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Oksana_A [137]
3 years ago
14

Which of the following terms have a GCF of 6x^3? Select two options. 12p^3r 27p^4q 45p^3q^6 54p^3 63p^3q^6

Mathematics
1 answer:
topjm [15]3 years ago
7 0

Answer: 12p^3r and 54p^3

Step-by-step explanation:

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7x=5y , find the slope and the y-intercept of each line whose equation is given.
nadezda [96]
Slope would be -7/5. The y intercept would be 5.
4 0
3 years ago
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Verify sine law by taking triangle in 4 quadrant<br>Explain with figure.<br>​
Ksivusya [100]

Proof of the Law of Sines

The Law of Sines states that for any triangle ABC, with sides a,b,c (see below)

a

 sin  A

=

b

 sin  B

=

c

 sin  C

For more see Law of Sines.

Acute triangles

Draw the altitude h from the vertex A of the triangle

From the definition of the sine function

 sin  B =

h

c

    a n d        sin  C =

h

b

or

h = c  sin  B     a n d       h = b  sin  C

Since they are both equal to h

c  sin  B = b  sin  C

Dividing through by sinB and then sinC

c

 sin  C

=

b

 sin  B

Repeat the above, this time with the altitude drawn from point B

Using a similar method it can be shown that in this case

c

 sin  C

=

a

 sin  A

Combining (4) and (5) :

a

 sin  A

=

b

 sin  B

=

c

 sin  C

- Q.E.D

Obtuse Triangles

The proof above requires that we draw two altitudes of the triangle. In the case of obtuse triangles, two of the altitudes are outside the triangle, so we need a slightly different proof. It uses one interior altitude as above, but also one exterior altitude.

First the interior altitude. This is the same as the proof for acute triangles above.

Draw the altitude h from the vertex A of the triangle

 sin  B =

h

c

      a n d          sin  C =

h

b

or

h = c  sin  B       a n d         h = b  sin  C

Since they are both equal to h

c  sin  B = b  sin  C

Dividing through by sinB and then sinC

c

 sin  C

=

b

 sin  B

Draw the second altitude h from B. This requires extending the side b:

The angles BAC and BAK are supplementary, so the sine of both are the same.

(see Supplementary angles trig identities)

Angle A is BAC, so

 sin  A =

h

c

or

h = c  sin  A

In the larger triangle CBK

 sin  C =

h

a

or

h = a  sin  C

From (6) and (7) since they are both equal to h

c  sin  A = a  sin  C

Dividing through by sinA then sinC:

a

 sin  A

=

c

 sin  C

Combining (4) and (9):

a

 sin  A

=

b

 sin  B

=

c

 sin  C

7 0
2 years ago
Need help with math probelm if do 5 stars and brainly points
PtichkaEL [24]

Step-by-step explanation:

let's first convert feet to inches

4 ft = 48 inches ( width )

6.5 ft = 78 inches ( length )

12.5 ft = 150 inches ( height )

each cube is 1/4 x 1/4 x 1/4

x-axis ( length )

78 ÷ 1/4 = 78 x 4 = 312 cubes

y-axis ( width )

48 x 4 = 192 cubes

z-axis ( height )

150 x 4 = 600 cubes

the total number of cubes fit in the closet is :

312 x 192 x 600 = 35,942,400 cubes

6 0
1 year ago
The function A = 15x - x2, where x is the width in yards, gives the area A of a llama pen in square yards. Make a table using 1/
Mnenie [13.5K]

Answer:

The width which gives the greatest area is 7.5 yd

Step-by-step explanation:

This is an application of differential calculus. Given the area as a function of the width, we simply need to differentiate the function with respect to x and equate to zero which yields; 15-2x=0 since the slope of the graph is zero at the turning points. Solving for x yields, x=7.5 which indeed maximizes the area of the pen

6 0
3 years ago
Solve the equation √x+9 - 9 = -4 show each step of your solution process
Serjik [45]

Answer:

16

Step-by-step explanation:

Start by adding 9 to both sides, obtaining:  √(x + 9) = 5.

Square both sides, obtaining:   x + 9 = 25.

Subtract 9 from both sides:  x = 16

Note that √(16+9) - 9 = -4, as required.


3 0
2 years ago
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