What number should be placed in the box to help complete the division calculation? (1 point) Long division setup showing an incomplete calculation. 19 is in the divisor, 8216 is in the dividend, and 4 hundreds and 3 tens is written in the quotient. 7600 is subtracted from 8216 to give 616. An unknown value represented by a box is being subtracted from 616.

Answer:

The unknown value is being subtracted from 702 is 650

Step-by-step explanation:

Long division setup showing an incomplete calculation

13 is in the divisor

3302 is in the dividend

2 hundreds and 5 tens is written in the quotient

2600 is subtracted from 3302 to give 702

An unknown value represented by a box is being subtracted from 702

We need to find this number

Lets write the steps above

∵ The dividend = 3302

∵ The divisor = 13

- 2 hundreds means 200 and 5 tens means 50

∵ The quotient = 200 + 50 + x

∵ Dividend = divisor × quotient

∴ (13 × 200) + (13 × 50) + (13 × x) = 3302

∵ 13 × 200 = 2600

- Subtract 2600 from the dividend

∴ 3302 - 2600 = 702

∵ 13 × 50 = 650

∴ 702 - 650 = 52 ⇒ 650 is the unknown value

∵ 13 × x = 13x

∵ 52 - 13x = 0

- Add 13 x to both sides

∴ 52 = 13x

- Divide both sides by 13

∴ x = 4

∴ 3302 ÷ 13 = 200 + 50 + 4

∴ 3302 ÷ 13 = 254

∴ From the steps above the missing number subtracted from

  702 is 650

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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.
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2. Pe mulțimea de numere reale se definește legea de compoziție asociativă
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2x
(x − 5).

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′
(x) = e
2x
(2x − 9), x ∈ R .
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x
√x
2+1
.

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2 + 1
2
0

dx = 2.

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(
−
4
)
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