Please give me the correct answer.​

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.

Using the together rate, it is found that it would take the apprentice 6 hours to make the same number of sets of glasses when working alone.

The together rate is the sum of each separate rate.

In this problem, the rates are:

Hence, applying the equation for the together rate:

[tex]\frac{1}{2} = \frac{1}{x} + \frac{1}{3}[/tex]

[tex]\frac{x + 3}{3x} = \frac{1}{2}[/tex]

[tex]2x + 6 = 3x[/tex]

[tex]x = 6[/tex]

It would take the apprentice 6 hours to make the same number of sets of glasses when working alone.

To learn more about the together rate, you can take a look at https://brainly.com/question/25159431

Answer:

3x-18=0

3x=18

x=18/3

x=6

Answer:

x = 11

Step-by-step explanation:

6x + 7 = 73   {Alternate interior angles}

    6x  = 73 - 7

    6x = 66

      x = 66/6

     x = 11

Answer:

(1,3)

Step-by-step explanation:

Coordinates are counted first how much spaces on the x-axis. Which in this case Is 1.

And how much spaces on the y- axis in this case 3.

To the right 1 and Up 3.

(1,3)

:)

Answer:

(1, 3)

Those are the coordinates.

Hope that helps!

Step-by-step explanation:

Answer:

the correct values are ( 3, -2)

Answer:

(3,-2)

Step-by-step explanation:

x=13/3+2/3y

9x-4y=35

9(13/3+2/3y)-4y=35

y=-2

x=13/3+2/3×(-2)

x=3

Answer:

4th option is the answer.

Answer:

15 units

Step-by-step explanation:

Calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (9, 10)

d = [tex]\sqrt{(9-0)^2+(10+2)^2}[/tex]

   = [tex]\sqrt{9^2+12^2}[/tex]

   = [tex]\sqrt{81+144}[/tex]

   = [tex]\sqrt{225}[/tex]

   = 15

Answer:

C≈28.27

Step-by-step explanation:

C=2πr

A=2·π·4.5

A≈28.27433

(round up by the nearest hundreth. very sorry if i get this question wrong.)

Answer:

Step-by-step explanation:

1) a ) 7x = 56

Divide both sides by 7

   7x/7 = 56/7

      x = 8

2) 6y = 35

Divide both sides by 6

6y/6 = 35/6

     [tex]y= 5\frac{5}{6}[/tex]

[tex]3a) \frac{x}{3}=10\\\\3*\frac{x}{3}=3*10\\\\x = 30\\\\\\\\d) \frac{c}{18}=\frac{1}{2}\\\\18*\frac{c}{18}=\frac{1}{2}*18\\\\c=9\\\\\\f) \frac{n}{8}=\frac{11}{4}\\\\8*\frac{n}{8}=\frac{11}{4}*8\\\\n=11*2\\\\n=22[/tex]

Answer:

1) a ) 7x = 56

Divide both sides by 7

  7x/7 = 56/7

     x = 8

2) 6y = 35

Divide both sides by 6

6y/6 = 35/6

Step-by-step explanation:

Answer:

18 un²

Step-by-step explanation:

Answer:

The answer is a is precipitation and air temperature

Step-by-step explanation:

Answer:C

Step-by-step explanation:

Answer:

The point of intersection of the two lines is;

(-9,-2)

Step-by-step explanation:

What we have to here is to get the equation of both lines, solve simultaneously and get the intersection points

For the first line;

The general form is

y = mx + b

formula for the slope is;

m = (y2-y1)/(x2-x1)

The points (3,4) and (-1,2)

m = (2-4)/(-1-3) = -2/-4 = 1/2

So the equation is;

y = 1/2x + b

To get b, let us substitute coordinates of the first point;

4 = 1/2 * 3 + b

4 = 3/2 + b

b = 4 - 3/2

b = (8-3)/2 = 5/2

So the equation is;

y = 1/2x + 5/2

For the second line;

Slope;

m = (-4-0)/(-6+12) = -4/6 = -2/3

The equation is;

y = -2x/3 + b

Let us substitute the first

0 = -2/3(-12) + b

0 = 8 + b

b = -8

The equation is;

y = -2x/3 - 8

Now , we want to get the intersection point

To do this, we have to solve both equations simultaneously;

Since we have an expression for y in both cases, let us equate both y

-2x/3-8 = 1/2x + 5/2

Multiply through by 6

-4x - 48 = 3x + 15

-4x-3x = 15 + 48

-7x = 63

x = 63/-7

x = -9

To get x;

Recall;

y = -2x/3 - 8

y = -2/3(-9) - 8

y = 6 - 8

y = -2

Answer:

1.rode

2. Participate

3. Prepared

i don't know about the other ones

9514 1404 393

Answer:

  ∠Y = 55°

Step-by-step explanation:

Complementary angles have a sum of 90°.

  ∠S + ∠Y = 90°

  (5∠Y -240°) +∠Y = 90°

  6∠Y = 330° . . . . . . . . . . . . add 240°, collect terms

  ∠Y = 55° . . . . . . . . . divide by 6

Answer:

first one

Step-by-step explanation:

answer:

you just have to shrink it down to 4cm then to 2cm

i wish i could help out more, but i would need to have access to the form

hopefully, this helps anyhow :)

good luck

have a great day !!

Answer:

3.5

7 divided by 50=3.5

3.5x2=7

Step-by-step explanation:

Answer:

A for the first one.

Second one, I'm not sure, but I'd guess it'd be A

Step-by-step explanation:

Answer:

To round 2.5 to the nearest cent consider the thousandths’ value of 2.5, which is 0 and less than 5. Therefore, the cents value of 2.5 remains 0. answer $2.5   rounded to the nearest cent = $2.50

Step-by-step explanation:

If you like to round 2.5 to the nearest cent, rendering the amount with only two numbers after the decimal point, then you have come to the right post.

Answer:

42 laps

Step-by-step explanation:

Answer:

-a^5b^17/8

Step-by-step explanation:

Answer:

Solution is positive and both are correct

Step-by-step explanation:

1) since negative times negative is positive and -27 and -35 are both negative then x needs to be positive

2) since positive divided by positive is positive and negative divided by negative is also positive (when the negative sign is in the middle of both numbers on a fraction bar it means both are negative) then both are correct

Answer:

Step-by-step explanation:

Okay so first you need to find out how much money it will cost in total.

$50*5

=$250

$250+$850=

$1,100

Now, $1,100 divided by 5

1,100/5

=220 hours

And there are 5 friends so divide the total amount hours by 5.

220/5

=44 hours

So you see, each friend will need to work 44 hours.

I hope this helped :)

Brainliest? ✨

Answer:

Step-by-step explanation:

F-^1(x)+x/10+1/5

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Since it gives us the amount of area of material to use we know we want to find how many times we can divide it into tablecloths.  So now we need to find how much each tablecloth is.

so first it tells us that each table has a radius of 2 ft, so we find the area using that.  area of a circle is [tex]\pi r^2[/tex] so plugging in 2 ft we get 4π square feet or 12.56.

It also says that each tablecloth needs to be 20% bigger, so we find what 20% larger than 4π is.  to do this you do 4pi*1.2 = 4.8π = 15.072 square feet.

Now, how many tablecloths with areas of 15.072 square feet can be made from 64 square feet.  Hopefully it's obvious you divide.  so 64/15.072 = 4.25

Since we want whole tablecloths and that .25 is a remainder, 4 whole tablecloths can be made.

Answer:

Option A) it has square roots of 2 is the answer

Answer:

200

Step-by-step explanation:

Answer:

Please check explanations

Step-by-step explanation:

Firstly, we calculate the area of the floor

That is the product of the sides

= 300 * 540 = 162,000 cm^2

What is left is to calculate the area of a tile

Since the tile is also rectangular, the area of each tile will be;

60 * 30 = 1,800 cm^2

Since we have both areas, we can now get the number of tiles needed to cover the floor

We can get this by dividing the area of the floor by the area of a tile

This is;

162,000/1,800 = 90

This means that 90 tiles will cover the floor

The cost of a tile

is £4.25

The cost of 90 tiles will be ;

£4.25 * 90 = £382.5

from here, we can see that the £400 is more than £382.5

So we can conclude that she has enough to spend on tiles