X/3+7=-5
X = ?
Solve for x

Step-by-step explanation:

Simplify.

Subtract 7 from both sides:

Multiply each side by 3 to remove the fraction:

A

Step-by-step explanation:

+ 7 = - 5 ( multiply through by 3 to clear the fraction )

x + 21 = - 15 ( subtract 21 from both sides )

x = - 36 → A

A

Step-by-step explanation:

+ 7 = - 5 ( multiply through by 3 to clear the fraction )

x + 21 = - 15 ( subtract 21 from both sides )

x = - 36 → A

7/10x =7/3

-7/3 =-7/10x

This is the answer cause I just took the test and these were the right answers.

Step-by-step explanation:

"Determine the number and type of roots for the equation using one of the given roots. Then find each root. (inclusive of imaginary roots.)"

Given one of the roots, we can use either long division or grouping to factor each cubic equation into a binomial and a quadratic.  I'll use grouping.

Then, we can either factor or use the quadratic equation to find the remaining two roots.

1. x³ − 7x + 6 = 0; 1

x³ − x − 6x + 6 = 0

x (x² − 1) − 6 (x − 1) = 0

x (x + 1) (x − 1) − 6 (x − 1) = 0

(x² + x − 6) (x − 1) = 0

(x + 3) (x − 2) (x − 1) = 0

The remaining two roots are both real: -3 and +2.

2. x³ − 3x² + 25x + 29 = 0; -1

x³ − 3x² + 25x + 29 = 0

x³ − 3x² − 4x + 29x + 29 = 0

x (x² − 3x − 4) + 29 (x + 1) = 0

x (x − 4) (x + 1) + 29 (x + 1) = 0

(x² − 4x + 29) (x + 1) = 0

x = [ 4 ± √(16 − 4(1)(29)) ] / 2

x = (4 ± 10i) / 2

x = 2 ± 5i

The remaining two roots are both imaginary: 2 − 5i and 2 + 5i.

3. x³ − 4x² − 3x + 18 = 0; 3

x³ − 4x² − 3x + 18 = 0

x³ − 4x² + 3x − 6x + 18 = 0

x (x² − 4x + 3) − 6 (x − 3) = 0

x (x − 1)(x − 3) − 6 (x − 3) = 0

(x² − x − 6) (x − 3) = 0

(x − 3) (x + 2) (x − 3) = 0

The remaining two roots are both real: -2 and +3.

"Find all the zeros of the function"

For quadratics, we can factor using either AC method or quadratic formula.  For cubics, we can use the rational root test to check for possible rational roots.

4. f(x) = x² + 4x − 12

0 = (x + 6) (x − 2)

x = -6 or +2

5. f(x) = x³ − 3x² + x + 5

Possible rational roots: ±1/1, ±5/1

f(-1) = 0

-1 is a root, so use grouping to factor.

f(x) = x³ − 3x² − 4x + 5x + 5

f(x) = x (x² − 3x − 4) + 5 (x + 1)

f(x) = x (x − 4) (x + 1) + 5 (x + 1)

f(x) = (x² − 4x + 5) (x + 1)

x = [ 4 ± √(16 − 4(1)(5)) ] / 2

x = (4 ± 2i) / 2

x = 2 ± i

The three roots are x = -1, x = 2 − i, x = 2 + i.

6. f(x) = x³ − 4x² − 7x + 10

Possible rational roots: ±1/1, ±2/1, ±5/1, ±10/1

f(-2) = 0, f(1) = 0, f(5) = 0

The three roots are x = -2, x = 1, and x = 5.

"Write the simplest polynomial function with integral coefficients that has the given zeros."

A polynomial with roots a, b, c, is f(x) = (x − a) (x − b) (x − c).  Remember that imaginary roots come in conjugate pairs.

7. -5, -1, 3, 7

f(x) = (x + 5) (x + 1) (x − 3) (x − 7)

f(x) = (x² + 6x + 5) (x² − 10x + 21)

f(x) = x² (x² − 10x + 21) + 6x (x² − 10x + 21) + 5 (x² − 10x + 21)

f(x) = x⁴ − 10x³ + 21x² + 6x³ − 60x² + 126x + 5x² − 50x + 105

f(x) = x⁴ − 4x³ − 34x² + 76x − 50x + 105

8. 4, 2+3i

If 2 + 3i is a root, then 2 − 3i is also a root.

f(x) = (x − 4) (x − (2+3i)) (x − (2−3i))

f(x) = (x − 4) (x² − (2+3i) x − (2−3i) x + (2+3i)(2−3i))

f(x) = (x − 4) (x² − (2+3i+2−3i) x + (4+9))

f(x) = (x − 4) (x² − 4x + 13)

f(x) = x (x² − 4x + 13) − 4 (x² − 4x + 13)

f(x) = x³ − 4x² + 13x − 4x² + 16x − 52

f(x) = x³ − 8x² + 29x − 52

The correct options are  (1) (5,10), (2) (3,-3), (3) x = -1, (4) , (5) 21s and (6) 0, -1, and 5.

Explanation:

Te standard form of the parabola is,

       .....(1)

Where,  (h,k) is the vertex of the parabola.

(1)

The given equation is,

Comparing this equation with equation (1),we get,

and

Therefore, the vertex of the graph is (5,10) and the fourth option is correct.

(2)

The given equation is,

To make perfect square add , i.e., . Since there is factor 3 outside the parentheses, so subtract three times of 9.

Comparing this equation with equation (1),we get,

and

Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.

(3)

The given equation is

To make perfect square add , i.e., . Since there is factor 4 outside the parentheses, so subtract three times of 1.

Comparing this equation with equation (1),we get,

and

The vertex of the equation is (-1,3) so the axis is x=-1 and the correct option is 2.

(4)

The given equation is,

To make perfect square add , i.e., .

Therefore, the correct option is  4.

(5)

The given equation is,

It can be written as,

It is a downward parabola. so the maximum height of the function is on its vertex.

The x coordinate of the vertex is,

Therefore,  after 21 seconds the projectile reach its maximum height and the correct option is first.

(6)

The given equation is,

Use factoring method to find the factors of the equation.

Equate each factor equal to 0.

Therefore, the zeros of the given equation is 0, -1, 5 and the correct option is 2.