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3 years ago

in each of the following divide the second number by the first number and find the quotient:3/4,-3/8

Mathematics

1 answer:

madam [21]3 years ago

5 0

Answer:

-3

Step-by-step explanation:

-3/8÷3/4

=-3/8×4/3

=-6/2

=-3

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Fine length of BC on the following photo.

MrMuchimi

Answer:

$BC=4\sqrt{5}\ units$

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

In the right triangle ACD

Find the length side AC

Applying the Pythagorean Theorem

$AC^2=AD^2+DC^2$

substitute the given values

$AC^2=16^2+8^2$

$AC^2=320$

$AC=\sqrt{320}\ units$

simplify

$AC=8\sqrt{5}\ units$

step 2

In the right triangle ACD

Find the cosine of angle CAD

$cos(\angle CAD)=\frac{AD}{AC}$

substitute the given values

$cos(\angle CAD)=\frac{16}{8\sqrt{5}}$

$cos(\angle CAD)=\frac{2}{\sqrt{5}}$ ----> equation A

step 3

In the right triangle ABC

Find the cosine of angle BAC

$cos(\angle BAC)=\frac{AC}{AB}$

substitute the given values

$cos(\angle BAC)=\frac{8\sqrt{5}}{16+x}$ ----> equation B

step 4

Find the value of x

In this problem

$\angle CAD=\angle BAC$ ----> is the same angle

equate equation A and equation B

$\frac{8\sqrt{5}}{16+x}=\frac{2}{\sqrt{5}}$

solve for x

Multiply in cross

$(8\sqrt{5})(\sqrt{5})=(16+x)(2)\\\\40=32+2x\\\\2x=40-32\\\\2x=8\\\\x=4\ units$

$DB=4\ units$

step 5

Find the length of BC

In the right triangle BCD

Applying the Pythagorean Theorem

$BC^2=DC^2+DB^2$

substitute the given values

$BC^2=8^2+4^2$

$BC^2=80$

$BC=\sqrt{80}\ units$

simplify

$BC=4\sqrt{5}\ units$

7 0

2 years ago

9 (1/3)^n-1 what is the tenth term

NARA [144]

Answer:

$a_{10}=\frac{1}{2187}$

Step-by-step explanation:

Simply plug in 10 for <em>n</em>

9(1/3)¹⁰⁻¹

9(1/3)⁹

9(1/19683)

9/19683

$a_{10}=\frac{1}{2187}$

7 0

3 years ago

What is the domain of this function?

krok68 [10]

A. {-1,3,5}

Hope this helps. :))

4 0

3 years ago

Write an expression for the sequence of operations described below.

Akimi4 [234]

Triple t ⇒ 3t
add the result to u ⇒ 3t + u
multiply what you have by v ⇒ (3t + u)v

Since it is instructed not to simplify, we perform the distributive property of multiplication.

(3t + u)v = 3tv + uv

5 0

3 years ago

What is the range of g(x) = 3|x − 1| − 1? A. (-∞, 1] B. [-1, ∞) C. [1, ∞) D. (-∞, ∞)

AVprozaik [17]

Answer:

B. [-1, ∞).

Step-by-step explanation:

g(x) = 3|x − 1| − 1

When x = 1 g(x) = 3(0) - 1 = -1.

As all negative vales of x will give positive values of |x - 1| then g(x) = -1 is its minimum value. The graph will be shaped like a letter V with the vertex at (1,-1).

Therefore the range is [-1, ∞).

6 0

3 years ago

in each of the following divide the second number by the first number and find the quotient:3/4,-3/8​

in each of the following divide the second number by the first number and find the quotient:3/4,-3/8