Select the correct answer
Consider the given solids with the dimensions shown. Which solids are similar?
Aonly figure 1 and figure 2
B.only figure 2 and figure 3
c.only figure 1 and figure 3
D. all three figures
E none of the figures

only figure 1 and figure 3 are similar.

Two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.

In figure 1, two of the sides (16 and 9 ) are perfect square and third is not.

If we take the ratio of three side as

16:9:12

(4)²:(3)²:(2√3)²

Similarly, In figure 3 two of the sides (64 and 36 ) are perfect square and third is not.

If we take the ratio of three side as

64:36:48

(8)²:(6)²:(4√3)²

Comparing the ratios of both figure, the figure 3  has twice the measurement of figure 1 sides.

Hence, only figure 1 and 3 are similar.

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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.
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.

Does anyone know the solution

Fill in the blank with a number to make the expression a perfect square.

y^2 + 6y + ?

please help :( ill give 40 points

Harold and his brother collected 2019 cans a 1-year period. Each boy collected the same number of cans. About how many cans did each boy collect? Explain how you found your answer.​

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4.
Find the value of y when x = 2.
y = 3x + 2
XON
Y
2
2
a) 2
b) 6
c) 7
d) 8

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triangle
rectangle
rhombus
square

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Phyllis invested $50,000 in two different types of stock. The first type earned 10% and the second type earned 15%. If the profit on the 15% stock was $2,500 more than the profit on the 10% stock, how much did Phyllis invest in the 15% stock?​

Which point represents
−
(
−
4
)
−(−4)minus, left parenthesis, minus, 4, right parenthesis on the number

Maya earned $225.oo at her job when she worked for 10 hours. What did she earn in one hour?

Mr. And mrs. Samson decide to go with design a and purchase the materials. Their total bill is 356.88. If they pay 220 in cash and charge the remainder, how much did they charge?

i need help with this please​

Directions: Write the
numerical expression
into word form. I it is in
word form, write it as a
numerical expression.
(8x2)-(3+5)

8x-2y=18 3x-y=5 What is the y value of the solution?

Help help help help help help

A camera is on sale for $130. After a 7.875% sales tax is added, what is the total cost of the camera?​

Please Help!!! I will try to give brainliest!!!

One angle of a triangle measures 134 degrees. The other two angles are in a ratio of 9:14. What are the measures of those two angles?

solve this question

​

Which system of inequalities is shown?

Your dinner bill is 93.24$

Select the correct answer.
When graphing an inequality, the boundary line needs to be graphed first. Which graph correctly shows the boundary line of the inequality?
y <1/3x+ 1

In Phoenix, Arizona, the average number of sunny days is 211 per year. About what percent of the year is Phoenix sunny?​