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3 years ago

Si "m" es el lado mayor de un triángulo, dos cuyos ángulos interiores miden 30° y 60°, entonces el perímetro del triángulo es

Mathematics

1 answer:

lions [1.4K]3 years ago

7 0

Answer:

$perimetro = \dfrac{(3 + \sqrt{3})m}{2}$

Step-by-step explanation:

triángulo 30°-60°-90°

$1~:~\sqrt{3}~:~2$

$1m~:~m\sqrt{3}~:~2m$

$\dfrac{m}{2}~:~\dfrac{m\sqrt{3}}{2}~:~m$

$perimetro = \dfrac{m}{2} + \dfrac{m\sqrt{3}}{2} + m$

$perimetro = \dfrac{m}{2} + \dfrac{m\sqrt{3}}{2} + \dfrac{2m}{2}$

$perimetro = \dfrac{m + m\sqrt{3} + 2m}{2}$

$perimetro = \dfrac{3m + m\sqrt{3}}{2}$

$perimetro = \dfrac{(3 + \sqrt{3})m}{2}$

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Please answer ASAP it’s really important please

bazaltina [42]

Answer:

Letter A.

Step-by-step explanation:

0 is not divisible, so the last the last two alternatives are impossible.

The second one doesn't work, so I'd stick to letter A.

6 0

3 years ago

Charlotte has been saving up to buy a home gym so she can work out at home without having to pay for a

Y_Kistochka [10]

The 15% discount for home gym, and the $889 cost of the Flex 3,000 gives;

1. f(x) = 0.85•x + 139.95

With the deal, Charlotte's before tax cost is $895.6
The deal cost is more than the initial price making the deal not worth it.

3. The domain is; 889 < x < ∞

The range is; 895.6 ≤ f(x) ‹ ∞

<h3>How can the function notation for the cost be found?</h3>

1. The percentage discount Charlotte gets = 15% = 0.15

Cost of the 6 months subscription = $139.95

f(x) = Final before tax

x = Price of the home gym equipment

Therefore;

Given the 15% off, we get;

f(x) = (1-0.15)•x + 139.95

Which gives;

f(x) = 0.85•x + 139.95

2. Question 1

Cost of the Flex3000, x = $889

Therefore;

f(889) = 0.85 × 889 + 139.95 = 895.6

Charlotte's before–tax cost with the deal is therefore, $895.6

Given that the workout channel holds no value to Charlotte, and the deal cost is higher than the initial cost, it isn't worth it for her to pay for the subscription to get the 15% discount

3. The domain if the Awesome Flex is the cheapest option, is the possible initial price of the home gym equipment.

The domain is therefore;

889 < x < ∞

The range is the possible values of the before tax cost.

The range is therefore;

895.6 ≤ f(x) ‹ ∞

Learn more about writing equations here:

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5 0

1 year ago

Suppose there are 4 defective batteries in a drawer with 10 batteries in it. A sample of 3 is taken at random without replacemen

SSSSS [86.1K]

Answer:

a.) 0.5

b.) 0.66

c.) 0.83

Step-by-step explanation:

As given,

Total Number of Batteries in the drawer = 10

Total Number of defective Batteries in the drawer = 4

⇒Total Number of non - defective Batteries in the drawer = 10 - 4 = 6

Now,

As, a sample of 3 is taken at random without replacement.

a.)

Getting exactly one defective battery means -

1 - from defective battery

2 - from non-defective battery

So,

Getting exactly 1 defective battery = ⁴C₁ × ⁶C₂ = $\frac{4!}{1! (4 - 1 )!}$ × $\frac{6!}{2! (6 - 2 )!}$

= $\frac{4!}{(3)!}$ × $\frac{6!}{2! (4)!}$

= $\frac{4.3!}{(3)!}$ × $\frac{6.5.4!}{2! (4)!}$

= $4$ × $\frac{6.5}{2.1! }$

= $4$ × $15$ = 60

Total Number of possibility = ¹⁰C₃ = $\frac{10!}{3! (10-3)!}$

= $\frac{10!}{3! (7)!}$

= $\frac{10.9.8.7!}{3! (7)!}$

= $\frac{10.9.8}{3.2.1!}$

= 120

So, probability = $\frac{60}{120} = \frac{1}{2} = 0.5$

b.)

at most one defective battery :

⇒either the defective battery is 1 or 0

If the defective battery is 1 , then 2 non defective

Possibility = ⁴C₁ × ⁶C₂ = 60

If the defective battery is 0 , then 3 non defective

Possibility = ⁴C₀ × ⁶C₃

= $\frac{4!}{0! (4 - 0)!}$ × $\frac{6!}{3! (6 - 3)!}$

= $\frac{4!}{(4)!}$ × $\frac{6!}{3! (3)!}$

= 1 × $\frac{6.5.4.3!}{3.2.1! (3)!}$

= 1× $\frac{6.5.4}{3.2.1! }$

= 1 × 20 = 20

getting at most 1 defective battery = 60 + 20 = 80

Probability = $\frac{80}{120} = \frac{8}{12} = 0.66$

c.)

at least one defective battery :

⇒either the defective battery is 1 or 2 or 3

If the defective battery is 1 , then 2 non defective

Possibility = ⁴C₁ × ⁶C₂ = 60

If the defective battery is 2 , then 1 non defective

Possibility = ⁴C₂ × ⁶C₁

= $\frac{4!}{2! (4 - 2)!}$ × $\frac{6!}{1! (6 - 1)!}$

= $\frac{4!}{2! (2)!}$ × $\frac{6!}{1! (5)!}$

= $\frac{4.3.2!}{2! (2)!}$ × $\frac{6.5!}{1! (5)!}$

= $\frac{4.3}{2.1!}$ × $\frac{6}{1}$

= 6 × 6 = 36

If the defective battery is 3 , then 0 non defective

Possibility = ⁴C₃ × ⁶C₀

= $\frac{4!}{3! (4 - 3)!}$ × $\frac{6!}{0! (6 - 0)!}$

= $\frac{4!}{3! (1)!}$ × $\frac{6!}{(6)!}$

= $\frac{4.3!}{3!}$ × 1

= 4×1 = 4

getting at most 1 defective battery = 60 + 36 + 4 = 100

Probability = $\frac{100}{120} = \frac{10}{12} = 0.83$

3 0

3 years ago

the sum of ages of father and his son is 60 years.if the difference between their ages is 40 years then find the age of father a

cluponka [151]

Answer:

Father's age is 50, Son's age is 10

Step-by-step explanation:

X+Y=60

X-Y= 40

Let X represent the Father's age while Y represents the Son's age;

therefore, from the two equations, the value of X is

X= 60-Y

X= 40+Y then putting in the value of x

(40+Y) + Y= 60,

40+2Y=60

2Y=60-40 =20

Y= 10,

Now that we know the value of Y, we can get the value of x

If X+Y=60, then

X+10=60,

X=60-10,

X= 50

8 0

3 years ago

Read 2 more answers

Maggie created this scale drawing of a soccer field, using a scale factor of 1 inch : 12 yards. She wants to make another scale

larisa [96]

The length and width of the new scale drawing is 36 inches and 24 inches respectively.

The given parameters:

Original scale of the soccer field, 1 inch : 12 yards

The original length and width of the soccer field is calculated as follows;

1 inch : 12 yards

original width = 6 x 12 yards = 72 yards
original length = 9 x 12 = 108 yards

For the new scale of 1 inch : 3 yards, the new length and width are represented as;

the new width:

$\frac{1 \ inch}{x} = \frac{3 \ yards}{72 \ yards} \\\\x = 24 \ inches$

the new length:

$\frac{1 \ inch}{x} = \frac{3 \ yards}{108 \ yards} \\\\x = 36\ inches$

Thus, the length and width of the new scale drawing is 36 inches and 24 inches respectively.

Learn more about scale drawing here:

7 0

2 years ago