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Ghella [55]
2 years ago
11

What value of c will make the expression x² + 6x + 4 + c a perfect square?

Mathematics
2 answers:
FinnZ [79.3K]2 years ago
8 0

Answer:

c= 5

Step-by-step explanation:

\text{If any  quadratic expression is a perfect square, then}\\ \\~~~~~~~\text{discriminant} = 0\\\\\implies b^2 -4ac = 0\\\\\implies 6^2 - 4 \cdot 1 (4+c) = 0~~~~~~~~~~~~~~~;[\text{Compare with the standard form}~ ax^2 +bx +c]\\\\\implies 36 - 16 - 4c =0 \\\\\implies 20-4c =0\\\\\implies 4c = 20\\\\\implies c = \dfrac{20}{4}\\\\\implies c= 5

fredd [130]2 years ago
6 0
<h2>Value Square</h2>

What value of c will make the expression x² + 6x + 4 + c a perfect square?

<h3>Solution:</h3>

  • Square = x² + 6x + 4 + c

Add and Subtract 9:

  • Square = c + x² + 6x + 4 =
  • c + x² + 6x + 4 + (9) - (9)

Complete the square:

  • Square = c - 5 + (x² + 6x + 9) =
  • c - 5 + (x + 3)²

Hence, the correct answer is Square = c + x² + 6x + 4 = c. + (x + 3)² - 5 or c = 5

#ProblemSolve

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A number between 61-107 and are multiples of 3,8,12
Sergeu [11.5K]
72 is the answer you are looking for here

3 0
3 years ago
Elizabeth has 1.32 pounds of candy. She wants to share it equally with herself and 3 friends. How much candy will each person re
lana66690 [7]

Answer:

1/3 pound per person

Step-by-step explanation:

(All)    (People)   (Amount per person)

1.32  /  4          = .33                        

.33 = 1/3

5 0
3 years ago
1. A professional basketball used for league play has a diameter of 25 cm. Which of the following is closest to the volume of th
yKpoI14uk [10]

Answer:

V = 8,181.23 cm^{3}

Step-by-step explanation:

Unfortunately, we are not given any answer choices to choose from but using the information provided we can find the actual volume of the basketball. A basketball is made in the shape of a sphere and the formula for the volume of a sphere is the following...

V = \frac{4}{3} * \pi  * r^{3}

radius of a circle/sphere is half of it's diameter. Since we are provided the diameter size we simply divide it by 2 which would give us 12.5cm. Now we simply plug this value into the formula and solve for V.

V = \frac{4}{3} * \pi  * 12.5^{3}

V = \frac{4}{3}  * \pi  * 1953.125

V = 8,181.23 cm^{3}

5 0
3 years ago
The greatest number that divide 60 and 84 without leaving a reminder ​
a_sh-v [17]

Step-by-step explanation:

HCF of 60 and 84 = 6

So the required greatest number that divides 60 and 84 without leaving remainder is 6.

6 0
3 years ago
Read 2 more answers
Limit of x^2-81/x+9<br> As x goes toward -9
Semmy [17]
Hello,

Use the factoration

a^2 - b^2 = (a - b)(a + b)

Then,

x^2 - 81 = x^2 - 9^2

x^2 - 9^2 = ( x - 9).(x + 9)

Then,

Lim (x^2- 81) /(x+9)

= Lim (x -9)(x+9)/(x+9)

Simplity x + 9

Lim (x -9)

Now replace x = -9

Lim ( -9 -9)

Lim -18 = -18
_______________

The second method without using factorization would be to calculate the limit by the hospital rule.

Lim f(x)/g(x) = lim f(x)'/g(x)'

Where,

f(x)' and g(x)' are the derivates.

Let f(x) = x^2 -81

f(x)' = 2x + 0
f(x)' = 2x

Let g(x) = x +9

g(x)' = 1 + 0
g(x)' = 1

Then the Lim stay:

Lim (x^2 -81)/(x+9) = Lim 2x /1

Now replace x = -9

Lim 2×-9 = Lim -18

= -18




7 0
3 years ago
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