Add the following complex numbers:
(6 - 21) + (11 +61)

The distance between the points is 6.7 units

The distance between two points is the number of points between them

The points are given as

(0, 5) and (3, -1)

The distance formula is given as

d = √(x2 - x1)^2 + (y2 - y1)^2

Substitute the given points in the above distance formula

So, we have

d = √(0 - 3)^2 + (5 + 1)^2

Evaluate the difference and the sum

d = √(-3)^2 + 6^2

Evaluate the exponents

d = √9 + 36

Evaluate the sum

d = √45

This gives

d = 6.7

Hence, the distance is 6.7 units

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Answer:

Step-by-step explanation:

3.14x6.25

19.625

Answer:

19.625

Step-by-step explanation:

Answer:

Indira should have written the equations Negative 6 + a = negative 3 and 1 + b = negative 2 in Step 2.

Step-by-step explanation:

The complete question is:

On a coordinate plane, point B(–6, 1) is translated to B prime(–3, –2). Indira uses these steps to find a rule to describe the translation. Step 1Substitute the original coordinates and the translated coordinates into (x, y) right-arrow (x + a, y + b):

B (negative 6, 1) right-arrow B prime (negative 6 + a, 1 + b) = B prime (negative 3, negative 2)

Step 2

Write two equations:

Negative 6 + a = negative 2. 1 + b = negative 3.

Step 3

Solve each equation:

Negative 6 + a = negative 2. a = negative 2 + 6. a = 4. 1 + b = 3. b = negative 3 minus 1. b = negative 4.

Step 4

Write the translation rule:

(x, y) right-arrow (x + 4, y minus 4)

Which corrects Indira’s first error?

Indira should have substituted B (negative 6, 1) right-arrow B prime (negative 3 + a, negative 2 + b) = B prime (negative 6, 1) in Step 1.

Indira should have written the equations Negative 6 + a = negative 3 and 1 + b = negative 2 in Step 2.

Indira should have solved the equations to find that a = negative 8 and b = negative 2 in Step 3.

Indira should have written the translation rule (x, y) right-arrow (x minus 4, y + 4) in Step 4.

Answer:

Transformation is the movement of a point from its initial position to a new position. Types of transformation is rotation, dilation, rotation or reflection.

Translation is the movement of a point in a given direction. It is represented by (x, y) ⇒ (x ± a, y ± b)

If a is positive then the point is moved right and if a is negative, the point is moved left. Also if b is positive, the point is moved up and if b is negative, the point is moved down

Step 1 is correct:

B (- 6, 1) ⇒ B' (- 6 + a, 1 + b) = B' (- 3, - 2)

Step 2 is not correct, Indira should have written the equations:

(-6 + a, 1 + b) = (-3, -2)

-6 + a = -3 and 1 + b = -2

a = 3 and b = -3

(x, y) ⇒ (x + 4, b - 3)

-

Answers:Indira should have substituted B (negative 6, 1) right-arrow B prime (negative 3 + a, negative 2 + b) = B prime (negative 6, 1) in Step 1.

Step-by-step explanation:

Answer:

A. -4

Step-by-step explanation:

Given the function f(x) = x + 3 for x ≤ -1 and 2x - c for x > -1, for the function to be continuous, the right hand limit of the function must be equal to its left hand limit.

For the left hand limit;

The function at the left hand occurs at x<-1

f-(x) = x+3

f-(-1) = -1+3

f-(-1) = 2

For the right hand limit, the function occurs at x>-1

f+(x) = 2x-c

f+(-1) = 2(-1)-c

f+(-1) = -2-c

For the function f(x) to be continuous on the entire real line at x = -1, then

f-(-1) = f+(-1)

On equating both sides:

2 = -2-c

Add 2 to both sides

2+2 = -2-c+2

4 =-c

Multiply both sides by minus.

-(-c) = -4

c = -4

Hence the value of c so that f(x) is continuous on the entire real line is -4

The value of 'c' is -4 and this can be determined by using the concept of continuous function and arithmetic operations.

Given :

f(x) is continuous on the entire real line when c f(x) = x + 3 for \(x \leq -1\), 2x - c for x > -1.

Remember for a continuous function, the left-hand limit is equal to the right-hand limit. So, determine the left-hand and right-hand limit.

The left-hand limit is calculated as:

f(-1) = (-1) + 3

f(-1) = 2    --- (1)

The right-hand limit is calculated as:

f(-1) = 2(-1) - c

f(-1) = -2 - c   --- (2)

Now, equate both the expression (1) and (2).

2 = -2 - c

c = -4

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Answer: 4

This problem requires basic division. If the restaurant divided 4/5 kg of butter with 1/5 kg on each dish, you would need to compute 4/5 divided by 1/5.

4/5 ÷ 1/5

Using the "KFC" method, or Keep, Change, Flip, you would keep the first number (in this case, 4/5), change the division sign, and flip the fraction to 5/1, or 5. We now have this:

4/5 x 5

To compute this equation, you must multiply the numerators of both of the numbers together. In this case, you would compute (4x5)/5, resulting with 20/5, or 4.

You can check this answer by re-multiplying the numbers together. 1/5 kg of butter per dish, multiplied by the total amount of dishes, 4, you would result in the original 4/5 kg of butter.

Hope this helps!

After answering the presented question, we can conclude that As a radius result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

In more modern parlance, the length of a circle or sphere is the same as its radius in classical geometry, which is one of the line segments from its centre to its circumference. The term was derived from the Latin word radius, which also refers to the spokes of a waggon wheel. The radius of a circle is the distance between its centre and any point on its periphery. It is usually denoted by "R" or "r." A radius is a line segment with one endpoint in the centre and one on the circle's circumference. The radius of a circle matches its diameter. The diameter of a circle is the segment that passes through its centre and has ends on the circle.

The formula for the volume of a sphere of radius "r" is:

V = (4/3)πr³

Substituting the specified radius value (r = 11 cm), we get:

V = (4/3)π(11)³ \sV = 5575.279 cm³

Now we must compute the weight of the titanium sphere, which can be found by multiplying its volume by its density:

Density = Volume Weight

Weight = 25121.811974 g Weight = 5575.279 cm3 4.506 g/cm3

When we divide 1000 by 1000 to convert grammes to kilogrammes, we get:

The weight is 25.121811974 kg.

As a result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

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Answer: Its answer A

Hope you feel soon better friend.

Presumably you've proven exercise 6, that the Laplace transform of \(t^k f(t)\) is \((-1)^k F^{(k)}(s)\).

Let F(s) = 1/s, whose inverse Laplace transform is f(t) = 1. Differentiate F with respect to s :

\(F'(s) = -\dfrac1{s^2}\)

By the claim from ex.6, this is the Laplace transform of t • f(t) = t.

Differentiate F again with respect to s :

\(F''(s) = \dfrac2{s^3}\)

and this is the Laplace transform of t² • f(t) = t². And so on.

We can prove the general claim by induction. Assume it's true for n = k, that \(t^k \leftrightarrow \frac{k!}{s^{k+1}}\). Then using the result of ex.6, we have

\(F(s) = \dfrac{k!}{s^{k+1}} \implies F'(s) = -\dfrac{(k+1)!}{s^{k+2}} \leftrightarrow t^{k+1}\)

QED

Answer:

X=60

m<QRS= 90

Step-by-step explanation:

assuming that it all adds up to 180

Add all like terms:

50+10+1/2x=180

1/2x+60=180

-60 -60

1/2x= 120

÷1/2= ÷1/2

x= 60

1. 1/2(60)+10

40

Answer:

The answer to your problem is, 7 friends can buy the meal on a budget of $41 which includes delivery charges of $6.

Step-by-step explanation:

We also should know what a formula is because it can explain how two expressions on each side of a sign are connected.

Example, 2x - 4 = 2.

The letter ‘ x ‘ is a preceding example.

So:

The total budget is $41.

Delivery charges are $6.

The equation is: 6 + az = 41

Z is the meal for each friend.

6 + 5z = 41

Calculate for ‘ z ‘

6 + 5z = 41

6 + 5(7) = 41

6 + 35 = 41

= 41

Thus the answer to your problem is, 7 friends can buy the meal on a budget of $41 which includes delivery charges of $6.

Answer:

2x4 is 8

Step-by-step explanation:

4 to times so 4+4 =8 thx

\(solution \\ x - y = 4 \\ now \\ 3(x - y) \\ = 3 \times 4 \\ = 12\)

hope this helps...

Good luck on your assignment...

Answer:

\(12\)

Step-by-step explanation:

\((x - y) = 4 \\ 3(x - y) = 3 \times (x - y) \\ 3 \times (x - y) \\ 3 \times 4 \\ = 12\)

hope this helps you.

The graph of the translated function is g ( x ) = ( x + 5 )² + 2

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x²

On simplifying , we get

The function is translated 5 units to the horizontal left direction:

And , when the function is translated 2 units in the vertical upward direction:

So , the translated function is

g ( x ) = ( x + 5 )² + 2

Now , the vertex of the function g ( x ) = ( x + 5 )² + 2 is (-5, 2)

Hence , the graph of the function is plotted and g ( x ) = ( x + 5 )² + 2

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equilateral and acute

Answer:

A, E, F

equilateral, acute, and isosceles

Step-by-step explanation:

Answer:

The amount or number to be divided is called the dividend

Answer:

If I'm correct it is the divisor.

Step-by-step explanation:

For example:

8 divided by 4 equals 2. I think 4 is the divisor and the 8 is the dividend. So I think it's the divisor, and I really apologize if the answer is incorrect.

Answer:

226 cm^3

The mass of plastic used to make cylinder is greater

Step-by-step explanation:

Given:-

- The density of cone material, ρc = 1.4 g / cm^3

- The density of cylinder material, ρl = 0.8 g / cm^3

Solution:-

- To determine the volume of plastic that remains in the cylinder after gouging out a hemispherical amount of material.

- We will first consider a solid cylinder with length ( L = 10 cm ) and diameter ( d = 6 cm ). The volume of a cylinder is expressed as follows:

                                  \(V_L =\pi \frac{d^2}{4} * L\)

- Determine the volume of complete cylindrical body as follows:

                                 \(V_L = \pi \frac{(6)^2}{4} * 10\\\\V_L = 90\pi cm^3\\\)

- Where the volume of hemisphere with diameter ( d = 6 cm ) is given by:

                                 \(V_h = \frac{\pi }{12}*d^3\)

- Determine the volume of hemisphere gouged out as follows:

                                 \(V_h = \frac{\pi }{12}*6^3\\\\V_h = 18\pi cm^3\)

- Apply the principle of super-position and subtract the volume of hemisphere from the cylinder as follows to the nearest ( cm^3 ):

                               \(V = V_L - V_h\\\\V = 90\pi - 18\pi \\\\V = 226 cm^3\)

Answer: The amount of volume that remains in the cylinder is 226 cm^3

- The volume of cone with base diameter ( d = 6 cm ) and height ( h = 5 cm ) is expressed as follows:

                               \(V_c = \frac{\pi }{12} *d^2 * h\)

- Determine the volume of cone:

                              \(V_c = \frac{\pi }{12} *6^2 * 5\\\\V_c = 15\pi cm^3\)

- The mass of plastic for the cylinder and the cone can be evaluated using their respective densities and volumes as follows:

                             \(m_i = p_i * V_i\)

- The mass of plastic used to make the cylinder ( after removing hemispherical amount ) is:

                           \(m_L = p_L * V\\\\m_L = 0.8 * 226\\\\m_L = 180.8 g\)

- Similarly the mass of plastic used to make the cone would be:

                           \(m_c = p_c * V_c\\\\m_c = 1.4 * 15\pi \\\\m_c = 65.973 g\)

Answer: The total weight of the cylinder ( m_l = 180.8 g ) is greater than the total weight of the cone ( m_c = 66 g ).

The volume of the remaining plastic in the cylinder is large, which

makes the weight much larger than the weight of the cone.

Responses:

Density of the plastic for the cone = 1.4 g/cm³

Density of the plastic used for the cylinder = 0.8 g/cm³

From a similar question, we have;

Height of the cylinder = 10 cm

Diameter of the cylinder = 6 cm

Height of the cone = 5 cm

(a) Radius of the cylinder, r = 6 cm ÷ 2 = 3 cm

Volume of a cylinder = π·r²·h

Volume of a hemisphere = \(\mathbf{\frac{2}{3}}\) × π×  r³

Volume of the cylinder after it has been hollowed out, V, is therefore;

Which gives;

\(V = \pi \times 3^2 \times 10 - \frac{2}{3} \times \pi \times 3^3 \approx \mathbf{ 226}\)

(b) Volume of the cone = \(\mathbf{\frac{1}{3}}\) × π × 3² × 5 ≈ 47.1

Mass of the cone = 47.1 cm³ × 1.4 g/cm³ ≈ 66 g

Mass of the hollowed cylinder ≈ 226 cm³ × 0.8 g/cm³ = 180.8 g

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The distance can be determined as,

Thus, the required distance is 25.

The most appropriate choice for compound interest will be given by-

1) If compounded monthly, amount = $9160

2)If compounded continuously, amount = $218

What is compound interest?

If the interest on a certain principal at a certain rate over a certain period of time increases exponentially (not linearly), the interest earned is known as compound interest.

If P is the principal, r is the rate and t is the time in years,

\(A = P(1+\frac{r}{100})^n\)

Here,

Principal = $28

Rate = 4%

Time = 2010 - 1855

         = 145 years

a) If compounded monthly

Amount =

\(28(1 + \frac{4}{1200})^{145\times 12}\\28(1 + \frac{1}{300})^{1740}\\28(\frac{300+1}{300})^{1740}\\28(\frac{301}{300})^{1740}\\28 \times 327.13\\\)

$9159.56

$9160

b) If compounded continuously

Amount =

\(28 \times e^{4\times 145}\\28e^{580}\\28 \times 7.78\\\)

$217.84

$218

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Answer:

9.5

Step-by-step explanation:

You're welcome have a nice

Answer:

-9 < x < 7

Step-by-step explanation:

If this is based on the question you asked earlier, the answer to your question is C) -9 < x < 7.

The domain represents all possible outputs for a function and typically deals with the x axis [With range dealing with the y-axis]

The given equation is

First, we subtract 10 from each side

Then, we divide the linear coefficient by half and elevated it to the square power.

Then, we add 9 on each side.

Now, we factor the trinomial.

At this point, we can deduct that the equation has no real solutions because there's no real number whose square power ends up in a negative number.

Answer:

yes

Step-by-step explanation:

Yes, the function rule is f(x) = 2x + 1.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

A function f (x) is graphed on the coordinate plane.

Function passes through two points (0, 1) and (1, 3).

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

y - 1 = 2(x - 0)

y = 2x + 1

Therefore, y = 2x + 1 is the required function.

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(a) Clicks Width of Door (inches)

1 3.3

2 3.63

3 3.99

4 4.39
(b) The function is y = 3  (1.1)ˣ.

(c) It would take about 15 clicks of the zoom-in button to make the door approximately 3 feet wide on the screen.

(d) It would take about 12 clicks of the zoom-out button to transform the display of the door from 3 feet wide back to a width of approximately 3 inches.

(a)

Clicks Width of Door (inches)

1 3.3

2 3.63

3 3.99

4 4.39

(b) Let x be the number of clicks and y be the width of the door on the screen. Then, we can write the algebraic rule as:

y = 3  (1.1)ˣ

(c) To make the door approximately 3 feet wide on screen, we need to convert 3 feet to inches, which is 36 inches. Then, we need to solve for x in the equation:

3 (1.1)ˣ = 36

Dividing both sides by 3, we get:

(1.1)ˣ = 12

Taking the logarithm of both sides (with base 1.1), we get:

x = log(12) / log(1.1) ≈ 14.7

So, it would take about 15 clicks of the zoom-in button to make the door approximately 3 feet wide on the screen.

(d) To transform the display of the door from 3 feet wide back to a width of approximately 3 inches, we need to find the number of clicks of the zoom-out button that will result in a width of approximately 3 inches. We can use the same formula as before, but with the initial width of 36 inches (since we are zooming out):

36 (0.9)ˣ = 3

Dividing both sides by 36, we get:

(0.9)ˣ = 1/12

Taking the logarithm of both sides (with base 0.9), we get:

x = log(1/12) / log(0.9) ≈ 11.5

So, it would take about 12 clicks of the zoom-out button to transform the display of the door from 3 feet wide back to a width of approximately 3 inches.

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Answer:

3 : 13 : 5 =_____ : _____ : 45 ?

3 : 13 : 5 = 27 : 117 : 45 .

Step-by-step explanation:

45/5=9

13×9=117

3×9=27

Answer:

a = 5q²

b = r²s

Step-by-step explanation:

The given identity is \(a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})\)

we have to use this identity to factor of two cubes given as \(125q^{6}-r^{6}s^{3}=(5q^{2})^{3}-(r^{2}s)^{3}\)

As this expression is in the form of a³- b³

Here a is 5q² and b is r²s.

Answer:

a=5q2  b=r2s the expression factored is also (5q2-r2s) (25q4+5q2r2s+1r4s2)

Step-by-step explanation:

Answer:

2 is really answer it is this question bro than ka for good point

Step-by-step explanation:

hello shreekant thanks 886A bubs 2 is answr

Answer:

  $28

Step-by-step explanation:

Each round trip will be double the price of a one-way trip, so will be ...

  2 × $3.50 = $7.00

Diego and his 3 friends will require a total of 4 round-trip tickets for a cost of ...

  4 × $7.00 = $28.00

Answer: (40, 28)

Step-by-step explanation:

(42+(-2), 33+(-5))=

(42-2, 33-5)=(40, 28)