All categories

2 years ago

3. How many solutions does the equation have?

Mathematics

1 answer:

Pepsi [2]2 years ago

3 0

An infinite number of solutions since the right side is equal the left side for every value of x.

You might be interested in

Haddie flipped a fair coin 12 times. The coin landed on heads 11 times and tails 1 time. She flips the coin a 13th time. How lik

Tpy6a [65]

Answer:

50/50. there is no outside force that decides otherwise

6 0

3 years ago

Solve x^2 - 8x = 3 by completing the square. Which is the solution set of the equation?

sp2606 [1]

1st one

Step-by-step explanation:

I have answered ur question

5 0

2 years ago

Read 2 more answers

Ariel’s pet baby polar bear ,Ryan weight 12.5 kilograms .Another polar bear ,Named Ronnie weights 11 kilograms.How many grams he

Mice21 [21]

Ryan is 1.5 kilograms heavier than Ronnie

1.5 kilograms is the same as 1500 grams

5 0

3 years ago

(15−x)∙4=10<br> pls pls answer asapppp

Novay_Z [31]

(15-12.5)*4=10

x=12.5

6 0

3 years ago

Select the correct answer.

Anika [276]

<h2>Answer:</h2><h3>A. $\displaystyle{\frac{-(-2) \pm \sqrt{(2)^{2}-4(1)(4)}}{2(1)} }$ </h3><h2 />

Find the values a, b, and c to substitute into the quadratic formula.

<h2>Remember:</h2><h3>Standard form</h3>

Notice how there are a, b, and c. Everything is left of the equal sign, leaving 0 on the right.

<h3>Quadratic formula</h3>

Notice how there are a, b, and c too, just like in standard form. After we find standard form, we can substitute a, b and c values into the quadratic formula.

$\displaystyle{x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a} }$

<h2>Step-by-step solution</h2>

Here are the steps we will follow:

Rearrange the equation from the question into standard form.
Determine the values for a, b, and c.
Substitute a, b, and c into the quadratic formula.
Compare options and simplify as needed.

<h3>Rearrange into standard form</h3>

Move everything to the left while keeping both sides equal.

x² + 1 = 2x – 3 Equation from the question

x² + 1 + 3 = 2x – 3 + 3 Add three to both sides.

x² + 1 + 3 = 2x -3 + 3 cancels out to 0.

x² + 4 = 2x Simplify.

x² + 4 – 2x = 2x – 2x Subtract 2x from both sides.

x² + 4 – 2x = 0 No numbers on the right side is the same as 0.

x² – 2x + 4 = 0 Rearrange to follow ax² + bx + c = 0.

<h3>Determine a, b, and c values</h3>

Find a, b, and c from standard form.

ax² + bx + c = 0 Standard form

x² – 2x + 4 = 0 No number attached to x² means a = 1.

a = 1, b = –2, and c = 4

<h3>Substitute into the quadratic formula</h3>

Substitute a = 1, b = –2, and c = 4 into the quadratic formula.

$\displaystyle{x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a} }$

Here is how our formula set up should look:

$\displaystyle{x=\frac{-(-2) \pm \sqrt{(-2)^{2}-4(1)(4)}}{2(1)} }$

<h3>Compare answer options</h3>

Let's compare formula set up to the options in the question.

The denominator is 2(1). So, the answer is <u>not option B</u>.

Inside the square root, it says –4(1)(4). So, the answer is <u>not option D</u>.

This leaves us with either option A or option C.

<h3>Simplify</h3>

Before the ±, it says –(–2). When simplified, –(–2) is 2.

Option C has –2. So, the answer is <u>not option C</u>.

Inside the square root, it says (–2)², which is equal to 2².

When solving exponents of negative numbers,

an odd exponent results in a negative product, and;
an even exponent results in a positive product.

The exponent 2 is even.

(–2)² = 4

∵ (–2)² = 4 and 2² = 4

∴ (–2)² = 2²

(–2)² is the same as 2².

Therefore, the answer is <u>option A</u>.

5 0

2 years ago