calculate the force needed to accelerate a car of mass 1500 kg by 5m/s

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.

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:

Step-by-step explanation:

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

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: n= 18

Step-by-step explanation: 3/8 of 48 is the same as 3/8 times 48

Answer:

18

Step-by-step explanation:

48 divided into 8 parts is 6

3x6=18

Answer:

3.5

7 divided by 50=3.5

3.5x2=7

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:

3x-18=0

3x=18

x=18/3

x=6

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:

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:

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:

(1,3)

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:

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:

-a^5b^17/8

Step-by-step explanation:

Answer:

the second one

Step-by-step explanation:

Answer:

Hope that answers your question

Answer:

1.rode

2. Participate

3. Prepared

i don't know about the other ones

Answer:

try 4.9

Step-by-step explanation:

Answer:

3.5 × 140

4.9g

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

Given

∠PDB = 110°

PDis the tangent to the circle whose centre is E

Construction

Join points D and E.

∠DPE= 90° [Since angle in a semi circle is 90°]

Also ∠PDE = 90° [Since radius ⊥ tangent]

From the figure we have,

∠PDB=∠PDE + ∠DBE

i.e. 110° = 90° + ∠DBE

Therefore, ∠DBE =20°

Now in ΔBED, BE = ED [Radii]

So, ∠EDB = ∠EBD =20°

In ΔBPD, we have

∠DPE = 90° & ∠DBE = 20°

Therefore, ∠DPB = 70°

Answer:

70 is the correct answer

Step-by-step explanation:

Answer:

first one

Step-by-step explanation:

Answer:

-13.6

Step-by-step explanation:

Open the bracket

-9.07-(-2.8+1.3).

-25.39+11.79

-13.6

Answer:

-7.57

i found the answer by solving the equation in the parenthises, then i subtract the answer i got with -9.07, and thats how i found out the answer is -7.57 (feel free to use a calculator to make sure its correct :D)

Answer:

18 un²

Step-by-step explanation:

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

Step-by-step explanation:

1-b 2-c 3-d 4-a yep I belive this is correct sorry if I'm wrong

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:

200

Step-by-step explanation:

Answer:

10% dicount

Step-by-step explanation:

76.50 / 85.00 = .9

The airplane cost 90% of its original value, meaning you have a 10% discount

10% of 85 =  .1 x 85 = 8.50

85.00 - 8.50 = 76.50

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