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3 years ago

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Need help with these questions, please

1 answer:

Zinaida [17]3 years ago

8 0

Number 29 would be y=-x +10

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what is the equation in standard form of the line that passes through the point (4,-8) and has a slope of 1/4

Sergio039 [100]

Y = mx + b
slope(m) = 1/4
(4,-8)....x = 4 and y = -8
now sub and find b, the y int
-8 = 1/4(4) + b
-8 = 1 + b
-8 - 1 = b
-9 = b
so ur equation is : y = 1/4x - 9....but we need it in standard form

y = 1/4x - 9
-1/4x + y = -9...multiply everything by -4
x - 4y = 36 <====

6 0

3 years ago

What are the solutions of the equation x6 + 6x3 + 5 = 0? Use factoring to solve.

lapo4ka [179]

Consider the equation $x^6+6x^3+5=0$ .

First, you can use the substitution $t=x^3$ , then $x^6=(x^3)^2=t^2$ and equation becomes $t^2+6t+5=0$ . This equation is quadratic, so

$D=6^2-4\cdot 5\cdot 1=36-20=16=4^2,\ \sqrt{D}=4,\\ \\ t_{1,2}=\dfrac{-6\pm 4}{2} =-5,-1$ .

Then you can factor this equation:

$(t+5)(t+1)=0$ .

Use the made substitution again:

$(x^3+5)(x^3+1)=0$ .

You have in each brackets the expression like $a^3+b^3$ that is equal to $(a+b)(a^2-ab+b^2)$ . Thus,

$x^3+5=(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25}) ,\\x^3+1=(x+1)(x^2-x+1)$

and the equation is

$(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25})(x+1)(x^2-x+1)=0$ .

Here $x_1=-\sqrt[3]{5} , x_2=-1$ and you can sheck whether quadratic trinomials have real roots:

1. $D_1=(-\sqrt[3]{5}) ^2-4\cdot \sqrt[3]{25}=\sqrt[3]{25} -4\sqrt[3]{25} =-3\sqrt[3]{25}$ .

2. $D_2=(-1)^2-4\cdot 1=1-4=-3$ .

This means that quadratic trinomials don't have real roots.

Answer: $x_1=-\sqrt[3]{5} , x_2=-1$

If you need complex roots, then

$x_{3,4}=\dfrac{\sqrt[3]{5}\pm i\sqrt{3\sqrt[3]{25}}}{2} ,\\ \\x_{5,6}=\dfrac{1\pm i\sqrt{3}}{2}$ .

6 0

3 years ago

Flogx=219.27 , G.M = 67.19 Find f

JulsSmile [24]

Let the answer be x.

Hence, f = x is the answer.

5 0

2 years ago

Horn Elementary School has 456 students. If there are exactly 24 students in each class, how many classes are there in the schoo

Ivan

Answer: There are 19 classes

Step-by-step explanation:

divide the total amount amount of students by the amount of students in each class

3 0

2 years ago

Read 2 more answers

If (x, y) is a solution to the system of equations, what is the value of x?

GREYUIT [131]

Answer:

B) -4

Step-by-step explanation:

(5/2)x + y = 2

x + (2/3)y = 4

y = 2 - (5/2)x

x + (2/3)(2 - (5/2)x) = 4

x + 4/3 - (5/3)x = 4

(-2/3)x = 8/3

-2x = 8

x = -4

3 0

2 years ago