calculate the difference quotients and approximate the slope of the tangent line

Answer:

l = 4a and b = 3a

Step-by-step explanation:

Given that,

The area of the rectangle, A = 12a²

Perimeter, P = 14a

The area and perimeter of a rectangle are given by :

A = lb

12a² = lb ....(1)

P = 2(l+b)

14a = 2(l+b) ....(2)

We need to solve equations (1) and (2). After solving we find that.

l = 4a and b = 3a

Hence, the dimensions of this rectangle are 4a and 3a.

Let k = 1, for a start. By definition of the Laplace transform,

\(\displaystyle F(s) = \int_0^\infty f(t) e^{-st} \, dt\)

Differentiate both sides with respect to s :

\(\displaystyle F'(s) = \frac{d}{ds} \int_0^\infty f(t) e^{-st} \, dt\)

\(\displaystyle F'(s) = \int_0^\infty \frac{\partial}{\partial s}  \left[f(t) e^{-st}\right] \, dt\)

\(\displaystyle F'(s) = \int_0^\infty -t f(t) e^{-st} \, dt\)

so that \(t f(t) \leftrightarrow (-1)^1 F^{(1)}(s) = -F'(s)\) is indeed true.

Suppose the claim is true for arbitrary integer k = n, which is to say that \(t^n f(t) \leftrightarrow (-1)^n F^{(n)}(s)\). Then if k = n + 1, we have

\(F^{(n+1)}(s) = \dfrac{d}{ds} F^{(n)}(s)\)

Consider the two cases:

• If k = n + 1 is even, then n is odd, so

\((-1)^n F^{(n)}(s) = -F^{(n)}(s) \leftrightarrow t^n f(t)\)

and it follows that

\(F^{(n+1)}(s) = \displaystyle \frac{d}{ds} \left[-\int_0^\infty t^n f(t) e^{-st} \, dt \right]\)

\(F^{(n+1)}(s) = \displaystyle -\int_0^\infty \frac{\partial}{\partial s}\left[ t^n f(t) e^{-st} \right] \, dt\)

\(F^{(n+1)}(s) = \displaystyle \frac{d}{ds} \left[-\int_0^\infty t^n f(t) e^{-st} \, dt \right]\)

\(F^{(n+1)}(s) = \displaystyle \int_0^\infty t^{n+1} f(t) e^{-st} \, dt\)

\(\implies F^{(n+1)}(s) = (-1)^{n+1} F^{(n+1)}(s) \leftrightarrow t^{n+1}f(t)\)

• Otherwise, if k = n + 1 is odd, then n is even, so

\((-1)^n F^{(n)}(s) = F^{(n)}(s) \leftrightarrow t^n f(t)\)

The rest of the proof is the same as the previous case.

So we've proved the claim by induction:

• \(t f(t) \leftrightarrow -F(s)\), and

• \(\bigg(t^n f(t) \leftrightarrow (-1)^n F^{(n)}(s)\bigg) \implies \bigg(t^{n+1} f(t) \leftrightarrow (-1)^{n+1} F^{(n+1)}(s)\bigg)\)

Answer:

Part A- The 1st box is 96 and the second box is 10.

PartB-

Part C-

Step-by-step explanation:

5x12=60

6x12=72

8x12=96

10x12=120

So the 1st box is 96 and the second box is 10.

5     $50

6     $60

8     $80

I know this because Harry receives $10 per hour so you have to multiply the number of hours by $10.

If Harry babysits for 5 hours, he would receive $60 but if he does yard work for 5 hours, he would receive $50. Harry would receive $10 more by babysitting than by doing yard work.

Hoped this helped.

The perimeter of the rectangle created by the given points (-4, 4), (3, 4), (-4, -3), and (3, -3) is 28 units. The length of each side is calculated, and the sum of all four sides gives the perimeter. Option D.

To find the perimeter of the rectangle created by the given points, we need to calculate the sum of the lengths of all four sides.

Let's calculate the length of each side:

Side 1: The distance between (-4, 4) and (3, 4) along the x-axis is 3 - (-4) = 7 units.

Side 2: The distance between (-4, 4) and (-4, -3) along the y-axis is 4 - (-3) = 7 units.

Side 3: The distance between (-4, -3) and (3, -3) along the x-axis is 3 - (-4) = 7 units.

Side 4: The distance between (3, -3) and (3, 4) along the y-axis is 4 - (-3) = 7 units.

Now, let's sum up the lengths of all four sides:

Perimeter = Side 1 + Side 2 + Side 3 + Side 4

Perimeter = 7 + 7 + 7 + 7

Perimeter = 28 units

Therefore, the perimeter of the rectangle created by the given points is 28 units. Option D is correct.

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Answer:

$33

Step-by-step explanation:

Let the amount of money Corey has be $x.

Amount of money Bryce have= $(x +16)

Total amount= $50

$x +$(x +16)= $50

2x +16= 50

2x= 50 -16

2x= 34

Divide both sides by 2:

x= 34 ÷2

x= 17

Amount of money Bryce have

= $(17 +16)

= $33

Problem 1

Answer: Yes a triangle can be formed with side lengths 5,5,3

--------------------

Explanation:

Take any two sides and add them up. If we get a sum larger than the third side, then a triangle is possible. This is the triangle inequality theorem.

5+5 = 10 is larger than 3

5+3 = 8 is larger than 5

This shows a triangle is possible. The triangle is isosceles because two sides are the same length.

==========================================================

Problem 2

Answer: Yes a triangle can be formed with side lengths 8,8,8

--------------------

Explanation:

This triangle is equilateral because all sides are the same length.

Take any two sides, add them up, and you'll find the sum is larger than the third side.

==========================================================

Problem 3

Answer: No a triangle cannot be formed with sides 7,8,15

--------------------

Explanation:

Yes it is true that

8+15 = 23 is larger than 7

7+15 = 22 is larger than 8

but

7+8 = 15 is not larger than 15

So this means a triangle is not possible.

Imagine you had 3 strips of paper that were 7 inches, 8 inches and 15 inches long. The 7 and 8 inch strips add to 15 inches, but those two smaller strips only form a straight line. We cannot pull them so a triangle forms. If we did, then the third side would be smaller than 15 inches. This is one way to get hands on to see why the triangle inequality theorem works.

==========================================================

Problem 4

Answer: Yes a triangle is possible with side lengths 5,6,10

--------------------

Explanation:

Same idea as before. We can take any two sides, add them, and get a sum larger than the third side. A triangle is possible.

9514 1404 393

Answer:

  x = ab/c

Step-by-step explanation:

The applicable theorem tells you the product of chord lengths is the same for the two crossing chords:

  ab = cx

  x = ab/c . . . . . divide by the coefficient of x

The axiom of regularity is a set theory principle which states that every non-empty set C contains an element that is disjoint from C.

The set theory concept rules that for every non-empty set C there is an element x of C such that x does not intersect C. The regularity axiom aims to establish that no non-empty set will have itself as an element.

The principle which is also called the axiom of foundation is a fundamental concept in set theory and credited to Zermelo–Fraenkel.

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Answer:

Hunter has 58 week until he have enough money for camp

Answer:

58 weeks

Step-by-step explanation:

Well, since he already has $90:

960 - 90 = 870.

So, now he has to save up to $870.

870 divided by 15= 58

So, Hunter has 58 weeks until he has enough money for camp.

Answer:

b

Step-by-step explanation:

Answer:

y=3x-36

Step-by-step explanation:

slope must be negative reciprocal

-1/3 changes to +3

then use point slope form with new points TO FIND NEW Y INTERCEPT

y=MX+B

0=3(12) + b

b= -36

new problem is y= 3x-36

Answer:

374

Step-by-step explanation:

L × W

22 × 17

374

The answer would be 374 due to the formula to find the perimeter of a rectangle, which is Length × Width.

Answer:

-5/12

Step-by-step explanation:

Answer: 3 1/12

Step-by-step explanation: First We Would Do 2 1/2 + -7/6 First. We Would Get 1 1/3 Because We Change The Mixed Fractions Into Improper Fractions. So We Would Do 5/2 + - 7/6. We Would Then Find A Common Denominator Which Would Be 12. So 7/6 Would Be 14/12 & 5/2 Would Be 30/12. If You Did The Math Correctly You Would Get 1 1/3. Now 1 1/3 - 1 3/4 Would Be 3 1/12. You Would Change The Fractions To Improper Fractions And Then Subtract. You Would Also Need To Find The Common Denominator Which Is 12.

Hoped This Helped!

Answer:

x = 90

Step-by-step explanation:

The given diagram shows a circle with intersecting chords, KM and JL.

To find the value of x, we can use the Angles of Intersecting Chords Theorem.

According to the Angles of Intersecting Chords Theorem, if two chords intersect within a circle, the angle formed at the intersection point is equal to half the sum of the measures of the arcs intercepted by the angle and its corresponding vertical angle.

Let the point of intersection of chords KM and JL be point P.

As the chords are straight lines, angle x° forms a linear pair with angle JPM.

Note: We cannot use the Angles of Intersecting Chords Theorem to find the value of x directly, since we have not been given the measures of the arcs KJ and ML. Therefore, we need to use the theorem to find m∠JPM first.

From inspection of the given diagram:

Using the Angles of Intersecting Chords Theorem, we can calculate the measure of angle JPM (shown in orange on the attached diagram):

\(\begin{aligned}m \angle JPM &=\dfrac{1}{2}\left(m\overset\frown{JM}+m\overset\frown{LK}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+(2x-30)^{\circ}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+2x^{\circ}-30^{\circ}\right)\\\\&=\dfrac{1}{2}\left(2x^{\circ}\right)\\\\&=x^{\circ}\end{aligned}\)

As angle JPM forms a linear pair with angle x°, the sum of the two angles equals 180°:

\(\begin{aligned}m \angle JPM+x^{\circ}&=180^{\circ}\\\\x^{\circ}+x^{\circ}&=180^{\circ}\\\\2x^{\circ}&=180^{\circ}\\\\\dfrac{2x^{\circ}}{2}&=\dfrac{180^{\circ}}{2}\\\\x^{\circ}&=90^{\circ}\\\\x&=90\end{aligned}\)

Therefore, the value of x is 90, which means that the two chords intersect at right angles.

The area of the circle created by the paint is given by the expression 4πt².

The area of the circle is 100π, which is approximately 314.16 in².

The circle will be at least 300 in² in 5 minutes. Yes.

To find the area of the canvas, we multiply the lengths of its sides:

Area = (3x + 5) × (2x + 1)

Expanding the expression:

Area = 6x² + 3x + 10x + 5

Combining like terms:

Area = 6x² + 13x + 5

The area of the canvas is given by the expression 6x² + 13x + 5.

Now, let's find the area of the circle created by the paint.

The area of a circle is given by the formula A = πr², where r represents the radius.

The radius is given by the spreading of paint, which is r(t) = 2t.

Substituting the value of r(t) into the formula, we have:

A[r(t)] = π(2t)²

Simplifying:

A[r(t)] = π(4t²)

A[r(t)] = 4πt²

Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.

Substitute t = 5 into the area formula:

A[r(5)] = 4π(5)²

A[r(5)] = 4π(25)

A[r(5)] = 100π

Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.

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Answer:

The number of parents spend their kids birthday parties

'n' = 1667

Step-by-step explanation:

Explanation:-

Given standard deviation of the Population = 62.5

Given the estimate error = 3 dollars

Level of significance =0.05

Z₀.₀₅ = 1.96

The margin of error defined by

\(M.E = \frac{Z_{0.05} S.D}{\sqrt{n} } \\3 = \frac{1.96 X 62.5}{\sqrt{n} }\)

cross multiplication , we get

3√n = 1.96 X 62.5

 √n = 40.833

Squaring on both sides, we get

n = 1667.34



The number of samples are 'n' = 1667

The values of the coordinates x and y is P ( 6 , 3 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( x , y )

Let the second point be Q ( 0 , 0 )

Now , the slope of the line is m₁ = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₁ = y / x

m₁ = 1/2

So , y/x = 1/2

And , x = 2y

Now , the third point is R ( 7 , 5 )

m₂ = ( 5 - y ) / ( 7 - x )

m₂ = 2

On simplifying , we get

( 5 - y ) / ( 7 - x ) = 2

Multiply by ( 7 - x ) , we get

5 - y = 14 - 2x

Adding 2x and subtracting 5 on both sides , we get

2x - y = 9

Substitute the value of x from m₁ , we get

2 ( 2y ) - y = 0

3y = 9

Divide by 3 on both sides , we get

y = 3

And , the value of x = 6

Hence , the coordinate of the point P is P ( 6 , 3 )

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Thanh's cost per month (four weeks) will be $300.00.The given fixed rate for Thanh is $49.00 per week. Thanh also pays $14.00 per week for the optional insurance and $12.00 weekly on gas.

To find Thanh's cost per month (four weeks), we need to multiply his weekly cost by 4.We can use the formula below to calculate Thanh's monthly cost.

Total weekly cost = Fixed rate + Insurance cost + Gas cost

Total weekly cost = $49.00 + $14.00 + $12.00

Total weekly cost = $75.00

The cost for Thanh per month (four weeks) = Total weekly cost × 4

Cost for Thanh per month (four weeks) = $75.00 × 4

Cost for Thanh per month (four weeks) = $300.00

Therefore, Thanh's cost per month (four weeks) will be $300.00.

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The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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Answer:

2 and 6

Step-by-step explanation:

Answer:

2 and 6

Step-by-step explanation:

Got a hundred on my test correct answer edge 2020

\((7 + 17 - 14 - 8)q = 14\)

\((24 - 22)q = 14\)

\(2q = 14\)

Divide both sides by 2

\( \frac{2q}{2} = \frac{14}{2} \\ \)

\(q = 7\)

There u go...

Have a great day ❤

The length of the transverse axis is 8.

Given the equation of hyperbola:\(\frac{(y-2)^{2} }{16}\)\(-\frac{(x+1)^{2} }{144 }\)\(=1\)

Rewrite this equation as \(\frac{(y-2)^{2} }{4^{2} }\)\(-\frac{(x+1)^{2} }{12^{2} }\)\(=1\)

When comparing this equation to the common hyperbola equation with a vertical transverse axis is \(\frac{(y-k)^{2} }{a^{2} }\)\(-\frac{(x+h)^{2} }{b^{2} }\)\(=1\)

\(h = -1\)

\(k= -2\)

\(a = 4\)

\(b = 12\)

The length of the transverse axis is\(2a = 2*4\)

                                                               \(=8.\)

The length of the transverse axis is 8.

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Answer: 84

Step-by-step explanation:

Question requires finding the 16th term in this sequence:

= -6 + ( n - 1 )(6)

= -6 + ( 16 - 1) (6)

= -6 + (15 * 6)

= 84

The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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Answer:

C) 120,000

Step-by-step explanation:

Let's use fractions.

7800 = x

---------- -------- . 325 5000 What we are going to do is multiply 325 times x and 7800 times 5000 . 7800 times 5000 equals 39,000,000. 325 times x equals 325x. The reason why we put the info this way is because we are trying to find the profit for a certain number of products . If we were trying the number of products we would put 5000 on top and the x on the bottom of the fraction the n croos multiply but this is not the case.

39,000,000 = 325x

----------------- --------

325 325

Next, we are going to divide 325 on both sides to get x ( in this case x equals the answer) by itself.

39,000,000 /325 = 120,000

325x / 325 = x

x = 120,000

The height of the stump is 3 ft.

The given equation represents the height of the frog, h(t), as a function of time, t. To find the height of the stump, we need to determine the height when the time, t, is equal to 0.

In the equation h(t) = -16t² + 64t + 3, we substitute t = 0:

h(0) = -16(0)² + 64(0) + 3

Since any term multiplied by zero is zero, we can simplify further:

h(0) = 0 + 0 + 3

Therefore, the height of the stump, at time t = 0, is 3 ft. This means that when the frog initially leaps from the stump, the height of the stump itself is 3 ft.

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Answer:

\(x=42; \ y=14\sqrt{5}.\)

Step-by-step explanation:

1. if the angles of the given triangle are 30-60-90°, then

2. y=0.5*28√5=14√5;

\(3. \ x=28\sqrt{5}*sin(60)=28\sqrt{3}*\frac{\sqrt{3} }{2}=42.\)

4. finally, x=42; y=14√5.

The possibility of selecting a 4 characters long password consisting of 3 letters and one number if letters cannot be repeated and the password must end with a number is 156000

An equation is an expression that shows the relationship between two or more number and variables.

The possibility of selecting the password = 26 * 25 * 24 * 10 = 156000

The possibility of selecting a 4 characters long password consisting of 3 letters and one number if letters cannot be repeated and the password must end with a number is 156000

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