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I think  this is supposed  to be

log ₄ 192   - log ₄ 3                ....if so......we  have

log ₄  (64 * 3)  -  log ₄ 3          and we can write

log ₄ 64  +  log ₄  3   -  log ₄ 3  =

log ₄ 64  =

log ₄ 4^3         and  we  can write

3 *  log ₄  4                      use  the  change-of-base theorem on  the log  part

3  *  ( log 4  / log 4) =

3 *  1   =

3

i believe the two triangles are similar, because of the mirror.

so we can get this ratio. let's have g represent the giraffe's height:

\(\frac{15}{4} = \frac{g}{5}\)

\(75 = 4g\) (cross multiply)

\(g = 18.75 \)

18.75 ~ 19, so our answer is 19 feet.

hope this helped! please let me know if you have any questions :)

Given right triangle ABCABC with altitude \overline{BD}BD drawn to hypotenuse ACAC. If BC=12BC=12 and DC=3,DC=3, what is the length of \overline{AC}?AC? (Note: the figure is not drawn to scale.)

-8 + 55x = 22

55x = 30 (we add 8 to both sides)

x = 30/55 = 6/11 (we divide 55 from both sides, then simplify)

hope this helped! please let me know if you are confused about anything i did 

Triangle CDB  is similar to triangle BDA

We have  this  relationship

CD / BD =  BD / AD

4 / 2  =  2 /  AD           cross-multiply

4AD  =   4

AD  =  1

\((x-h)^2 + (y - k)^2 = r^2\)

The center point of the circle is: (-3, -2)

The radius of the circle is: 5

Which means the equation is:

\((x -(-3))^2 + (y -(-2))^2 = 5^2\)

\((x+3)^2 + (y + 2)^2 = 25\)

7x + 20 + 5x + 2y + 7x + 20 + 90 = 360

19x + 2y + 130 = 360

19x + 2y = 230

7x + 90 + 20 = 180

7x = 70

x = 10

19x + 2y = 230

19(10) + 2y = 230

190 + 2y = 230

2y = 40

y = 20

Since  AB  = BC....then  angles  BAC   and  BCA  are equal

Call angle ABC = x

Then  angles  BAC  and  BCA = (3/2) x

So   

(3/2)x  + (3/2) x  +  x  =180

3x  + x  =180

4x = 180

x = 180 / 4 =  45°

So angle  BCA = (3/2) 45  =  67.5 =  angle ECD

And  because  CD = CE....then angles CED  and CDE  are equal

So

Angle CDE    =   (180  - 67.5)  /  2  =  56.25°   =   "angle D"

Connect PB

Then triangle  PAB is  a right triangle   with legs  PA  and  AB  and hypotenuse  PB

PA  =  1             AB =  9  + 1 =   10 

PB  =   sqrt  ( AB^2  + PA^2)   =  sqrt  ( 10^2  + 1^2)  = sqrt (101)

Likewise angle PTB  is right  since  a radius  drawn to a tangent  meets  the  tangent at a  90°  angle

So triangle PTB is also right

So PB is  the  hypotenuse of  this triangle  and PT  and TB  are legs  with  TB  = 9

So

PT =  sqrt  (  PB^2  - TB^2)  =  sqrt  (101 - 9^2)  =  sqrt ( 101  - 81)  = 

sqrt (20)  =

sqrt(4) * sqrt (5)  =

2 sqrt (5) cm

We  have  a triangular prism  a the  top

Its  base area =  (1/2)8 * 4  =  16

And its  volume = 5 * 16  =   80 cm^3

And  we have  a  rectangular  solid  whose  volume = 5 * 8 * 6 =  240 cm^3

So.....the  total volume =  (80 + 240) =  320 cm^3

Angle  BCA  =   8(5)   = 40°

Angle BAC  = 4(5)  = 20°

Then angle  ABC  =  180 - 40  - 20  =  180  - 60    = 120 °

And  because opposite angles of a parralleogram  are  equal, then angle  B  =120° 

Since DB  is a transversla  cutting parallels  AB and Dc,  then angle  CBE  = angle ADE  = 36°

And angle  AED  = 90°

So...in  triangle ADE,   angle   DAE  =   180  - angle AED   - angle ADE  =   

180  - 90   -  36    =

90  - 36  = 

54° 

By pythagoras' theorem: 

the slant height of the cone \((l) = \sqrt{18^2 + 5^2}\)

\(l = \sqrt{349}\)

This means the slant height is √349 inches, or about 18.68 inches

The volume is the length times the width times the height:
4 x 5 x 6 = 120 m³

22x + 8 + 24x + 6 + 12x - 2 = 360

58x + 12 = 360

58x = 348

x = 6 

By pythagoras' theorem:

\(x = \sqrt{10^2 + 24^2}\)

\(x = \sqrt{676}\)

\(x = 26\)

The two points are: (-5, 3) and (3, 5)

To find the slope, use this equation:
\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

\(m = \frac{5 - 3}{3 - (-5)}\)

\(m = \frac{2}{8}\)

\(m = \frac{1}{4}\)

Now we can plug in one of the points and find the y intercept:

(3, 5)
\(y = mx + b\)

\(5 = \frac{1}{4} \cdot 3 + b\)

\(5 = \frac{3}{4} + b\)

\(b = \frac{17}{4}\)

This means the equation of the line is:
\(y = \frac{1}{4}x + \frac{17}{4}\)

The correct value of c is -2.

508 - 58 = 450 miles. 
He's driving 45 miles per hour over 450 miles, which means it took him 450/45 = 10 hours to drive the rest of the way
 

7x + 5 = 11x - 27

32 = 4x

x = 8

7x + 5

= 7(8) + 5 

= 56 + 5

= 61, which means your answer is B

Another way to write this is (9*2)/(10*3).

(9*2)/(10*3)

18/30 (simplify and divide by 6 on both sides)

3/5

I hope this helped. :))

=^._.^=

As follows:

I'll leave you to finish the calculation.

Reposts include the address of the original question,.  NOT the question itself.

First you need to figure out the gradient of the first line.   Can you do that?

the gradient of the second line is the negative reciprocal of the first, that is m

Sub the pint in to find b

Add m and b together.

It's 6x