All categories

4 years ago

given the equation Square root of x minus 5 + 7 = 11 Solve for x and identify if it is an extraneous solution.

2 answers:

8 0

Sqrt(x) - 5+7 =11
combine like terms
-5 +7 = 2

sqrt(x) + 2 = 11
subtract 2 from each side

sqrt(x) = 9

square both sides

x = 9^2

x = 81

an extraneous solution would be an invalid solution

in this case it is not an extraneous solution

ddd [48]4 years ago

5 0

Answer:

x=21 and solution is not extraneous.

Step-by-step explanation:

Given : Expression $\sqrt{(x-5)}+7=11$

To find : The solution for x and identify if it is an extraneous solution?

Solution :

Expression $\sqrt{(x-5)}+7=11$

$\sqrt{(x-5)}=11-7$

$\sqrt{(x-5)}=4$

Taking square both side,

$(\sqrt{(x-5)})^2=4^2$

$x-5=16$

$x=21$

Substituting the value back in the equation to find this is an extraneous solution or not.

$\sqrt{(21-5)}+7=11$

$\sqrt{(16)}+7=11$

$4+7=11$

$11=11$

This is true.

Which means solution is not an extraneous solution.

You might be interested in

PLEASE HELP!!!!

Lunna [17]

NOTES:

Given a quadratic function in standard format (y = ax² + bx + c), the direction of the parabola is as follows:

if "a" is positive, then opens UP
if "a" is negative, then opens DOWN

Given a quadratic function in standard format (y = ax² + bx + c), the vertex can be found as follows:

the Axis Of Symmetry (x-value) is: x = $\frac{-b}{2a}$
y-value is found by plugging in the AOS for "x" in the equation

****************************************************************************************

1) y = x² + 11x + 24

a = +1 so the parabola opens UP

x = $\frac{-b}{2a}$ = $\frac{-11}{2(1)}$ = $-\frac{11}{2}$

y = $(-\frac{11}{2})^{2}$ + 11 $(-\frac{11}{2} )$ + 24 = $-\frac{25}{4}$

vertex $(-\frac{11}{2}$ , $-\frac{25}{4})$ is in Quadrant 3 and is below the x-axis

This COULD be the graph of the rain gauge.

The graph should contain the vertex, x-intercepts (-3, 0) and (-8, 0), and y-intercept (0, 24)

******************************************************************************************

2) y = -x² - 6x - 8

a = -1 so the parabola opens DOWN

x = $\frac{-b}{2a}$ = $\frac{-(-6)}{2(-1)}$ = $\frac{6}{-2}$ = -3

y = -(-3)² - 6(-3) - 8 = -9 + 18 - 8 = 1

vertex (-3, 1) is in Quadrant 2 and is above the x-axis

This could NOT be the graph of the rain gauge.

The graph should contain the vertex, x-intercepts (-2, 0) and (-4, 0), and y-intercept (0, -8)

******************************************************************************************

3) y = x² - 2x + 3

a = 1 so the parabola opens UP

x = $\frac{-b}{2a}$ = $\frac{-(-2)}{2(1)}$ = $\frac{2}{2}$ = 1

y = (1)² - 2(1) + 3 = 1 - 2 + 3 = 2

vertex (1, 2) is in Quadrant 1 and is above the x-axis

This could NOT be the graph of the rain gauge.

The graph should contain the vertex, y-intercept (0, 3), and its mirror image (2, 3). There are no x-intercepts

******************************************************************************************

4) y = x² + 4x + 4

a = 1 so the parabola opens UP

x = $\frac{-b}{2a}$ = $\frac{-4}{2(1)}$ = -2

y = (-2)² + 4(-2) + 4 = 4 - 8 + 4 = 0

vertex (-2, 0) is in Quadrant 2 and is on the x-axis

This COULD be the graph of the rain gauge.

The graph should contain the vertex, y-intercept (0, 4), and its mirror image (-4, 4). The x-intercept is the vertex.

Compared to the other four graphs, this is most likely the equation for the rain gauge!

******************************************************************************************

5) y = 3x² + 21x + 30

a = +3 so the parabola opens UP

x = $\frac{-b}{2a}$ = $\frac{-21}{2(3)}$ = $-\frac{7}{2}$

y = 3 $(-\frac{7}{2})^{2}$ + 21 $(-\frac{7}{2} )$ + 30 = $-\frac{27}{4}$

vertex $(-\frac{7}{2}$ , $-\frac{27}{4})$ is in Quadrant 3 and is below the x-axis

This COULD be the graph of the rain gauge.

The graph should contain the vertex, x-intercepts (-2, 0) and (-5, 0), and y-intercept (0, 30)

*******************************************************************************************

4 0

4 years ago

Read 2 more answers

Vectors; please help: 2y+w-u=?

andreyandreev [35.5K]

Answer:

idkdikdidkidkidk

Step-by-step explanation:

5 0

4 years ago

A local grocery store tested spinach samples for E coli bacteria using two different tests. The first test has a 94% probability

Afina-wow [57]

Answer: Probability that both tests detect the bacteria is 83.66%.

Step-by-step explanation:

Since we have given that

Probability of the first test giving accurate results = 84%

Probability of the second test is accurate = 89%

Probability of both tests detect the bacteria is given by

$\frac{94}{100}\times \frac{89}{100}\\\\=0.94\times 0.89\\\\=0.8366\\\\=83.66\%$

Hence, Probability that both tests detect the bacteria is 83.66%.

6 0

3 years ago

Read 2 more answers

An observer (O) spots a plane flying at a 55° angle to his horizontal line of sight. If the plane is flying at an altitude of 21

xz_007 [3.2K]

Answer:

B. 25,636 feet

Step-by-step explanation:

sin(55) = h/x

h = 21,000

sin(55) = 21,000/x

x = 21,000/sin(55)

x = 25636.27 ≈ 25,636 feet

Hope this helped! :)

3 0

3 years ago

Read 2 more answers

Please help me on this problem!

USPshnik [31]

There is no solution since the lines are parallel. (See attached graph)

<h2>Hope this helps!</h2>

6 0

3 years ago

Read 2 more answers