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3 years ago

T is between S and U ST = X-6, SU = 10 units, and TU = 2x - 8. Find the length of ST.

Mathematics

1 answer:

abruzzese [7]3 years ago

3 0

Answer:

Step-by-step explanation:

|<-------------- 10 --------------------->|

S-------------------T--------------------U

X-6 2X - 8

FIND: ST

SOLUTION:

ST + TU = SU

x - 6 + 2x - 8 = 10

combine like terms:

3x - x = 10 + 8 + 6

x = 24/3

x = 8

plugin the value of x= 8 into the ST = x - 6

ST = x - 6

ST = 8 - 6

ST = 2

proof:

x - 6 + 2x - 8 = 10

8 - 6 + 2(8) - 8 = 10

10 = 10 ---OK

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dolphi86 [110]

The other 2 angles of given right angles are 61.93° and 28.072°, if a triangle with side lengths 8, 15, and 17 is a right triangle by the converse of the Pythagorean Theorem.

Step-by-step explanation:

The given is,

Right angled triangle,

Side lengths are 8, 15, and 17

Step:1

The given triangle is right angle triangle by the converse of Pythagorean theorem, so the trigonometric ratio,

Ref the attachment,

For angle a,

...................................................(1)

Where, Opp - 8

Hyp - 17

From equation (1),

= 0.470588

(0.470588)

a = 28.072°

For angle b,

...................................................(1)

Where, Opp - 15

Hyp - 17

From equation (1),

= 0.882352

(0.882352)

b = 61.93°

Step:2

Check for solution for right angle triangle,

90 ° = Other 2 angles

90 ° = a + b

90 ° = 28.072° + 61.93°

90 ° = 90 °

Result:

The other 2 angles of given right angles are 61.93° and 28.07°, if a triangle with side lengths 8, 15, and 17 is a right triangle by the converse of the Pythagorean Theorem.

7 0

3 years ago

Find the ratio in simplest form.<br><br> 30:6<br><br> A. 1:5<br> B. 4:1<br> C. 5:1

nekit [7.7K]

ANSWER

The simplest form of the ratio
$30:6$
is

$5:1$

EXPLANATION

The ratio given to us is
$30:6$

We can divide each term in ratio by the same number.

To find the ratio in the simplest form we divide the terms in the ratio by their highest common factor, which is
$6.$

This implies that,

$30:6 = \frac{30}{6} : \frac{6}{6}$

We simplify this to obtain,

$30:6 = 5: 1$

The correct answer is C.

Alternatively,

$30:6 = \frac{30}{6}$

$30:6 = \frac{5}{1}$

This implies that,

$30:6 = 5:1$

6 0

3 years ago

Read 2 more answers

4. k/6 = 8/16 5. 5.4/7 = 27/h 6. 8/11 = 4/y+2

kupik [55]

Answer:

4. $k=3\\$