Help with line equations?

Answers

Answer 1

Answer: First question

$line:~~~~y=x+3$

$curve:~~~~x^2+y^2=29$

now we have to replace the y of curve by the y of line, therefore

$x^2+(x+3)^2=29$

$x^2+x^2+6x+9=29$

$2x^2+6x+9-29=0$

$2x^2+6x-20=0$

we can multiply each member by $(1)/(2)$

$\boxed{\boxed{x^2+3x-10=0}}$

Now we have to find the roots of this funtion

$x^2+3x-10=0$

Sum and produc or Bhaskara

Then we find two axis

$\boxed{x_1=2~~and~~x_2=-5}$

now we replace this values to find the Y, we can replace in curve or line equation, I'll prefer to replace it in line equation.

$y=x+3$

$y_1=x_1+3$

$y_1=2+3$

$\boxed{y_1=5}$

$y_2=x_2+3$

$y_2=-5+3$

$\boxed{y_2=-2}$

Therefore

$\boxed{\boxed{P_1(2,5)~~and~~P_2(-5,-2)}}$
_______________________________________________________________

The second question give to us

$y=ax+b$

$P_1(2,13)$

$P_2(-1,-11)$

We just have to replace the value then we'll get a linear system.

point 1

$13=2a+b$

point 2

$-11=-a+b$

then our linear system will be

$\begin{Bmatrix}2a+b&=&13\n-a+b&=&-11\end{matrix}$

I'll multiply the second line by -1 and I'll add to first one

$\begin{Bmatrix}2a+(a)+b+(-b)&=&13+(-11)\n-a+b&=&-11\end{matrix}$

$\begin{Bmatrix}3a&=&24\n-a+b&=&-11\end{matrix}$

$\begin{Bmatrix}a&=&8\n-a+b&=&-11\end{matrix}$

therefore we can replace the value of a, at second line

$\begin{Bmatrix}a&=&8\n-8+b&=&-11\end{matrix}$

$\begin{Bmatrix}a&=&8\nb&=&-11+8\end{matrix}$

$\boxed{\boxed{\begin{Bmatrix}a&=&8\nb&=&-3\end{matrix}}}$

then our function will be

$\boxed{\boxed{y=8x-3}}$

_________________________________________________________________

The third one, we have

$line:~~~~y=3x-4$

$curve:~~~~y=x^2-2x-4$

This resolution will be the same of our first question.

Let's replace the y of curve by the y of line

$3x-4=x^2-2x-4$

$0=x^2-2x-4-3x+4$

therefore

$\boxed{\boxed{x^2-5x=0}}$

now we have to find the roots of this function.

$x^2-5x=0$

put x in evidence

$x*(x-5)=0$

$\boxed{x_1=0~~and~~x_2=5}$

then

$y=3x-4$

$y_1=3x_1-4$

$y_1=3*0-4$

$\boxed{y_1=-4}$

$y_2=3x_2-4$

$y_2=3*5-4$

$y_2=15-4$

$\boxed{y_2=11}$

our points will be

$\boxed{\boxed{P_1(0,-4)~~and~~P_2(5,11)}}$

I hope you enjoy it ;)

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How to solve this one

Answers

Answer:

Step-by-step explanation:

w^3 + 4w^2 + 5w - 12

I WILL ANSWER SO TIMMY GET CROWN

Joe works on an assembly line that fills boxes with various toy trinkets. Every sixth box gets a red ball and every eighth box gets a blue whistle. How often does a box get both a red ball and a blue whistle?

Answers

So we know that every 6th box gets a red ball and every 8th box gets a whistle, so now multiply 6, 8 until you get the same numberf EX: 6x1=6 8x1=8 and so on

Given the functions f (x) = x^2 + 4 and g (x) = 3x+ 8 what is a solution for the equation ? x^2 + 4 = 3x + 8 A. 0 B. 1 C. 2 D. 4

Answers

Answer:

Step-by-step explanation:

Let's solve your equation step-by-step.

x2+4=3x+8

Step 1: Subtract 3x+8 from both sides.

x2+4−(3x+8)=3x+8−(3x+8)

x2−3x−4=0

Step 2: Factor left side of equation.

(x+1)(x−4)=0

Step 3: Set factors equal to 0.

x+1=0 or x−4=0

x=−1 or x=4

Answer:

x=−1 or x=4

How many subsets does the set {1, 2, 3} have? 6 7 8

Answers

there are 8 sub sets

Answer: There are 8 subsets

Explanation: I got it right on my test.

If (x^2 – 4) ÷ (x + 2) = x – 2, which polynomial should fill in the blank below?(x + 2) ´ ______ = x^2 – 4

A. x^2 – 4
B. x – 2
C. x + 2
D. x^2 – 2

Answers

Option (b) $(x-2)$ is the correct answer.

A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

So, $(x+2)*(x-2)$

$=x^(2) -2x+2x-4$

$=x^(2) -4$

Therefore, LHS is equal to RHS.

Hence, $(x-2)$ is the polynomial that should be filled in that place.

Learn more about polynomial, refer to:

brainly.com/question/1600696

#SPJ2

The answer is x-2 because dividing is the opposite of mutiplying. Hope this helps.

Serena has $50 to spend. She buys 5 packages of hotdog buns and 5 packages of beef hotdogs. Each package of buns cost $3.85 and each package of beef hotdogs cost $4.20. How much money does Serena have left after these purchases?

Answers

she will have 9.75 left