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vivado [14]
2 years ago
11

Which set of values could be the side lengths of a 30-60-90 triangle?

Mathematics
2 answers:
navik [9.2K]2 years ago
6 0
A triangle with 30°, 60° & 90° angles is called a semi equilateral triangle.

In such a triangle the hypotenuse equal the side of the equilateral triangle,  and the opposite side to the angle 30° is equal half the side of the equilateral or half the hypotenuse.

Assume the side equal 8 & the other 8/2 = 4. let's calculate the 3rd side by applying Pythagoras:

8²  = 4² + x² ;  64 = 16 + x²  or x² = 64-16 ; x² =48 and
x =√48 = √16. 3 = 4√3

So the 3 sides are 8, 4 and 4√3 (answer B)
jeyben [28]2 years ago
3 0
If we say that side "a" is the shortest (adjacent), side "b" is the second shortest (opposite), and side "c" is the longest (hypotenuse): then angle A would be 30°,  angle B would be 60°, and angle C would be 90°

tan B = b/a
 or
a tan B = b

they have 4 as the smallest value in all four options, so we know that a=4

4 tan 60° = b
tan 60° = √3
so, 4 tan 60° = 4√3
b=4√3

that leaves two options left, so now we find "c":

c^2 = (a^2) + (b^2)
OR
c= \sqrt{a^{2} + b^{2}}

c= \sqrt{4^{2}+(4\sqrt{3})^{2}}

c= \sqrt{16+48} \\ c=\sqrt{64} \\ c=8

so a=4, b=4√3, and c=8

Making your answer B
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A fertilizer company manufactures 10-pound bags of fertilizer with a standard deviation of 0.24 pounds per bag. The bag weights
Ksju [112]

Answer:

the probability that a sample of 4 bags will have a mean weight less than 9.8 pounds is 0.05

Step-by-step explanation:

Given the data in the question;

μ_x = 10 pound bags

standard deviation s_x = 0.24 pounds

sample size n = 4

The bag weights are normally distributed so;

p( x' less than 9.8 ) will be;

p(  (x'-μ_x' / s_x')   <   (9.8-μ_x' / s_x')  )

we know that;

μ_x' = μ_x = 10

and s_x' = s_x/√n = 0.24/√4

so; we substitute

p(  z  <  ( (9.8 - 10) / (0.24/√4)  )

p(  z  <  -0.2 / 0.12   )

p(  z  <  -1.67   )

{ From z-table }

⇒ p(  z  <  -1.67   ) = 0.0475 ≈ 0.05

Therefore, the probability that a sample of 4 bags will have a mean weight less than 9.8 pounds is 0.05

3 0
3 years ago
-8(1+8n)-8(6-4n)=-24
Naily [24]

-8(1 + 8n) - 8(6 - 4n) = -24

-8 - 64n - 48 + 32n = -24

-32n - 56 = -24

-32n = 32

n = -1

3 0
3 years ago
Please help!!! I need this done today!!
Kryger [21]

Answer:

1) distance travelled = 75mi

time taken = 3 hrs.

speed = distance/time

= 75/3 = 25 mi/hr.

now, if time = 1.6 hrs.

Distance = speed x time

= 25 x 1.6 = 40.0 mi

---------------------------------------------------------------------------------------------

2) earning for 8 hrs. of work = $120.

therefore, rate of earning per hr. = 120/8 = $15/hr.

so, earning in 11 hrs. = 15 x 11 = $165


8 0
3 years ago
Factorise -75ab² - 15ac
Verdich [7]

Answer:

1)  -15·a·(5·b² + c)

2) h < 4

3) 4·x² - 9

4) 1792

5)  156°

6) 2t cm

7) 2·a·m·(2·m - 3)

8)  10 cm

9) 0.00051

10)  #47,250

11)  -10·p·q

12) 1.35 × 10⁻⁴

13) 320°

14) 20 cm

15) 12·x²·y²

16) 6.36 × 10⁵

17) 4 cm

18)  225°

19) 1034 cm²

20) 29

Step-by-step explanation:

1) The given expression is -75·a·b - 15·a·c

Which can be expressed as -15·a·(5·b² + c)

2) The height, h < 2 × 12/6 = 4

h < 4

3) (2·x - 3)·(2·x + 3) = 4·x² - 9

4) The selling price = 1.12 × 200 × 8 = 1792

5) The interior angle of a polygon is given by the relation;

(n - 2)×180/n for 15, we get;

(15 - 2)×180/15 = 156°

6) 2t cm

7) 4·a·m² - 6·a·m = 2·a·m·(2·m - 3)

8) Slant height = √(8² + 6²) = 10 cm

9) 51 × 10⁻⁵ = 0.00051

10) Cash price = #54,000 × (1 - 0.125) = #47,250

11) -40·p·q÷(-2)² = -10·p·q

12) 0.003 × 0.045 = 1.35 × 10⁻⁴

13) N40°W = 320°

14) The base diameter of the cylinder = √(4 × (700×π cm³/7)/π) = 20 cm

15) The LCM of 2·x²·y, 3·x·y² is 12·x²·y²

16) 636,000 = 6.36 × 10⁵

17) 1/3·π·r²·h₁ = π·r²·h₂

h₂/h₁ = 1/3·π·r²/( π·r²) = 1/3

h₂/12 =  1/3

h₂ = 12/3 = 4 cm, the height of the cylinder = 4 cm

18) The angle = 180 + 45 = 225°

19) The total surface area = 22/7×14²/4 +  22/7 ×14 × 20 = 1034 cm²

20) The number is 58/2 = 29.

4 0
3 years ago
Given that EF is a diameter of circle D, which of the following arcs must be a major arc?
Rainbow [258]

Answer:

Arc ECG is the major arc

Step-by-step explanation:

Arc ECG is made by an angle which is greater than 180°.

All the other arcs listed are made by angles which are 180° or less than.

The greater the angle measure the greater the arc length.

8 0
2 years ago
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