Find the measure of the missing angles

A) The distance that a force of 3 newtons would stretch the rubber band is; 0.015 m

B) The amount of work it takes to stretch the rubber band this far is; 0.0225 J

From Hookes's law, as long as the elastic limit is not exceeded the extension is directly proportional to the force applied.

F = Ke

Where;

F = force

K = force constant

e = extension

Thus,  for a restoring force of magnitude 2 newtons ;

2 N = K(1 × 10⁻²) m

K = 2 N /(1 × 10⁻²) m

K = 200 N/m

a) For a force of 3 newtons, we have;

3N = 200 N/m × a

Where a is the extension in meters

a = 3N/200 N/m

a = 0.015 m

b) The formula to find the work done is;

P.E = ¹/₂Ke²

P.E = ¹/₂ * 200 * 0.015²

P.E = 0.0225 J

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Answer:

5.3%

Step-by-step explanation:

% Increase = Increase / Original Number × 100.

68/1283 * 100

= 5.3%

Answer:

2.23606798 i

or sqrt(-5)

Step-by-step explanation:

Answer:

Zoe is not correct because equilateral triangles are acute triangles with three sides of equal length. Acute triangles can sometimes be equilateral triangles.

Step-by-step explanation:

Answer:

Coplanar is when all 3 points are on the same plane

Noncoplanar is when they are not

For ex:

Coplanar->

.x, .z, and .s are all on the plane R

Noncoplanar->

.x, and .z are on plane R

.s is on plane Y

Answer:

1600

Step-by-step explanation:

20 x 40 = 800 Per week or 1600 for 2 weeks.

Answer:

I hope this helps.

Step-by-step explanation:

Answer: C

Step-by-step explanation:

The rest of the quadrilaterals provided have 2 pairs of parallel lines.

The choice is:

Explanation:

The quadrilateral that has exactly one pair of parallel lines is called a trapezoid.

Here's what a trapezoid looks like :

\(\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\linethickness{0.3mm}\qbezier(0,0)(0,0)(1,3)\qbezier(5,0)(5,0)(4,3)\qbezier(1,3)(1,3)(4,3)\qbezier(3,0)(8.2,0)(0,0)\put(-0.5,-0.3){$\sf A$}\put(5.3,-0.3){$\sf B$}\put(4.2,3.1){$\sf C$}\put(0.6,3.1){$\sf D$}\end{picture}\)

Answer:

(A)

Step-by-step explanation:

That rule isn't used in the elimination methods for systems of equations, but, rather, it is used in substitution methods. The other rules are used in elimination.

Please tell me if I got it wrong.  I really hope it is correct.

A. Add the left side of equation 2 to the left side of equation 1.

B. Multiply equation 2 by 3. Then subtract the result from equation 1.

C. Add equation 2 to equation 1.

Answer:

An integer is any positive whole number or its opposite. Here, opposite means sign. So a positive integer has a negative opposite and vice versa

Step-by-step explanation:

-5 and 5 are an example.

Answer:

true

Step-by-step explanation:

Answer:

3x+8

Step-by-step explanation:

PEMDAS

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

2(x +6)-4 +x

2x+12 (distributive property)

2x+12-4+x

3x+8

Hope this helps :)

Answer:

3x+12

Step-by-step explanation:

Follow the PEMDAS/GEMDAS order. First, distribute the 2 to the numbers in the parenthesis:

2(x+6)-4+x

      ↓

2x+16-4+x

Then, subtract the numbers without a variable (the numbers without x):

2x+16-4+x

      ↓

 2x+12+x

Then, add the variables together (the numbers with x):

2x+12+x

     ↓

 3x+12

Hope this is the answer you need.

Answer:

C

Step-by-step explanation:

The answer you selected is correct

The y-intercept should be (0, -2)

The slope should be 1

Answer:

bbbdbrhrhfhdbfhfhchchfhffh

Huda's error in evaluating (3) squared incorrectly led to the incorrect final result.

The correct answer should be -20, not 34.

Huda's error was that she evaluated (3) squared incorrectly.

Instead of calculating 3 squared as 9, she mistakenly considered it as 3. This error led to incorrect subsequent calculations and the final result of 34, which is not the correct answer.

To evaluate the expression correctly, let's go through the steps:

Negative 3 (8 minus 5) squared minus (negative 7) \(= -3(3)^2 - (-7)\)

First, we simplify the expression within the parentheses:

\(-3(3)^2 - (-7) = -3(9) - (-7)\)

Next, we evaluate the exponent:

-3(9) - (-7) = -3(9) + 7

Now, we perform the multiplication and addition/subtraction:

-3(9) + 7 = -27 + 7 = -20

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Answer:

120

Step-by-step explanation:

Answer: 120

Hope that helped!(:

The unknown angle in the cyclic quadrilateral is as follows:

m∠CML = 109 degrees

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle.

The sum of angles in a cyclic quadrilateral is 360 degrees.

Therefore, let's find m∠CML as follows:

Using the arc angle and opposite angle of a quadrilateral theorem,

6x + 25 = 1 / 2 (7x + 14 + 106)

6x + 25 = 1 / 2(7x + 120)

6x + 25 = 7 / 2 x + 60

6x - 7 / 2 x  = 60 - 25

6x - 3.5x = 35

2.5x = 35

divide both sides by 2.5

x = 35 / 2.5

x = 14

Therefore,

m∠CML = 6x + 25 = 6(14) + 25 = 84 + 25 = 109 degrees

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The required perimeter of the triangle with vertices (-9,-6), (-5, 0), and (10,-7) is 42.72 units.

The distance between two points (x₁, y₁) and (x₂, y₂) in the plane can be found using the distance formula,

d = √((x₂- x₁² + (y₂ - y₁)²)

Here

Using the above formula, we can find the length of each side of the triangle:

Length of the first side:

d = √((-5 - (-9))² + (0 - (-6))²)
   = √(4² + 6²)
   = √52 = 7.2

Similarly, the length of the second and third sides:

d =√274 = 16.5

Length of the third side:

d =  √362 = 19.02

Finally, the perimeter of the triangle is the sum of the lengths of its sides, P = 7.2 + 16.5 + 19.02
P = 42.72 units

So, the perimeter of the triangle is approximately 42.72 units.

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Answer:

The  equation is  \(x^2 + y^2 +z^2 + 14 x + 3y \ + 14z + 86.25=0\)

Step-by-step explanation:

From the question we are told that  

    The  diameter endpoints is   (-8, -3, -10) and (-6, 1, -4)

Generally the equation of a sphere with center coordinates (a, b , c ) and  radius  r   is mathematically represented as

           \((x - a )^2 + (y -b )^2 + (z -c)^2 = r^2\)

Now since we are given the endpoints of the diameter then we can obtain the center coordinates as follows

         \((a, b , c) = [ \frac{ -8 +(-6)}{2} , \frac{-3 + (1)}{ 2} , \frac{ -10 + (-4)}{2} ]\)

         \((a, b , c) = [ -7 , -1.5 , -7 ]\)

Now the length of the diameter is evaluated as

    \(|d| = \sqrt{ (-8 - (-6 ))^2 + ( -3 - (1) )^2 + ( -10 - (-4))^2 }\)

   \(|d| = \sqrt{56 }\)

   \(|d| = \sqrt{4 * 14 }\)

   \(|d| = 2 \sqrt{ 14 }\)

Now the radius is mathematically represented as

    \(r = \frac{|d|}{2}\)

    \(r = \frac{ 2 \sqrt{14} }{2}\)

    \(r = \sqrt{14}\)

So

   \((x - -7 )^2 + (y --1.5 )^2 + (z --7)^2 = ( \sqrt{14} )^2\)

   \((x +7 )^2 + (y +1.5 )^2 + (z +7)^2 = 14\)

    \(x^2 + 14 x + 49 + y^2 + 3y + 2.25 +z^2 14z + 49 = 14\)

    \(x^2 + y^2 +z^2 + 14 x + 3y \ + 14z + 86.25=0\)

Answer:

Step-by-step explanation:

Nathan invented a robotic bug when can crawl 6cm in 24 secs

so, to crawl 1cm it would take (24÷6) secs, i.e, 4secs

therefore, to crawl 42cm the bug would take (42×4) secs = 168 secs

So, to crawl forty-two centimeters the bug would take 168 secs or, 1min 48 secs.

The solution of x in the inequality is x > 2

The inequality is given as:

5x + one third(3x + 6) > 14

Rewrite properly as:

5x + 1/3(3x + 6) > 14

Open the brackets

5x + x + 2 > 14

Subtract 2 from both sides of the inequality

5x + x + 2 - 2> 14 - 2

Evaluate the difference

5x + x > 12

Evaluate the like terms

6x > 12

Divide both sides of the inequality by 2

x > 2

Hence, the solution of x in the inequality is x > 2

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Answer:

x > 2, like the other guy said

Step-by-step explanation:

I hope this helps

Answer:

3x²–2x+1=0

3x²+x–3x+1=0

(3x²+x)-(3x+1)=0

x(3x+1)-1(3x+1)=0

either (x-1) (3x+1)=0

x=1 or x=-⅓

Answer:

130° and 310°

Step-by-step explanation:

the bearing of A from B is the measure of the clockwise angle from a north line at B to A

the angle at B and A are same- side interior angles and sum to 180°

angle at B = 180° - 50° = 130°

the bearing of A from B is then 130°

the bearing of B from A is the measure of the clockwise angle from the north line at A to B

the complete angle about A = 360° then clockwise angle from north line at A to B is

360° - 50° = 310°

the bearing of B from A is 310°

There is no unique output for the manufacturing sector that can satisfy the given final demand for transportation and manufacturing.

To determine the output for the manufacturing sector, we can set up a system of equations based on the given information. Let's denote the output for the transportation sector as T and the output for the manufacturing sector as M.

From the given information, we know that:

- Production of a dollar's worth of transportation requires an input of $0.20 from transportation and $0.15 from manufacturing.

- Production of a dollar's worth of manufacturing requires an input of $0.40 from transportation and $0.30 from manufacturing.

Using these statements, we can set up the following equations:

0.20T + 0.15M = $60 million (equation 1)

0.40T + 0.30M = $80 million (equation 2)

We can solve this system of equations to find the values of T and M

Multiplying equation 1 by 2, we have:

0.40T + 0.30M = $120 million (equation 3)

Now, subtracting equation 2 from equation 3, we get:

(0.40T + 0.30M) - (0.40T + 0.30M) = $120 million - $80 million

This simplifies to:

0 = $40 million

This means that the left-hand side of the equation is zero, and there is no valid solution that satisfies both equations simultaneously.

Therefore, there is no unique output for the manufacturing sector that can satisfy the given final demand for transportation and manufacturing. The given information seems to be inconsistent or incomplete.

It's important to note that the problem could be resolved by providing additional information or correcting any errors in the given data. Without further clarification, it is not possible to determine the output for the manufacturing sector.

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The missing coordinates of given vectors a, b, c, d, and e are 0,0,0, -0.8, and 0. Then, the vectors are \(\vec{u}=\left[\begin{array}{ccc}-0.6\\0.8\\0\end{array}\right]\), \(\vec{v}=\left[\begin{array}{ccc}0\\0\\1\end{array}\right]\), and \(\vec{w}=\left[\begin{array}{ccc}-0.8\\-0.6\\0\end{array}\right]\)

We refer to two vectors as being orthogonal if they are perpendicular to one another. So these vectors' dot product will be zero. Let the given three vectors be \(\vec{u}\), \(\vec{v}\), and \(\vec{w}\). And the unknowns be a, b, c, d, and e.

Then, the vectors are written as

\(\vec{u}=\left[\begin{array}{ccc}-0.6\\0.8\\a\end{array}\right]\), \(\vec{v}=\left[\begin{array}{ccc}b\\c\\1\end{array}\right]\), and \(\vec{w}=\left[\begin{array}{ccc}d\\-0.6\\e\end{array}\right]\)

First, take \(\vec{u}\) and consider unit length, we get,

\(1=\sqrt{(-0.6)^2+(0.8)^2+a^2}\\1=1+a^2\\a=0\)

For \(\vec{v}\), we get,

\(1=\sqrt{(b)^2+(c)^2+1^2}\\1=1+b^2+c^2\\b=0\;\text{and}\;c=0\)

We know that \(\vec{w}\) is orthogonal to both vectors, then,\(\vect{w}\cdot{\vec{v}=0\). Substituting, the values of \(\vec{v}\) and \(\vec{w}\), we get,

\(\begin{aligned}\langle d, -0.6, e\rangle \;\cdot\;\langle 0, 0, 1\rangle&=0\\e&=0\end{aligned}\)

Also, \(\vect{u}\cdot{\vec{w}=0\),  Substituting, the values of \(\vec{u}\) and \(\vec{w}\), we get,

\(\begin{aligned}\langle -0.6, 0.8, 0\rangle \;\cdot\;\langle d, -0.6, e\rangle&=0\\-0.6d-0.48+0&=0\\-0.6d&=0.48\\d&=-0.8\end{aligned}\)

Therefore, the required answers for a, b, c, d, and e are 0,0,0, -0.8, and 0.

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There were approximately 6056 no votes.

Let's assume the number of yes votes is represented by the variable "5x," where x is a positive constant.

Similarly, the number of no votes can be represented by "8x" since the ratio of yes votes to no votes is 5 to 8.

The total number of votes is given as 9854, so we can set up the following equation:

\(5x + 8x = 9854\)

Combining like terms, we have:

\(13x = 9854\)

To solve for x, we divide both sides of the equation by 13:

\(x = \frac{9854 }{13}\)

\(x \approx 757.23\)

Since x represents a positive constant, we round it to the nearest whole number, giving us x = 757.

Now, we can find the number of no votes by multiplying x by the ratio of no votes:

No votes \(= 8x\)

\(= 8 \times 757\)

\(= 6056\)

Therefore, there were approximately 6056 no votes.

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Answer:

x =28

Step-by-step explanation:

Divide the numbers

Combine multiplied terms into a single fraction

Eliminate fraction denominators

Simplify

Divide both sides of the equation by the same term

Answer:

1.99%. (2% rounded)

Step-by-step explanation:

The total number of ways to select 4 children out of 40 is given by the combination formula:

C(40,4) = 40! / (4! * (40-4)!) = 91,390

The number of ways to select 4 girls out of 16 is given by the combination formula as well:

C(16,4) = 16! / (4! * (16-4)!) = 1,820

Therefore, the probability of selecting 4 girls out of the group of 40 children is:

P(4 girls) = C(16,4) / C(40,4) = 1,820 / 91,390 ≈ 0.0199 or 1.99%

So the probability that all 4 helpers will be girls is approximately 1.99%

Hope this helps!.

Answer:

From an email exchange with Professor Stewart:"It’s actually a fairly simple equation, mathematically speaking. What caused trouble was the complexity of the system the mathematics was intended to model.... You don’t really need to be a rocket scientist to understand that lending hundreds of billions of dollars to people who have no prospect of ever paying it back is not a great idea...."People took a theoretical equation too seriously, overreached its assumptions, used it to justify poor decisions, and built a trillion dollar house of cards on it. This made the crisis inevitable:"I think that the crisis became inevitable once the financial instruments being traded in gigantic quantities became so complex that no one could understand either their value or the risks they entailed. When markets trade real goods for real money, excesses can only grow to the limits of what is actually out there. When they trade virtual goods (derivatives) for virtual money (leverage), there’s no real-world limit, so the markets can gallop off into Cloud Cuckoo 

Step-by-step explanation:

Physicist: If you have plenty of chalkboard space and absolutely nothing better to do, you can write down numbers, letters (Greek if you’re δυσάρεστος), and mathematical operators and eventually you’ll have the longest equation ever written down.  So if you really want to see the most complicated equation ever, call in sick for a few weeks.  A better question might be “what is the most (but not needlessly) complicated equation?”.There are plenty of equations that are infinitely long, but often they’re simple enough that we can write them compactly.  For example,   This equation goes on forever, but it’s fairly straight forward: every term you flip the sign and increase the denominator from one odd number to the next.  You can write it in mathspeak as .  Like π itself, this sum goes on forever, but it isn’t complicated.  You can describe it simply and in such a way that anyone (with sufficient time and chalk) can find as many digits of π as they like.  This is the basic idea behind “Kolmogorov Complexity“; the length of the shortest possible set of written instructions that can produce a given result (never mind how long it takes to actually compute it).If you’re looking for an equation that needs to be complicated, a good place to look is physics (I mean, what else do you really need math for?).  If you want to describe the behavior of a ball flying through the air it’s not enough to say “it goes up then down”; there’s a minimum amount of math that goes into accurately calculating the path of falling objects, and it’s more complicated than that.Arguably, the universe is pretty complicated.  But like π, it is deceptively so (we hope).  If you want to do something like, say, describe the gravitational interactions of every star in the galaxy, you’d do it by numbering the stars (take your time: star 1, star 2, …, star n), determine the position and mass of each,  and , and then find the force on each star produced by all the others.  In practice this is absurd (there are a few hundred billion stars in the Milky Way, but we can’t see most of them because there’s a galaxy in the way), but the equation you would use is pretty straight forward.  The force on star k is: .  This is just Newton’s law of gravitation, , repeated for every possible pair of stars and added up.  So while the situation itself is complicated, the equation describing it isn’t.  Evidently, if you want an equation that genuinely needs to be complicated, you don’t need a complicated situation, you need complicated dynamics.

If is confusing than I can use a different example:)

Answer:

82

Step-by-step explanation:

205/5=41 jumps per minute

41*2= 82 jumping jacks

hope this helps :))

Answer:

1.75x?

Step-by-step explanation:

I'm not sure if it has to be multiple numbers