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Morgarella [4.7K]
4 years ago
14

2x+3 less than or equal to 5

Mathematics
2 answers:
rjkz [21]4 years ago
6 0
2x+3 \leq 5 \\  \\ (2x+3)-3 \leq (5)-3 \\  \\ 2x \leq 2 \\  \\   \frac{2x}{2}  \leq  \frac{2}{2}  \\  \\ x \leq 1 \\  \\x=( -\infty} ,1]
ycow [4]4 years ago
3 0
2x + 3 ≤ 5
<u>      -3   -3</u>
      2x ≤ 2
      <u>2x</u> ≤ <u>2</u>
       2     2
       x =  1
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What are the dimensions of the largest 30-60-90 triangle that will fit inside a 45-45-90 triangle with leg length 14in.? Sketch
SSSSS [86.1K]
The dimensions would be 7√2, 7√6 and 14√2.

A 45-45-90 triangle has two equal legs and a hypotenuse that is equal to the leg multiplied by the square root of two (t, t, t√2).

A 30-60-90 triangle has legs that are equal to t, t√3, and 2t.  

The longest side on the 45-45-90 triangle will be 14√2.  This will also be the longest side of the 30-60-90 triangle; this gives us

2t = 14√2

Dividing both sides by 2, we have
2t/2 = 14√2/2
t = 7√2

We now have t and 2t; we lack t√3:

t = 7√2
t√3 = 7√2(√3) = 7√6.
8 0
3 years ago
Find the value of each trigonometric ratio. Simplify if you can.
alina1380 [7]

Answer:

5/13

Step-by-step explanation:

cos=adj/hyp=10/26=5/13

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3 years ago
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4 years ago
Find the Cartesian coordinates of the given polar coordinates. Then plot the point. (a) (2, π) (x, y) = WebAssign Plot WebAssign
Allisa [31]

Answer:

(a) ∴(x,y)= (-2,0)

(b) ∴(x,y)= (-2,-2\sqrt3)

(c) ∴(x,y)=(2\sqrt2,-2\sqrt 2)

Step-by-step explanation:

To convert from polar coordinate to Cartesian Coordinate(x,y)

  • x = r cos θ
  • y = r sin θ

(a)

Here r = 2 and θ = π

x= 2 cos π = -2

y=  2 sin π =  0

∴(x,y)= (-2,0)

(b)

Here r = 4 and \theta=-\frac{2\pi}{3}

x= 4 cos (-\frac{2\pi}{3})  =4\times (-\frac12) = - 2

y=  4 sin (-\frac{2\pi}{3})  =4\times (-\frac{\sqrt3}{2}) ==-2\sqrt3

∴(x,y)= (-2,-2\sqrt3)

(c)

Here r= -4  and \theta= \frac{3\pi}{4}

x=-4 cos (\frac{3\pi}{4})=-4 \times (-\frac1{\sqrt2)}=2\sqrt2

y=-4 sin(\frac{3\pi}{4})=-4\times \frac{1}{\sqrt2} =-2\sqrt 2

∴(x,y)=(2\sqrt2,-2\sqrt 2)

3 0
3 years ago
The ratio of pine trees to oak trees in the park is 3 to 8. If there are 14 pine trees,about many oak trees are there?
a_sh-v [17]

3 pine trees for every 8 oak trees

14 / 3 = 4 2/3

8 x 4 2/3 = 21 1/3, which rounds to 21

21 oak trees

5 0
3 years ago
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