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3 years ago

10

Solve the following exponential equations. 4^x + 7(2^x) + 12 = 0

1 answer:

andrey2020 [161]3 years ago

6 0

Answer:No value of x

Step-by-step explanation:

Given

$4^x+7(2^x)+12=0$

Let $2^x=y$

$y^2+7y+12=0$

$y^2+3y+4y+12=0$

$y(y+3)+4(y+3)=0$

$(y+3)(y+4)=0$

$y=-3,-4$

$2^x=-3$

or $2^x=-4$

so there is no value of x for which $2^x=-3 or -4$

because minimum value of $^x=1$

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Given 4x+6/2=9 prove x=3

Montano1993 [528]

Steps:

Step 1: Simplify both sides of the equation.

4x+3=9

Step 2: Subtract 3 from both sides.

4x+3−3=9−3

4x=6

Step 3: Divide both sides by 4.

4x /4 = 6 /4

Answer: x= 3/2

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<em><u>Hope this helps.</u></em>

8 0

2 years ago

Read 2 more answers

A rancher wants to fence in an area of 1500000 square feet in a rectangular field and then divide it in half with a fence down t

VLD [36.1K]

Answer:

6000 ft

Step-by-step explanation:

Let length of rectangular field=x

Breadth of rectangular field=y

Area of rectangular field= $1500000$ square ft

Area of rectangular field= $l\times b$

Area of rectangular field= $x\time y$

$1500000=xy$

$y=\frac{1500000}{x}$

Fencing used ,P(x)= $x+x+y+y+y=2x+3y$

Substitute the value of y

P(x)= $2x+3(\frac{1500000}{x})$

$P(x)=2x+\frac{4500000}{x}$

Differentiate w.r.t x

$P'(x)=2-\frac{4500000}{x^2}$

Using formula: $\frac{dx^n}{dx}=nx^{n-1}$

$P'(x)=0$

$2-\frac{4500000}{x^2}=0$

$\frac{4500000}{x^2}=2$

$x^2=\frac{4500000}{2}=2250000$

$x=\sqrt{2250000}=1500$

It is always positive because length is always positive.

Again differentiate w.r.t x

$P''(x)=\frac{9000000}{x^3}$

Substitute x=1500

$P''(1500)=\frac{9000000}{(1500)^3}>0$

Hence, fencing is minimum at x=1 500

Substitute x=1 500

$y=\frac{1500000}{1500}=1000$

Length of rectangular field=1500 ft

Breadth of rectangular field=1000 ft

Substitute the values

Shortest length of fence used= $2(1500)+3(1000)=6000 ft$

Hence, the shortest length of fence that the rancher can used=6000 ft

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3 years ago

To drive to work, Dave has to drive 20 miles east and then 15 miles north. If there were a direct road going northeast, how many

suter [353]

By the Pythagorean theorem:

$x= \sqrt{20^2+15^2}= \sqrt{400+225}= \sqrt{625}=25 \ miles$

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3 years ago

Marisol is making a rectangular wooden frame. She wants the length of the frame to be no more than 12 inches. She has less than

evablogger [386]

<span>l ≤ 12
2l + 2w < 30
the second and fourth option are saying she can make the length longer than twelve and the third option forgets to double the length and width so it is accurate. The first option is the right answer.</span>

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2 years ago

A number cube is rolled 25 times and lands on 2 five times. What is the experimental probability of landing on 2?

olga nikolaevna [1]

Answer:

5/25, 1/5, or 20%

Step-by-step explanation:

Based on the experiment the dice lands on 2 five times, giving you the experimental probability

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1 year ago