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dolphi86 [110]
2 years ago
8

Find an integer $x$ such that $\frac{2}{3} < \frac{x}{5} < \frac{6}{7}$.

Mathematics
2 answers:
julsineya [31]2 years ago
6 0

Answer:

5

Step-by-step explanation

Aops Question

alexandr1967 [171]2 years ago
5 0

Answer:

4

Step-by-step explanation:

It's AoPS question

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Find the point on the line y = 3x + 2 that is closest to the origin.
anzhelika [568]
1.
the slope of the line y=3x+2 is the coefficient of x, that is 3.

2.
the slope of any line perpendicular to the line y=3x+2, is m, such that:

3*m=-1

so m= \frac{-1}{3}

3. 
so any line with equation y=-1/3x+k is perpendicular to y=3x+2.

moreover, the line y=-1/3x (so k=0) is the line passing through the origin
(0, 0) and perpendicular to y=3x+2


4. This means that the closest point of y=3x+2 to the origin is the intersection point of lines y=3x+2 and y=-1/3x

5.
to find this point:

3x+2=(-1/3)x
x(3+1/3)=-2
x(9/3+1/3)=-2

x*10/3=-2

x= \frac{-2*3}{10} = \frac{-6}{10}=-0.6


thus y is :  (-1/3)(-6/10)=0.2



Answer: (-0.6, 0.2)

3 0
3 years ago
Which would be the BEST formula to model the volume of the bus shown?
Elenna [48]

Answer:

1.) D

2.) C

Step-by-step explanation:

3 0
2 years ago
Solve BCD Round the answer to the nearest hundredth
lesya [120]

Answer:

A

Step-by-step explanation:

The measure of angle D can be found using the Interior Angle Sum of a Triangle.

The angles of a triangle add to 180. This means:

90 + 21 + x = 180.

111 + x = 180

x = 69

The solution is A.

Angle B is smaller than Angle D which means CD will be smaller than BC.

7 0
3 years ago
*80 POINTS!!!! PLEASE HELP ME I HAVE BEEN WAITING FOR MORE THAN AN HOUR!!!!!!!!!! MARKING AS BRAINLIEST!! PLEASE SHOW WORK AND E
ruslelena [56]

Answer:

  D.  tan(-π/6)

Step-by-step explanation:

The tangent function is periodic with a period of π, so ...

  tan(5π/6) = tan(5π/6 ± kπ) . . . for any integer k

For k = -1, we have ...

  tan(5π/6) = tan(5π/6 -π) = tan(-π/6)

7 0
3 years ago
Please answer for extra points !
MatroZZZ [7]

Answer:

the answer is D

Step-by-step explanation:

I don't know how to explain it very well but the line starts at 2 then ends at 8

6 0
2 years ago
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