7 more than the quantity 3 times 2

miv72 [106K]

$2x+y=0\qquad\text{subtract 2x from both sides}\\\\y=-2x\\\\\text{Put it to the second equation}\ 5x+3y=-11:\\\\5x+3(-2x)=-11\\\\5x-6x=-11\\\\-x=-11\qquad\text{change the signs}\\\\\boxed{x=11}\\\\\text{Put the value of x to the first equation:}\\\\y=-2(11)\\\\\boxed{y=-22}\\\\Answer:\ \boxed{x=11\ and\ y=-22}$

4 0

3 years ago

2. Given a directed line segment with endpoints A(3, 2) and B(6, 11), what is the point that

KATRIN_1 [288]

Answer:

The point of division is (5 , 8)

Step-by-step explanation:

* Lets explain how to solve the problem

- If point (x , y) divides the line whose endpoints are $(x_{1},y_{1})$

and $(x_{2},y_{2})$ at ratio $m_{1}:m_{2}$ , then

$x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$ and

$y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

* Lets solve the problem

- The directed line segment with endpoints A (3 , 2) and B (6 , 11)

- There is a point divides AB two-thirds from A to B

∵ The coordinates of the endpoints of the directed line segments

are A = (3 , 2) and B = (6 , 11)

∴ $(x_{1},y_{1})$ is (3 , 2)

∴ $(x_{2},y_{2})$ is (6 , 11)

∵ Point (x , y) divides AB two-thirds from A to B

- That means the distance from A to the point (x , y) is 2/3 from

the distance of the line AB, and the distance from the point (x , y)

to point B is 1/3 from the distance of the line AB

∴ $m_{1}:m_{2}$ = 2 : 1

∵ $x=\frac{(3)(1)+(6)(2)}{2+1}=\frac{3+12}{3}=\frac{15}{3}=5$

∴ The x-coordinate of the point of division is 5

∵ $y=\frac{(2)(1)+(11)(2)}{2+1}=\frac{2+22}{3}=\frac{24}{3}=8$

∴ The y-coordinate of the point of division is 8

∴ The point of division is (5 , 8)

6 0

3 years ago

A microorganism is a pathogen that _______

sergij07 [2.7K]

Answer:

A. can cause disease

Step-by-step explanation:

7 0

3 years ago

1.Find the zeros of f(x) = x2 - 9

Marat540 [252]

So for the first one it is (x-3)(x+3) this is because it is a difference of squares so you square root the 9 and the minus you do both +and - in order to keep up the -9
The zeros are:x=3 and x=-3 ( this is because you change the sign in the bracket

the others should be pretty simple to do for number 2 its a complex
the third is a simple trinomial
and fourth is simple trinomial as well

6 0

3 years ago

hey, can someone please double check these questions for me / or help me solve them if they are incorrect? thank you U-U

zzz [600]

Question 11

The directrix is a horizontal line, which means the parabola opens either upward or downward. In this case, it opens downward. This is because all answer choices have a negative leading coefficient. Also, it's because the focus is below the directrix.

For vertically opening parabolas, we use this form

4p(y-k) = (x-h)^2

where (h,k) is the vertex and p is the focal distance, aka the distance from the vertex the focus. To find (h,k), we start at the focus (0,-4) and move directly up until we reach the directrix y = 4. We'll arrive at (0,4). The midpoint of (0,-4) and (0,4) is (0,0) which is the vertex's location. So (h,k) = (0,0).

Note that in moving from (0,-4) to (0,4) is a span of 4 units. So this is the value of p.

Plug h = 0, k = 0, p = 4 into the equation mentioned and solve for y

4p(y-k) = (x-h)^2

4*4(y-0) = (x-0)^2

16y = x^2

y = (1/16)x^2

The only adjustment we need to make is to change the 1/16 to -1/16 so that the parabola opens downward.

<h3>Answer: Choice D. y = -(1/16)x^2</h3>

===============================================

Question 3

The given equation is in the form y = ax^2+bx+c

In this case,

a = 2
b = 4
c = 3

Let's compute the x coordinate of the vertex h

h = -b/(2a)

h = -4/(2*2)

h = -1

This h value is plugged into the original function to find k

f(x) = 2x^2+4x+3

f(-1) = 2(-1)^2+4(-1)+3

f(-1) = 1

We find that h = -1 and k = 1 pair up together. In short, (h,k) = (-1,1) is the vertex.

<h3>Answer: Choice B. (-1,1)</h3>

8 0

2 years ago