log2 (X^2+3x+2)=1 state the universe and solve each of the following for x.​

Answers

Answer 1

By "state the universe" I suppose you mean "domain". log₂(x ² + 3x + 2) is defined for

x ² + 3x + 2 = (x + 1) (x + 2) > 0   →   x < -2   or   x > -1

(To solve the inequality, consider values of x between the ones that make the expression exactly equal to 0, in this case x = -2 and x = -1. We have, for instance, for x = -3, that (-3)² + 3(-3) + 2 = 2 > 0, so x ² + 3x + 2 > 0 for all x < -2.)

Now solve the equation: Write both sides as powers of 2 to eliminate the logarithm on the left:

[tex]\log_2(x^2+3x+2)=1\implies 2^{\log_2(x^2+3x+2)}=2^1\implies x^2+3x+2=2[/tex]

Solve the remaining quadratic:

x ² + 3x + 2 = 2

x ² + 3x = 0

x (x + 3) = 0

x = 0   or   x = -3

Both of these solutions are within the presribed domain (-3 < -2 and 0 > -1), so we're done.


Related Questions


Sales tax in Rally County is 8%. What would the amount of tax be on a $50 restaurant bill? Express your answer in the form of a decimal

Answers

54.00
50x4%=4
50+4=54

19. Macy bought new tires for her car. She chose tires that cost $73 each. However, the tire store was offering a Buy 3Get 1 Free Sale. After this special sale, she had to pay % sales tax . What was , Macy's final cost for all 4 tires?

Answers

Answer:

$219 without tax

Step-by-step explanation:

im not sure how to calculate tax

hope this helps :)

The length of the diogonals of a rectangular garden is 34m. If it's longer side measures 30m, find the perimeter of garden. ​

Answers

Answer:

92 m

Step-by-step explanation:

Use the Pythagorean theorem to find the length of the shorter side.

Let w = length of the shorter side.

[tex]w^{2} + 30^{2} = 34^{2} \\ w^{2} + 900 = 1156\\w^{2} = 256\\w = \sqrt{256} = 16[/tex]

The perimeter is 2l + 2w = 2(30) + 2(16) = 60 + 32 = 92 m

how do i convert 84 3/4 percent into a decimal.

Answers

Answer:

84 3/4% = 0.8475

Hopes this helps:

Answer: 84.75

Which statement is true about the following pair of rectangles?

Two rectangles are shown. To the left, a larger rectangle has a lower side labeled 60 centimeters and a left side labeled 30 centimeters. To the right, a smaller rectangle has an upper side labeled 6 centimeters and a right side labeled 3 centimeters.
A. They are not similar because Start Fraction 6 over 60 End Fraction≠ Start Fraction 30 over 3 End Fraction.
B. They are not similar because Start Fraction 30 over 3 End Fraction = Start Fraction 60 over 6 End Fraction.
C. They are not similar because Start Fraction 3 over 6 End Fraction ≠ Start Fraction 30 over 60 End Fraction.
D. They are similar because Start Fraction 3 over 6 End Fraction = Start Fraction 30 over 60 End Fraction.

Answers

Answer:

probably D

Step-by-step explanation:

the tiles on cathy's bathroom floor are square shaped and each tile covers an area of 90 square inches. simplify an expression to represent the side length of each tile.

Answers

Answer:

[tex]\huge\boxed{\sf L = 3\sqrt{10} }[/tex]

Step-by-step explanation:

Area of a square tile = 90 square inches

Let the side length of tile be "L"

Condition:

Area = 90

L * L = 90

L² = 90

Taking sqrt on both sides

L = √90

L = 3√10

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807


Tell which equation you would choose to solve for one of the variables. Explain.
x+ 4y = 30
x – 2y = 0

Answers

Answer:

i would choose to solve x+2y=0 because it is simple and ez

Step-by-step explanation:

i took test and got 100 % brainliest plz

4 2/3 - 3 1/8
Leave your answer as a mixed fraction

Answers

Answer:

Here.is the answer.

Step-by-step explanation:

Hope it helps.....

When spinning a ten-number spinner (with numbers 1-10), what are the odds of the arrow landing on 8?​

Answers

There is a 10% to land on any of the numbers since there are 10 of them. :).

1+1
(You don't have to answer its for talking)

Answers

Answer:

Step-by-step explanation:

1 +1  =   2   g a y   n i g  g a s

20 POINTS AND BRAINIEST!

You want to sell lemonade by the park. Different brands of lemonade have different formulas. You want to sell the lemonade that tastes the most “lemony.” You use 4 cups of lemon concentrate and 6 cups of water.
What fraction of the TOTAL mixture is lemon concentrate? What percentage is this?

Answers

Answer:

4/10

Step-by-step explanation:

you add the amount of cups of concentrated lemon plus the amount of water and it is 10. and then it asks for the faction of lemon concentrate out of 10. so it would be 4/10

Hope this helps!!

Subtract and simplify. plz show all work!
(−5y^2 − 9y− 4) − (−2y^2 − y + 8)

Answers

the answer is −
3
y
2

8
y

12

HELP WHAT PERCENT IS THE SALES TAX????

Answers

Answer:

first one is 6 cents(6 percent) second one 14 cents (14%)

Step-by-step explanation:

is just didviding them

-8, 22, 52, 82, ...
Find a 20

Answers

Answer:

Step-by-step explanation:

It is an arithmetic sequence with common difference d = 30.

a₂₀ = a₁ + (20-1)d = -8 + 19·30 = 562

Will give brainiest to correct answer

20a + 32

Answers

Answer:

wouldn't it just be the same? It would still be 20a+32

Answer:

4(5a+8)

Step-by-step explanation:

Factor 20a+32

20a+32

=4(5a+8)

What is the measure of the missing angle

Answers

Answer:

45 degrees xxxxxxxxxx

Step-by-step explanation:

simple geo

Systems of equation:substitution
The 2 problems in here i need done by 11:00pm est
8:00pm pst

Answers

Step-by-step explanation:

8)

describe y in terms of x

y=5+x

so now replace y with terms of x

5+x+3x=37

4x=32

x=8

y=13

9)

do the same here

x=y+1

2y+x=19

2y+y+1=19

3y=18

x=6

y=7

Plz, answer this question plz!

Answers

Answer:

The answer is

F: 362,880

Step-by-step explanation:

9 X 8 X 7 X 6 X 5 X 4  X 3 X 2 X 1

You multiply 9 all the way back to 1 giving you the answer of 362,880

overheads are added to the?​

Answers

Answer:" In business, overhead or overhead expense refers to an ongoing expense of operating a business. Overheads are the expenditure which cannot be conveniently traced to or identified with any particular cost unit, unlike operating expenses such as raw material and labor." as said by wiki

Step-by-step explanation:

Help me please with this math question

Answers

34 34/100. 17

27. 27/100. 13.5

21. 21/100. 10.5

18. 18/100. 9

I think this is right!

Is 1.5 a solution to 2x- 19 = −4−8x?

Answers

Answer:

yes

Step-by-step explanation:

Yes. You have to plug in 1.5 as x, and if the equation is true then it is a solution.

walk if it walks at a constant pace for 15
minutes. At the same rate, how many
kilometers can the tortoise walk in 1 hour?
Write your answer as a decimal.
Minutes H
0
+
15
Meters H
400


PLEASE HELP ME TODAY

Answers

Answer: 4.00

Step-by-step explanation: There are 60 minutes in 1 hour. So, 60/15 gives you your answer. 60/15 = 4, but it says write it as a decimal. So, your answer will be 4.00.

You have 5 3/4 cups of sunflower seeds and 1 1/4 cups of peanuts for birdseed. You use 2/3 of the total mixture each week. How many weeks your birdseed mixture last

Answers

Answer:

Step-by-step explanation:

The bird food lasts 1½ weeks.

Your birdseed mixture last till 10 and a half weeks.

What is an improper fraction?

A fraction that has the numerator higher than or equal to the denominator is said to be an improper fraction.

Given:

You have 5[tex]\frac{3}{4}[/tex] cups of sunflower seeds and 1[tex]\frac{1}{4}[/tex] cups of peanuts for birdseed.

The total mixture,

= 5[tex]\frac{3}{4}[/tex] + 1[tex]\frac{1}{4}[/tex]

= 23/4 + 5/4

= 28/4

= 7 cups.

You use 2/3 of the total mixture each week.

That means,

the number of weeks,

= 7 x 3/2

= 21/2

= 10.5 weeks.

Therefore, the mixture will last till 10 and a half weeks.

To learn more about the improper fraction;

brainly.com/question/21449807

#SPJ2

what is the value of x ?

Answers

Answer:

10

Step-by-step explanation:

4 + 5x-x + 19 simplify expressions using like terms

Answers

6x+23, that’s the answer but it makes be at least have 20 words lol

somebody help I need your help​

Answers

Answer:

a

Step-by-step explanation:

sorry if im wrong

Answer:

hsdcfvjfcdn cfv bb

Step-by-step explanation:dvbvgfdsxdcfvfcdsdxc

Scrbkfvjtfcbjt hffcjtfbnid. Jrcvnfccb

Answers

Answer:

yeah i know the secret codeto Sy evvceryvcx evtrtyev ivyreviqvvt. qut

Step-by-step explanation:

PLEASE MARK BRAINLIEST!!!!!!!!!!!!!!!!!!!!


Reflections, Rotations, and Translations give two congruent shapes (The Image and Pre-Image)
True
O False

Answers

I’m pretty sure it’s true

What is the area of the trapezoid?

Answers

Answer:

108

Step-by-step explanation:

b1+b2/2×h

so 12+15/2×8

12+15=27

27÷2=13.5

13.5×8=108

108 is the answer

find x to the nearest tenth

Answers

Answer:

x = 18.0

Step-by-step explanation:

You must memorize the definitions of the trig functions and then these types of problems are easy.

In your problem,  sin of an angle = opposite side/hypotenuse

So,  sin 51 = 14/x

      x sin 51  = 14

            x = 14/sin 51 = 18.0

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