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4 years ago

Given: cos∅ =-4/5 , sinФ = -12/13 , ∅ is in the third quadrant, and Ф is in the fourth quadrant. Evaluate Sin(∅+Ф)

Mathematics

1 answer:

galina1969 [7]4 years ago

4 0

Answer:

63/65

Step-by-step explanation:

the angles are in fourth and third quadrants so all the sin and cos values are minus

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Triangle ABC has AB=5, BC=7, and AC=9. D is on AC with BD=5. Find the length of DC

e-lub [12.9K]

Answer:

$DC=\frac{8}{3}\ units$

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The triangle ABD is an isosceles triangle

because

AB=BD

The segment BM is a perpendicular bisector segment AD

In the right triangle ABM

Applying the Pythagorean Theorem

$BM^2=AB^2-AM^2$

we have

$AB=5\ units\\AM=x\ units$

substitute

$BM^2=5^2-x^2$

$BM^2=25-x^2$ -----> equation A

In the right triangle BMC

Applying the Pythagorean Theorem

$BM^2=BC^2-MC^2$

we have

$BC=7\ units\\MC=AC-AM=(9-x)\ units$

substitute

$BM^2=7^2-(9-x)^2$

$BM^2=49-(81-18x+x^2)$

$BM^2=49-81+18x-x^2$

$BM^2=-x^2+18x-32$ ----> equation B

equate equation A and equation B

$-x^2+18x-32=25-x^2$

solve for x

$18x=25+32\\18x=57\\\\x=\frac{57}{18}$

Simplify

$x=\frac{19}{6}$

Find the length of DC

$DC=AC-2x$

substitute the given values

$DC=9-2(\frac{19}{6})$

$DC=9-\frac{19}{3}\\\\DC=\frac{8}{3}\ units$

8 0

3 years ago

What sign of a null hypothesis must always include?

IrinaVladis [17]

Answer:

Option d - Equality

Step-by-step explanation:

To find : What sign of a null hypothesis must always include?

Solution :

The Null hypothesis is defined as a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.

The Null hypothesis represent by $H_o$

$H_o$ always has a symbol with an equal in it.

Therefore, Option d is correct.

Equality sign of a null hypothesis must always include.

5 0

3 years ago

Given the functions f(x)=4x+8 and g(x)=2x-12 Find f(x)+g(x)

Bingel [31]

Answer:

6x - 4

Step-by-step explanation:

f(x) + g(x)

= 4x + 8 + 2x - 12 ← collect liketerms

= 6x - 4

6 0

3 years ago

Read 2 more answers

Shen is on the swim team. Each week he swims a total of 5000 meters. How many kilometers does he swim each week?

Volgvan

Answer:

5 km

Step-by-step explanation:

to convert m to km you have to divide by 1000.

5000/1000=5

hope this helps!

7 0

3 years ago

What is the quotient of (4x^3-3x^2+5x+6) divided by (x+6)

musickatia [10]

The answer is in the picture below I used the square rooting method hope this is the answer you need!

3 0

3 years ago