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3 years ago

Simplify the expression. 10h + 6 - 5h + 3. PLEASE EXPLAIN HOW YOU GOT THE ANWSER!

1 answer:

7 0

Simplify the h's bysubtracting 5h (since it is negative) from 10h then add 6 and 3. Your simplified expression should be 5h+9.

Also it may be good to know that you can only add and subtract numbers of like form. Ex. 4v and 7v; 9 and 768; 98767jk and 6jk; 12 and 21

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Find the measures of the angles of the triangle whose vertices are A = (-3,0) , B = (1,3) , and C = (1,-3).A.) The measure of ∠A

alekssr [168]

Answer:

$\theta_{CAB}=128.316$

$\theta_{ABC}=25.842$

$\theta_{BCA}=25.842$

Step-by-step explanation:

A = (-3,0) , B = (1,3) , and C = (1,-3)

We're going to use the distance formula to find the length of the sides:

$r= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$

$AB= \sqrt{(-3-1)^2+(0-3)^2}=5$

$BC= \sqrt{(1-1)^2+(3-(-3))^2}=9$

$CA= \sqrt{(1-(-3))^2+(-3-0)^2}=5$

we can use the cosine law to find the angle:

it is to be noted that:

the angle CAB is opposite to the BC.

the angle ABC is opposite to the AC.

the angle BCA is opposite to the AB.

to find the CAB, we'll use:

$BC^2 = AB^2+CA^2-(AB)(CA)\cos{\theta_{CAB}}$

$\dfrac{BC^2-(AB^2+CA^2)}{-2(AB)(CA)} =\cos{\theta_{CAB}}$

$\cos{\theta_{CAB}}=\dfrac{9^2-(5^2+5^2)}{-2(5)(5)}$

$\theta_{CAB}=\arccos{-\dfrac{0.62}}$

$\theta_{CAB}=128.316$

Although we can use the same cosine law to find the other angles. but we can use sine law now too since we have one angle!

To find the angle ABC

$\dfrac{\sin{\theta_{ABC}}}{AC}=\dfrac{\sin{CAB}}{BC}$

$\sin{\theta_{ABC}}=AC\left(\dfrac{\sin{CAB}}{BC}\right)$

$\sin{\theta_{ABC}}=5\left(\dfrac{\sin{128.316}}{9}\right)$

$\theta_{ABC}=\arcsin{0.4359}\right)$

$\theta_{ABC}=25.842$

finally, we've seen that the triangle has two equal sides, AB = CA, this is an isosceles triangle. hence the angles ABC and BCA would also be the same.

$\theta_{BCA}=25.842$

this can also be checked using the fact the sum of all angles inside a triangle is 180

$\theta_{ABC}+\theta_{BCA}+\theta_{CAB}=180$

$25.842+128.316+25.842$

$180$

6 0

3 years ago

Read 2 more answers

X= Length= Width= WILL GIVE BRAINLIEST + 5 star

babymother [125]

Answer:

x = 20

Length = 20ft

Width = 12ft

Step-by-step explanation:

A = 240

x^2 - 8x = 240

x^2 - 8x - 240 = 0

x^2 - 20x + 12x - 240 = 0

x(x-20) + 12(x-20) = 0

(x+12)(x-20) = 0

x = 20

x = -12 (which we discard since x is a length)

So the dimensions are 20ft and 20-8 = 12ft

7 0

3 years ago

Yall I really need help! Please

bulgar [2K]

There are 5 vowels.
There are 26 letters in total.
Then, the probability of choosing a vowel is 5/26

8 0

3 years ago

Find the LCM of k2 + 3k + 2 and 2k2 + 14k + 20.

Archy [21]

Answer:

2(k+1)(k+2)(k+5)

5 0

3 years ago

Given that and , determine which lines are parallel

777dan777 [17]

What lines and here is how parallel looks

_________
_________

these lines r parallel
and parallel lines r lines that go on forever but NEVER touch

7 0

3 years ago