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Tanya [424]
3 years ago
10

Point A is at (-7,5) and point B is at (7,3) what is the midpoint

Mathematics
1 answer:
AleksandrR [38]3 years ago
8 0

Answer:

The midpoint between A(-7, 5) and B (7, 3) is: (0, 4)

Step-by-step explanation:

Given the points

  • A (-7, 5)
  • B (7, 3)

Determining the midpoint between A(-7, 5) and B (7, 3)

M.P_{AB\:}=\:\:\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)

\left(x_1,\:y_1\right)=\left(-7,\:5\right),\:\left(x_2,\:y_2\right)=\left(7,\:3\right)

             =\left(\frac{7-7}{2},\:\frac{3+5}{2}\right)

             =\left(0,\:4\right)

Therefore, the midpoint between A(-7, 5) and B (7, 3) is: (0, 4)

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Find the arc length of ADC. Round to the nearest hundredth.<br> BA = 6.5 cm
MakcuM [25]
2190.5 cm.

360 degrees - 23 degrees = 337 degrees

337 degrees x 6.5 cm = 2190.5 cm
7 0
3 years ago
Use the ordinary division of polynomials to find the quotient and remainder when the first polynomial is divided by the second.
Vanyuwa [196]

The quotient and remainder when the first polynomial is divided by the second are -4w^2 - 7w - 21 and -71 respectively

<h3>How to determine the quotient and remainder when the first polynomial is divided by the second?</h3>

The polynomials are given as:

-4w^3 + 5w^2 - 8, w - 3

Set the divisor to 0.

So, we have

w - 3 = 0

Add 3 to both sides

w = 3

Substitute w = 3 in -4w^3 + 5w^2 - 8 to determine the remainder

-4(3)^3 + 5(3)^2 - 8

Evaluate the expression

-71

This means that the remainder when -4w^3 + 5w^2 - 8 is divided by w - 3 is -71

The quotient (Q) is calculated as follows:

Q = [-4w^3 + 5w^2 - 8]/[w - 3]

The numerator can be expressed as follows:

Numerator = -4w^3 + 5w^2 - 8

Subtract the remainder.

So, we have:

Numerator = -4w^3 + 5w^2 - 8 + 71

This gives

Numerator = -4w^3 + 5w^2 + 61

So, the quotient becomes

Q = [-4w^3 + 5w^2 + 61]/[w - 3]

Expand

Q = [(w - 3)(-4w^2 - 7w - 21)]/[w - 3]

Evaluate

Q = -4w^2 - 7w - 21

Hence, the quotient and remainder when the first polynomial is divided by the second are -4w^2 - 7w - 21 and -71 respectively

Read more about polynomials at:

brainly.com/question/4142886

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6 0
2 years ago
In Problems 23–30, use the given zero to find the remaining zeros of each function
Talja [164]

Answer:

x =  2i, x = -2i and x = 4 are the roots of given polynomial.

Step-by-step explanation:

We are given the following expression in the question:

f(x) = x^3 - 4x^2+ 4x - 16

One of the zeroes of the above polynomial is 2i, that is :

f(x) = x^3 - 4x^2+ 4x - 16\\f(2i) = (2i)^3 - 4(2i)^2+ 4(2i) - 16\\= -8i+ 16+8i-16 = 0

Thus, we can write

(x-2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

Now, we check if -2i is a root of the given polynomial:

f(x) = x^3 - 4x^2+ 4x - 16\\f(-2i) = (-2i)^3 - 4(-2i)^2+ 4(-2i) - 16\\= 8i+ 16-8i-16 = 0

Thus, we can write

(x+2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

Therefore,

(x-2i)(x+2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16\\(x^2 + 4)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

Dividing the given polynomial:

\displaystyle\frac{x^3 - 4x^2 + 4x - 16}{x^2+4} = x -4

Thus,

(x-4)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

X = 4 is a root of the given polynomial.

f(x) = x^3 - 4x^2+ 4x - 16\\f(4) = (4)^3 - 4(4)^2+ 4(4) - 16\\= 64-64+16-16 = 0

Thus, 2i, -2i and 4 are the roots of given polynomial.

4 0
3 years ago
Simplify tan9x-tan5x / 1+tan9xtan5x​
Wittaler [7]

Answer:

The given expressions simplifies to tan (4x).

Step-by-step explanation:

Here, the given expression is : \frac{tan9x - tan5x}{1+ tan9xtan5x}

By TRIGONOMETRIC IDENTITY:

tan (A-B)  = \frac{tanA - tanB}{1+ tanAtanB}

Putting this identity here, and taking A = 9 x, B = 5 x, we get

\frac{tan9x - tan5x}{1+ tan9xtan5x} = tan (9x-5x)

= tan(4x)

Hence, the given expressions simplifies to tan (4x).

5 0
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The population of a certain country is approximated by the following equation, where x is the number of years since 1980 and P i
marissa [1.9K]

Answer:

In 2010 the population become 206,123,000.

Step-by-step explanation:

Consider the provided equation.

P=2.748x + 126.199

Where P represents the population in millions.

We need to determine the year in which the country had population of 206,123,000.

As P is in millions so divide 206,123,000 by one million.

\frac{206,123,000 }{1,000,000}= 206.123

Substitute P = 206.123 in above equation.

206.123=2.748x + 126.199

79.924=2.748x

x=\frac{79.924}{2.748}

x=29.08

30 year from 1980 the population become 206,123,000.

In 2010 the population become 206,123,000.

6 0
3 years ago
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