If AB = 3 cm and BC = 4 cm, which does AC equal <br><br>A. 3 cm <br>B. 4 cm<br>C. 5 cm<br>D. 6 cm

Solve equation by using the quadratic formula.

Sati [7]

Answer: 1: x=3, x=1

2: x= -5

3: There are 2 real solutions.

4: There are 2 real solutions.

5: There are no real solutions.

6. There is 1 real solution.

7.

8. x= -6, x = -2

9. x = -1/6, x=1

10.

Explanation:

1. The quadratic formula is

Substituting our known information we have:

2. Rewriting the quadratic in standard form we have x²+10x-25=0. Substituting this into the quadratic formula gives us:

3. The discriminant is b²-4ac. For this problem, that is 20²-4(-4)(25)=400--400=800. Since this is greater than 0, there are 2 real solutions.

4. The discriminant in this problem is 7²-4(2)(-15)=49--120=49+120=169. This is greater than 0, so there are 2 real solutions.

5. The discriminant in this problem is 1²-4(-2)(-28)=1-224=-223. Since this is less than 0, there are no real solutions.

6. If the discriminant of a quadratic is 0, then by definition there is 1 real solution.

7. Rewriting the quadratic we have 3x²-4x-2=0. Using the quadratic formula we have:

8. Factoring this trinomial we want factors of 12 that sum to 8. 6*2 = 12 and 6+2=8, so those are our factors. This gives us:

(x+6)(x+2)=0

Using the zero product property we know that either x+6=0 or x+2=0. Solving these equations we get x= -6 or x= -2.

9. Factoring this trinomial we want factors of 6(-1)=-6 that sum to -5. (-6)(1)=-6 and -6+1=-5, so this is how we "split up" the x term:

6x²-6x+1x-1=0

We group together the first two and the last two terms:

(6x²-6x)+(1x-1)=0

Factor the GCF out of each group. In the first group, that is 6x:

6x(x-1)+(1x-1)=0

In the second group, the GCF is 1:

6x(x-1)+1(x-1)=0

Both terms have a factor of (x-1), so we can factor it out:

(x-1)(6x+1)=0

Using the zero product property, we know either x-1=0 or 6x+1=0. Solving these equations we get x=1 or x=-1/6.

10. Substituting our information into the quadratic formula we get:

Step-by-step explanation:

5 0

2 years ago

Given g(x) = -x + 5, solve for x when g(x) = 3.

Elan Coil [88]

Both equal g(x) so put them together

-x+5=3 then solve for x

-x=3-5
-x=-2
-2 divided by -x =2

x=2

5 0

3 years ago

On one side of the balance scale, Henry placed a 6-gram weight. On the other side of the scale, he placed a ballet slipper.

olchik [2.2K]

Answer:

<u><em>A. 6,000 miligrams</em></u>

Explanation:

A <em>balance scale</em> is balanced when the weights on both sides are equal. Then, since the image shows that both sides are equal, the weight of the <em>6-gram weight</em>, placed by Henry on one side of the balance scale is equal to the weight of the <em>ballet slipper </em>placed on the other side.

Weight of the balance slipper = weight of the 6-gram weight

Weight of the balance slipper = 6 grams

<u>Conversion of units: </u>

6 grams × 1,000miligrams/1gram = 6,000 miligrams

Weight of the balance slipper = 6,000 miligrams

That is the option A.

7 0

4 years ago

Function (T/F) Please help.

Anna007 [38]

Answer:

False

Step-by-step explanation:

it has more than one dot in the same row, which means it has the same number more than once in the x - axis.

3 0

3 years ago

Read 2 more answers

Which statement best describes the function below?

marta [7]

<h2>Answer:</h2>

A. It is a many-to-one function.

<h2>Step-by-step explanation:</h2>

Hello! It will be a pleasure to help to figure out what's the correct answer to this problem. First of all, we have the following function:

$f(x) = 2x^3 + 2x^2-x$

When plotting this function, we get the red graph of the function shown below. So let's solve this as follows:

<h3>A. It is a many-to-one function.</h3>

True

A function is said to be many-to-one there are values of the dependent variable (y-values) that corresponds to more than one value of the independent variable (x-values). To test this, we need to use the Horizontal Line Test. So let's take the horizontal line $y=0.5$ , and you can see from the first figure below that $y=0.5$ is mapped onto $x=-1.241 \ x=-0.344 \ and \ x=0.585$ . so this is a many-to-one function.

<h3>B. It is a one-to-one function.</h3><h3>False</h3>

Since this is a many-to-one function, it can't be a one-to-one function.

<h3>C. It is not a function.</h3>

False

Indeed, this is a function

<h3>D. It fails the vertical line test.</h3>

False

It passes the vertical line test because any vertical line can intersect the graph of the function at most once. An example of this is shown in the second figure below.

6 0

4 years ago

If AB = 3 cm and BC = 4 cm, which does AC equal A. 3 cm B. 4 cmC. 5 cmD. 6 cm