(3x+3/x^2-25)-(x-5/x^2-25)

This is Mrs. Galicia’s solution for the equation. Is Mrs. Galicia’s solution correct? Explain in complete sentences also, what a

horrorfan [7]

Given:

Given that Mrs. Galicia’s solution for the equation.

We need to determine whether Mrs. Galicia’s solution is correct or not.

Also, we need to determine the correct solutions.

Mrs. Galicia’s solution:

Step 4: $(x-4)^2=25$

Step 5: $x-4=25$

After step 4, Mrs. Galicia’s did not take square root on both sides to determine the value of x.

Thus, Mrs. Galicia’s made in mistake in step 5, by solving the equation without taking square root on both sides.

Hence, Mrs. Galicia’s solution is wrong.

Correct solutions:

The equation is $x^{2} -8x-9=0$

Solving, we get;

$x^2-8x=9$

Completing the square, we have;

$x^2-8x+16=9+16$

$(x-4)^2=25$

Taking square root on both sides, we get;

$x-4=\pm 5$

Thus, the values of x are given by

$x-4=5$ and $x-4=-5$

$x=9$ and $x=-1$

Thus, the correct solutions are x = 9 and x = -1

6 0

3 years ago

If f(x) = 6x - 4 and g(x) = 2x^3, find g(3) - f(4)

Korolek [52]

To solve the problem, simply plug in the value for x in both functions, as shown below:

$f(4) = 6(4) - 4$

--> $f(3) = 24 - 4$

---> $f(3) = 20$

$g(3) = 2(3)^3$

--> $g(3) = 2 * (3^3)$

---> $g(3) = 2 * 27$

----> $g(3) = 54$

$g(3) - f(4) = 54 - 20$ , so the answer is 34.

7 0

4 years ago

A dump truck driver is delivering loads of sand for making sandbags to protect homes from flooding. Each load contains 12 m3 of

DaniilM [7]

Answer:

57

Step-by-step explanation:

The volume of a cone is given by the formula ...

V = (1/3)πr²h

For a pile with a radius of 8.5 m and a height of 9 m, the volume is ...

V = (1/3)π(8.5 m)²(9 m) = 216.75π m³ ≈ 680.94 m³

Then the number of truckloads required to create that size pile will be ...

(680.94 m³)/(12 m³/truck) = 56.745 trucks

Even a partial truck load entails another trip, so ...

57 truck loads of sand are needed.

5 0

3 years ago

Identify the values of variables x, y, and z based on the image given of the angles formed by a transversal and parallel lines

Paul [167]

Answer:

$x=62\\y=94\\z=94$

Step-by-step explanation:

Let's start by identifying relevant angle theorems for two parallel lines cut by a transversal.

Alternate Interior Angles Theorem

Two angles that are on different sides of the transversal and inside of the two parallel lines are congruent (=).

Alternate Exterior Angles Theorem

Two angles that are on different sides of the transversal and outside of the two parallel lines are congruent (=).

Same-side Interior Angles Theorem

Two angles that are on the same side of the transversal and inside of the two parallel lines are supplementary (= 180).

Same-side Exterior Angles Theorem

Two angles that are on the same side of the transversal and outside of the two parallel lines are supplementary (=180).

Corresponding Angles Theorem

Two angles on a figure that correspond are congruent (=).

_

Now, let's look at the figure and apply these theorems.

$z$ and $86$ are same-side exterior angles, meaning they're supplementary:

$z+86=180$

Subtract $86$ from both sides of the equation:

$z=94$

Now that we know our $z$ value, let's recognize that $z$ ( $94$ )corresponds to $x+32$ , meaning they're congruent:

$x+32=94$

Subtract $32$ from both sides of the equation:

$x=62$

Let's find the value of the angle:

$(62)+32$

Add:

$94$

Since the corresponding angles are of the same value, they're congruent, proving our $x$ & $z$ values correct.

_

Since $y$ and the angle represented by the expression $x+32$ ( $94$ °) are alternate-interior angles, they are congruent:

$y=94$

5 0

4 years ago

7.0 is ten times as much as

icang [17]

Answer:

0.7

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers