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Andre45 [30]
3 years ago
6

Use the discriminant to answer the questions. 32x - 4 = 4x2 + 60 For the equation shown, choose the description of the solutions

. One real, rational Two real, rational Two real, irrational Two complex
Mathematics
2 answers:
sp2606 [1]3 years ago
8 0

One real, rational, Option A

kenny6666 [7]3 years ago
3 0

Answer:

one real solution

Step-by-step explanation:

Use the discriminant to answer the questions. 32x - 4 = 4x^2 + 60

Move all the terms to one side and make right hand side 0

32x - 4 = 4x^2 + 60

subtract 4x^2 from both sides

-4x^2 + 32x -4 = 60

Subtract 60 from both sides

-4x^2 + 32x - 64=0

a= -4, b= 32, c= -64

discriminant is b^2 - 4ac

(32)^2 - 4(-4)(-64)= 1024 -1024=0

Discriminant b^2 - 4ac=0

so the equation has only one real solution

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What is the solution to the linear equation?
antoniya [11.8K]

Answer:

\large\boxed{p=1}

Step-by-step explanation:

\dfrac{2}{5}+p=\dfrac{4}{5}+\dfrac{3}{5}p\qquad\text{multiply both sides by 5}\\\\5\!\!\!\!\diagup^1\cdot\dfrac{2}{5\!\!\!\!\diagup_1}+5p=5\!\!\!\!\diagup^1\cdot\dfrac{4}{5\!\!\!\!\diagup_1}+5\!\!\!\!\diagup^1\cdot\dfrac{3}{5\!\!\!\!\diagup_1}p\\\\2+5p=4+3p\qquad\text{subtract 2 from both sides}\\\\5p=2+3p\qquad\text{subtract 3p from both sides}\\\\2p=2\qquad\text{divide both sides by 2}\\\\p=1

4 0
3 years ago
Read 2 more answers
(iii) If a, b, c are rational numbers, then<br>a x (b-c) #ax b-ax c. true or false ​
sp2606 [1]

Answer:

false

Step-by-step explanation:

answer:ab-ac=ab-ac

3 0
3 years ago
Help!!!!!<br> Suppose f(x) = x2. What is the graph of g(x) = f(3x)?
STALIN [3.7K]

Answer:

we conclude that g(x) = 9x² is the result of f(x) vertically stretched by multiplying each of its y-coordinates by 9.

Also, check the attached graph is matched with option B.

Hence, option (B) is the correct graph.

Step-by-step explanation:

Given

  • f(x) = x²
  • g(x) = f(3x)

so

  • g(x) = (3x)² = 9x²

Thus, the graph of g(x) = 9x² is shown below.

From the graph, it is clear that at x = 0, y = 0

So, the y-intercept is at (0, 0).

Clearly

  • f(x) = x²
  • g(x) = 9x²

Note that the vertex of the graph also lies at (0, 0), because it is clear that g(x) = 9x² is the result of f(x) vertically stretched by multiplying each of its y-coordinates by 9.

Since 9 > 0, it means g(x) = 9x² is vertically stretched by multiplying each of its y-coordinates by 9.

Therefore, we conclude that g(x) = 9x² is the result of f(x) vertically stretched by multiplying each of its y-coordinates by 9.

Also, check the attached graph is matched with option B.

Hence, option (B) is the correct graph.

7 0
3 years ago
there are 32 students in ms keys he homeroom. of the students 3/8 are boys. how many boys are in the homeroom
algol13

Answer: 12 out of the 32 would be boys. Hope this helps.

7 0
4 years ago
Read 2 more answers
Eloise started to solve a radical equation in this way: square root of negative 2x plus 1 − 3 = x square root of negative 2x plu
Rasek [7]

Answer:

Both solutions cannot satisfy the original equation as Eloise makes mathematical error in solving for those solutions. Check Explanation for the breakdown of her steps and the right way to go about solving this.

Step-by-step explanation:

Radical equation is square root of negative 2x plus 1 − 3 = x

In mathematical terms,

√(-2x + 1) - 3 = x

Them her steps,

She adds 3 to both sides,

square root of negative 2x plus 1 − 3 + 3 = x + 3

In mathematical terms,

√(-2x + 1) - 3 + 3 = x + 3

On simplification, she obtains,

square root of negative 2x plus 1 = x + 3

√(-2x + 1) = x + 3

Then, she goes ahead to subtract 1 from both sides,

square root of negative 2x plus 1 − 1 = x + 3 − 1

√(-2x + 1) - 1 = x + 3 - 1

It was at this point that she makes the mistake that scatters everything; she removed the 1 from under square root to take the (- 1) she introduced (without much thoughts). She then obtains

square root of negative 2 x = x + 2

√(-2x) = x + 2 (wrong step, that scatters the process)

She then squares both sides

(square root of negative 2x)² = (x − 4)²

-2x = (x - 4)²

Here, Eloise makes another error, albeit, this is a typographical error. She wrote (x - 4) instead of (x + 2)

From then on, anything she does, whether wrong or right, it will not give the right answer.

−2x = x² − 8x + 16

Then she makes more errors, (-8x) changes to 8x with the introduced 2x on the left hand side doesn't account for this change.

−2x + 2x = x² + 8x + 16 + 2x

0 = x² + 10x + 16

0 = (x + 2)(x + 8)

x+2 = 0 or x+8 = 0

x = -2 or x = -8

Which is evidently wrong.

The correct solving method should have been from the point

√(-2x + 1) = x + 3

Square both sides

-2x + 1 = (x + 3)²

x² + 6x + 9 = - 2x + 1

x² + 8x + 8 = 0

Solving the equation quadratically.

x = - 1.17 or - 6.83

The true value of x that satisfies the given equation that Eloise attempted to solve are -1.17 and -6.83.

Hope this Helps!!!

8 0
3 years ago
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