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
wlad13 [49]
2 years ago
15

Use completing the square to determine which of the following gives the solutions to 3x2 - 24x + 40 = 28.

Mathematics
1 answer:
jeka942 years ago
5 0

Answer:

x=4+2\sqrt{3}

x=4-2\sqrt{3}

Step-by-step explanation:

<u>Completing the square</u>

when  ax^2+bx+c=0

Given equation:

3x^2-24x+40=28

Subtract 40 from both sides:

\implies 3x^2-24x=-12

Divide both sides by 3:

\implies x^2-8x=-4

Add the square of half the coefficient of x to both sides:

(\frac{b}{2})^2=(\frac{-8}{2})^2=16

\implies x^2-8x+16=-4+16

Factor the left side and simplify the right side:

\implies (x-4)^2=12

Square root both sides:

\implies x-4=\pm\sqrt{12}

Add 4 to both sides and simplify the radical:

\implies x=4\pm\sqrt{4 \cdot 3}

\implies x=4\pm\sqrt{4}\sqrt{3}

\implies x=4\pm2\sqrt{3}

You might be interested in
In the summertime your friend wants to have a snow cone stand at a local grocery store parking lot. You want to make sure he act
Vitek1552 [10]
a) The total monthly cost is the sum of the fixed cost and the variable cost. If q represents the number of cones sold in a month, the monthly cost c(q) is given by 
   c(q) = 300 + 0.25q

b)
If q cones are sold for $1.25 each, the revenue is given by
   r(q) = 1.25q

c)
Profit is the difference between revenue and cost.
   p(q) = r(q) - c(q)
   p(q) = 1.00q - 300
. . . . . . slope-intercept form

d)
The equation in part (c) is already in slope-intercept form.
   q - p = 300
. . . . . . . . . . . . standard form
The slope is the profit contribution from the sale of one cone ($1 per cone).
The intercept is the profit (loss) that results if no cones are sold.

e) With a suitable graphing program either form of the equation can be graphed simply by entering it into the program.
   Slope-intercept form. Plot the intercept (-300) and draw a line with the appropriate slope (1).
   Standard form. It is convenient to actually or virtually convert the equation to intercept form and draw a line through the points (0, -300) and (300, 0) where q is on the horizontal axis.

f) Of the three equations created, we presume the one of interest is the profit equation. Its domain is all non-negative values of q. Its range is all values of p that are -300 or more.

g) The x-intercept identified in part (e) is (300, 0). You need to sell 300 cones to break even.

h) Profit numbers are
   425 cones: $125 profit
   550 cones: $250 profit
   700 cones: $400 profit
7 0
3 years ago
The cost to take a taxi includes a flat rate, plus a charge for the number of miles the taxi travels.
Alenkasestr [34]

Answer:

412$

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Pls help I’m lost Pls PLS I NEED YALL TO ANSWER QUICK
Margaret [11]

Answer:1/2

Step-by-step explanation:

3/6 =1/2

5 0
3 years ago
Ms. Green has 3 % yards of fabric. One bandana requires 1/4 of a yard of fabric. How many bandanas can
Nikitich [7]

Answer:

12

Step-by-step explanation:

number of bandana that can be made = total yards of fabric ÷ yards needed to make one bandanna

3 ÷ 1 /4

= 3 x 4 = 12

7 0
3 years ago
What is the distance between the following points?
Elenna [48]

Answer:

11

Step-by-step explanation:

there are 11 spaces between the points

just count the number of spaces, no calculations needed.

6 0
3 years ago
Other questions:
  • There are 38 pockets on an american roulette wheel: 18 red, 18 black, and 2 green. if you were to randomly spin an american roul
    15·1 answer
  • 9 please please :D.
    10·2 answers
  • Find the percent change from the first value to the second.<br><br> 50;36
    6·1 answer
  • find the volume of the composite figure ( also I'm not going to redo this question becuase, u should be able to zoom in) Ok, ple
    14·2 answers
  • What is 3000 divided by 200 to the 6 power
    15·2 answers
  • 2 over 3 multiplied by 3 minus 5
    8·1 answer
  • X+X+(60% of X)=180<br><br> Ez points plus brainliest
    8·1 answer
  • Explain two ways you might reduce motor vehicle insurance premiums.
    15·1 answer
  • The price of a pair of shoes increases from $58 to $61 What is the percent increase to the nearest percent?
    9·2 answers
  • Each of the 16 creates on a freight elevator weighs 150 pounds. The freight elevator has a weight limit 2 tons. How many more cr
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!