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
Ratling [72]
3 years ago
15

Complete the square on the following quadratic

Mathematics
1 answer:
OlgaM077 [116]3 years ago
8 0
X² + 10x +2 = 0 .Complete the square of (x² + 10x + ??)
We know that (10x) is equal to twice the square root of the 1st (x) by ??
10x = 2.x.(??) and ?? = 5 and its square is 25. Then I have to add 25 and subtract 25 so that not to change the equation:
 (x² + 10x + 25) -25 +2 =0
 (x+5)² -23
You might be interested in
Solve for x: 3x − 24 = 81
LenKa [72]

3x - 24 = 81

Add 24 to each side.

3x - 24 + 24 = 81 + 24

3x = 105

Divide each side by 3.

(3x)/3 = 105/3

x = 35

Answer: x = 35

5 0
3 years ago
Read 2 more answers
What is the result of substituting for y in the bottom equation<br> y=x+3<br> y=x^2+2x-4
8_murik_8 [283]

The solutions are (2.1925, 5.1925) and (-3.1925, -0.1925)

<em><u>Solution:</u></em>

Given that,

y = x + 3 ------- eqn 1\\\\y = x^2 + 2x - 4  ----- eqn 2

<em><u>We have to substitute eqn 1 in eqn 2</u></em>

x + 3 = x^2 + 2x - 4

\mathrm{Switch\:sides}\\\\x^2+2x-4=x+3\\\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}\\\\x^2+2x-4-3=x+3-3\\\\\mathrm{Simplify}\\\\x^2+2x-7=x\\\\\mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}\\\\x^2+2x-7-x=x-x\\\\\mathrm{Simplify}\\\\x^2+x-7=0

\mathrm{Solve\:with\:the\:quadratic\:formula}\\\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=1,\:c=-7\\\\x =\frac{-1\pm \sqrt{1^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}

x = \frac{-1 \pm \sqrt{ 1 + 28}}{2}\\\\x = \frac{ -1 \pm \sqrt{29}}{2}

x = \frac{ -1 \pm 5.385 }{2}\\\\We\ have\ two\ solutions\\\\x = \frac{ -1 + 5.385 }{2}\\\\x = 2.1925

Also\\\\x = \frac{ -1 - 5.385 }{2}\\\\x = -3.1925

Substitute x = 2.1925 in eqn 1

y = 2.1925 + 3

y = 5.1925

Substitute x = -3.1925 in eqn 1

y = -3.1925 + 3

y = -0.1925

Thus the solutions are (2.1925, 5.1925) and (-3.1925, -0.1925)

6 0
3 years ago
IM TIMEDDD HELP!! Which shows a rational number plotted correctly on a number line?
IrinaVladis [17]
I guess the one with 2
6 0
3 years ago
Read 2 more answers
A brand of grape juice that's is 25% grape juice is mixed with another brand that is 75% grape juice. The result is 7 gallons of
garri49 [273]

Answer:

5.6 gallons.

Step-by-step explanation:

If we take x gallons of 25% grape juice then it will contain \frac{x}{4} gallons of pure grape juice.

Again, if we take y gallons of 75% grape juice then it will contain \frac{3y}{4} gallons of pure grape juice.

If we mix them then the total volume will become x + y = 7 gallons  ...... (1)

Again the mixture will become 35% juice.

So, \frac{\frac{x}{4} +\frac{3y}{4} }{x+y} =\frac{35}{100}

⇒ 0.25x + 0.75y = 0.35x + 0.35y

⇒0.1x = 0.4y

⇒x = 4y........ (2)

Now, solving equations (1) and (2) we get, 5y = 7, ⇒ y = 1.4 gallons

Hence, x = 4y = 5.6 gallons

Therefore, the 25% grape juice was mixed by 5.6 gallons. (Answer)

4 0
3 years ago
ANSWER ASAP PLEASE !!!
Sauron [17]
3/7 = 0.43 (approx.)
4/9 = 0.44 (approx.)

Hence, 4/9 is bigger. 
6 0
3 years ago
Read 2 more answers
Other questions:
  • Use rectangular model to record the partial quotients 852/6.
    7·1 answer
  • Given f(x) =5 - 3x, if f(x) = -19, find x
    8·1 answer
  • If the outliers are not included what is the mean of the data set, 79 79 80 82 50 78 83 79 81 82
    5·1 answer
  • You can get a quart bottle of cola for $1.50 or a liter bottle for $1.57. Which is the better buy in terms of price per volume?
    5·1 answer
  • Help with trig please.
    8·2 answers
  • Given the following perfect square trinomial, fill in the missing term. <br><br> x2 − 16x + ____
    10·1 answer
  • One inch is about 2.54 centimeters. About how many centimeters is 4.5 inches.
    6·1 answer
  • A, C, E<br> A, C, D<br> B, D, E<br> C, D, E
    7·1 answer
  • Please help me with this!!!!
    10·1 answer
  • What is the volume of this object?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!