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3 years ago

70 POINTS! PLEASE HELP! Explain the difference between the following equation formats: Slope-Intercept, Point-Slope and Standard

Mathematics

1 answer:

katrin2010 [14]3 years ago

7 0

Answer and Step-by-step explanation:

1. slope intercept

2. point-slope form

3. standard

Explanation:

1. A slope intercept form equation is when it's set up as y = m x + b

m = slope

b = y-intercept

2. A point-slope form is when a line passes through a point

and the equation is set up as y −b = m ( x−a)

m = slope

(a, b) A point that the line passes through

3. standard lope form is when the equation is set up as

Ax + By = C

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HELP!!!! I think its C but I'm not sure!

MA_775_DIABLO [31]

Answer:

The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are $x=1\pm i\sqrt{7}$ .

Step-by-step explanation:

Consider the provided information.

Algebra's fundamental theorem states that: Every polynomial equation of degree n with complex coefficients has n roots in the complex numbers.

Now consider the provided equation.

$2x^2-4x+16=0$

The degree of the polynomial equation is 2, therefore according to Algebra's fundamental theorem the equation have two complex roots.

Now find the root of the equation.

For the quadratic equation of the form $ax^2+bx+c=0$ the solutions are: $x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Substitute $a=2,\:b=-4,\:\ and \ c=16$ in above formula.

$x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:2\cdot \:16}}{2\cdot \:2}$

$x_{1,\:2}=\frac{4\pm \sqrt{16-128}}{4}$

$x_{1,\:2}=\frac{4\pm \sqrt{-112}}{4}$

$x_{1,\:2}=\frac{4\pm 4i\sqrt{7}}{4}$

$x_{1,\:2}=1\pm i\sqrt{7}$

Hence, the fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are $x=1\pm i\sqrt{7}$ .

4 0

3 years ago

The measures of the angles of a triangle are shown in the figure below. Find the measure of the smallest angle.

nataly862011 [7]

Answer:

(2x+18) degrees

Step-by-step explanation:

A triangle is a total of 180 degrees, so you would do:

(2x+18)+55+(4x+11)=180

(2x+4x)+(18+55+11)=180 <- take out parentheses and add like terms

6x+84=180 <- subtract 84 from both sides of the equation

6x=96 <- divide 6 from each side

x=16

Now that you know what x is you would plug it into each of the angles

Angle 1: 2x+18 --> 2(16)+18= 32+18= 50

Angle 2: 55

Angle 3: 4x+11 --> 4(16)+18= 64+18= 82

Then out of these three angles of the triangle, angle 1 (2x+18) would be the smallest.

4 0

3 years ago

Read 2 more answers

Plz help me with Geometry

Greeley [361]

Answer:

the second one

Step-by-step explanation:

6 0

3 years ago

A playground is being designed where children can interact with their friends in certain combinations. If there is 1 child, ther

mariarad [96]

<h2>Answer:</h2>

Recursive equation for the pattern followed is given by,

$a_{n}=a_{n-1}+(n-1)^{2}$

<h2>Step-by-step explanation:</h2>

In the question,

The number of interaction for 1 child = 0

Number of interactions for 2 children = 1

Number of interactions for 3 children = 5

Number of interaction for 4 children = 14

So,

We need to find out the pattern for the recursive equation for the given conditions.

So,

We see that,

$a_{1}=0\\a_{2}=1\\a_{3}=5\\a_{4}=14\\$

Therefore, on checking, we observe that,

$a_{n}=a_{n-1}+(n-1)^{2}$

On checking the equation at the given values of 'n' of, 1, 2, 3 and 4.

At,

n = 1

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{1}=a_{1-1}+(1-1)^{2}\\a_{1}=0+0=0\\a_{1}=0$

which is true.

At,

n = 2

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{2}=a_{2-1}+(2-1)^{2}\\a_{2}=a_{1}+1\\a_{2}=1$

Which is also true.

At,

n = 3

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{3}=a_{3-1}+(3-1)^{2}\\a_{3}=a_{2}+4\\a_{3}=5$

Which is true.

At,

n = 4

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{4}=a_{4-1}+(4-1)^{2}\\a_{4}=a_{3}+9\\a_{4}=14$

This is also true at the given value of 'n'.

Therefore, the recursive equation for the pattern followed is given by,

$a_{n}=a_{n-1}+(n-1)^{2}$

3 0

3 years ago

186.73 x (-0.0175) Please help!!

marishachu [46]

Answer:

186.73 x (-0.0175) = −3.267775

3 0

3 years ago