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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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HS: Algebra 2A [M] (Prescriptive) (GP)/ 5 Quadratic Functions
ipn [44]

Answer:

Linear, the linear term is -21x and the constant term is -20. Last option is the answer

Step-by-step explanation:

We are given the following function:

y = (x - 5)(5x + 4) - 5x^2

First we have to simplify y, before solving the question:

y = (x - 5)(5x + 4) - 5x

Applying the distributive property:

y = 5x^2 + 4x - 25x - 20 - 5x^2

y = 0x^2 - 21x - 20

y = -21x - 20

No quadratic term, so it is linear.

The linear term is -21x and the constant term is -20.

4 0
3 years ago
Evaluate -9x when x = 2
11111nata11111 [884]

Answer:

-18

Step-by-step explanation:

x=2 so,

-9(2) = -18

hope this helps

3 0
3 years ago
Read 2 more answers
Please show me a graph of the inequality statement f(x) is less than or equal to 2x squared + 4x
Nikitich [7]

Answer:

Step-by-step explanation:

4 0
3 years ago
Find the reference angle for the given angle. Show work
Katarina [22]
Answer: 44 degrees

=========================================================

Since the given angle -404 is not between 0 and 360, we add 360 to it to get:
-404 + 360 = -44

We add another 360 to that result
-44 + 360 = 316
now we have a value between 0 and 360

Rules:
* If the angle is between 0 and 90, we stop here and simply write down that value

* If the angle x is between 90 and 180, then we compute 180-x

* If the angle x is between 180 and 270, then we compute x-180

* If the angle x is between 270 and 360, then we compute 360-x

* Note in the three rules above, the order of subtraction is always (larger angle)-(smaller angle) = reference angle

* The reference angle has one segment on the x axis (aka the reference angle is adjacent to the x axis)

Based on that, we see that 316 is between 270 and 360, so we use the rule that
360-x
In this case, x = 316

So,
360-x = 360-316 = 44

The reference angle is 44 degrees and looks like what you see in the attached image.

4 0
3 years ago
Read 2 more answers
A rectangular swimming pool is 25 ft long and 20 1/2 ft wide, and it must be filled to a depth of 4 1/2 ft. One cubic foot of wa
bazaltina [42]

ANSWER

307½ gallons of water

EXPLANATION

The volume of the rectangular swimming pool is

V = l \times w \times h

where l=25ft and w=20½ ft.

when it is filled to a depth of 4½ ft ,then the height is , h=4½ ft.

We substitute these values into the formula to get:

V = 25\times 20.5\times 4.5

V = 2306.25 {ft}^{3}

If one cubic foot of water is 7½ gallons, then 2306.25 cubic feet will be

\frac{2306.25}{7.5}  = 307.5gallons

We need 307.5 gallons of water to fill the pool.

4 0
3 years ago
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