SUBIECTUL I

1. 1p Să se determine primul termen al unei progresii aritmetice (an

)n≥1 știind că rația este

egală cu 5 și suma primilor zece termeni ai progresiei este egală cu 245.
2. 1p Să se determine punctele de intersecție ale graficului funcției
f: R → R, f (x) = x

2 − 7x + 12, cu axele de coordonate.
3. 1p Să se determine numărul real a pentru care vectorii
u⃗ = (a − 2)i + (3a − 1)j și v = 2i +4j sunt coliniari.
4. 1p Să se calculeze ctg x, știind că sin x =
√3
2
, x ∈ (0, 90°
).
5. 1p Să se determine soluțiile reale ale ecuației 49x+2 = 7
x
2+5
.

6. 1p Să se rezolve ecuația : Ax
2+Cx
2 = 0, x∈ N , x≥ 2.

SUBIECTUL II
1 Se consideră matricea A(a) = (

1 0 √a
1 0 1
a 1 1

), unde a ∈ (0, ∞).

a) 0.5p Arătați că det(A(4)) = 1.
b) 0.5p Demonstrați că det(A(a) ∙ A(1) − A(a + 1)) > 0, pentru orice a ∈ (0, ∞).

2. Pe mulțimea de numere reale se definește legea de compoziție asociativă
x ∘ y = √3(xy + 4) − 3(x + y).
a) 0.5p Arătați că √3 ∘ 2 = √3.
b) 0.5pDemonstrați că x ∘ y = √3(x − √3)(y − √3) + √3, pentru orice numere reale x și y.
SUBIECTUL III

1 0.5p Se consideră funcția f: R → R, f(x) = e
2x
(x − 5).

Arătați că f

(x) = e
2x
(2x − 9), x ∈ R .
2. 0.5p Se consideră funcția f: R → R, f(x) =
x
√x
2+1
.

Arătați că ∫ f(x)√x
2 + 1
2
0

dx = 2.

Answers

Answer 1

Answer:

there was a tipikal answers of this question


Related Questions

What is 15.56 rounded to the nearest tenth?​

Answers

The answer is 15.6 cuz your round 0.56

Answer: 15.6

Step-by-step explanation:

In 15.56, the digit in the tenths place is the second 5. 15.56. So look at the hundredths place (6). If the digit in the hundredths place is smaller than 5, round down. If it's 5 or more, round up. 6 > 5, so we round the tenths place up by one number to get 15.6.

is the function linear or not

Answers

☆Answer :

Linear.

[tex] \rm {6x}^{2} = 12[/tex]

[tex] \rm {x}^{2} = 12 \div 6[/tex]

[tex] \rm {x}^{2} = 2[/tex]

[tex] \rm x = \sqrt{2} [/tex]

29 years ago, James put some money into a savings account with 8% interest compounded quarterly (4 times a year). He just remembered it and saw that there was now $7328 in it. Find the original amount he invested.

Answers

Answer:

$0.97

Step-by-step explanation:

7328*100/108^(4*29)

a bunch of math later, with rounding...

0.97

*note-may be wrong

On a busy construction site at 1:00 p.m. the sound level is 124 dB, while at 4:00 p.m. it is 100dB. How
many times as intense as the sound of the construction site at 4:00 p.m. is the sound at 1:00 p.m.?

Answers

Answer:

1.24 times as intense

Step-by-step explanation:

The intensity of the sound decreases by 24% at construction site from 4:00 p.m. to 1:00 p.m.

What is the average rate of change?

Let the function y = f(x).

Then the average rate of change will be

Average rate of change = (y₂ - y₁) / (x₂ - x₁)

On a busy construction site at 1:00 p.m. the sound level is 124 dB, while at 4:00 p.m. it is 100dB.

Then the intense as the sound of the construction site at 4:00 p.m. is the sound at 1:00 p.m. will be

⇒ (100 – 124) / 100

⇒ -0.24

Then the intensity of the sound decreases by 24% at construction site from 4:00 p.m. to 1:00 p.m.

More about the average rate of change link is given below.

https://brainly.com/question/23715190

#SPJ2

increase 2.75 by 1/4

Answers

Answer:

1/4 in decimal form is 0.25. You can convert any fraction into a decimal by just diving the numerator by the denominator.

Every time you see a fraction sign basically “—“ it jsut means divide by.

Now you can just divide. 1/4= 0.25

now we Increase which just means add

2.75+0.25 =3

7 inches 6 inches and 6 inches make a triangle?

Answers

Answer:

^

Step-by-step explanation:

The left and right sides of the triangle must be 6 and the bottom must be 7. This creates an equilateral triangle where 2 sides are equal.

Please help & solve for x thank you!

Answers

9514 1404 393

Answer:

  x = 23.1

Step-by-step explanation:

The parallel lines make the left segments proportional to the right segments. This lets us write the equation ...

  x/14 = 33/20

Multiplying by 14, we get ...

  x = 14(33/20) = 7(33/10) = 23.1

A man walks 50km a day he gets R1 for every 1000 steps. How much money will he have at the end of his 50km walk if 1,6Km is = to 2000 steps.​

Answers

we have 1,6Km is = to 2000 steps => 1 km = 1250 steps

=>  50km = 1250 x 50 = 62500 steps

so he'll have: 62500/1000 = 62,5 R1

ok done. Thank to me :>

Samantha is training to be a paramedic.
She works in the emergency room
of a hospital as part of the training
requirements. So far, she has completed
619 hours. If Samantha worked a total of
58 days so far, about how many hours
did she work each day?

Answers

About 10hours a day is the answer
10 hours per day , did you need to show any work or just an answer?

I just need the properties in order help plz

Answers

[tex] \: \: \: \: [/tex]

[tex]6x - 30 - 3x = - 12[/tex]

move the variable to the left hand side and change its sign, move the constant to the right hand side and change its sign

[tex]6x - 30 = - 12[/tex]

collect like terms and calculate the sum

[tex] 3x = - 18[/tex]

divide both sides of the equation by 3

[tex]x = 3[/tex]

hope it helps

[tex] \: \: \: \: \: [/tex]

[tex]\sf \longmapsto6(x−5)=3x−12[/tex]

Simplify both sides

[tex]\sf \longmapsto(6)(x)+(6)(−5)=3x+−12[/tex]

[tex]\sf \longmapsto6x+−30=3x+−12[/tex]

[tex]\sf \longmapsto \: 6x - 30 = 3x - 12[/tex]

Subtract 3x from both sides

[tex]\sf \longmapsto \: 6x−30−3x=3x−12−3x[/tex]

[tex]\sf \longmapsto3x−30=−12[/tex]

Add 30 to both sides

[tex]\sf \longmapsto3x−30+30=−12+30[/tex]

[tex]\sf \longmapsto3x=18[/tex]

Divide both sides by 3

[tex]\sf \longmapsto \: \dfrac{3x}{3} = \dfrac{18}{3} [/tex]

[tex]\sf \longmapsto \: x = 6[/tex]

[tex] \boxed{\sf \: x = 6 }[/tex]

60 children went to the beach.. 4/5 of them could swim. How many 60 children went to the beach. children could not swim?​

Answers

Answer:

75

Step-by-step explanation:

60 divided by 4/5 is 75

If 4/5 can swim, then 1/5 cant

1/5 of 60 is basically 60/5 which is 12

12 children can’t swim

Please help me ASAP

Answers

Step-by-step explanation:

a= 3×(-2)+3=-6+3=3

b=3×(-1)+3=-3+3=0

c=3×1+3=3+3=6

d=2×3+3=6+3=9

-------------------------

a=3, b=0, c=6, d=9

Good work!

hooke’s law states that the extension or elastic string beyond its natural length as the force applied. if a weight of 9 9 pounds attached to s spring causes it to a length of 20 inches?

Answers

Answer:

https://brainly.com/question/25709302

1. Suppose that in the population of American college students the average number of alcoholic drinks consumed per week is 22. What is the probability of randomly selecting a sample (n = 30) with a mean of 24 and a standard deviation of 5? (Hint: Tell me the two probabilities it will be between using a 2-tailed value)

Answers

ANSWER

im not sure on the full awnser.

Help help me help help

Answers

The co ordinates of M would be (-2,6)

49-6(4x-7) pls help me.

Answers

Here’s the answer! Hope this helps.

Help pls ASAP plssss is sims ska and d

Answers

The answer is -1 because the line goes through it

If you got $4 552 from your father and $1 478 from your mother and you spend $625. How much money do you now have to the nearest thousand?​

Answers

Answer:

simply add what you got from your mother and father then subtract from what you spent then the remaining is the answer

ANSWER: $5000

You get all together $6,030 from your parents and after you spend $625 you will have $5,405 left and be cause your rounding to the nearest thousand you check if the hundred in your number is above 5 because if it is below 5 you round down making it $5000 but if it were above 5 you would round up making it $6000 but because your amounts hundred is below 5, you will round down making your answer $5000

The speed of an object is the ratio of its distance traveled to time. If the speed of a bicycle is 4.5 meters per second, what is the distance traveled in 9 seconds?

Answers

Answer:

Step-by-step explanation:

9(4.5) = 40.5 m

A construction company can remove 3/8 tons of dirt from a construction site each hour. How long will it take them to remove 24 tons of dirt from the site

Answers

Answer:

64 hours

Step-by-step explanation:

(3\8) times 64 (hours) equals 24 (tons of dirt)

What would you do if you found out that you wrote a cheque of $78 but it was recorded as $98 in check register?

Answers

Step-by-step explanation:

I'll go to the cashier and says it's wrong cheque

the book is sold for 5.4 dollars at a profit of 8% on the cost price what was the cost price
please help

Answers

Answer:

5.4*0.08=0.432 or

43 cents

Hope This Helps!!!

Evaluate


[2- |-2/3 -2(-1/5)|] (-13)


What is the value of the expression?


Enter your answer as a simplified fraction in the box.

Answers

Answer: the answer - 2/15

Step-by-step explanation: i took the test

The value of the expression [2- |-2/3 -2(-1/5)|] ÷ (-13) is -2/15

What is an expression?

Numbers, symbols and operators grouped together that show the value of something.

Given that an expression [2- |-2/3 -2(-1/5)|] ÷ (-13)

[2- |-2/3 -2(-1/5)|] ÷ (-13)

= [2 - 4/15]/ (-13)

= 26/15*1/(-13)

= -2/15

Hence, The value of the expression [2- |-2/3 -2(-1/5)|] ÷ (-13) is -2/15

For more references on expression, click;

https://brainly.com/question/14083225

#SPJ5

Towns A, B, C, and X are located along a straight highway. Town B is between A and C, and the distance from A to C is
41 miles. BC is 2 miles more than twice AB.
Town X is between A and B, 6 miles from A. Find XC.
a. 13 miles
c. 41 miles
b. 28 miles
d. 35 miles

Answers

Answer:  35 miles, but this is not an answer option.

Step-by-step explanation:

A   X   B       C

AC = 41 miles

BC = 2AB + 2  

AX = 6

AX + XC = 41        [This is the key equation.  We want XC and AX is given as 6]

6 + XC = 41          

XC = 35 miles

None of the answer options show this value.

I don't know why, since:

a.  "the distance from A to C is 41 miles." means AC = 41, and

b.  "Town X is between A and B, 6 miles from A" means AX = 6

If we say that AX + XC = 41, then 6 + XC = 41 and XC = 35

I don't know why this would be incorrect, so I'll leave it to someone else to spot the problem.

What is 608 + 17.25?

Answers

Answer:

625.25

Step-by-step explanation:

the answer is 625.25

Answer: 625.25

Step-by-step explanation:

4(2x - 1) + 3(2x + 5)​

Answers

Answer:

14 x + 11

Step-by-step explanation:

4*(2x - 1) + 3*(2x + 5)​ =

8x - 4 + 6x + 15 =

14 x + 11

Which of the equations will be a true statement if
p
=
10
3
p
=
10
3
? Select the two choices that apply.





A.
3
.
4
÷
p
=
0
.
034
3
.
4
÷
p
=
0
.
034
B.
437
÷
p
=
0
.
437
437
÷
p
=
0
.
437
C.
53
.
45
÷
p
=
53
.
45
53
.
45
÷
p
=
53
.
45
D.
6
,
340
÷
p
=
6
.
34
6
,
340
÷
p
=
6
.
34
E.
2
,
458
.
2
÷
p
=
24
.
582
2
,
458
.
2
÷
p
=
24
.
582
I will mark brainless

Answers

Answer:

afd

Step-by-step explanation:

Jorge wants to find the height of the house, help him find it.

Answers

I think we need more explanation

Solve for x given that
4x + 2
7

Answers

Answer:

x = - 1/2 or -0.5

Step-by-step explanation:

Steps on the pic above

Fast indeed help on this !! ( ty )

Answers

Answer:

32

Step-by-step explanation:

First, draw some line for about 4 lines in the double number line.

Now in the bottom, it counts by 15 according to the word problem.

And in the top, count by 8.

Now finally, if you reach 60, write your final number. 32.

woohoo you did it lol

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