Halla la forma general de la recta que pasa por los puntos P( -10, -7) y Q(-6, -2)

Alecsey [184]

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

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

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

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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 ;)

5 0

3 years ago

There are 12 girls and 16 boys . What is the largest number in each group?

lianna [129]

Answer:

Step-by-step explanation:

The largest number of groups they can be split into and have the same number of boys and girls on each team is 6 groups

Given:

Number of girls = 12

Number of boys = 16

Find the highest common factor of 12 and 16

12 = 1, 2, 4

18 = 1, 2,4

The highest common factor of 12 and 16 is 4

Number of girls in each group = 12/4

= 3 girls

Number of boy in each group = 18/4

= 4.5 boys=5

Therefore, the group can be split into 4 groups to have 3 girls and 5 boys in each group

8 0

2 years ago

Can somebody plz help answer all these questions (like what to add to solve it)

kirza4 [7]

18. 9
19. 5
20. 12
21. 8
22. 2

6 0

2 years ago

Read 2 more answers

How can you determine the domain and range of function.

Mice21 [21]

Answer:

The domain of a function is the complete set of possible values of the independent variable.

In plain English, this definition means:

The domain is the set of all possible x-values which will make the function "work", and will output real y-values.

When finding the domain, remember:

The denominator (bottom) of a fraction cannot be zero

The number under a square root sign must be positive in this section

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Hong has been given a list of 6 bands and asked to place a vote. his vote must have the names of his favorite and second favorit

mixas84 [53]

This requires us to find the number of permutations of 6 different bands taken 2 at a time:
$6P2=\frac{6!}{(6-2)!}=30\ different\ votes.$

7 0

2 years ago