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madreJ [45]
3 years ago
14

Help with these questions please!

Mathematics
1 answer:
Orlov [11]3 years ago
8 0

Answer:

9.  (1)

10. (2)

11.  (3)

12. (2)

Step-by-step explanation:

9. Given the equation of the parabola

(y-3)^2=8(x-2)

If the equation of the parabola is in form (y-y_0)^2=2p(x-x_0), then (x_0,y_0) are the coordinates of its vertex and p is parabola's parameter. So, the vertex is at (2,3) and p = 4.

This parabola goes in positive x-direction, so the focus is at

F\left(\dfrac{p}{2}+x_0,y_0\right)\\ \\F(2+2,3)\\ \\ F(4,3)

and the equation of the directrix is

x=-\dfrac{p}{2}+x_0\\ \\x=-2+2\\ \\x=0

Correct option is (1)

10. The diagram shows the absolute value function with vertex at (3,0). From the graph you can see that the left part of the graph determines increasing function (when going by the graph, you'll go up) and the right part of the graph determines the decreasing function (when going by the graph, you'll go down). So,

  • increasing for x\in (-\infty ,3);
  • decreasing for x\in (3,\infty).

11. Given

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

and

g(x)=-x^3+5

<u>Definition:</u> Function f(x) is an even function, if for all x from the domain, f(-x)=f(x)

<u>Definition:</u> Function f(x) is an odd function, if for all x from the domain, f(-x)=-f(x)

Consider function f(x):

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

So, the function f(x) is an even function and is not an odd function. Thus, option (3) is false

12. Consider function

f(x)=-x^2+12x-4

Find the discriminant:

D=b^2-4ac=12^2-4\cdot (-1)\cdot (-4)=144-16=128

Since the discriminant is greater than 0, the function has 2 different rational roots. These roots are irrational, because \sqrt{128}=8\sqrt{2} is an irrational number.

So, correct option is (2)

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Can you please answer this question ​
schepotkina [342]

Answer:

1/40

219/250

69/16

Step-by-step explanation:

1.

0.025=(025)/(1000)=1/40

2.

0.876=876/1000=219/250

3.

4.3125=43125/10000=1725/400=69/16

4 0
3 years ago
What is the answer to -5x+5y=-10 and 3x-3y=5 using substitution
IceJOKER [234]

Answer:

for the 1st one the answer is x= 3 y=1 and the second one is x= 5 and y = 3 and 1/3

Step-by-step explanation: so basically for the first one -5 times x which is 3 is -15 right? and then 5 times y which is 1 is 5 right so -15 plus 5 = -10

second one is x = 5 and y = 3 and 1/3 because 5*x which is 5 is = to 15 right? and then 3 times y which is equal to 3 and 1/3 is equal to 10 which when you do 15-10 in pretty sure it equals 5 correct me if im wrong

Hope this helps xD ;)

7 0
3 years ago
Using the graph, determine the coordinates of the vertex of the parabola.
nadezda [96]

Answer:

The coordinates of the vertex is (6,4).

Step-by-step explanation:

The vertex is the highest or lowest point on the parabola (curved line).

6 0
2 years ago
A rectangle has a width of 2cm and a perimeter of 25cm. Find the length and the area .
Gwar [14]

2w + 2l = 25

2 * 2 + 2l = 25

<em><u>Simplfiy.</u></em>

4 + 2l = 25

<em><u>Subtract 4 from both sides.</u></em>

2l = 21

<em><u>Divide both sides by 2.</u></em>

l = 10.5

Now that we have the value of l, we can find the area.

A = lw

A = 10.5 * 2

A = 21.

The length is 10.5cm.

The area of the rectangle is 21cm^2

5 0
3 years ago
Please help mee! The picture is up there :)
Gala2k [10]

Answer:0

the answer is 5

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
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