2^{2x}-5\cdot2^{x}+4=0

Answers

Answer 1

This is a polynomial in [tex]2^x[/tex] that can be factorized:

[tex]2^{2x}-5\cdot2^x+4 = 0[/tex]

[tex]\left(2^x\right)^2-5\cdot2^x+4=0[/tex]

[tex]\left(2^x-4\right)\left(2^x-1\right)=0[/tex]

[tex]2^x-4=0\text{ or }2^x-1=0[/tex]

[tex]2^x=4\text{ or }2^x=1[/tex]

Since 4 = 2² and 1 = 2⁰, you get the two solutions x = 2 and x = 0.


Related Questions

Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=2x, BE=y+10, CE=x+2 and DE=4y−8. Find the length of AC.

Answers

Answer: 8 units

Step-by-step explanation:

The diagonals of a parallelogram bisect each other, so you can set AE and CE equal to each other, as well as BE and ED

2x=x+2

x=2

AC=2x+x+2

AC=3x+2

SUbstitute x

AC=3(2)+2

AC=6+2

AC=8

HELP ANSWER ASAP. what is the radius of a circle in which a 30 arc is 2pi inches long?

Answers

Answer:

I believe it's 12 in.

Step-by-step explanation:

hope this helps you!

On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), crosses the x-axis at (negative 0.7, 0), (0.76, 0), and (2.5, 0), and crosses the y-axis at (0, 2).
Which statement is true about the graphed function?

F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞

Answers

Answer:

F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)

Step-by-step explanation:

The minimum value of the curve = (1.9, -5.7),

The maximum value = (0, 2)

The point the function crosses the x-axis (the x-intercept) = (-0.7, 0), (0.76, 0), and (2.5, 0)

The point the function crosses the y-axis (the y-intercept) = (0, 2)

The given points can be plotted using MS Excel, from which we have;

F(x) is less than 0 over the interval from x = -∞, to x = -0.7, and the interval from x = 0.76 to x = 2.5

The correct option is therefore, F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)

Answer:

A. F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).

Step-by-step explanation:

I want a simple explanation on how to get the answer to this question not just the answer.

Answers

the answer is= there are 126 5p coins

the reason for this is that
-630 is simplified to 5,
-so 1/5 is really 126/630,
(630 divided by 5 is 126)
- and so 2/5 is 126 x 2 =252/630
- there are only 3 parts left, and if 1p has more parts than 5p,
-then 1p takes up 2/5 of the bag
-and 5p takes up 1/5 of the bag

The area of a square is given as (s3)6.

What is its perimeter?

Answers

Step-by-step explanation:

what does this problem description really say ? what is the area of that square ?

36 ?

s3×6 ?

s³×6 ?

5³×6 ?

2³×6 ?

(5×3)×6 ?

(2×3)×6 ?

and these are just the options that I can see right away without really thinking about it.

in any case, the solution is to draw the square root of the area, and then multiply the result by 4.

why ?

because the area of a square is the square of the length of one of its side - like for any rectangle the area is length×width, but in a square length = width, so the area is length×length = length².

therefore, sqrt(area) = sqrt(length²) = length.

and the perimeter of the square is the way all around the whole square (4 sides), which is then

length + length + length + length = 4×length

from all the possibilities I listed up there, only 36 and (2×3)×6 lead to nice round numbers.

as the area would be in both cases 36.

sqrt(36) = 6

and the perimeter would be 6×4 = 24

The weekly wages of employees of Volta gold are normally distributed about a mean of$1250 with a standard deviation of $120. Find the probability of an employee having a weekly wage lying 1) between $1320 and $970 2) over $1290 3) under $1400

Answers

Answer:

1) 0.7104 = 71%

2) 0.6615 = 66%

3) 0.8944 = 89%

Step-by-step explanation:

1)

Z(low)=-2.333 0.009815329

Z(upper)=0.583 0.720165536

2)

Z(low)=0.333 0.63055866

Z(upper)=8322.908 1

3)

Z(low)=-10.417 0

Z(upper)=1.25 0.894350226

5-7
To rationalize the denominator of
9- 114 · you should multiply the expression by which fraction?
o
5+
g-ſ14
9-14
9-14
9+ 14
9+
14
14
14

Answers

Answer:

the third option

Step-by-step explanation:

what does that mean ?

to "rationalize" it is to transform it into a rational number (that is a number that can be described as a/b, and is not an endless sequence of digits after the decimal point without a repeating pattern).

a square root of a not square number is irrational (not rational).

so, what this question is asking us to get rid of the square root part in the denominator (the bottom part).

for this we need to multiply to and bottom with the same expression (to keep the whole value of the quotient the same) that, when multiplied at the bottom, eliminates the square root.

what can I multiply a square root with to eliminate the square root ? the square root again - we are squaring the square root.

so, what works for 9 - sqrt(14) as factor ?

we cannot just square this as

(9- sqrt(14))² = 81 -2sqrt(14) + 14

we still have the square root included.

but remember the little trick :

(a+b)(a-b) = a² - b²

without any mixed elements.

so, we need to multiply (9-sqrt(14)) by (9+sqrt(14)) to get

81-14 = 67 which is a rational number.

therefore, the third answer option is correct.

follow the rule

[tex]\\ \sf\longmapsto \dfrac{a+b}{c-d}[/tex]

To rationalize the above fraction we need to change the sign of denominator patt and multiply with both numerator and denominator

Like

[tex]\\ \sf\longmapsto \dfrac{a+b(c+d)}{(c-d)(c-d)}[/tex]

Here correct option is C

Can you help me out plz

Answers

Answer:

An isometry preserves all the following except orientation .

If the side of an equilateral triangle is 3.5cm. Perimeter od triangle is _____ cm.​

Answers

If the side of an equilateral triangle is 3.5cm. Perimeter od triangle is 10.5_ cm.

Answer: Perimeter = 10.5 cm

Step-by-step explanation:

Concept:

Here, we need to know what is an equilateral triangle.

An equilateral triangle is a triangle in which all three sides have the same length.

Perimeter = 3a

a = side length

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

a = 3.5 cm

Given formula

Perimeter = 3a

Substitute the value into the formula

Perimeter = 3 (3.5)

Simplify

Perimeter = 10.5 cm

Hope this helps!! :)

Please let me know if you have any questions

5. The average weight of a blue whale is 4 x 105 pounds. The average weight of an elephant is 1 x 10 pounds. How many more times heavier is a blue whale than an elephant in pounds? ​

Answers

Answer:

42 more times

Step-by-step explanation:

1) 4×105=420 (pounds)-blue whale

2) 1×10=10 (pounds)- elephant

3) 420:10=42

The amount of times that the blue whale is more heavier than the elephant in pounds is; 40 times heavier.

We are given;

Average weight of blue whale; W_w = 4 × 10^(5) pounds

Average weight of elephant; w_e = 1 × 10⁴ pounds

Now, we want to find how much more heavier the blue whale is than the elephant. Thus we will just divide W_w by W_e to get;

W_w/W_e = (4 × 10^(5))/(1 × 10⁴)

According to laws of exponents;

a¹²/a³ = a¹² ¯ ³ = a^(9)

Applying that to our question gives;

4(10^(5 - 4)) = 4 × 10 = 40

Read more about exponents at; https://brainly.com/question/18248071

HELP is it a, b, c , or d?

Answers

Answer:

B

when you input the first value of y which is -2

-2+2=(4/5)(x+9)

0=(4x+36)/5

multiply both sides by 5

0=4x +36

4x =-36

divide both sides by 4

x=-9

if you like my answer mark as brainliest

Simplify: 0.9(2b-1)-0.5b+1

Answers

Answer:

Step-by-step explanation:

0.9*2b = 1.8b

0.9*-1 = -0.9

So far we have 1.8b-0.9. It can't be simplified further.

Then, we add the 2nd part, -0.5b+1.

We have:

1.8b-0.9-0.5b+1. Next we combine like terms.

1.8b-0.5b = 1.3b.

-0.9+1 = 0.1

Then we put it together.

1.3b+0.1 is our answer.

Hope this helped! Have a nice day :D

Hi there!  

»»————- ★ ————-««

I believe your answer is:

1.3b + 0.1

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Simplifying...}}\\\\0.9(2b-1)-0.5b+1\\--------------\\\rightarrow 1.8b - 0.9 - 0.5b + 1\\\\\rightarrow 1.8b - 0.5b - 0.9 + 1\\\\\rightarrow \boxed{1.3b +0.1}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

Can you answer me this question please? I have doubts. Thank you​

Answers

Answer:

9Step-by-step explanation:Step-by-step explanation:you have 2 bars right ? the taller one has a frequency of 12 Step-by-step explanation:you have 2 bars right ? the taller one has a frequency of 12 so the half of the taller one is 6 which is smaller than the 2nd one right ? so the frequency of the smaller one is surely greater than half of the big which is 6 so the frequency should be from 6 upwards ....

hi pls help. pls explain a bit thank you:)

Answers

Answer:

[tex]a^3b^2c^6[/tex]

Step-by-step explanation:

[tex]n^x*n^y=n^{x+y}[/tex]

so

[tex]a^6*a^{-3}*a^0=a^{6-3+0}=a^3[/tex]

[tex]b^3*b^1*b^{-2}=b^{3+1-2}=b^2[/tex]

[tex]c^4*c^2=c^{4+2}=c^6[/tex]

put it all together

[tex]a^3b^2c^6[/tex]

Can someone help me out plz

Answers

Answer:

The answer is 43.52 you're welcome

find the measure of the missing angles in the kite​

Answers

Answer:

Step-by-step explanation:

In a kite, the angles between the two non- congruent side have the same degree.

x = 114 degrees

In a quadrilateral the sum of the inner angles is 360 degrees

88 + (114 * 2) + y = 360

88 + 228 + y = 360

316 + y = 360

y = (360 - 316)

y = 44 degrees

please help, i will give brainliest!

Answers

Answer:

hope that helps i don't know it either tho

I need 26/50 simplified so I can answer an assignment

Answers

Answer:

13/25

Step-by-step explanation:

Find: 26/50 simplified

Step 1: Find the GCF (Greatest Common Factor) of 26 and 50

26: 1, 2, 13 & 26

50: 1, 2, 5, 10, 25 & 50

The GCF (Greatest Common Factor) will be 2

Then simplify 26/50 by 2

26/50 = 13/25

The sum of two numbers is 75. If one exceeds the other by 35, find the numbers.

Answers

Answer:

20 and 55

Step-by-step explanation:

Let's assume, we have two numbers 'x' and 'y'.

Now, all we know is:

one number exceeds the other by 35 (i.e  their difference is 35)sum of two numbers is 75

So we form two equations:

x + y = 75_____(i)

and x - y =  35

so, x = y+35 _____(ii)

Put the value of x from (ii) into (i)

x + y = 75

y + 35 + y = 75

2y = 40

y = 20

Put value of y back in (ii)

x = y+35

x = 20 + 35

x = 55

The first number is 20, and the second number is 55.

Given that the sum of two numbers is 75, one exceeds the other by 35, we need to find the numbers.

Let's assume the first number is x.

According to the problem, the second number exceeds the first by 35, so the second number can be expressed as (x + 35).

The sum of the two numbers is given as 75, so we can set up the equation:

x + (x + 35) = 75

Simplifying the equation, we get:

2x + 35 = 75

Subtracting 35 from both sides:

2x = 40

Dividing both sides by 2:

x = 20

Therefore, the first number is 20, and the second number is (20 + 35) = 55.

Learn more about numbers click;

https://brainly.com/question/24908711

#SPJ4

8. Solve the following triangle for all missing sides and angles.
Part I: Find the measure of angle B. (1 point)
Part II: Use the law of sines to find the length of side a. (2 points)
Part III: Use any method to find the length of side c. (2 points)

Answers

Answer:

Step-by-step explanation:

find the missing side of the triangle​

Answers

Answer:

197 is the missing side of the triangle

x= 197 ! i did it on a sheet of paper

Nicole Tobin receives a salary of $250
per week plus a commission of 15% of all
sales over $1,500. Find her earning
during a week in which sales totaled
$3,000.

Answers

Answer:

Earnings = 475

Step-by-step explanation:

She gets a straight salary of                                            250

She sold  3000 worth of merchandise            3000

She receives a commission on anything over 1500             Subtract

She gets a commission on                                 1500

15%  of 1500 = 15/100 * 1500                                         225

Earnings                                                                          475  

find the missing side​

Answers

Answer:

x ≈ 14.7

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan73° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{48}{x}[/tex] ( multiply both sides by x )

x × tan73° = 48 ( divide both sides by tan73° )

x = [tex]\frac{48}{tan73}[/tex] ≈ 14.7 ( to the nearest tenth )

X = 48/tan(73) = 14.675

hlppppppppppppppp mehhhhhhhhhhhhhhh

Answers

Answer:

120

Step-by-step explanation:

Given,

t = 2

s = 10

3 t^2 s

= 3 x 2^2 x 10

= 3 x 4 x 10

= 120

Answer:

Step-by-step explanation:

Hello!

t² = 2²=4

3*4*10 = 120

can someone help me figure out how much my final exam is weighted?

in the grade book there are:
6 assignments for 10 points each
52 assignments for 20 points each (it’s not a typo i promise there was actually 52)
5 assignments for 30 points each
5 assignments for 40 points each
and 1 assignment for 60 points (aka the final exam)

my grade is an average of all of these different assignments combined. How much is my exam weighted- can you even calculate this? (i just want to know so i can see what score i need to get to pass with an a)

Answers

Answer:

About 4%

Step-by-step explanation:

6x10=60

52x20=1040

5x30=150

5x40=200

1x60=60

Total Points available:1510

Final Exam is 60 points

60/1510=0.0397

please! help me i need it rn

Answers

The answer is d 1 1/2 of chicken for 3 salads

Answer:

It is the last option.

Jordan needs 1 1/2 cups of diced chicken for 3 salads.

To make this easy for you.

1. start on the x axis which is number of salads.

2. Go to the number 3 (of the x axis which is the number of salads)

3. Find your way up to the point marked.

4. see what is your number in the y-axis (in this case it is 1 1/2.

Step-by-step explanation:

I hope it helps!

About how many cells are in the human body?

You can assume that a cell is a sphere with radius 10-3 cm and that the density of a cell is approximately the density of water which is 1g/cm3.

Answers

Answer:

In other words: The human body consists of some 37.2 trillion cells.

Step-by-step explanation:

can somebody explain how they got 37.2 trillion cells.!!!

please helpppp

Comparing Distance
Is there a relationship between the distance and the sum? Is there a relationship between the distance and the difference?

A 5-column table with 3 rows. Column 1 is labeled a with entries 1, 4, negative 6. Column 2 is labeled b with entries 2, negative 1, negative 3. Column 3 is labeled a + b with entries 3, 3, negative 9. Column 4 is labeled a minus b with entries negative 1, 5, negative 3. Column 5 is labeled Distance with entries 1 unit, 5 units, 3 units.

Which describes the relationship between the distance and the difference?
The distance is always the opposite of the difference.
The distance is exactly the difference.
The distance is the absolute value of the difference.
The distance is not related to difference.
NEED HELP FOR EDGUNITY

Answers

Answer:

C. The distance is the absolute value of the difference.

Step-by-step explanation:

See the table made based on the given values.

It is easy to note that the numbers in the distance column are same as numbers in the a - b column but all numbers being positive.

So we can say that:

distance = |a - b|

Correct choice is C

Factor.
20x2 – 19x + 3

Answers

Answer:

Here is your answer!

In Natalie's class, 18 children listed math as their favorite subject while 15 said English was their favorite
subject. Eleven children liked both subjects equally well and 3 children didn't like either math or English. How
many children are in the class?

Answers

25 is your answer if i am sure, the question was confusing tho.

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