Solve for x. help pls im stressed

A _____ has two-fold rotational symmetry.

Neko [114]

The answer is D. line.

5 0

3 years ago

Find the roots of:

Elena-2011 [213]

$\large\displaystyle\text{$\begin{gathered}\sf \pmb{1) \ 2x^3-7x^2+8x-3=0 } \end{gathered}$}$

Synthetic division is used since the equation is of the third degree. The divisors of -3 are 1, -1, 3, +3. So:

| 2 -7 8 -3

1 | 2 -5 3

| 2 -5 3 0

1 | 2 -3

2 -3 0

So the factorization is (x-1)² (2x-3)=0. So:

$\bf{ x_1=x_2=1 \qquad x_2=\dfrac{3}{2} }$

$\large\displaystyle\text{$\begin{gathered}\sf \pmb{2) \ x^3-x^2-4=0 } \end{gathered}$}$

Synthetic division is used since the equation is of the third degree. The divisors of -4 are 1, -1, 2, -2, 4, -4. So:

| 1 -1 0 -4

2 | 2 2

1 2 2 0

So the factorization is (x-2)(x²+x+2)=0 . When calculating the discriminant of the trinomial, it is concluded that it has no roots since the result is negative. So you only have one solution.

$\bf{ 1^2-4(2)(2)=1-16=-15 < 0 \quad \Longrightarrow \quad x=2 }$

$\large\displaystyle\text{$\begin{gathered}\sf \pmb{3) \ 6x^3+7x^2-9x+2=0 } \end{gathered}$}$

Synthetic division is used since the equation is of the third degree. The divisors of 2 are 1, -1, 2, -2. So:

| 6 7 9 2

-2 | -12 10 -2

6 -5 1 0

So the factorization is (x+2)(6x²-5x+1)=0 . The quadratic equation is solved by the general formula:

$\bf{ x_{2, 3}&=\dfrac{5\pm \sqrt{(5)^2-4(6)(1)}}{2(6)}=\dfrac{5\pm \sqrt{25-24}}{12}=\dfrac{5\pm 1}{12} }}$

$\large\displaystyle\text{$\begin{gathered}\sf \begin{matrix} x_1=-2&\ \ \ \ \ \ x_{2}=\dfrac{6}{12} \qquad &\ \ \ x_3=\dfrac{4}{12}\\ &\ \ \ x_2=\dfrac{1}{2} \qquad &x_3=\dfrac{1}{3} \end{matrix} \end{gathered}$}$

6 0

2 years ago

Which table of ordered pairs represents a proportional relationship?

Anna11 [10]

Answer: a

Step-by-step explanation: i took the test

6 0

3 years ago

Write a linear function f with the values f(10)=5 and f(2)=-3

Nutka1998 [239]

Answer:

$f(x)=x-5$

Step-by-step explanation:

step 1

Find the slope m

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have the ordered pairs

(10,5) and (2,-3)

substitute the values

$m=\frac{-3-5}{2-10}$

$m=\frac{-8}{-8}$

$m=1$

step 2

Find the equation of the line in slope intercept form

$f(x)=mx+b$

we have

$m=1$

$point\ (10,5)$

substitute and solve for b

$5=(1)(10)+b$

$5=10+b$

$b=-5$

The linear function is equal to

$f(x)=x-5$

3 0

3 years ago

What is the place value of the number 5 in 2,257,926

Norma-Jean [14]

Answer:

5 is in the ten thousands place.

Step-by-step explanation:

Since the number to the left of 5, 2, is in the hundred thousands place, and the number to the right, 7, is in the thousands place, 5 is in the ten thousands place.

I hope this helped! :-)

8 0

3 years ago

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