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
IRINA_888 [86]
3 years ago
14

Solve for x...........................

Mathematics
1 answer:
yaroslaw [1]3 years ago
5 0

Answer:

Option A is correct, i.e. x = -3, x = 7.

Step-by-step explanation:

Given the equation is x² -4x -21 = 0.

We can compare it with general quadratic equation i.e. ax² +bx +c =0.

then a = 1, b = -4, c = -21.

We can use Quadratic formula as follows:-

x = ( -b ± √(b²-4ac) )/2a

x = ( +4 ± √(16-4*1*-21) )/2*1

x = ( +4 ± √(16+84) )/2

x = ( +4 ± √(100) )/2

x = ( +4 ± 10 )/2

x = (4+10)/2 or x = (4-10)/2

x = 14/2 or x = -6/2

x = 7 or x = -3

Hence, option A is correct, i.e. x = -3, x = 7.

You might be interested in
It costs $34.95 to rent a jet ski for four hours plus $15.75 for each additional hour. You have $100. Can you rent the jet ski f
irakobra [83]

Answer:

yes

Step-by-step explanation:

34.95 + 15.75(4)

34.95 + 63 = 97.95

5 0
3 years ago
Read 2 more answers
A stereo system is being installed in a room with a rectangular floor measuring 11 11 feet by 10 10 feet and a a 9 9​-foot ceili
lisabon 2012 [21]

Answer:

idkhhfrdssefghujhgjjuuu

5 0
3 years ago
A rectangle container that has a length of 30 cm,a width of 20 cm,and a height of 24 cm is filled with water to a depth of 15 cm
Ket [755]
<span>V(h 24) = 30 cm*20 cm*24 cm = 14400 cm³ =  14,4 liters</span>
<span>V(h 15) = 30 cm*20 cm*15 cm =    9000 cm³  =  9 liters</span>
<span>                         + 6,5 liters = + 6500 cm³      </span>
9 liters +   6,5 liters = 15,5 liters         =>   15,5 liters -14,4 liters = 1,1 liters
now  15500 cm³   =>    1100 cm³ =1,1 liters  too much !!
Answer:  1,1 liters of water overflow the container.<span>
</span>
7 0
3 years ago
Read 2 more answers
The graphs of the quadratic functions f(x) = 6 – 10x2 and g(x) = 8 – (x – 2)2 are provided below. Observe there are TWO lines si
natta225 [31]

Answer:

a) y = 7.74*x + 7.5

b)  y = 1.148*x + 6.036

Step-by-step explanation:

Given:

                                  f(x) = 6 - 10*x^2

                                  g(x) = 8 - (x-2)^2

Find:

(a) The line simultaneously tangent to both graphs having the LARGEST slope has equation

(b) The other line simultaneously tangent to both graphs has equation,

Solution:

- Find the derivatives of the two functions given:

                                f'(x) = -20*x

                                g'(x) = -2*(x-2)

- Since, the derivative of both function depends on the x coordinate. We will choose a point x_o which is common for both the functions f(x) and g(x). Point: ( x_o , g(x_o)) Hence,

                                g'(x_o) = -2*(x_o -2)

- Now compute the gradient of a line tangent to both graphs at point (x_o , g(x_o) ) on g(x) graph and point ( x , f(x) ) on function f(x):

                                m = (g(x_o) - f(x)) / (x_o - x)

                                m = (8 - (x_o-2)^2 - 6 + 10*x^2) / (x_o - x)

                                m = (8 - (x_o^2 - 4*x_o + 4) - 6 + 10*x^2)/(x_o - x)

                                m = ( 8 - x_o^2 + 4*x_o -4 -6 +10*x^2) /(x_o - x)

                                m = ( -2 - x_o^2 + 4*x_o + 10*x^2) /(x_o - x)

- Now the gradient of the line computed from a point on each graph m must be equal to the derivatives computed earlier for each function:

                                m = f'(x) = g'(x_o)

- We will develop the first expression:

                                m = f'(x)

                                ( -2 - x_o^2 + 4*x_o + 10*x^2) /(x_o - x) = -20*x

Eq 1.                          (-2 - x_o^2 + 4*x_o + 10*x^2) = -20*x*x_o + 20*x^2

And,

                              m = g'(x_o)

                              ( -2 - x_o^2 + 4*x_o + 10*x^2) /(x_o - x) = -20*x

                              -2 - x_o^2 + 4*x_o + 10*x^2 = -2(x_o - 2)(x_o - x)

Eq 2                       -2 - x_o^2 + 4*x_o+ 10*x^2 = -2(x_o^2 - x_o*(x + 2) + 2*x)

- Now subtract the two equations (Eq 1 - Eq 2):

                              -20*x*x_o + 20*x^2 + 2*x_o^2 - 2*x_o*(x + 2) + 4*x = 0

                              -22*x*x_o + 20*x^2 + 2*x_o^2 - 4*x_o + 4*x = 0

- Form factors:       20*x^2 - 20*x*x_o - 2*x*x_o + 2*x_o^2 - 4*x_o + 4*x = 0

                              20*x*(x - x_o) - 2*x_o*(x - x_o) + 4*(x - x_o) = 0

                               (x - x_o)(20*x - 2*x_o + 4) = 0  

                               x = x_o   ,     x_o = 10x + 2    

- For x_o = 10x + 2  ,

                               (g(10*x + 2) - f(x))/(10*x + 2 - x) = -20*x

                                (8 - 100*x^2 - 6 + 10*x^2)/(9*x + 2) = -20*x

                                (-90*x^2 + 2) = -180*x^2 - 40*x

                                90*x^2 + 40*x + 2 = 0  

- Solve the quadratic equation above:

                                 x = -0.0574, -0.387      

- Largest slope is at x = -0.387 where equation of line is:

                                  y - 4.502 = -20*(-0.387)*(x + 0.387)

                                  y = 7.74*x + 7.5          

- Other tangent line:

                                  y - 5.97 = 1.148*(x + 0.0574)

                                  y = 1.148*x + 6.036

6 0
3 years ago
Choose the equation of the line that is equal to the x-axis.
stiv31 [10]

Answer:

C) x=y

hope it helps.

<h3>stay safe healthy and happy.</h3>
8 0
2 years ago
Other questions:
  • 5 inches equals how many feet
    8·2 answers
  • Suppose a quarter of all the elephants in an African wildlife refuge have ear tags. If there are exactly 60 tagged elephants, wh
    7·1 answer
  • We’re does 1 3/5 go on a number line
    13·1 answer
  • If a train travels 30 miles per hour how long will it take for the train to drive 180 miles
    12·1 answer
  • greg plans to buy a book for $5.00 and some music CDs for $4.00 each. the greatest total amount o money that greg plans to spend
    15·1 answer
  • Someone please help me ​
    6·2 answers
  • [FOLLOW-UP FOR LAST QUESTION] Whenever inappropriate, unacademic, or irrelevant (or plain idiotic) questions are asked on Brainl
    11·2 answers
  • It would be nice if someone can help me. i’m failing school and i really need help. thank you:).
    6·1 answer
  • The equation v=68t represents the number of views v for a video after t hours. Identify the independent and dependent variables.
    14·1 answer
  • The difference in measure of two complemenatary angles is 12 find the measure of the angles
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!