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3 years ago

Find the missing side of the triangle.

Mathematics

1 answer:

Ronch [10]3 years ago

6 0

Answer:

x=1

Step-by-step explanation:

Since you know two sides and are trying to find the missing side, you can use the Pythagorean Theorem. So fashion the equation like this:

x^2 + 3^2 = sqrt10^2. After simplify, which leads to x^2 + 9 =10. Then have the variable to one side by subtracting 9 on both sides. This leads to x^2=1. Finally, square root both sides which leads to 1. Note that any root of 1 is 1. So your answer becomes x=1.

Hope this helps!

You might be interested in

Write the following as an inequality.

JulsSmile [24]

Answer:

$-4\leq x$

that is the required inequality

6 0

3 years ago

Which are the solutions of the quadratic equation x2 =-5-3

alexdok [17]

Answer: x = 2 • ± √2 = ± 2.8284

Step-by-step explanation:

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 8 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step 1 :

x2 - 8 = 0

Step 2 :

Solving a Single Variable Equation :

2.1 Solve : x2-8 = 0

Add 8 to both sides of the equation :

x2 = 8

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

x = ± √ 8

Can √ 8 be simplified ?

Yes! The prime factorization of 8 is

2•2•2

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 8 = √ 2•2•2 =

± 2 • √ 2

The equation has two real solutions

These solutions are x = 2 • ± √2 = ± 2.8284

Two solutions were found :

x = 2 • ± √2 = ± 2.8284

Not sure what you need help with, but I hope I helped you somehow.

5 0

3 years ago

PLEASE GUYS HELP ITS DUE TONIGHT

KATRIN_1 [288]

Answer:

20. AB = 42

21. BC = 28

22. AC = 70

23. BC = 20.4

24. FH = 48

25. DE = 10, EF = 10, DF = 20

Step-by-step explanation:

✍️Given:

AB = 2x + 7

BC = 28

AC = 4x,

20. Assuming B is between A and C, thus:

AB + BC = AC (Segment Addition Postulate)

2x + 7 + 28 = 4x (substitution)

Collect like terms

2x + 35 = 4x

35 = 4x - 2x

35 = 2x

Divide both side by 2

17.5 = x

AB = 2x + 7

Plug in the value of x

AB = 2(17.5) + 7 = 42

21. BC = 28 (given)

22. AC = 4x

Plug in the value of x

AC = 4(17.5) = 70

✍️Given:

AC = 35 and AB = 14.6.

Assuming B is between A and C, thus:

23. AB + BC = AC (Segment Addition Postulate)

14.6 + BC = 35 (Substitution)

Subtract 14.6 from each side

BC = 35 - 14.6

BC = 20.4

24. FH = 7x + 6

FG = 4x

GH = 24

FG + GH = FH (Segment Addition Postulate)

$4x + 24 = 7x + 6$ (substitution)

Collect like terms

$4x - 7x = -24 + 6$

$-3x = - 18$

Divide both sides by -3

$x = 6$

FH = 7x + 6

Plug in the value of x

FH = 7(6) + 6 = 48

25. DE = 5x, EF = 3x + 4

Given that E bisects DF, therefore,

DE = EF

5x = 3x + 4 (substitution)

Subtract 3x from each side

5x - 3x = 4

2x = 4

Divide both sides by 2

x = 2

DE = 5x

Plug in the value of x

DE = 5(2) = 10

EF = 3x + 4

Plug in the value of x

EF = 3(2) + 4 = 10

DF = DE + EF

DE = 10 + 10 (substitution)

DE = 20

4 0

3 years ago

Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. Enter

andreev551 [17]

Answer:

Step-by-step explanation:

In each case, draw the right triangle which produces the inverse trig value. That is, label the two sides as needed, and calculate the third side.

It should be clear that

$tan(sin^{-1} x/4) = x/\sqrt{16-x^{2} }$

$sin(tan^{-1} x/4) = x/\sqrt{16+x^{2} }$

sin(2α) = 2 sinα cosα

So,

$1/2 sin(2sin^{-1} x/4) = (1/2)(x/4) * x/\sqrt{16-x^2} = x^{2} /(8\sqrt{16-x^2})$

See what you can do with the others.

6 0

3 years ago

1. It is a three-digit whole number.

taurus [48]

Answer:

660

Step-by-step explanation:

4x5x11x3 = 660

8 0

3 years ago