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Yuki888 [10]
3 years ago
13

Please help and explain how you did it

Mathematics
1 answer:
jenyasd209 [6]3 years ago
5 0
To determine the lengths of the sides from shortest to longest, you need to calculate the corresponding angles. The higher angles will correspond to longer sides.

To find the angles, you have to solve for x. You’re already given that angle A is 76. To find the others, you know that angle C is 180-(16x+16) since it’s supplemental to the exterior angle. Then, you know the sum of the angles of the entire triangle is 180, so add up A, B, and C

A+B+C=180
76+6x+(180-16x-16)=180
240-10x=180
-10x=-60
x=6

So to find angle B, you use 6x or 6(6)=36.

To find angle C, you use 180-(16x-16) or 180-16(6)-16=68

So now match up the angles with their corresponding sides to find the length from shortest to longest.

Angle A (76) corresponds with BC
Angle B (36) corresponds with AC
Angle C (68) corresponds with AB

Again, the higher the degree, the longer the corresponding side, so AC is shortest, AB is next, and BC is the longest.
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Mau bought a television for 330.The tax rate is 8% what is the total amount paid for the television
nika2105 [10]
If the tax rate is 8%, we need to find 108% of the price, or 330 times 1.08, which is $356.4
7 0
3 years ago
In the year 2012, 12% of the residents of the US moved to a different residence. Suppose that several
balandron [24]

Answer:

Approximately normal

Step-by-step explanation:

4 0
3 years ago
In a pizza restaurant, you can get a basic pizza with two toppings: cheese and tomato.
poizon [28]

The number of different topping combination illustrates combination

Ross have 6 different topping combination to select from

<h3>The number of different combination</h3>

The given parameters are:

Extra toppings, n = 4

Toppings to select, r = 2

The number of extra topping that Ross can select is then calculated  using the following combination formula

Toppings = nCr

This gives

Toppings = 4C2

Evaluate the combination expression

Toppings = 6

Hence, Ross have 6 different topping combination to select from

Read more about combination at:

brainly.com/question/11732255

7 0
2 years ago
There are 80 people waiting to tour the science museum. The tour guide takes 4 groups of 16 people each. The remaining people wi
Anna11 [10]

Answer:

16 people

Step-by-step explanation:

Given that :

Number of people to tour = 80

Number per group = 16

Number of groups = 4

Total number of people who make up the entire groups :

Number per group * number of groups

16 * 4 = 64

The number of people in the last tour group :

80 - 64

= 16 people

7 0
3 years ago
For 0 ≤ ϴ &lt; 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va
Black_prince [1.1K]

Answer:

3 solutions:

\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is tan(\frac{\theta}{2}) so let's focus on that part of the equation first.

We know that:

tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}

therefore:

cos(\frac{\theta}{2})\neq0

so we need to find the angles that will make the cos function equal to zero. So we get:

cos(\frac{\theta}{2})=0

\frac{\theta}{2}=cos^{-1}(0)

\frac{\theta}{2}=\frac{\pi}{2}+\pi n

or

\theta=\pi+2\pi n

we can now start plugging values in for n:

\theta=\pi+2\pi (0)=\pi

if we plugged any value greater than 0, we would end up with an angle that is greater than 2\pi so,  that's the only angle we cannot include in our answer set, so:

\theta\neq \pi

having said this, we can now start solving the equation:

tan(\frac{\theta}{2})=sin(\theta)

we can start solving this equation by using the half angle formula, such a formula tells us the following:

tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}

so we can substitute it into our equation:

\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)

we can now multiply both sides of the equation by sin(\theta)

so we get:

1-cos(\theta)=sin^{2}(\theta)

we can use the pythagorean identity to rewrite sin^{2}(\theta) in terms of cos:

sin^{2}(\theta)=1-cos^{2}(\theta)

so we get:

1-cos(\theta)=1-cos^{2}(\theta)

we can subtract a 1 from both sides of the equation so we end up with:

-cos(\theta)=-cos^{2}(\theta)

and we can now add cos^{2}(\theta)

to both sides of the equation so we get:

cos^{2}(\theta)-cos(\theta)=0

and we can solve this equation by factoring. We can factor cos(\theta) to get:

cos(\theta)(cos(\theta)-1)=0

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

cos(\theta)=0

\theta=cos^{-1}(0)

\theta={\frac{\pi}{2}, \frac{3\pi}{2}}

Equation 2:

cos(\theta)-1=0

we add a 1 to both sides of the equation so we get:

cos(\theta)=1

\theta=cos^{-1}(1)

\theta=0

so we end up with three answers to this equation:

\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}

7 0
2 years ago
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