-value interval is a difference of m units.
Part I. Please find attached the graph of y = x + 3, created with MS Excel, which shows that the differences between the y-values is 2 units over each x-value interval of 2 units.
a) The difference between the x-values is; k
The difference between the y-values is; m·k
The difference in the y-value is; m·k
Please find attached the completed tables in the following section
What are linear functions?The equation of a linear function is; y = m·x + c
Where;
m = The slope of the graph = (y₂ - y₁)/(x₂ - x₁)
(x₁, y₁), and (x₂, y₂), are ordered pair of data on the graph of the linear function
c = The y-intercept of the linear function
(y₂ - y₁)/(x₂ - x₁) = m
(y₂ - y₁) = m × (x₂ - x₁)
Δy = m × Δx
When Δx = 1, we get;
Δy = m
Therefore, the y-value of a linear function increases by m, the slope value, when the x-value increases by 1, which indicates that the linear function grows by equal differences over the same interval of the input value of the function
Part I; Please find a graph of the linear function, y = 1·x + 3, which shows that each equivalent interval of 2 units in the x-axis, produces a difference in the y-value or y-axis of 2 units.
a) Considering the interval p and p + k, let y₁ represent the y-value at p and let y₂ represent the y-value at p + k, we get;
Slope, m = (y₂ - y₁)/((p + k) - p) = (y₂ - y₁)/k
Therefore;
(y₂ - y₁)/k = m
(y₂ - y₁) = m × k
Therefore, the increase in the y-value, for an increase in the x-value of k is a constant, m·k = (y₂ - y₁)
Therefore the difference in the y-value for the specified x-values is a constant m·k
The possible equation in the question obtained from a similar question on the website is; y = -(1/2)·x + 10
The completed tables are;
[tex]\begin{tabular}{ | c | c | c | c | }\cline{1-4}& Interval; p = 2& p+ k = 6&\\ \cline{1-4}x-value & 2 & 6 & 4 \\\cline{1-4}y-value & y = (-1/2)\cdot (2)+10 =9 & y = (-1/2)\cdot (6)+10=\underline{7} & -2 \\\cline{1-4}\end{tabular}[/tex]
[tex]\begin{tabular}{ | c | c | c | c | }\cline{1-4}& Interval; p = 10& p+ k = 14&\\ \cline{1-4}x-value & 10 & 14 & 4 \\\cline{1-4}y-value & y = (-1/2)\cdot (10)+10 =\underline{ 5 }& y = (-1/2)\cdot (14)+10=3 & -2 \\\cline{1-4}\end{tabular}[/tex]
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Show work and number
The measure of length of the triangle is solved and
a) x = 4.9 units
b) x = 14 units
c) x = 4.8 cm
d) b = 68.5 units
Given data ,
Let the triangle be represented as ΔABC
where the measure of the lengths of the sides are given as
a)
The measure of hypotenuse AC = 12
The measure of angle ∠BAC = 66°
So , from the trigonometric relations , we get
cos θ = adjacent / hypotenuse
cos 66° = x / 12
So , x = 12 cos ( 66 )°
x = 4.9 units
b)
The measure of base of triangle BC = 20 units
And , the angle ∠BAC = 55°
So , from the trigonometric relations , we get
tan θ = opposite / adjacent
tan 55° = 20/x
x = 20 / tan55°
x = 14 units
c)
The measure of base of triangle BC = 4 cm
And , the angle ∠BAC = 57°
So , from the trigonometric relations , we get
sin θ = opposite / hypotenuse
sin 57° = 4/x
x = 4 / sin 57°
x = 4.8 cm
d)
The measure of base of triangle BC = 38 units
And , the angle ∠BAC = 61°
So , from the trigonometric relations , we get
tan θ = opposite / adjacent
tan 61° = b/38
b = 38 x tan 61°
b = 68.5 units
Hence , the trigonometric relations are solved.
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100 Points! Geometry question. Photo attached. Find x and y. Please show as much work as possible. Thank you!
Answer: 36
Step-by-step explanation: 3y by 56
How many solutions does the system of equations below have? y=-3/4x+1/6
The solution is the point (0, 1/6) y = 1/6
Given the equation y = (-3/4)x + 1/6, which represents a linear equation, there is no "system" of equations involved since there is only one equation.
In this case, the equation is in slope-intercept form (y = mx + b),
where m represents the slope (-3/4) and b represents the y-intercept (1/6).
The slope-intercept form allows us to determine various properties of the equation.
Since there is only one equation, the solution to this equation is a single point on the Cartesian plane.
Each pair of x and y values that satisfy the equation represents a solution.
For example, if we choose x = 0, we can substitute it into the equation to find the corresponding y value:
y = (-3/4)(0) + 1/6
y = 1/6
Therefore, the solution is the point (0, 1/6).
In summary, the given equation has a unique solution, represented by a single point on the Cartesian plane.
Any value of x plugged into the equation will yield a corresponding y value, resulting in a unique point that satisfies the equation.
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