Refer to this diagram for the next five statements (Questions 1–5). Write the correct postulate, theorem, property, or definition that justifies the statement below the diagram.
Given: ∠MRS ≅ ∠MRO
Answers
In the given figure the equation m∠MRS + m∠MRO = m∠SRO is the postulate describing the linear pair of angles.
From the given figure, It is given that -
∠MRS ≅ ∠MRO
Now, what that means is that ∠MRS is congruent to ∠MRO.
Thus, to understand this concept of equality or congruence, we can prove it since from the given image, we see that -
m∠MRS = m∠MRO = 90°
Since they are both right angles then we can say that the correct theorem is the definition of a right angle triangle.
It can be seen that m∠SRO = 180°
Also, m∠MRS + m∠MRO = 180°
It is seen that the angles form a linear pair and lie on the same plane.
Therefore, the correct postulate is linear pair.
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Related Questions
1. [6 marks] Solve the following system of linear equations using Gaussian elimination (write all steps)⎩⎨⎧2x−3y−5z=−6x+2y+8z=113x−y+3z=5
Answers
The solution to the system of linear equations is (47/16, -161/40, 49/8).
To solve the system of linear equations using Gaussian elimination, we first need to write the equations in matrix form.
[2 -3 -5 | -6]
[-6 2 8 | 11]
[3 -1 3 | 5]
Next, we need to use elementary row operations to transform the matrix into reduced row echelon form (RREF). This means that the matrix will have a leading 1 in each row, and all other entries in that column will be 0.
Step 1: Divide the first row by 2 to get a leading 1.
[1 -3/2 -5/2 | -3]
[-6 2 8 | 11]
[3 -1 3 | 5]
Step 2: Add 6 times the first row to the second row to eliminate the -6 in the second row.
[1 -3/2 -5/2 | -3]
[0 5 7 | 7]
[3 -1 3 | 5]
Step 3: Subtract 3 times the first row from the third row to eliminate the 3 in the third row.
[1 -3/2 -5/2 | -3]
[0 5 7 | 7]
[0 7/2 13/2 | 14]
Step 4: Divide the second row by 5 to get a leading 1.
[1 -3/2 -5/2 | -3]
[0 1 7/5 | 7/5]
[0 7/2 13/2 | 14]
Step 5: Add 3/2 times the second row to the first row to eliminate the -3/2 in the first row.
[1 0 -1/2 | -1/2]
[0 1 7/5 | 7/5]
[0 7/2 13/2 | 14]
Step 6: Subtract 7/2 times the second row from the third row to eliminate the 7/2 in the third row.
[1 0 -1/2 | -1/2]
[0 1 7/5 | 7/5]
[0 0 4/5 | 49/10]
Step 7: Divide the third row by 4/5 to get a leading 1.
[1 0 -1/2 | -1/2]
[0 1 7/5 | 7/5]
[0 0 1 | 49/8]
Step 8: Add 1/2 times the third row to the first row to eliminate the -1/2 in the first row.
[1 0 0 | 47/16]
[0 1 7/5 | 7/5]
[0 0 1 | 49/8]
Step 9: Subtract 7/5 times the third row from the second row to eliminate the 7/5 in the second row.
[1 0 0 | 47/16]
[0 1 0 | -161/40]
[0 0 1 | 49/8]
Now the matrix is in RREF, and we can read off the solutions:
x = 47/16
y = -161/40
z = 49/8
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BRAINLIEST PLEASE HELP WITH GOOD EXPLANATION
Answers
Range of a function.
We have:
F(x) = 3x + 7, x∈ {-1, 0, 1, 2}Find the Range.
Substitute to F(x):
x = -1, x = 0, x = 1 and x = 2:
F(-1) = 3(-1) + 7 = -3 + 7 = 4
F(0) = 3(0) + 7 = 0 + 7 = 7
F(1) = 3(1) + 7 = 3 + 7 = 10
F(2) = 3(2) + 7 = 6 + 7 = 13
The Range:
{4, 7, 10, 13}An ant crawls 12 feet in 10 minutes. How far can it crawl in 20 minutes and in 30 minutes?
Answers
Answer:
We can use the given information to find the ant's crawling speed and then use that to calculate how far it can crawl in a given amount of time.
The ant crawls 12 feet in 10 minutes, so its crawling speed is:
12 feet / 10 minutes = 1.2 feet/minute
To find how far the ant can crawl in 20 minutes, we can multiply its crawling speed by the time:
Distance in 20 minutes = crawling speed x time
Distance in 20 minutes = 1.2 feet/minute x 20 minutes
Distance in 20 minutes = 24 feet
Therefore, the ant can crawl 24 feet in 20 minutes.
To find how far the ant can crawl in 30 minutes, we can use the same formula:
Distance in 30 minutes = crawling speed x time
Distance in 30 minutes = 1.2 feet/minute x 30 minutes
Distance in 30 minutes = 36 feet
Therefore, the ant can crawl 36 feet in 30 minutes.
Answer:
20 mins=24 feet
30 mins=36 feet
Step-by-step explanation:
if 12 feet = 10 mins and 10 times 2 = 20 then 12 times 2 =24
same for 30 mins.
10 times 3= 30 then 12 times 3= 36
Find the diviative of the following
[tex] y = ( \sqrt{1 + 2x)} 5[/tex]
Answers
Answer:
Step-by-step explanation:
1+2x)5
First you minus the 1 with the 5
Which you'll get a four then divide it by 2
Which you'll get x=2
But then times it by 5
Then you get y=10
Answer:
[tex]\dfrac{d}{dx}\left(\sqrt{1\:+\:2x}\right)5 = \boxed{\dfrac{5}{\sqrt{1+2x}}}[/tex]
Step-by-step explanation:
Given [tex]y = \left(\sqrt{1\:+\:2x}\right)5[/tex]
we are asked to find [tex]\dfrac{dy}{dx}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{d}{dx}\left(\sqrt{1\:+\:2x}\right)5\\\\= 5\dfrac{d}{dx}\left(\sqrt{1+2x}\right)\\\\[/tex]
Find [tex]\dfrac{d}{dx}\left(\sqrt{1+2x}\right)[/tex]:
[tex]Let \;u = 1 + 2x\\\\f(u) = \sqrt(u)\\\\[/tex]
[tex]\mathrm{Apply\:the\:chain\:rule}:\quad \dfrac{df\left(u\right)}{dx}=\dfrac{df}{du}\cdot \dfrac{du}{dx}[/tex]
[tex]= \dfrac{d}{du}\left(\sqrt{u}\right)\dfrac{d}{dx}\left(1+2x\right)[/tex]
[tex]\dfrac{d}{du}\left(\sqrt{u}\right) = \dfrac{d}{du}\left(u^{\dfrac{1}{2}}\right)\\\\= \dfrac{1}{2}u^{\dfrac{1}{2}-1}\\\\= \dfrac{1}{2\sqrt{u}}\\\\\\[/tex]
Substitute back u = 1 + 2x
[tex]= \dfrac{1}{2\sqrt{1+2x}}[/tex]
[tex]\dfrac{d}{dx}(1 + 2x) =\dfrac{d}{dx}(1)} + \dfrac{d}{dx}{2x}\\\\= 0 + 2 \\\\= 2\\[/tex]
Therefore
[tex]\dfrac{dy}{dx} = \dfrac{d}{dx}\left(\sqrt{1\:+\:2x}\right)5\\\\= 5\dfrac{d}{dx}\left(\sqrt{1+2x}\right)\\\\[/tex]
[tex]= 5\cdot \dfrac{1}{2\sqrt{1+2x}}\cdot \:2\\\\= 5\cdot \dfrac{1}{\sqrt{1 + 2x}}\\\\=\dfrac{5}{\sqrt{1+2x}}[/tex]
21. \( \frac{\tan ^{2} t}{\sec t}=\sec t-\cos t \) 22. \( \frac{\cot ^{2} t}{\csc t}=\csc t-\sin t \) 24. \( \frac{1-\sin \theta}{\operatorname{hsos} \theta}=\sec \theta-\tan \theta \) 25. \( \frac{\s
Answers
21. tan^2 t/sec t = sec t-cos t
First, we can simplify the left-hand side of the equation by dividing tan^2 t by sec t. Remember that tan t = sin t/cos t and sec t = 1/cos t:
tan^2 t/sec t = (sin^2 t/cos^2 t)/(1/cos t) = sin^2 t/cos t
Now we can subtract cos t from both sides of the equation:
sin^2 t/cos t - cos t = sec t - cos t
Next, we can multiply both sides of the equation by cos t to get rid of the fraction:
sin^2 t - cos^2 t = sec t*cos t - cos^2 t
Finally, we can use the Pythagorean identity sin^2 t + cos^2 t = 1 to simplify the left-hand side of the equation:
1 - cos^2 t - cos^2 t = sec t*cos t - cos^2 t
0 = sec t*cos t - 2*cos^2 t
22. cot^2 t/csc t = csc t-sin t
First, we can simplify the left-hand side of the equation by dividing cot^2 t by csc t. Remember that cot t = cos t/sin t and csc t = 1/sin t:
cot^2 t/csc t = (cos^2 t/sin^2 t)/(1/sin t) = cos^2 t/sin t
Now we can subtract sin t from both sides of the equation:
cos^2 t/sin t - sin t = csc t - sin t
Next, we can multiply both sides of the equation by sin t to get rid of the fraction:
cos^2 t - sin^2 t = csc t*sin t - sin^2 t
Finally, we can use the Pythagorean identity sin^2 t + cos^2 t = 1 to simplify the left-hand side of the equation:
1 - sin^2 t - sin^2 t = csc t*sin t - sin^2 t
0 = csc t*sin t - 2*sin^2 t
24. (1−sin θ)/cos θ = sec θ−tan θ
First, we can simplify the left-hand side of the equation by dividing 1-sin θ by cos θ:
(1−sin θ)/cos θ = (1/cos θ) - (sin θ/cos θ) = sec θ - tan θ
So the equation is already simplified and both sides are equal.
25. (sin t/csc t) + (cos t/sec t) = 1
First, we can simplify the left-hand side of the equation by dividing sin t by csc t and cos t by sec t. Remember that csc t = 1/sin t and sec t = 1/cos t:
(sin t/csc t) + (cos t/sec t) = (sin t/(1/sin t)) + (cos t/(1/cos t)) = sin^2 t + cos^2 t
Now we can use the Pythagorean identity sin^2 t + cos^2 t = 1 to simplify the left-hand side of the equation:
1 = 1
So the equation is already simplified and both sides are equal.
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Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answers
The options which satisfy the given diagram are
m∠5 + m∠6 = 180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
What is Angle Sum Property?The sum of the interior angles of a triangle is 180°.
What is Exterior Angle Theorem?The exterior angle of a triangle is equal to the sum of its interior opposite angles.
Let the Triangle be ABC and the exterior angle be ∠D , then
∠A + ∠B + ∠C = 180°
∠A + ∠B = ∠D , ∠A and ∠B are interior opposite angles of the triangle
So, the Options that satisfied
m∠5 + m∠6 = 180° { linear pair}
m∠2 + m∠3 = m∠6 {exterior angle theorem}
m∠2 + m∠3 + m∠5 = 180° {Angle Sum Property}
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Which equation shows the volume of the rectangular prism as a product of its edge lengths?
Answers
The equation that shows the volume of the rectangular prism as a product of its edge lengths is (5/3)(1/3)(2/3) = 10/27 in cube. Option 2 is the correct answer.
What is volume and how to calculate it?The quantity of space within a three-dimensional object is its volume. The fundamentals of such forms are described in our page on three-dimensional shapes. Calculating volume is probably not something you will do as frequently as calculating area in the real world.
Even so, it may still be significant. Knowing how to calculate volume will help you determine things like how much room you have for packing when moving house, how much room you need for an office, or how much jam you can put into a jar. It can also be helpful for deciphering what the media means when they discuss a dam's capacity or a river's flow.
The volume of the rectangular prims is given by the formula:
V = lwh
Substituting the values we have:
V = (5/3)(1/3)(2/3) = 10/27
Hence, the equation that shows the volume of the rectangular prism as a product of its edge lengths is (5/3)(1/3)(2/3) = 10/27 in cube. Option 2 is the correct answer.
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x=-4y-23
2x+2y=-4
solve using linear combination method
Answers
Answer:
(5,7)
x = 5
y = 7
please help me its so confusing
Answers
The total surface area of the cube is 3.84 m². The solution has been obtained by using the area of cube.
What is area of a cube?The total surface area of a given cube is said to be equal to the sum of all the surface areas of the cube's faces, according to the definition of surface area. Given that the cube has six faces, its total surface area will be equal to the sum of its six faces.
We are given a cube with side length 0.8 metres.
We know that total surface area of a cube is given by 6a².
Now, by substituting a = 0.8 in the formula, we get
⇒Total surface area of cube = 6 (0.8)²
⇒Total surface area of cube = 6 (0.64)
⇒Total surface area of cube = 3.84 m²
Hence, the total surface area of the cube is 3.84 m².
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Bobby has 3/4 of a cake. If he shares 1/8 slice with morgan then how much does he have?
Answers
The fraction of cake left with Bobby is 5/8.
What is subtraction of fractions?Subtracting fractions include the subtraction of two or more fractions with the same or different denominators. Like fractions can be subtracted directly but for unlike fractions we need to make the denominators same first and then subtract them.
Given that, Bobby has 3/4 of a cake. He shared 1/8 slice with Morgan.
Slice of cake left = 3/4 -1/8
= 6/8 -1/8
= 5/8
Therefore, the fraction of cake left with Bobby is 5/8.
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what is 36/12÷ one whole
Answers
Answer:
12/36 ÷ 2/2 = 6/18
12/36 ÷ 3/3 = 4/12
12/36 ÷ 4/4 = 3/9
All of these equations are equal to one another since they are all being divided by a whole, they are all just being expressed differently.
I hope this helped & Good Luck <3 !!!
Answer:
12/36 ÷ 1 = 0.0333333.......
Step-by-step explanation:
36/12 ÷ 1 =3
12 divided by 36 gives 0.333...... and the result divided by 1 gives the same answer. The same process applies to 36 divided by 12, which gives 3. The result which is three is divided by 1 which gives the same three.
NB: Any number divided by 1 is still the same number. Example: 1200/1 = 1200
Hope it helps.
There are 15 sacks of rice in a van. If each sacks weight 110kg, what is the total weight of all sacks
Answers
Answer:
Step-by-step explanation:
So all that you have to do is just multiply 15 by 110kg and you'll get a answer of 1500kg total.
The ratio of 1 Bertha to form 1 Florence is 12:20 if there are 120 pupils in Florence calculate how many pupils are in Bertha
Answers
There are 72 pupils in bertha if the ratio of 1 Bertha to form 1 Florence is 12:20 if there are 120 pupils in Florence.
The problem can be solved by using the concept of ratios and inverse ratios. It involves setting up a proportion based on the given ratio and using algebra to solve for the unknown quantity.
If the ratio of Bertha to Florence is 12:20, then the ratio of Florence to Bertha is 20:12 (inverse ratio).
Let the number of pupils in Bertha be x. Then, the number of pupils in Florence would be:
20/12 * x = 120
Simplifying:
x = 120 * 12/20
x = 72
Therefore, there are 72 pupils in Bertha.
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Nora created a tiled mosaic for display in her local art museum. The numbers of tiles in the rows of the mosaic form an arithmetic sequence. The first row of the mosaic has 8 tiles and the second row has 12 tiles.
a. Write an explicit formula representing this sequence.
b. Determine the number of tiles in the 13th row.
Answers
a. The explicit formula for the sequence is: an = a + (n - 1)d
b. There are 56 tiles in the 13th row.
What is arithmetic sequence?
An arithmetic sequence is one in which each phrase grows by adding or removing a certain constant, k.
a. Let's denote the number of tiles in the first row as a, and the common difference between consecutive rows as d. Then, the number of tiles in the second row would be a + d, the third row would be a + 2d, and so on. Since the second row has 12 tiles and the first row has 8 tiles, we have:
a + d = 12
a = 8
We can solve this system of equations to find the value of d:
a + d = 12
8 + d = 12
d = 4
Therefore, the explicit formula for the sequence is:
an = a + (n - 1)d
where a = 8 and d = 4.
b. To find the number of tiles in the 13th row, we can plug in n = 13 into the formula:
a13 = 8 + (13 - 1)4
a13 = 8 + 48
a13 = 56
Therefore, there are 56 tiles in the 13th row.
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Answer: a. an= 8+4(n-1)
b. a13=60
Step-by-step explanation:
There are 60 tiles in the 13th row.
a13=4(13)+8
52+8
16severings of a drink you need 8 scoops & 1gallon. You need to make 32 servings how many scoops and gallons do you need
Answers
Answer:
Step-by-step explanation:
based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number8957647h3ny4y4y7
Grace purchases a $3,800 appliance set. She can't afford to pay cash, so she uses the installment plan, which requires a 12% down payment. How much is the down payment?
Answers
Answer:
$456
Step-by-step explanation:
12% = 0.12
3800 x 0.12 = $456
So, the down payment is $456
X=3800 x12/100
X=456
Down payment is equal to $456
Determine the x- and y-intercept(s) of the equation. Write each answer as an ordered pair. If one does not exist, write none in the blank. Enter your answer without blank spaces. y=(x+2)^2-9 a. x-intercepts: blank1 - Word Answer -2 You are incorrect and blank2 - Word Answer -9 You are incorrect b. y-intercept: blank3 - Word Answer -37/4 You are incorrect
Answers
blank1 - Word Answer (-5,0)
blank2 - Word Answer (1,0)
blank3 - Word Answer (0,-5)
The x- and y-intercept(s) of an equation are the points where the graph of the equation crosses the x- and y-axis respectively. To find the x-intercept(s), we set y=0 and solve for x. To find the y-intercept, we set x=0 and solve for y.
a. x-intercepts:
0=(x+2)^2-9
9=(x+2)^2
±3=x+2
x=-5 or x=1
So the x-intercepts are (-5,0) and (1,0).
b. y-intercept:
y=(0+2)^2-9
y=4-9
y=-5
So the y-intercept is (0,-5).
Therefore, the correct answers are:
blank1 - Word Answer (-5,0)
blank2 - Word Answer (1,0)
blank3 - Word Answer (0,-5)
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Hi due today pls help! Ty! question attached
iz Compund intrests
Answers
Answer:
write relation between work and power
Given that the curves are formed from quarter circles, find the area of the shaded region. Give your answer in terms of T. 12m 12m
Answers
the area of the shaded region:
[tex]= 2(the \ area \ of \ a \ quarter \ circle) - (the \ area \ of \ the \ square)\\[/tex]
[tex]= 2\Big(\dfrac{\pi 12^{2} }{4}\Big) - 12^{2} = \dfrac{144 \pi}{2} - 144 = 72 \pi - 144\\[/tex]
[tex]= 72 (\pi - 2) \ m^{2}[/tex]
Answer:
72π-144 m²
Step-by-step explanation:
You want the area of a shaded region consisting of the overlap of two quarter circles in a 12 m square.
SegmentsIf we draw a diagonal from upper left to lower right through the figure, the shaded area is divided into two 90° segments of a circle of radius 12 m.
The formula for the area of a segment is ...
A = 1/2r²(θ -sin(θ))
where θ is the measure of the central angle.
For θ = π/2 radians, this is ...
A = 1/2r²(π/2 -1) . . . . . half the shaded area
Shaded areaThen the whole shaded area is ...
2 × 1/2r²(π/2 -1) = (12 m)²(π/2 -1) = 72π -144 m²
The area of the shaded region is 72π -144 m².
__
Additional comment
If we expand the shaded area formula, we get ...
A =1/2πr² -r²
This is recognizable as twice the area of a quarter circle, less the area of the square.
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please help for 20 points !!
Answers
The [tex]4\frac{3}{8}-2\frac{1}{8}[/tex] [tex]=2\frac{1}{8}[/tex] This is the correct way to solve the equation it.
What sort of equation would that be?The meaning of an equations in algebra is a logical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Does equation imply issue?When we say we're "solving" an equation, we truly mean we're "solving" the issue or "answering" the question since, in most circumstances, a formula reflects a problem (or query) of some type. A mathematical phrase with two equal sides and an equal sign is called an equation.
Given,
[tex]4\frac{3}{8}-2\frac{1}{8}[/tex]
[tex]=2\frac{1}{8}[/tex]
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PLEASE HURRY, TEST QUESTION!!!!
Question- The original radius of a sphere is 6 centimeters. Explain how the surface area of the sphere would change if the radius was halved to 3 centimeters. Round your answers to the nearest whole number.
Answers
Step-by-step explanation:
Refer to pic.............
. Write your claim, which may or may not be the same as the claim you wrote for question 1. Make sure that your claim (a) takes a clear stand, (b) gives an opinion \
HELP ASAP!
Answers
Claim: The current education system should be reformed to ensure that students of all backgrounds are able to pursue education and reach their full potential.
What does claim mean?A claim is a statement made by an individual or organization that seeks to establish a legal right or entitlement to something. It is similar to a demand or request but is used in a legal context.
Points in support of the claim:
1. The current education system is not equitable and fails to provide equal opportunities to all students regardless of their background.
2. Students from low-income families are more likely to attend schools with fewer resources and less rigorous curriculums.
3. These students are often at a disadvantage when it comes to competing for college admissions and other opportunities.
4. Education reform can help to bridge the gap between different socioeconomic backgrounds and ensure that all students have access to quality education.
5. Reforms should focus on providing equal resources and opportunities to all students, regardless of their financial or social backgrounds.
6. This can help to create a more equitable education system, which will benefit all students, regardless of their background.
Conclusion:
Education reform is essential for ensuring that all students, regardless of their background, have access to quality education and the opportunities to reach their full potential. The current education system is not equitable and fails to provide equal opportunities to all students, leaving some at a disadvantage. Therefore, steps must be taken to reform the education system and bridge the gap between different socioeconomic backgrounds. This will help to create a more equitable education system that benefits all students, regardless of their backgrounds.
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Identify Points on a Coordinate Grid
Write the ordered pair for each point.
3. A
4. B
5. C
6. D
7. E
8. F
Answers
(3, 5): Point A is located at the coordinates (3, 5) on the Cartesian plane, meaning it is 3 units to the right of the origin and 5 units above the origin.
What is Coordinate?Coordinates are points on a graph used to determine the position of a particular location. Coordinates can be expressed in two-dimensional (2D) or three-dimensional (3D) formats. In 2D, a point is determined by two numbers—its x and y values—which are the distances from the point to the origin along each axis. In 3D, an additional z-value is needed to indicate the distance from the origin along the third axis. Coordinates are used in a variety of applications, including navigation, mapping, surveying, and astronomy.
B. (2, -3): Point B is located at the coordinates (2, -3) on the Cartesian plane, meaning it is 2 units to the right of the origin and 3 units below the origin.
C. (-4, -2): Point C is located at the coordinates (-4, -2) on the Cartesian plane, meaning it is 4 units to the left of the origin and 2 units below the origin.
D. (0, 0): Point D is located at the coordinates (0, 0) on the Cartesian plane, meaning it is at the origin.
E. (-2, 1): Point E is located at the coordinates (-2, 1) on the Cartesian plane, meaning it is 2 units to the left of the origin and 1 unit above the origin.
F. (5, -4): Point F is located at the coordinates (5, -4) on the Cartesian plane, meaning it is 5 units to the right of the origin and 4 units below the origin.
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If the scale factor of a dilation is 8: 7, what kind of image does it create?
Answers
A dilation with a scale factor of 8:7 creates an image that is eight times larger than the original.
What is scale factor?A scale factor is a numerical value which is used to multiply or divide a given measurement. It is used to compare the sizes of two different objects, or to enlarge or reduce the size of an object. The scale factor can be used to calculate the area, perimeter, and volume of an object. For example, if an object is enlarged by a scale factor of 2, its area will increase by a factor of 4. Similarly, if an object is reduced by a scale factor of 0.5, its area will be reduced by a factor of 0.25.
This means that all of the points in the original image are moved away from the center of the dilation by a factor of eight. This creates an image that is eight times wider and seven times taller than the original. This type of dilation is also known as an enlargement. By enlarging the image, it is possible to see more detail and make the image easier to see. Additionally, it may also be possible to see features that were previously too small to be seen.
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Find the eritical numbers, if any, the function \( f(x)=-x+\sin (2 x), 0 \leq x \leq \pi \). (Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list.
Answers
These are the Critical numbers of the function within the given interval.
Therefore, the answer is \(x=\frac{\pi }{6}, \frac{5 \pi }{6}\).
The Critical numbers of a function are the values of x that make the derivative of the function equal to zero. To find the eritical numbers of the given function, we need to find the derivative of the function and set it equal to zero.
The derivative of the function \(f(x)=-x+\sin (2 x)\) is \(f'(x)=-1+2\cos (2 x)\).
Setting the derivative equal to zero, we get:
\(-1+2\cos (2 x)=0\)
\(\cos (2 x)=\frac{1}{2}\)
Using the inverse cosine function, we get:
\(2 x=\cos ^{-1}\left(\frac{1}{2}\right)\)
\(2 x=\frac{\pi }{3}\) or \(2 x=\frac{5 \pi }{3}\)
Dividing both sides by 2, we get:
\(x=\frac{\pi }{6}\) or \(x=\frac{5 \pi }{6}\)
These are the Critical numbers of the function within the given interval.
Therefore, the answer is \(x=\frac{\pi }{6}, \frac{5 \pi }{6}\).
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Using the numbers 1 to 9 (one time each), fill in the boxes to make
the equation true.
0:0=00:0=00:00
Answers
Using the numbers 1 to 9 (one time each), the boxes can be filled in the following way to make the equation true. 2:2 = 3×3:9 = 4×4 =16.
What do you mean by proportion?An arithmetic contrast among two numbers is known as a percentage. Two sets of provided numbers are considered to be approximately equal with respect to one another in conformity with the rules of proportion if they increase or decrease by the same ratio.
We must create the equation to prove the equality by utilizing each of the numerals 1 through 9 once. Any of the numbers between 1 and 9 are equivalent to 1 and 2.
Let the ratio equal 1.
The comparable ratios are therefore 1:1, 2:2, and 3:3.
2:2 = 3×3:9 = 4×4 =16
Therefore, using the numbers 1 to 9 (one time each), the boxes can be filled in the following way to make the equation true. 2:2 = 3×3:9 = 4×4 =16.
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Are these proportion yes or no?
1/3 , 7/21
2/5 , 40/16
48/9 , 16/3
Answers
1) The ratios 1/3 , 7/21 are in proportion.
2) The ratios 2/5 , 40/16 are not in proportion.
3) the ratios 48/9 , 16/3 are in proportion.
We know that two ratios are said to be in proportion when both the ratios are equivalent.
Consider 1/3 , 7/21
Here 7/21 = (7 × 1)/(7 × 3)
= 1/3
This means 1/3 = 7/21
Thus, the ratios 1/3 , 7/21 are in proportion.
Consider 48/9, 16/3
Here 48/9 = (16 × 3)/(3 × 3)
= 16/3
This means 48/9 = 16/3
Thus, the ratios 48/9, 16/3 are in proportion.
Now consider 2/5 , 40/16
Here 40/16 = (8 × 5)/(8 × 2)
= 5/2
This means 2/5 ≠ 5/2
Thus, the ratios 2/5 , 40/16 are not in proportion.
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Find
x
to the nearest tenth of a degree. Show your work. Set up the trigonometric ratio for right triangles that you would use to find
x
. You are nor asked to find
x
. 3. a. b. 4 Approximate
x
to the nearest tenth of a degree. 5. Consider the following right triangle. Set up the trigonometric ratio for right triangles that you would use to find
x
. Then find
x
Answers
The approximate value of x to the nearest tenth of a degree is 36.9 degrees.
To find x to the nearest tenth of a degree, we can use trigonometric ratios for right triangles. First, we need to determine which trigonometric ratio to use based on the given information.
If we are given the opposite side and the adjacent side of the right triangle, we can use the tangent ratio:
tan(x) = opposite/adjacent
If we are given the opposite side and the hypotenuse, we can use the sine ratio:
sin(x) = opposite/hypotenuse
If we are given the adjacent side and the hypotenuse, we can use the cosine ratio:
cos(x) = adjacent/hypotenuse
Once we have determined the appropriate trigonometric ratio, we can plug in the given values and solve for x. To find x to the nearest tenth of a degree, we can use a calculator to find the approximate value of x and then round to the nearest tenth.
For example, if we are given a right triangle with an opposite side of 3 and an adjacent side of 4, we can use the tangent ratio to find x:
tan(x) = 3/4
x = tan^-1(3/4)
Using a calculator, we find that x is approximately 36.87 degrees. To the nearest tenth of a degree, x is approximately 36.9 degrees.
Therefore, the approximate value of x to the nearest tenth of a degree is 36.9 degrees.
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whats the answer to this?
Answers
it should be +60 not +78
when you multiply 18x by X - 3 you obtain 18x² - 54x . Subtract what you have gotten from 18x²-6x you obtain 60x
vow solve this equation for r. (r-3.5)(4)=(r)((9)/(4)) 4r-14=(9)/(4)r -14=-(7)/(4)r 8=r
Answers
From the given equation the value of r is 8.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
To solve this equation for r, we need to isolate r on one side of the equation. First, we add 14 to both sides of the equation:
4r-14+14 = (9/4)r+14
4r = (9/4)r+14
Then, we subtract (9/4)r from both sides:
4r - (9/4)r = (9/4)r+14 - (9/4)r
(5/4)r = 14
Finally, divide both sides of the equation by (5/4) to isolate r:
r = 14/(5/4) = 8
Therefore, the value of r is 8.
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