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3 years ago

How many integer solutions are there to the equation x1+x2+x3=0 if x1,x2,x3 > -5?

1 answer:

4 0

x1+x2+x3=0 if x1,x2,x3 > -5?
and the solutions are integer
x1= - 4 and x2+x3=4 we count (-4;4;0), (-4;0;4), (-4;3;1), (-4;1;3), (-4; 2;2), (-4;2;2)
x1= -3 and x2+x3=3 we count (-3; 0;3), (-3;3;0), (-3;1;2), (-3;2;1)
x1= -2 and x2+x3=2 we count (-2;0;2). (-2;2;0), (-2;1;1)
x1= -1 and x2+x3=1 we count (-1;0;1), (-1;1;0)
x1=0 and (0;0;0), (0;1;-1), (0;-1;1)
There are 42 solutions
Have fun

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State of the triangles in each pair of similar. If so, State how you know they are similar and complete the similarity statement

Vinil7 [7]

Answer:

b. not similar

Step-by-step explanation:

The given sides* have the ratio 30:39 = 10:13 in one triangle and the ratio 20:27 = 10:13.5 in the other triangle. Since these ratios are different, the triangles cannot be similar.

____

* These are the sides bracketing the vertical angles at T. If the triangles were similar, the three sides would have to have the ratios 10 : 13 : 13.5.

However, the geometry shown would require that the angle opposite side 13.5 in one triangle have the same measure as the angle opposite side 13 in the other triangle. That is not possible, so it is not possible for these triangles to be similar.

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3 years ago

There is a parallelogram ABCD with diagonals AC and BD. The diagonals AC and BD intersects each other at point E. Side AB is con

grandymaker [24]

Answer:

SAS theorem

Step-by-step explanation:

Given

$\square ABCD$

$\[ \lvert \[ \lvert AB =\[ \lvert \[ \lvert CD$

$\angle BAC = \angle DCA$

Required

Which theorem shows △ABE ≅ △CDE.

From the question, we understand that:

AC and BD intersects at E.

This implies that:

$\[ \lvert \[ \lvert AE = \[ \lvert \[ \lvert EC$

and

$\[ \lvert \[ \lvert BE = \[ \lvert \[ \lvert ED$

So, the congruent sides and angles of △ABE and △CDE are:

$\[ \lvert \[ \lvert AB =\[ \lvert \[ \lvert CD$ ---- S

$\angle BAC = \angle DCA$ ---- A

$\[ \lvert \[ \lvert BE = \[ \lvert \[ \lvert ED$ or $\[ \lvert \[ \lvert AE = \[ \lvert \[ \lvert EC$ --- S

Hence, the theorem that compares both triangles is the SAS theorem

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2 years ago

What is the volume of the planter that measures 60l, 60w. 60h?

andre [41]

The volume of the planter that measures 60 l, 60 w. 60 h (D) 216000 cm³

Explanation:

Length, l = 60 cm

Width, w = 60 cm

Height, h = 60 cm

Volume, v = ?

We know,

Volume = length ×width × height

Substitute the values in the formula.

$v = 60 X 60 X 60\\\\v = 216,000 cm^3$

Therefore, the volume of the planter is 216,000 cm³

8 0

3 years ago

michelle and rosa are researching the deepest lakes in the united states for a school project. lake tahoe has a depth of 1,644 f

Hatshy [7]

Answer:

Rosa is closer to the correct depth.

Step-by-step explanation:

To show that two measurements are nearly equivalent, we must convert one of the measurements to the other unit.

1 m = 3.281 ft

$\text{Depth } = \text{1644 ft} \times \dfrac{\text{1 m}}{\text{3.281 ft}} = \textbf{501.1 m}$

Neither is correct but Rosa is closer to the correct depth.

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2 years ago

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pentagon [3]

Answer:

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2 years ago