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.

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

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 :>

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.

Answer:

64 hours

Step-by-step explanation:

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

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]

im not sure on the full awnser.

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.

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

Answer:

625.25

Step-by-step explanation:

the answer is 625.25

Answer: 625.25

Step-by-step explanation:

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

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

Answer:

https://brainly.com/question/25709302

Answer:

75

Step-by-step explanation:

60 divided by 4/5 is 75

Answer:

5.4*0.08=0.432 or

43 cents

Hope This Helps!!!

Answer:

afd

Step-by-step explanation:

Answer:

x = - 1/2 or -0.5

Step-by-step explanation:

Steps on the pic above

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.

Answer:

Step-by-step explanation:

9(4.5) = 40.5 m

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

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!

Answer:

Step-by-step explanation:

4*(2x - 1) + 3*(2x + 5)​ =

8x - 4 + 6x + 15 =

14 x + 11

Step-by-step explanation:

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

Answer:

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

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

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.

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

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

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

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

[tex]x = 3[/tex]

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

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

[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]

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

[tex]\sf \longmapsto3x−30=−12[/tex]

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

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

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

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

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

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