1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
SVETLANKA909090 [29]
3 years ago
8

Help with line equations?

Mathematics
1 answer:
Alecsey [184]3 years ago
5 0
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 \frac{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\\-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)\\-a+b&=&-11\end{matrix}

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

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

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

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

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

\boxed{\boxed{\begin{Bmatrix}a&=&8\\b&=&-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 ;)
You might be interested in
4x+12+2=23<br> Solve the multi step equation
Eduardwww [97]

Answer: x = 9/4

Step-by-step explanation:

4x+12+2=23

4x+14 = 23

4x = 9

x = 9/4

7 0
3 years ago
Read 2 more answers
Where were some of the first tunnels built
QveST [7]
<span>In Babylonia, tunnels were used extensively for irrigation; and a brick-lined pedestrian passage some 3,000 feet (900 meters) long was built about 2180 to 2160 BC under the Euphrates River to connect the royal palace with the temple. Hopefully this answer helps
</span>
6 0
3 years ago
A and B are complementary angles. If A = (x – 23)° and m
Lana71 [14]

Answer:

∠ B = 85°

Step-by-step explanation:

Complementary angles sum to 90° , then

x - 23 + 2x + 29 = 90 , that is

3x + 6 = 90 ( subtract 6 from both sides )

3x = 84 ( divide both sides by 3 )

x = 28

Then

∠ B = 2x + 29 = 2(28) + 29 = 56 + 29 = 85°

5 0
2 years ago
What is the percentage:<br><br> 16 out of 20
gtnhenbr [62]
16/20= .80
.80 x 100%
=80%
3 0
3 years ago
HELP???????????????????????????????????????????????????????? pls? (10 points) (image down below to make it easier to understand.
prisoha [69]

Answer:

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Other questions:
  • What is the rational number between -1/6 and -2/6
    14·1 answer
  • Need help with radical expression!!! It’s asking for a set of all x where the expression is defined in interval form!
    15·1 answer
  • Nibbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
    14·1 answer
  • What adds to 11 and multiplies to -150
    9·1 answer
  • Suppose you just received a shipment of twelve televisions. Three of the televisions are defective. If two televisions are rando
    11·1 answer
  • 11,792.7 in word form
    13·1 answer
  • There are many cones with a height of 12 inches. Let r represent the radius and V represent the volume of these cones.
    11·2 answers
  • How do I do this? <br> I need to simplify the answers
    11·2 answers
  • Find the discriminant and describe the nature of the root(s) of the equation: 6x2 - 2x - 4 = 0)
    10·1 answer
  • Find the center of the circle whose equation is (x - 5) 2 + (y + 3) 2 = 6.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!