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ozzi
2 years ago
14

Find the missing side lengths. Leave your answer as radicals in simplest form.

Mathematics
1 answer:
nika2105 [10]2 years ago
7 0

\sqrt{2Answer:

Step-by-step explanation:

take 45 degree as reference angle

use sin rule

sin 45=opposite/hypotenuse

1/\sqrt{2=x/2\sqrt{2

do cross multiplication

x\sqrt{2=\sqrt{2 *\sqrt{2

x\sqrt{2=2

x=2/\sqrt{2

x=\sqrt{2

pythagoras theorem

a^2+b^2=c^2

(\sqrt{2 )^2+y^2=(2\sqrt{2 )^2

2+y^2=8

y^2=8-2

y=\sqrt{6

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Find the perimeter of the triangle with vertices ​A(negative 2​,2​,3​), ​B(4​,negative 4​,3​), and ​C(7​,6​,4​).
gayaneshka [121]

Answer:

P\approx 28.872\,\text{units}

Step-by-step explanation:

We are given coordinates of each of the vertices of the triangle ABC, hence we can use the distance formula to find the lengths of each of the side.

the distance formula is generally written as:

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

for the side AB: A(-2,2,3) and B(4,-4,3)

AB = \sqrt{(-2-4)^2+(2-(-4))^2+(3-3)^2}

AB = \sqrt{(-6)^2+(6)^2+(3-3)^2}

AB = \sqrt{72}

for the side BC: B(4,-4,3) and C(7,6,4)

BC = \sqrt{(4-7)^2+((-4)-6)^2+(3-4)^2}

BC = \sqrt{110}

for the side CA: C(7,6,4) and A(-2,2,3)

CA = \sqrt{(7-(-2))^2+(6-2)^2+(4-3)^2}

CA = \sqrt{98}

Now we all the sidelengths:

to find the perimeter we need to just sum the three side lengths:

P = AB + BC + CA

P = \sqrt{72} + \sqrt{110} + \sqrt{98}

P\approx 28.872\,\text{units}

this is the perimeter of triangle ABC

6 0
3 years ago
(PLEASE HELP)
stich3 [128]

Answer:

C

Step-by-step explanation:

Because you should be subtract each other by 20x to transfer from side to another side.

4 0
3 years ago
Read 2 more answers
What are the roots of the polynomial equation x3-7x=6x-12?
Ilia_Sergeevich [38]
This is not a polynomial equation unless one of those is squared.  As it stands x=-.833.  If you can tell me which is squared I can help solve the polynomial.

Ok, that is usually notated as x^3 to be clear.   I'll solve it now.

x^3-13x-12=0

Then use factor theorum to solve x^3-13x-12/x+1 =0
So you get one solution of x+1=0
x=-1

Then you have x^2-x-12 now you complete the square.

Take half of the x-term coefficient and square it. Add this value to both sides. In this example we have:

The x-term coefficient = −1

The half of the x-term coefficient = −1/2

After squaring we have (−1/2)2=1/4

When we add 1/4 to both sides we have:

x2−x+1/4=12+1/4

STEP 3: Simplify right side

x2−x+1/4=49/4

STEP 4: Write the perfect square on the left.

<span>(x−1/2)2=<span>49/4
</span></span>

STEP 5: Take the square root of both sides.

x−1/2=±√49/4

STEP 6: Solve for x.

<span>x=1/2±</span>√49/4

that is,

<span>x1=−3</span>

<span>x2=4</span>

<span>and the one from before </span>

<span>x=-1</span>

7 0
3 years ago
Read 2 more answers
is M a midpoint of line AB? AB=44, MB=22 a)maybe b)can't determine c)yes d)no (please explain how you got your answer)
Elza [17]

Answer:

Yes

Step-by-step explanation:

Yes, M is the midpoint of AB.

The length of the whole line AB is 44. So, if any midpoint is drawn on it, The two parts of the line will be equal and half of the total lines measure.

Whole line's measure = AB = 44

If any Midpoint say "M" is drawn on it, the measures of divided line would be halved.

AM = BM = 44/2 = 22

5 0
2 years ago
22<br> Solve for x.<br> 3x - 5 = 10<br> x equals.....<br> help
kramer

Answer:

x = 5

Step-by-step explanation:

3x - 5 = 10

We want to isolate the x.

3x - 5 = 10\\+5\;\;\;\;\;\;\;\;\;         +5

3x = 15

Now, we want the x not to have a coefficient. We want it just to be x =. We will do this via inverse operations. Since 3 x is 3 multiplied by x, we will divide each side by 3.

\frac{3x}{3} \;=\;\frac{15}{3}

x = 5

~InLoveWithPugs

Moderator\\Math \ Enthusiast

7 0
2 years ago
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