Consider the diagram shown. Choose all the true statements.
If Θ = 2 rad, then r > s.
If Θ = 1 rad, then r ≤ s.
If s = 1/2r, then 2Θ = 1.
If s/2r=1, then Θ = 2
Answers
Answer:
If Θ = 1 rad, then r ≤ s
If s = 1/2r, then 2Θ = 1
If s/(2r)=1, then Θ = 2
Step-by-step explanation:
we know that
The arc length s is equal to
[tex]s=r\theta[/tex]
where
r is the radius
[tex]\theta[/tex] is the central angle in radians
Verify each statement
case 1) If Θ = 2 rad, then r > s
The statement is false
Because
For Θ = 2 rad
substitute
[tex]s=r(2)\\s=2r[/tex]
so
[tex]s>r[/tex]
case 2) If Θ = 1 rad, then r ≤ s
The statement is true
Because
For Θ = 1 rad
substitute
[tex]s=r(1)[/tex]
[tex]s=r[/tex]
so
[tex]r\leq s[/tex] ---> is true
case 3) If s = 1/2r, then 2Θ = 1
The statement is true
Because
For s=1/2r
substitute
[tex]\frac{1}{2}r=r\theta[/tex]
[tex]\theta=\frac{1}{2}[/tex]
[tex]2\theta=1[/tex]
case 4) If s/2r=1, then Θ = 2
The statement is true
Because
For Θ = 2
substitute
[tex]s=r(2)\\\\\frac{s}{2r}=1[/tex]
Related Questions
Average snowfall for Boise
Answers
Answer:
20 inches
Step-by-step explanation:
hope this helps you
in 2014 there were about 126 million women in the United States, and women were about 51.4% of the total population. what was the total population in 2014?
Answers
Answer:
Step-by-step explanation
51.4% of the total population is 126 million
let x be the total population
turn ur percent to a decimal
0.514x = 126,000,000
x = 126 / 0.514
x = 245,136,186.77 <==
Answer:
245 millions
Step-by-step explanation:
51.4 > 126million
100 > X
X=100*126/51,4
X=245.1
Complete the following equation: a2 = b2 + c2 - ______.
2 bc cos A
2 ca cos B
2 ab cos C
none of the above
Answers
Answer:
2 bc cos A
Step-by-step explanation:
Cosine rule
The missing part of the equation is 2bc cos A. This equation is a form of the Law of Cosines from trigonometry, which provides a relationship between the lengths of the sides of a triangle and one of its angles.
Explanation:The equation presented is a variant of the Law of Cosines in trigonometry. To complete the equation accurately, we need to choose the right trigonometric relationship between sides a, b, c, and one of the angles. The correct completion of the equation is 2bc cos A.
The Law of Cosines can be stated in three different ways depending on the specific circumstances:
a² = b² + c² - 2bc cos Ab² = a² + c² - 2ac cos Bc² = a² + b² - 2ab cos CLearn more about Law of Cosines here:https://brainly.com/question/32188599
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Please help me with the question. You must solve for x.
Answers
Answer:
[tex]x= (3, \frac{3}{10} )[/tex]
Step-by-step explanation:
The figure is composed of two similar triangles; therefore,
[tex]\frac{7x}{19x-4} =\frac{7x+8}{(5x+5)+(19x-4)}[/tex] this says the ratio of the sides is same for the two triangles.
we simplify and a rearrange to get
[tex]7x(24x+1)=(7x+8)(19x-4)[/tex]
which we expand and get
[tex]168x^2+7x=133x^2+124x-32[/tex]
[tex]35x^2-117x+32=0[/tex]
this quadratic equation has solutions
[tex]x=3.04[/tex]
[tex]x=0.30[/tex]
As integers and simplified fractions these are
[tex]x= (3, \frac{3}{10} )[/tex]
39 points!!!!! HURRY AND SHOW STEPS.... Point B is collinear with A and C and partitions AC in a 3:4 ratio. B is located at (4,1) and C is located at (12,5). Find the coordinates of endpoint A.
Answers
Answer:
(11,3)
Step-by-step explanation:
Find the value of the y-intercept of the line whose equation is 5x - 3y = -12.
Answers
To find the y-intercept, rewrite the equation of the line in slope-intercept form:
Slope-intercept form: y = mx + b (b is the y-intercept)
This is how you get your equation in slope-intercept form:
5x -3y = -12
-3y = -5x - 12
-3y/-3 = (-5x -12)/-3
y = (5/3)x + 4
The answer is 4.
Please let me know if you understand in the comments!
The volume of a sphere is 288pi cm^3
What is the radius of the sphere?
Answers
Answer:
radius = 6 cm
Step-by-step explanation:
The volume (V) of a sphere is calculated as
V = [tex]\frac{4}{3}[/tex] πr³ ← r is the radius
Given V = 288π, then
[tex]\frac{4}{3}[/tex] πr³ = 288π
Multiply both sides by 3 to clear the fraction
4πr³ = 864π ( divide both sides by 4π )
r³ = 216 ( take the cube root of both sides )
r = [tex]\sqrt[3]{216}[/tex] = 6
Thus the radius of the sphere is 6 cm
To find the sphere's radius from its given volume of 288pi cm^3, we use the volume formula V = (4/3) π r³ and solve for r, resulting in a radius of 6 cm.
Explanation:The student is asking for the radius of a sphere given its volume, which is 288pi cm³. To find the radius, we need to use the formula for the volume of a sphere:
V = (4/3) π r³
Where V is the volume and r is the radius. We can solve for r by rearranging the formula:
r = √[3V / (4π)]
In this case, substituting the given volume into the equation:
r = √[3(288π) / (4π)]
r = √[864π / (4π)]
r = √[216]
The radius of the sphere is 6 cm.
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-2°F ___ -6°F
=?
>?
<?
Answers
Answer:
-2 °F > -6 °F
Step-by-step explanation:
-2 is to the right of -6 on the number line, so is the greater of the two values. The temperature has to go up from -6 to get to -2. Thus, ...
-2 °F > -6 °F
what is the fraction of 66.7%
Answers
Evaluate each expression if d = 12 and e = 1/3 2d-5
Answers
Answer:
19
Step-by-step explanation:
Plug it in
What is the exact value of cos (67.5° )?
Answers
The exact value of cos(67.5°) is found using half-angle identities in trigonometry, which leads to the solution √(2 - √2)/2.
Explanation:To find the exact value of cos (67.5°), we can use the half-angle identity for cosine which states that cos(θ/2) = ± √ ((1+cosθ)/2). In this case, to find the cosine of 67.5 degrees, we effectively need to calculate the half-angle of 135 degrees.
Thus, cos(67.5°) = cos(135°/2) = √ ((1+cos135°)/2) = √ ((1 - √2/2)/2). This further simplifies to √(2 - √2)/2.
This is because the cosine of 135 degrees equals -√2/2 (as it's in the second quadrant where cosine is negative).
Therefore, the exact value of cos(67.5°) is √(2 - √2)/2.
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A two-column proof
O uses a visual representation of the logical flow of steps needed to reach a conclusion
o contains a table with a logical series of statements and reasons that reach a conclusion
O contains a set of sentences explaining the steps needed to reach a conclusion,
O uses inductive reasoning to prove a statement.
Answers
Answer:
B contains a table with a logical series of statements and reasons that reach a conclusion.
Step-by-step explanation:
A two-column proof
uses a visual representation of the logical flow of steps needed to reach a conclusion.
contains a table with a logical series of statements and reasons that reach a conclusion.
contains a set of sentences explaining the steps needed to reach a conclusion.
uses inductive reasoning to prove a statement.
The area of a rectangle is 17 1/2 in and it’s shorter side is 3 1/2in.draw a diagram that shows this information. What is the length of the longer side
Answers
Answer: 5
Step-by-step explanation:
17 1/2 is equal to 17.5
3 1/2 is equal to 3.5
Since 17.5 is the area, you must divide by 3.5, which equals 5
To find the length of the longer side of a rectangle with an area of 17 1/2 square inches and a shorter side of 3 1/2 inches, divide the area by the width to get the length. The length of the longer side is 5 inches.
Explanation:The question is asking how to find the length of the longer side of a rectangle given that the area of the rectangle is 17 1/2 square inches and one of the shorter sides is 3 1/2 inches. To find the length of the other side, which we will call length, use the formula for the area of a rectangle which is area = length × width. Since the area and width (shorter side) are known, the equation can be set up as follows:
17 1/2 = length × 3 1/2To find the length, divide the area by the width:Length = (17 1/2) / (3 1/2)Convert mixed numbers to improper fractions:Length = (35/2) / (7/2)Multiply by the reciprocal of the divisor:Length = (35/2) × (2/7)Simplify the fractions:Length = 5Therefore, the length of the longer side of the rectangle is 5 inches.
Convert the decimal to a fraction.
0.6 repeating
Answers
Round 9.3959 to the nearest hundredth
Answers
Answer:
The answer is 9.396
Step-by-step explanation:
Which of the following inequalities could be the result of the first step in solving the inequality
3(x – 4) < 8x + 13 for x?
AX-45 x+13
B x-458x+10
(C3x – 4 5 8x+13
D
3x – 12 5 8x + 13
Answers
In the inequality 3(x – 4) < 8x + 13, the first step is to distribute the 3 on the left-hand side. That results in the inequality 3x – 12 < 8x + 13. Therefore, the correct answer from the options given is (D) 3x – 12 < 5 8x + 13.
Explanation:The question is asking for the inequality that could result after the first step when solving the given inequality 3(x – 4) < 8x + 13. The first step involves distributing the multiplication on the left side of the inequality. Therefore, 3 multiplied by x gives 3x and 3 multiplied by -4 gives -12. This leads to the inequality 3x – 12 < 8x + 13.
So, the correct answer from the options given is:
(D) 3x – 12 < 5 8x + 13.
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if the circumference of one of the world's largest pizzas is 215 feet, what is its radius? Use 3.14 to approximate pi. Round to the nearest tenth.
Answers
Answer: 34.2
Step-by-step explanation:
What is the simplified expression for 6 (2 (y + x))?
6 y + 12 x
12 y + 12 x
12 y + 8 x
8 y + 8 x
Answers
Step-by-step explanation:
6(2(y+x))=6(2x+2y)=12x+12y
Answer:
12y + 12x
Step-by-step explanation:
You're welcome.
(2,-1)
Is one of many solutions to the inequality:
X - 3y<1
True or false?
Answers
Answer:
False
Step-by-step explanation:
lets find out..
x - 3y < 1.....check (2,-1)....x = 2 and y = -1
now we sub
2 - 3(-1) < 1
2 + 3 < 1
5 < 1.......so is 5 less then 1 ? NO, it is not...so (2,-1) IS NOT a solution
Answer:false
Step-by-step explanation:
Which of the following lengths cannot be the lengths of the sides of a triangle?
A. 4,6,9
B. 3,4,2
C. 2,2,3
D. 1, 1, 2
Answers
Jenna and Callie collect stamps. Jenna has 20 less than twice the number of stamps that Callie has. Write an expression that represents the number of stamps that Jenna has.
Answers
The expression that represents the number of stamps that Jenna has is 2x - 20
Step-by-step explanation:
Let us revise some algebraic expressions
a is 5 more than b ⇒ a = b + 5a is 3 less than b ⇒ a = b - 3a is twice b ⇒ a = 2 bThe sum of a and b ⇒ a + bThe difference of a and b ⇒ a - bThe quotient of a and b ⇒ a ÷ bThe product of a and b ⇒ a × b∵ Jenna and Callie collect stamps
∵ Jenna has 20 less than twice the number of stamps that Callie has
- Assume that Callie has x stamps, that means to find the number
of stamps of Jenna multiply x by 2 and subtract 20 from the product
∵ Callie has x stamps
∵ Twice means × 2
∴ Jenna has = 2(x) - 20
∴ Jenna has = 2x - 20
The expression that represents the number of stamps that Jenna has is 2x - 20
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Identify the property and equation that satisfies the following statement: The solution of an equation is x = –2. Addition Property of Equality; x + 6 = 8 Substitution Property of Equality; x + 8 = 6 Division Property of Equality; x + 8 = 6 Subtraction Property of Equality; x + 6 = 8
Answers
Answer: identity is subtraction property of equality equation is x + 8 = 6
Substitution Property of Equality; x + 8 = 6
Take the equation x + 8 = 6. subtract 8 from both sides using the subtraction property of equality x + 8 - 8 = 6 - 8 simplify x + 0 = -2 x = -2
The Addition Property of Equality and the equation x + 6 = 8 are the property and equation that satisfy the statement 'The solution of an equation is x = –2'. This is because when you subtract 6 from both sides of the equation, x equals -2.
Explanation:To find the property and equation that fits the statement 'The solution of an equation is x = –2', we need to understand the basic properties of equality and apply those in this context.
Following the statement, it seems that the Addition Property of Equality fits the best here. The Addition Property of Equality states that when we add the same number to both sides of an equation, the equation remains balanced and the solution is the same. Now, if we think of an equation 'x + 6 = 8', and solve it using the Addition Property by subtracting 6 from both sides, we get the solution x = -2.
That means the property that satisfies the statement is Addition Property of Equality and the equation that satisfies the statement is x + 6 = 8.
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what is StartFraction one-half EndFraction x is less than or equal to 18.x ≤ 18
Answers
Answer:
[tex]x\leq 36[/tex]
The solution for [tex]x[/tex] is all real numbers less that or equal to 36.
Step-by-step explanation:
Given expression:
[tex]\frac{1}{2}x\leq18[/tex]
To find the solution for [tex]x[/tex]
Solution:
In order to solve for [tex]x[/tex] , we will make sure to isolate the unknown variable [tex]x[/tex] on left side alone by doing math operations on both sides of the inequality.
We have:
[tex]\frac{1}{2}x\leq18[/tex]
Multiplying both sides by 2.
[tex]2.\frac{1}{2}x\leq18\times 2[/tex]
The 2 on left side will cancel each other leaving [tex]x[/tex] alone.
Thus, we have:
[tex]x\leq 36[/tex]
Thus, solution for [tex]x[/tex] is all real numbers less that or equal to 36.
Answer:
D
Step-by-step explanation:
For which equation is y=7 a solution
A)7y= 1
B)y - 26= -19
C)y + 7 = 0
D) y/2 = 7
Answers
Find the distance between the points with the given coordinates (-4, 9) and (1, -3).
Answers
Answer: 13
Step-by-step explanation:
The formula for finding distance between two points is given by :
D = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
[tex]x_{1}[/tex] = -4
[tex]x_{2}[/tex] = 1
[tex]y_{1}[/tex] = 9
[tex]y_{2}[/tex] = -3
Substituting the values into the formula , we have :
D = [tex]\sqrt{(1 -(-4))^{2} +(-3-9)^{2}}[/tex]
D = [tex]\sqrt{(5)^{2}+(-12)^{2}}[/tex]
D = [tex]\sqrt{25+144}[/tex]
D = [tex]\sqrt{169}[/tex]
D = 13
Therefore : the distance between the points is 13
what is x-13+2x+1=180
Answers
Answer:
64
Step-by-step explanation:
x-13+2x+1=180
3x-13+1=180
3x-12=180
3x=180+12
3x=192
x=192/3
x=64
Answer:
X=83
Step-by-step explanation:
UH TOO LAZY TO EXPLAIN. lol
Use the formula d=rt to find the average speed of a car if the car traveled 320 miles in 8 hours.
Answers
Answer:
320 miles = (8 hours)(r)
r = 40 mph
If h(x) = 6 - X, what is the value of (h*h)(10)?
Answers
The value of [tex]\bold{ h(h(10))=10}[/tex]
Solution:
Given: [tex]h(x) = 6 - x[/tex]
To find: The value of (h*h)(10)
We know that, [tex](h*h)(x)=h(h(x))[/tex]
which is,
[tex]\Rightarrow h(h(x))=6-(6-x)=x[/tex]
On solving we get,
[tex]\Rightarrow6-6+x=x[/tex]
So, for x = 10 it will be,
[tex]h(h(10))=10[/tex]
Hence, the required value is 10.
35 POINTS!!!! PLEASE HELP! (2.01)A polygon is shown on the graph: A polygon is shown on a coordinate plane. Vertex A is at 1 comma 5, vertex B is at 0 comma 1, vertex C is at 6 comma 1, and Vertex D is at 5 comma 5. If the polygon is translated 2 units down and 4 units left, what will the coordinates of the new image be? Use prime notation in expressing the new coordinates.
Answers
Answer:
A’ is (3,-3)
B’ is (-1,-4)
C’ is (-1,2)
D’ is (3,1)
Step-by-step explanation:
the other person gto one wrong this is what it should be
have a good day hope this helped
I have a pic to show you
79 percent of 145 is what?