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2 years ago

The perimeter of a triangle is 7 m. The longest side is twice the length of the shortest side. The sum of the

Mathematics

1 answer:

34kurt2 years ago

3 0

Answer:

See below in bold.

Step-by-step explanation:

Let the length of the shortest side be x, then the longest side = 2x.

Also x + y = 2x + 1 where y = length of the middle side,

Simplifying:

2x - x - y = -1

x - y = -1 (A)

Also as the perimeter = 7:

x + 2x + y = 7

3x + y = 7 (B)

Adding (A) and (B):

4x + 0 = 6

x = 6/4 = 1.5

Plug x = 1.5 into equation B:

3(1.5) + y = 7

y = 7 - 4.5 = 2.5.

Answer:

So the shortest side = 1.5, middle = 2.5 and longest = 2*1.5 = 3.

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Distributive property of 1/2(8x+2)

sdas [7]

Answer:

4x+1

Step-by-step explanation:

1/2 *(8x+2)=1/2*8x+1/2*2=4x+1

5 0

2 years ago

Show that √(1-cos A/1+cos A) =cosec A - cot A

Gennadij [26K]

Hi there!

$\sqrt{\frac{1-cosA}{1+cosA}} =$

We can begin by multiplying by its conjugate:

$\sqrt{\frac{1-cosA}{1+cosA}} * \sqrt{\frac{1+cosA}{1+cosA}} = \\\\\sqrt{\frac{(1-cosA)(1 + cosA)}{(1+cosA)(1 + cosA)}} =$

Simplify using the identity:

$1 - cos^2A = sin^2A$

$\sqrt{\frac{(1-cos^2A)}{(1+cosA)^2}} =\\\\\sqrt{\frac{(sin^2A)}{(1+cosA)^2}} =$

Take the square root of the expression:

${\frac{sinA}{1+cosA} =$

Multiply again by the conjugate to get a SINGLE term in the denominator:

${\frac{sinA}{1+cosA} * {\frac{1-cosA}{1-cosA} =\\$

Simplify:

${\frac{sinA(1-cosA)}{1-cos^2A} =$

Use the above trig identity one more:

${\frac{sinA(1-cosA)}{sin^2A} =$

Cancel out sinA:

${\frac{(1-cosA)}{sinA} =$

Split the fraction into two:

${\frac{1}{sinA} - \frac{cosA}{sinA} =$

Recall:

$1/sinA = cscA\\\\cosA/sinA = cotA$

Simplify:

$\frac{1}{sinA} + \frac{cosA}{sinA} = \boxed{cscA - cotA}$

5 0

2 years ago

Please help me calculate the value of y with steps

Nutka1998 [239]

The value of y in the triangle is 7.5

<h3>How to calculate the value of y?</h3>

The given parameter is the triangle

On the triangle, we have the following equivalent ratio

y : 8 = y + 15 : 20

Express as fraction

y/8 = y + 15/20

Cross multiply

20y = 8y + 90

Collect the like terms

20y - 8y = 90

Evaluate

12y = 90

Divide by 12

y = 7.5

Hence, the value of y in the triangle is 7.5

Read more about triangles at

brainly.com/question/17335144

#SPJ1

5 0

1 year ago

At the start of a science experiment, the temperature is 10 degrees Celsius. If the temperature decreases by a constant rate of

notka56 [123]

Answer:

-5 If it is one of your answers it will be -5

Step-by-step explanation:

If you take 10 and have 3 decrease every minute and did it for 5 minutes it will go 10 7 4 1 -2 -5 That is 5 minutes of the temperature decreasing by 3 I hope it is right.

3 0

2 years ago

In how many ways can 6 competitors finish a race assuming there are no ties?In how many ways can we sit n people on r < n cha

VLD [36.1K]

Answer: a) 720, b) $^nC_r=\dfrac{n!}{(n-r)!r!}$ c) 336, d) 30240 e) 120.

Step-by-step explanation:

Since we have given that

a) Number of competitors = 6

We need to find the number of ways that 6 competitors can finish a race and there are no ties.

So, Number of ways would be

$6!=720$

b) number of people = n

Number of chairs = r (r<n)

so, the number of ways we can sit n people on r<n chairs is given by

$^nC_r=\dfrac{n!}{(n-r)!r!}$

c) If there are three awards :

Gold, silver, bronze.

We need to find the number of ways that these medals can be awarded.

Number of ways is given by

$^8P_3\\\\=336$

d) Number of 5-digit zip codes are possible is given by

$^{10}P_5=30240$

e) Number of poeple = 10

Number of people required in committee = 3

Number of different 3 person committee that are selected from 10 people is given by

$^{10}C_3=120$

Hence, a) 720, b) $^nC_r=\dfrac{n!}{(n-r)!r!}$ c) 336, d) 30240 e) 120.

6 0

3 years ago