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fiasKO [112]
3 years ago
10

1)

Mathematics
1 answer:
algol133 years ago
3 0
You will try all the cases and see if all the equations will match after substituting or no.
1.
5x
put x = 1/2
2.5 isn't equal to 20

4=15x
put x =1/2
15 × 1/3 =7.5
7.5 isn't equal to 4

-4x = 60
put x = 1/2
-4×1/2 = -2
-2 isn't equal to 60

30 = 60x
pit x = 1/2
60 × 1/2 = 30
30 = 30

Therefore, the correct answer is D. 30 = 60x

2. Answer is B. -4 , 4

Put x = -4
l 5 × -4 l = l-20l = 20
20 = 20

Put x = 4
l 5 × 4 l = l20l = 20
20 = 20
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The answer is 50


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Factor f(x)=x4-x3-7x2+13x-6 completely. Then Sketch the graph
Dennis_Churaev [7]

ANSWER TO QUESTION 1


f(x)=(x-2)(x+3)(x-1)^2.



EXPLANATION


The function given to us is,


f(x)=x^4-x^3-7x^2+13x-6


According to rational roots theorem,


\pm1,\pm2,\pm3,\pm6 are possible rational zeros of  


f(x)=x^4-x^3-7x^2+13x-6.


We find out that,


f(-3)=(-3)^4-(-3)^3-7(-3)^2+13(-3)-6


f(-3)=81+27-63-39-6



f(-3)=6-6



f(-3)=0


Also




f(2)=(2)^4-(2)^3-7(2)^2+13(2)-6



f(2)=16-8-28+26-6



f(2)=6-6



f(2)=0


This implies that  


x-2 and x+3 are factors of



f(x)=x^4-x^3-7x^2+13x-6 and hence (x-2)(x+3)=x^2+x-6 is also a factor.



We perform the long division as shown in the diagram.



Hence,


f(x)=(x-2)(x+3)(x-1)^2.


ANSWER TO QUESTION 2

Sketching the graph

We can see from the factorization that the roots  

x=2 and x=-3 have a multiplicity of 1, which is odd. This means that the graph crosses the x-axis at this intercepts.


Also the root x=1 has a multiplicity of 2, which is even. This means the graph does not cross the x-axis at this intercept.



Now we determine the position of the graph on the following intervals,


x\le -3


f(-4)=(-4)^4-(-4)^3-7(-4)^2+13(-4)-6


f(-4)=150\:>0



-3\le x \le 1


f(0)=-6\:


1\le x\le 2


f(1.5)=-0.56\:



x \ge 2



f(3)=24\:>0



We can now use these information to sketch the function as shown in diagram



4 0
3 years ago
PLS HELP ME. THIS IS THE LAST QUESTION !!! i’ll give you brainliest and 15 points !! pls show work.
nata0808 [166]

Answer:

The answer is 9

Step-by-step explanation:

Since the diagram is rhombus

Then

pq = qr = rs = sp \\ 2y + 3 = 5y - 6 \\ 5y - 2y = 6 + 3 \\ 3y = 9 \\ y = 3

Then

qr = 2y + 3 \\  = 2 \times 3 + 3 \\  = 9

If you need any explanation in math you can communicate with me on Whats on this number +201557831028 or face, email,instaand anything

8 0
3 years ago
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