Subtract and simplify: (3x^2 + 7) – (x^2 – 6x – 4)Question 3 options:

2x^2 + 6x + 3


4x^2 – 6x + 3


2x^2 + 6x + 11


4x^2 + 3

Answer:

This problem has two number solutions. The solutions are x = ±√ 1.500 = ± 1.22474.

Step-bystepexplanation:

Step 1 :

Equation at the end of step 1 :

0 - ((0 - 2x2) + 3) = 0

Step 2 :

Trying to factor as a Difference of Squares :

2.1 Factoring: 2x2-3

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 2 is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Equation at the end of step 2 :

2x2 - 3 = 0

Step 3 :

Solving a Single Variable Equation :

3.1 Solve : 2x2-3 = 0

Add 3 to both sides of the equation :

2x2 = 3

Divide both sides of the equation by 2:

x2 = 3/2 = 1.500

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

x = ± √ 3/2

The equation has two real solutions

These solutions are x = ±√ 1.500 = ± 1.22474

Answer:

P(x)=(x-2)(x-4)(x+3)(x+6)

Step-by-step explanation:

Given: P(x)=x⁴+3x³-28x²-36x+144

It is a polynomial with degree 4.

It should maximum four factor.

Hit and trial error method.

Put x = 2 into P(x)

P(2)=2⁴+3×2³-28×2²-36×2+144

P(2) = 0

So, x-2 would be factor of P(x)

Now divide x⁴+3x³-28x²-36x+144 by x-2 to get another factors

Put x = 4

now divide by x-4

Now factor

Complete factor of P(x)

P(x)=(x-2)(x-4)(x+3)(x+6)

Answer: 0.5 or 3/6 or 1/2

Step-by-step explanation:

1/6 x 3 = 1/6 + 1/6+ 1/6 = 3/6 = 1/2

Answer:

Step-by-step explanation:

Since L is the midpoint of MN, by the definition of midpoint:

We can picture the following segment:

M----------L----------N

We know that and . Since the two segments are equivalent, we can set them equal to each other:

Now, let's solve for x. Subtract -7 from both sides:

Subtract 3x from both sides:

Divide both sides by -1:

So, the value of x is 10.

With this, we can find the remaining lengths.

We know that ML is .

Substitute 10 for x. So, the length of ML is:

We know that LN is . So, the length of LN is:

Finally, MN will be the combined lengths of ML and LN. So:

And we're done!

The lengths of each segment are:

ML = 27, LN = 27, and MN = 54.

We have,

Let's use the information given to find the values of ML, LN, and MN.

ML = 2x + 7

LN = 3x - 3

L is the midpoint of MN, which means that ML is equal to LN:

2x + 7 = 3x - 3

Now, let's solve for x:

Move the x term to one side of the equation:

2x - 3x = -3 - 7

-x = -10

Now, multiply both sides by -1 to get rid of the negative sign:

x = 10

Now that we have the value of x, we can find the lengths ML, LN, and MN:

ML = 2x + 7

ML = 2(10) + 7

ML = 20 + 7

ML = 27

LN = 3x - 3

LN = 3(10) - 3

LN = 30 - 3

LN = 27

MN = ML + LN

MN = 27 + 27

MN = 54

Thus,

The lengths of each segment are:

ML = 27, LN = 27, and MN = 54.

Learn more about midpoints of linesegments here:

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Given that the same-side interiorangles formed by two parallel lines and a transversal have an angle ratio of 1:14, the eight angles formed are:

m<1 = 12°

m<2 = 168°

m<3 = 168°

m<4 = 12°

m<5 = 12°

m<6 = 168°

m<7 = 168°

m<8 = 12°

Applying the knowledge of ratio, transversal and parallel lines, we can determine the measures of all 8 angles that are formed when a transversal intersects two parallel lines as shown in the image attached below.

Let < 1 and < 6 be the two same-side interior angles whose measures are in the ratio, 1:14.

Thus:

• m<1 : m<6 = 1 : 14

Recall:

Same-side interior angles are always supplementary. That is,

m<1 + m<6 = 180 degrees.

Let's apply ratio to find the measure of <1 and <6.

• m<1 = ratio of <1 / sum of ratio x 180

• m<6 = ratio of <6 / sum of ratio x 180

Since we know the measure of <1 and <6, we can find the measure of others as follows:

• m<2 = m<6 = 168° (corresponding angles are congruent)

• m<3 = m<6 = 168° (alternate interior angles are congruent)

• m<4 = m<1 = 12° (vertical angles are congruent)

• m<5 = m<1 = 12° (corresponding angles are congruent)

• m<7 = m<6 = 168° (vertical angles are congruent)

• m<8 = m<4 = 12° (corresponding angles are congruent)

In conclusion, given that the same-side interiorangles formed by two parallel lines and a transversal have an angle ratio of 1:14, the eight angles formed are:

m<1 = 12°

m<2 = 168°

m<3 = 168°

m<4 = 12°

m<5 = 12°

m<6 = 168°

m<7 = 168°

m<8 = 12°

Learn more here:

brainly.com/question/15937977

Answer:

At the intersection of the first parallel line with the transversal, a = 12°, c = 168°, d = 12°, e = 168°. Counting counterclockwise from a.

At the first intersection of the second parallel line with the transversal, b = 168°, f = 12°, g = 168°, h = 12°. Counting clockwise from b.

Step-by-step explanation:

Let a be the first interior angle. Since they are in 1:14, the second same side interior angle is b = 14a.

We know that the sum of interior angles equals 180°.

So, a + b = 180°

a + 14a = 180°

15a = 180°

a = 180/15

a = 12°

At alternate angle to the other interior angle, b adjacent to a is c = b = 14a = 14 × 12 = 168°

The angle vertically opposite to a is d = a = 12°

The angle vertically opposite to a is b = e = 168°

At the intersection of the second parallel line and the transversal, the angle alternate to a is f = a = 12°

the angle vertically opposite to angle b is g = b = 168°

the angle vertically opposite to f is h = 12°