The ratio of students to laptops in a school is 3:2. If there are 1,200 students, how many laptops are there?

Answer:

They are all positive because you must go right.

They are all negative because you must go down.

Step-by-step explanation:

Example. (1,-4)

You go over one.

Down 4

Answer:

Step-by-step explanation:

1) r = 5mm; d = 10 mm

2) r = 6 cm; d = 12 cm

3) r = 9 m; d = 18 m

4) r = 8 km; d = 16 km

5) r = 11 m; d = 22 m

6) r = 15 mm; d = 30 mm

7) r = 13 km; d = 26 km

8) r = 7 cm; 14 cm

Answer:

3. D

4. A

5. B

Step-by-step explanation:

Answer:

1.

(x+1)(x+2)>x(x+3)

x^2+2x+x+2>x^2+3x

x^2+3x+2>x+3x

2>0

2.

(x+2)^2>x(x+4)

x^2+4x+4>x^2+4x

4>0

Step-by-step explanation:

1.

Suppose x is the lowest number in the set of 4 consecutive numbers, then x+1, x+2, and x+3 are then the next numbers in the sequence since they are the next whole numbers.

Then, to follow the conditions of the problem, we make the equation:

(x+1)(x+2)>x(x+3)

Using the formula of (a+b)(c+d)=ac+ad+bc+bd, we can expand both sides of the equation into this:

x^2+2x+x+2>x^2+3x

=x^2+3x+2>x^2+3x

We can then cancel x^2+2x from both sides and we are left with 2>0.

2.

Again, suppose x is the lowest value in the set of consecutive numbers. In this case, odd numbers increase by 2 each time so the series of numbers are:

x, x+2, x+4

Therefore, to follow the conditions of the problem, we make the equation:

(x+2)^2>x(x+4)=

(x+2)(x+2)>x(x+4)

Using the same formula of (a+b)(c+d)=ac+ad+bc+bd, we get:

x^2+4x+4>x^2+4x

Cancel x^2+4x from both sides and we are left with 4>0

Hope this helps!

Answer:

D

Step-by-step explanation:

Where the graphs intersect each other is where the solution is. The graphs intersect each other at the points (0,-8) and (4,8). Hope this helps!

Answer:

6

Step-by-step explanation:

Answer:

Use PEMDAS

(Parentheses, Exponents, Multiplication and Division, Addition and Subtraction)

18 - 3 (5) + 2

18 - 15 + 2

3 +2

5

Answer:

5

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

first find the median of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.

Answer:

-1 and 4/3

Step-by-step explanation:

Given the quadratic equation;

f(x) = 3x^2-x-4

To get all potential roots, we will equate f(x) = 0

3x^2-x-4 = 0

3x^2-4x+3x-4 = 0

x(3x-4)+1(3x-4) = 0

(x+1)(3x-4) = 0

x+1= 0 and 3x-4 = 0

x = -1 and 3x = 4

x = -1 and x= 4/3

Hence the potential roots are -1 and 4/3

Answer:

4*s= 520

s= 130

area=s*s=130*130=16900m^2

Step-by-step explanation:

Answer:

7 cars

Step-by-step explanation:

The computation of the number of cars to be filled is shown below:

A car that is 90% full and the total people is 20 so 90% would be

= (.90)(20)

= 18

A car that is 65% full and the total people is 20 so 65% would be

= (.65)(20)

= 13

Now

Total number of people = (5)(18) + (3)(13).

= 129

Now the number of cars to be filled is

= 129 ÷ 20

= 6.45

= 7 cars

Answer:

-1, -2, and -3

Step-by-step explanation:

-1 + -2 + -3 = -6

Answer:

(4 , - 35)

Step-by-step explanation:

X²-8x-19 =(x-4)² -35

y = a (x-h)² + k    a=1   , (h , k) -> (4 , - 35)

Answer:

3. 15 baskets

4. 16 tries

Step-by-step explanation:

3.

3: 4 is ratio so 3:4=x:20, 3/4=x/20, and you get x=15

4. ratio is still 3:4, 3:4=12:x, 3/4=12/x, x=16, so 16 tries

1) Power of a Product

2) Power Rule (or Power of a Power)

Answer:

-Number 1 is Power of a Power Property, I think

-Number 2 is Power of a Power Property

Answer:

D) 22

Step-by-step explanation:

Since it gives you two rays just set them equal and solve for X.

6x - 14 = 3x +4

      +14        +14

6x = 3x + 18

-3x   -3x

3x = 18

/3    /3

x = 6

Then plug x into either one of the equations

6(6) - 14

36 - 14

22

Answer:

D. 22

Step-by-step explanation:

Answer:

∠1 = 42°

∠2 = 48°

∠4 = 48°

∠3 = 21°

∠5 = 21°

Step-by-step explanation:

Given:

∠WZY = 138°

Find:

∠1

∠2

∠3

∠4

∠5

Computation:

WZ = ZY

So,

∠3 = ∠5

So,

∠3 + ∠5 + 138 = 180

2∠3 = 42

∠3 = 21°

∠5 = 21°

∠1 = 180 - 138

∠1 = 42°

∠W = ∠Y

∠X + ∠Y + ∠W = 180

42 + ∠Y + ∠W = 180

∠Y = 69

∠2 = 69 - 21

∠2 = 48°

∠4 = 48°

Answer:

6 feet per minute

Step-by-step explanation:

Answer:

6 feet per minute.

Step-by-step explanation:

5ft + 1ft = 6ft per minute.

Step-by-step explanation:

2*22/7*48=301.714 .This the answer

Answer:

Yeah, what they said above.

Step-by-step explanation:

Answer:

≥

..................................................

Answer:

1234567890

Step-by-step explanation:

?

Answer:

5: 2 or 10: 4

Step-by-step explanation:

as a ratio, this would be 5: 2.

Im not sure if it's asking you to also make a new ratio that fits this, but if it is you could multiply both sides by 2 to get

10 : 4

Very quickly: since tan(30°) = 1/√3,

(1 + tan(30°)) / (1 - tan(30°)) = (1 + 1/√3) / (1 - 1/√3)

… = (√3 + 1) / (√3 - 1)

… = (√3 + 1)² / ((√3)² - 1²)

… = ((√3)² + 2√3 + 1²) / (3 - 1)

… = (3 + 2√3 + 1) / 2

… = (4 + 2√3) / 2

… = 2 + √3

On the other side, we have sin(30°) = 1/2 and sin(60°) = √3/2, so

(1 + sin(60°)) / (1 - sin(30°)) = (1 + √3/2) / (1 - 1/2)

… = (1 + √3/2) / (1/2)

… = 2 (1 + √3/2)

… = 2 + √3

and we're done, both sides are equal.

We can also prove this algebraically:

Force the denominator on the left side into a difference of squares:

(1 + tan(30°)) / (1 - tan(30°)) × (1 + tan(30°)) / (1 + tan(30°))

… = (1 + tan(30°))² / (1 - tan²(30°))

Expand the numerator:

… = (1 + 2 tan(30°) + tan²(30°)) / (1 - tan²(30°))

Recall that 1 + tan²(x) = sec²(x) :

… = (sec²(30°) + 2 tan(30°)) / (1 - tan²(30°))

Since sec(x) = 1/cos(x) and tan(x) = sin(x)/cos(x), multiply through every term by cos²(30°) :

… = (sec²(30°) + 2 tan(30°)) / (1 - tan²(30°)) × cos²(30°) / cos²(30°)

… = (1 + 2 sin(30°) cos(30°)) / (cos²(30°) - sin²(30°))

Recall that sin(2x) = 2 sin(x) cos(x) and cos(2x) = cos²(x) - sin²(x) :

… = (1 + sin(2×30°)) / cos(2×30°)

… = (1 + sin(60°)) / cos(60°)

Finally, recall that cos(90° - x) = sin(x), so cos(60°) = sin(30°) = 1/2, and we can write 1/2 = 1 - 1/2, so

… = (1 + sin(60°)) / (1 - sin(30°))

as required.