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3 years ago

Determine if the three lengths can be the measures of the sides of a triangle.

Mathematics

1 answer:

wolverine [178]3 years ago

7 0

Answer:

yes

Step-by-step explanation:

For the lengths to form a triangle, the sum of any 2 must be greater than the third, that is

3 + 9 = 12 > 8

3 + 8 = 11 > 9

9 + 8 = 17 > 3

Thus the 3 lengths can form a triangle

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A car was valued at $39,000 in the year 1995. The value depreciated to $11,000 by the year 2003.

denis23 [38]

Answer:

14.6328% , $5836.03

Step-by-step explanation:

Here we are going to use the formula

$A_{0}(1-r)^n = A_{n}$

$A_{0}$ = 39000

r=?

$A_{8}$ = 11000

n=8

Hence

$39000(1-r)^8 = 11000$

$(1-r)^8 = \frac{11000}{39000}$

$(1-r)^8 = 0.2820$

$(1-r) = 0.2820^{\frac{1}{8}$

$(1-r) = 0.2820^{0.125}$

$(1-r) = 0.8536$

$(1-0.8536=r$

$r = 0.1463$

Hence r= 0.1463

In percentage form r = 14.63%

Now let us see calculate the value of car in 2003 that is after 12 years

we use the main formula again

$A_{0}(1-r)^n = A_{n}$

$A_{0}$ = 39000

r=0.1463

$A_{12}$ = ?

n=12

$39000(1-0.14634)^{(12} = A_{12}$

$39000(0.8536)^{12} = A_{12}$

$39000*0.1497 = A_{12}$

$A_{12}=5840.34$

Hence the car's value will be depreciated to $5840.34 (approx) by 2003.

5 0

3 years ago

A circle with circumference 6 has an arc with a 60° central angle.

erica [24]

Answer:

length of an arc = 1unit

Step-by-step explanation:

given that the circumference of a circle = 6

central angle = 60

length of the arc =?

recall that the circumference of a circle = 2πr

6 = 2πr

r = 6/2π

now to calculate the length of an arc

recall,

length of an arc = 2πr(Ф/360)

length of an arc = 2π(6/2π) × 60/360

length of an arc = 6 × 60/360

length of an arc = 360/360

length of an arc = 1unit

therefore the length of the arc whose circumference is 6 and arc angle is 60° is evaluated to be 1unit

5 0

3 years ago

Let the vector \mathbf{v}v have an initial point at (1, -2)(1,−2) and a terminal point at (0, 0)(0,0). Plot the vector \mathbf{v

ASHA 777 [7]

Given that the initial point of the vector is (1,-2) and the termination point of the vector is (0,0).

So, the tail of the vector is at point (1,-2) and the head of the vector is at (0,0). The vector, $\vec{v}$ , has been shown in the figure.

The magnitude of the vector:

$|\vec{v}|=\sqrt{(1-0)^2+(-2-0)^2}=\sqrt{1+4}=\sqrt{5}$

The direction of a vector is the angle made by a vector with the positive direction of the x-axis.

From the figure, $\theta = 180 \degree\tan ^{-1} \left|\frac {0-(-2)}{0-1}\right|$

$\theta = 180 ^{\circ} - \tan^{-1}(2) = 180 ^{\circ} - 63.43^{\circ}$

$\theta =116.57 ^{\circ}$

Hence, the required vector having a magnitude $\sqrt {5}$ and direction $116.57 ^{\circ}$ has been shown in the figure.

4 0

4 years ago

A garden snail traveled 1⁄40 of a mile in 1⁄2 an hour. What was the speed of the snail?

abruzzese [7]

There are several information's of immense importance already given in the question. Based on those information's the answer to the question can be easily deduced.
The total distance that has been traveled by the garden snail in question = 1/40 mile
Time taken by the garden snail to travel the distance given in question = 1/2 hour.
Then
Speed of the snail = Distance traveled/ Time taken
   = (1/40)/(1/2) miles per hour
   = 2/40 miles per hour
   = 1/20 miles per hour
So the speed of the garden snail as can be seen from the above deduction is 1/20 miles per hour. I hope the procedure is simple enough for you to understand.

6 0

3 years ago

What percent of 141 is 35.4

melamori03 [73]

Step-by-step explanation:

35.4/141x100%=25.1% (3s.f.)

6 0

3 years ago

Read 2 more answers