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3 years ago

The measures of the angles of a triangle are in the extended ratio 4 : 5 : 6. What is the measure of the smallest angle?

1 answer:

8 0

The sum of the interior angles of a triangle is 180 degrees

4x + 5x + 6x = 180
15x = 180
x = 180/15
x = 12

The measure of the smallest angle = 4x = 4*12 = 48°

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The volume of a tetrahedron is 1 6 of the volume of a parallelepiped whose sides are formed using the vectors coming out of one

Irina18 [472]

Answer: The volume of the tetrahedron is 2 units.

Step-by-step explanation:

Let A = (1, 1, 1)

B = (1, 5, 5)

C = (2, 2, 1)

The volume of a tetrahedron is given as

V = (1/6)|AB, AC, AD|

Where |AB, AC, AD| is the determinant of the matrix of AB, AC, AD.

We need to determine AB, AC, and AD

Suppose A = (a1, a2, a3)

B = (b1, b2, b3)

C = ( c1, c2, c3)

AB = ( b1 - a1, b2 - a2, b3 - a3)

Similarly for AB, AC, BC, etc.

AB = (1 - 1, 5 - 1, 5 - 1)

= (0, 4, 4)

AC = (1, 0, 2)

AD = (1, 1, 0)

Volume =

(1/6) |0 4 4|

|1 0 2|

|1 1 0|

= (1/6)[0(0 - 2) - 4(0 - 2) + 4(1 - 0)

= (1/6)(0 + 8 - 4)

= (1/6)(12)

V = 12/6 = 2 units

5 0

3 years ago

What expression is equivalent to 5 to the 6th power?PlZZZ HElP

Akimi4 [234]

Answer:

$5^6 = 125 * 125$

Step-by-step explanation:

The given expression can be represented as:.5⁶

Required

Find equivalent expression

$5^6$

Express 6 as 3 + 3

$5^6 = 5^{3+3}$

Apply the following law of indices

$a^{m+n} = a^m * a^n$

So, we have:

$5^6 = 5^{3} * 5^{3}$

Express $5^3$ as 125

$5^6 = 125 * 125$

Hence, option (b) is equivalent

8 0

3 years ago

Alyssa has 6/8 of a cup caramel dip for apples if she uses 1/4 cup of dip for each cup how many apples can Alyssa dip?

Vitek1552 [10]

Answer:

2/8 is left

Step-by-step explanation:

because 6/8 - (1/4 = 2/8) = 4/8 = 1/2

8 0

3 years ago

Read 2 more answers

If x² - y² = 55, and x - y = 11, then y = a. 8 b. 5 c. 3 d. -8 e. -3

irina1246 [14]

X^2-y^2=55
this means that
(x+y)(x-y)=55
we know that x-y=11 so we can write
(x+y)(11)=55
x+y=55/11 we divide by 11 and we obtain
x+y=5

x-y=11 this means
x=y+11 we replace in the other equation (x+y=5)

y+11+y=5
2y=5-11
2y=-6
y=-3
and you find out that also
x=8

7 0

3 years ago

Solve and explain. 4 and 5.

Pavlova-9 [17]

Answer:

Step-by-step explanation:

4. 2 2/3 = 2 4/6

1/2 = 3/6

3/6 + 2 4/6 = 3 1/6

95÷3 1/6=30

5. 500,000

4 0

3 years ago