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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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Natasha_Volkova [10]

Answer:

<u>11 feet 2 inches</u>

Step-by-step explanation:

ill add the inches first

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26inches= 2ft 2inches

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<u>11 feet 2 inches</u>

7 0
2 years ago
Solve the value for v.
NemiM [27]

Answer:

Hey mate !!

Your answer is so simple :)

<h2>V= 9°</h2>

Go through the explanation to understand.

Step-by-step explanation:

In the given question,

We see that 105° and it's adjacent angle (i.e. 8v+3° ) forms a supplementary angle. Which means the sum of 8v+3°+105° is 180°

<h3>Therefore,</h3>

According to the question

105 + 8v + 3 = 180

=  > 105 + 8v = 180 - 3

=  > 8v =  177 - 105

=  > 8v = 72

=  > v =  \frac{72}{8}

=  > v = 9

Answer the value of v is 9° .

Hope it helps you!!

#IndianMurga ツ

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2 years ago
The volume of a cube is 27 cubic meters. what is its surface area in square meters?
erma4kov [3.2K]

To find the answer, take the measurement of an edge of the cube, multiply it by 6, and then square that number.

Ex:

Edge = 16

Faces in 1 cube = 6

     6 * 16 = 96

96^2 (which is just 96 * 96)= 9,216


I hope this helps! :)

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3 years ago
Solve for the surface area of the shape 6m 6m 6m 6m 4m
algol13

Answer:

28

Step-by-step explanation: add all sides together

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