1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
alexdok [17]
3 years ago
7

What is the value of X?

Mathematics
1 answer:
Ugo [173]3 years ago
4 0

∆ABC similar to ∆CBD

DB/AC = CB/AB

\frac{x}{7.5}  =  \frac{7.5}{x + 3}  \\ x(x + 3) =  {7.5}^{2}  =  { (\frac{15}{2}) }^{2}  \\  {x}^{2}  + 3x =  \frac{225}{4}  \\ 4 {x}^{2}  + 12x = 225 \\ 4 {x}^{2}  + 12x + 9 = 216 \\  {(2x + 3)}^{2}  = 216 \\ 2x + 3 = 6 \sqrt{6}  \\ x =  - 1.5 + 3 \sqrt{6}

approximately 6.1485

You might be interested in
HELP PLEASE HELP ITS THE LAST QUESTION
andrew-mc [135]
C and d hope it help
7 0
3 years ago
PLEASE ANSWER THIS QUESITON !! WILL GIVE BRAINLIEST !!
Scilla [17]

Answer:

26

Step-by-step explanation:

You can determine the slant height of this cone by forming a right triangle with the radius, and height. Therefore, the slant height is:

sqrt(10^2 + 24^2) = sqrt676 = 26

4 0
3 years ago
Read 2 more answers
Square root of 2tanxcosx-tanx=0
kobusy [5.1K]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/3242555

——————————

Solve the trigonometric equation:

\mathsf{\sqrt{2\,tan\,x\,cos\,x}-tan\,x=0}\\\\ \mathsf{\sqrt{2\cdot \dfrac{sin\,x}{cos\,x}\cdot cos\,x}-tan\,x=0}\\\\\\ \mathsf{\sqrt{2\cdot sin\,x}=tan\,x\qquad\quad(i)}


Restriction for the solution:

\left\{ \begin{array}{l} \mathsf{sin\,x\ge 0}\\\\ \mathsf{tan\,x\ge 0} \end{array} \right.


Square both sides of  (i):

\mathsf{(\sqrt{2\cdot sin\,x})^2=(tan\,x)^2}\\\\ \mathsf{2\cdot sin\,x=tan^2\,x}\\\\ \mathsf{2\cdot sin\,x-tan^2\,x=0}\\\\ \mathsf{\dfrac{2\cdot sin\,x\cdot cos^2\,x}{cos^2\,x}-\dfrac{sin^2\,x}{cos^2\,x}=0}\\\\\\ \mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left(2\,cos^2\,x-sin\,x \right )=0\qquad\quad but~~cos^2 x=1-sin^2 x}

\mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left[2\cdot (1-sin^2\,x)-sin\,x \right]=0}\\\\\\ \mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left[2-2\,sin^2\,x-sin\,x \right]=0}\\\\\\ \mathsf{-\,\dfrac{sin\,x}{cos^2\,x}\cdot \left[2\,sin^2\,x+sin\,x-2 \right]=0}\\\\\\ \mathsf{sin\,x\cdot \left[2\,sin^2\,x+sin\,x-2 \right]=0}


Let

\mathsf{sin\,x=t\qquad (0\le t


So the equation becomes

\mathsf{t\cdot (2t^2+t-2)=0\qquad\quad (ii)}\\\\ \begin{array}{rcl} \mathsf{t=0}&\textsf{ or }&\mathsf{2t^2+t-2=0} \end{array}


Solving the quadratic equation:

\mathsf{2t^2+t-2=0}\quad\longrightarrow\quad\left\{ \begin{array}{l} \mathsf{a=2}\\ \mathsf{b=1}\\ \mathsf{c=-2} \end{array} \right.


\mathsf{\Delta=b^2-4ac}\\\\ \mathsf{\Delta=1^2-4\cdot 2\cdot (-2)}\\\\ \mathsf{\Delta=1+16}\\\\ \mathsf{\Delta=17}


\mathsf{t=\dfrac{-b\pm\sqrt{\Delta}}{2a}}\\\\\\ \mathsf{t=\dfrac{-1\pm\sqrt{17}}{2\cdot 2}}\\\\\\ \mathsf{t=\dfrac{-1\pm\sqrt{17}}{4}}\\\\\\ \begin{array}{rcl} \mathsf{t=\dfrac{-1+\sqrt{17}}{4}}&\textsf{ or }&\mathsf{t=\dfrac{-1-\sqrt{17}}{4}} \end{array}


You can discard the negative value for  t. So the solution for  (ii)  is

\begin{array}{rcl} \mathsf{t=0}&\textsf{ or }&\mathsf{t=\dfrac{\sqrt{17}-1}{4}} \end{array}


Substitute back for  t = sin x.  Remember the restriction for  x:

\begin{array}{rcl} \mathsf{sin\,x=0}&\textsf{ or }&\mathsf{sin\,x=\dfrac{\sqrt{17}-1}{4}}\\\\ \mathsf{x=0+k\cdot 180^\circ}&\textsf{ or }&\mathsf{x=arcsin\bigg(\dfrac{\sqrt{17}-1}{4}\bigg)+k\cdot 360^\circ}\\\\\\ \mathsf{x=k\cdot 180^\circ}&\textsf{ or }&\mathsf{x=51.33^\circ +k\cdot 360^\circ}\quad\longleftarrow\quad\textsf{solution.} \end{array}

where  k  is an integer.


I hope this helps. =)

3 0
3 years ago
If AD=BD, which of the following relationships can be proved and why?
myrzilka [38]

Answer: The answer would be b, the side-angle-side postulate. :)

Step-by-step explanation:

This would be due to the definition of a bisector, and the reflexive property.

3 0
3 years ago
Anyone by chance know how to answer this geometry question I need help so bad
NemiM [27]

Answer:

x = -8 and BDC is 68 degrees.

Step-by-step explanation:

Combine -7x+12 and -8x+48 to get -15x+60.  Since BDA is a straight angle put the above equation to get -15x+60=180.  Subtract 60 from both sides to get -15x=120.  Divide -15 both sides to get -8 as your x value.  Plug in -8 to BDC, since both negatives are being multiplied, it would turn to a positive number which is 56, add 12 to get 68 as your final result for BDC.

8 0
3 years ago
Other questions:
  • Which expression can be used to determine the length of segment ZY?
    5·2 answers
  • What percent of 400 is 20?
    9·2 answers
  • HELP PLEASE!!! I'm desperate! I don't understand.
    13·1 answer
  • How do u make y=4x into standard form
    15·1 answer
  • James and Sarah went out to lunch the price of a lunch for both of them was $20 they tipped their server 20% of that amount. How
    8·1 answer
  • Isaac is purchasing two pairs of shoes—one pair for $37.00 and the second pair for $42.00. The state sales tax applied to Isaac’
    10·1 answer
  • What are the coordinates (x, y) at which the graphs of 2x + 3y = 12 and 2x - y = 4 intersect?
    11·2 answers
  • How much would you pay for a boat that costs $35,000 if you buy it on
    5·1 answer
  • Which statement must be true ?
    15·2 answers
  • 1. The factors of a2 - 9 are
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!