Ask question

Ask question

All categories

Nookie1986 [14]

3 years ago

5

Solve for x

2%20%20%7B%7D%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20" id="TexFormula1" title="8 {}^{2 + x} + 2 {}^{3x} = 32 {}^{ \frac{1}{2} } " alt="8 {}^{2 + x} + 2 {}^{3x} = 32 {}^{ \frac{1}{2} } " align="absmiddle" class="latex-formula">

1 answer:

Stella [2.4K]3 years ago

7 0

Answer:

8^2+x + 2^ 3x = 32^ 1/2

2^3(2+x) + 2^3x = 2^5^1/2

All two's will cancel out

3(2+x) + 3x = 5^1/2

6+3x + 3x = 5^1/2

6 +6x = 2.23

6x = 2.23 - 6

6x = -3.77

x = -3.77÷ 6

x = -0.63

You might be interested in

The depth of a lake in Lexington changes over time due to rainfall and evaporation. A few months ago, the depth was 1,300 feet.

SVETLANKA909090 [29]

Answer:

The Depth of the lake had increased by 19%.

Step-by-step explanation:

Given:

Depth of lake few months ago = 1300 ft

depth of lake currently = 1547 ft

We need to find the percent of increase in depth of lake.

Solution:

First we will find the increase in depth of lake.

Increase in depth of lake can be calculated by subtracting Depth of lake few months ago from depth of lake currently.

framing in equation form we get;

increase in depth of lake = $1547-1300= 247\ ft$

Now to find the percent of increase in depth of lake we will divide increase in depth of lake from Depth of lake few months ago and then multiply by 100.

framing in equation form we get;

percent of increase in depth of lake = $\frac{247}{1300}\times 100 = 19\%$

Hence the Depth of the lake had increased by 19%.

6 0

3 years ago

The perimeter of a rectangular baking sheet is 58 inches and its area is 201.25 in.2. What are the length and width of the bakin

anzhelika [568]

Answer:

$Length=17.5\ in\\\\Width=11.5\ in$

Step-by-step explanation:

The formula for calculate the Area of a rectangle is:

$A=lw$

Where "l" is the lenght and "w" is the width.

And the formula for calculate the peimeter of a rectangle is:

$P=2l+2w$

Where "l" is the lenght and "w" is the width.

We know that the perimeter of the rectangular baking sheet is 58 inches and its area is 201.25 in². Then:

$A=201.25\ in^2\\\\P=58\ in$

<u>The steps are:</u>

1. Solve for the "l" from the formula $A=lw$ :

$A=lw\\\\l=\frac{A}{w}\\\\\l=\frac{201.25}{w}$

2. Substitute $l=\frac{201.25}{w}$ into the formula $P=2l+2w$ and solve for "w":

$58=2(\frac{201.25}{w})+2w\\\\58=\frac{402.5}{w}+2w\\\\58=\frac{402.5+2w^2}{w}\\\\58w=402.5+2w^2\\\\2w^2-58w+402.5=0$

Applying the Quadratic formula $x=\frac{-b\±\sqrt{b^2-4ac}}{2a}$ , we get:

$x=w=\frac{-(-58)\±\sqrt{(-58)^2-4(2)(402.5)}}{2(2)}\\\\w_1=17.5\\\\w_2=11.5$

3. Substitute $w_1=17.5$ into $l=\frac{201.25}{w}$ :

$l=\frac{201.25}{17.5}=11.5$

4. Substitute $w_2=11.5$ into $l=\frac{201.25}{w}$ :

$l=\frac{201.25}{11.5}=17.5$

Therefore, since the value of the lenght of a rectangle must be greater that the value of the width, we can conclude that the lenght and the width of the rectangular baking sheet are:

$l=17.5\ in\\\\w=11.5\ in$

8 0

3 years ago

A person on a runway sees a plane approaching. The angle of elevation from the runway to the plane is 11.1° . The altitude of th

Gnoma [55]

Answer:

The horizontal distance from the plane to the person on the runway is 20408.16 ft.

Step-by-step explanation:

Consider the figure below,

Where AB represent altitude of the plane is 4000 ft above the ground , C represents the runner. The angle of elevation from the runway to the plane is 11.1°

BC is the horizontal distance from the plane to the person on the runway.

We have to find distance BC,

Using trigonometric ratio,

$\tan\theta=\frac{Perpendicular}{base}$

Here, $\theta=11.1^{\circ}$ ,Perpendicular AB = 4000

$\tan\theta=\frac{AB}{BC}$

$\tan 11.1^{\circ} =\frac{4000}{BC}$

Solving for BC, we get,

$BC=\frac{4000}{\tan 11.1^{\circ} }$

$BC=\frac{4000}{0.196}$ (approx)

$BC=20408.16$ (approx)

Thus, the horizontal distance from the plane to the person on the runway is 20408.16 ft

8 0

3 years ago

(x - 3) - 2(x + 6) = -5

vekshin1

Answer:

Alright solve for x by multiplying both sides of the equation then isolating the variable

x = - 10 Hope this helps :)

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Guys please last one ok

den301095 [7]

Located at -3 and 5
:)

7 0

3 years ago

Read 2 more answers