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Reika [66]
2 years ago
12

HELP PLEASE, if you can answer number 2 and 3 also I would appreciate it

Mathematics
1 answer:
Inessa [10]2 years ago
6 0
Number 2 is 14 units
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Given △ABC. m∠A>m∠B>m∠C. Perimeter=30. Which side of △ABC may have length 7?
lisabon 2012 [21]

<u>Solution-</u>

As given in △ABC,

m\angle A>m\angle B>m\angle C

As from the properties of trigonometry we know that, the greater the angle is, the greater is the value of its sine. i.e

\sin A>\sin B>\sin C

According to the sine law,

\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}

In order to make the ratio same, even though m∠A>m∠B>m∠C, a must be greater than b and b must be greater than c.

\Rightarrow a>b>c

Also given that its perimeter is 30. Now we have to find out whose side length is 7. So we have 3 cases.

Case-1. Length of a is 7

As a must be the greatest, so b and c must be less than 7. Which leads to a condition where its perimeter won't be 30. As no 3 numbers less than 7 can add up to 30.

Case-2. Length of b is 7

As b is greater than c, so c must 6 or less than 6. But in this case the formation of triangle is impossible. Because the triangle inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. If b is 7 and c is 6, then a must be 17. So no 2 numbers below 7 can add up to 17.

Case-3. Length of c is 7

As this is the last case, this must be true.

Therefore, by taking the aid of process of elimination, we can deduce that side c may have length 7.


5 0
3 years ago
Joy and Peter were each walking along a straight road. joy walked 1800 meters in 1/3 hour. Peter walked 1/2 of joys distance in
Citrus2011 [14]

Answer:

what is it asking to find then i can help

Step-by-step explanation:

6 0
2 years ago
Identify the rule for fg when f(x) = –3x – 6 and g(x) = x2 – x – 6.
stellarik [79]

Answer:

f(g) = -3( x^2 -x-6) -6 = -3x^2+3x+12

4 0
2 years ago
Which two transformations must be applied to the graph of y = ln(x) to result in the graph of y = –ln(x) + 64?
stiks02 [169]

Answer: A) reflection over the x-axis, plus a vertical translation

Step-by-step explanation:

Ok, when we have a function y = f(x)

> A reflection over the x-axis changes a point (x, y) to a point (x, -y), then for a function (x , y = f(x)) the point will change to (x, -y =- f(x))

then for a funtion g(x), this tranformation can be written as h(x) = -g(x).

> A vertical translation of A units (A positive) up for a function g(x) can be written as: h(x) = g(x) + A.

Then in this case we have:

y = g(x) = ln(x)

and the transformed function is h(x) = -ln(x) + 64

Then we can start with h(x) = g(x)

first do a reflection over the x-axis, and now we have:

h(x) = -g(x) = -ln(x)

And now we can do a vertical translation of 64 units up

h(x) = -g(x) + 64 = -ln(x) + 64

Then the correct option is:

A) reflection over the x-axis, plus a vertical translation

3 0
2 years ago
A company purchased a machine for $970,000. the machine has a useful life of 12 years and a residual value of $4,500. it is esti
harina [27]
Cost less salvage value = 970,000 - 4500 = 965,500
Capacity of machine = 1,000,000 units.
units consumed at the end of second year = 200,000 + 300,000 = 500,000 units.
Capacity remaining = 1,000,000 - 500,000 = 500,000 units
Book value at end of second year = (500,000/1,000,000)*965,500 + 4500
= $487,250
8 0
3 years ago
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