Prove that the difference between squares of consecutive even numbers is always a multiple of 4. Note: Let n stand for any integer in your working. Total marks: 4

Answer:

Step-by-step explanation:

Attached is the sample space for rolling two dice

Answer:

see below

Step-by-step explanation:

4(5n-7)+10n+2

Distribute

20n -28 +10n+2

Combine like terms

30n-26

Assuming you meant =

4(5n-7)=10n+2

Distribute

20n -28 =10n+2

Subtract 10n from each side

20n-10n-28 = 10n-10n+2

10n-28 =2

Add 28 to each side

10n-28+28=28+2

10n=30

Divide by 10

10n/10 =30/10

n=3

9(x+3)=4x-3

Distribute

9x+27 = 4x-3

Subtract 4x from each side

9x-4x+27 = 4x-4x-3

5x +27 =-3

Subtract 27 from each side

5x+27-27 = -3-27

5x = -30

Divide by 5

5x/5 = -30/5

x=-6

2(12-8x)=x-11x

Combine like terms

2(12-8x) = -10x

Divide by 2

12-8x = -5x

Add 8x to each side

12-8x+8x = -5x+8x

12 = 3x

Divide by 3

12/3 =3x/3

4=x

Answer:

See explaination

Step-by-step explanation:

Assuming that these are three different problems:

1) 4(5n-7) = 10n+2

Distribute:

4(5n-7) = 10n+2

20n - 28 = 10n + 2

Combine like terms, isolate, and solve:

10n = 30

n = 3

2) 9(x+3) = 4x-3

Distribute:

9(x+3) = 4x-3

9x+27 = 4x - 3

Combine like terms, isolate, and solve:

5x = -30

x = -6

3) 2(12-8x) = x-11(i assumed the extra x was a typo)

distribute:

24-16x = x-11

Combine like terms, isolate, and solve:

35 = 17x

x = 35/17

Answer:

300 euros

Step-by-step explanation:

1200 x 5 x 5=30000/100=300

Answer:

£1531.53

Step-by-step explanation:

Times 1200 by 1.05 then times the new answer by 1.05 until done 5 times

Answer:

Congruent angles have the same angle and side measure. Thus angle Q is 47 degrees and PR is 9 cm.

Step-by-step explanation:

Answer:

B. 4 would be your answer.

Step-by-step explanation:

7 x 3 = 21

4 x 3 = 12

:)

Answer:

B. 4.

Step-by-step explanation:

Let the number be x then

x/7 = 12/21

Crossmultiply:

x = 7*12 / 21

x =  12 / 3 = 4.

Answer:

last one

Step-by-step explanation:

the domain includes all real numbers and the range is y>0

Answer:

I think that y=17.5 when x=7

Answer:

117.00

Step-by-step explanation:

I = prt  where i is the interest , p is the principal r is the rate and t is the time in years

2 years 6 months is 2.5 years

I = 1200 * .039* 2.5

I =117

Answer:

y = - 3x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line

m = [tex]\frac{-1-2}{0+1}[/tex] = - 3

The line crosses the y- axis at (0, - 1) ⇒ c = - 1

y = - 3x - 1 ← equation of line

Answer:

-93

Step-by-step explanation:

it decreases by four every time, so take -4 times 22 and then subtract 5.

The solution for equation is at (-2, 0).

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

Both linear equations with one variable and those with two variables exist.

Given equations,

y = x + 2

y = x² + 5x + 6

substitute value of y in second equation

x + 2 = x² + 5x + 6

x² + 4x + 4 = 0

x² + 2x + 2x +4 = 0

x(x +2) + 2(x + 2) = 0

(x + 2)(x + 2) = 0

x = -2

and y = x + 2

y = -2 + 2 = 0

Hence, the solution of equation is at x  = -2 and y = 0.

Learn more about linear equation here:

brainly.com/question/29739212

#SPJ7

Answer:

make them the same

Step-by-step explanation:

hope this helps

Answer:

[tex] A) \: x = - 10 \\ B) \: x = 7 [/tex]

Step-by-step explanation:

[tex]A) \\ = > 2(x + 3) = x - 4 \\ \\ = > (2 \times x) + (2 \times 3) = x - 4 \\ \\ = > 2x + 6 = x - 4 \\ \\ = > 2x - x + 6 = - 4 \\ \\ = > x + 6 = - 4 \\ \\ = > x = - 4 - 6 \\ \\ = > x = - 10 \\ \\ \\ B) \\ = >4(5x-2)=2(9x+3) \\ \\ = > (4 \times 5x) - (4 \times 2) = (2 \times 9x) + (2 \times 3) \\ \\ = > 20x - 8 = 18x + 6 \\ \\ = > 20x - 18x - 8 = 6 \\ \\ = > 2x - 8 = 6 \\ \\ = > 2x = 6 + 8 \\ \\ = > 2x = 14 \\ \\ = > x = \frac{14}{2} \\ \\ = > x = 7[/tex]

Answer:

28.5 ft

Step-by-step explanation:

The height of a ball is given by the equation ƒ(x) = −16x² + 45x + 2.5 where x is the tome the ball travels. To find the height of the ball after a seconds, we substitute a in place of x, the equation becomes:

ƒ(a) = −16a² + 45a + 2.5.

Therefore if the height of the ball is needed to be found after 2 seconds, we find f(2).

ƒ(2) = −16(2)² + 45(2) + 2.5 = -64 + 90 + 2.5 = 28.5 ft

f(2) = 28.5 ft

Answer:

The length and width of the rectangle are 23 m and 7 m respectively.

Step-by-step explanation:

P = 2L + 2W

P (perimeter of the rectangle) = 60 m

L (length of the rectangle) = 2 + 3W. W is the width of the rectangle

Therefore, L = 2 + 3W

P = 2L + 2W

60 = 2(2 + 3W) + 2W

60 = 4 + 6W + 2W

60 - 4 = 8W

56 = 8W

W = 56/8 = 7 m

L = 2 + 3W = 2 + 3(7) = 2 + 21 = 23 m

L = 23 m

W = 7 m

Answer:

the inverse is f^-1(x)=3x+6

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

trust me bro  i gotchu

Answer:

A) The fish was out of water for 0.6875 seconds.

B) Maximum height = 5.672

Step-by-step explanation:

Height is modeled by;

y = -16t² + 11t

A) To find total time of the fish out of water, we need to find the x - intercept. That is the points where y = 0

So, 0 = -16t² + 11t

So the roots of this equation are;

t = 0 or 0.6875

Thus,the fish was out of water for 0.6875 seconds.

B) y = -16t² + 11t

The x coordinate of the vertex is at - b/2a

For y = -16t² + 11t

a = -16, b = 11, c = 0

So, -b/2a = -11/(2*-16) = 11/32

The maximum height will be at the y-coordinate of the vertex.

Thus, we need to find f(11/32)

f(11/32) = -16(11/32)² + 11(11/32) = 1.890625 + 3.78125 = 5.671875 ≈ 5.672

Answer:

B

Step-by-step explanation:

If they have no solutions, the lines must not intersect.

If they don't intersect, they must be parallel

Answer:

1209 acres

Step-by-step explanation:

On the farm, 3/4 of the acre is planted with blue spruce trees.

There are 1612 acres on the farm. Therefore, the number of acres planted with blue spruce trees is:

3/4 * 1612 = 1209 acres

Answer:

Step-by-step explanation:

cause 100 cats can catch 100 bunnies in 300 min

Answer:

Question 1

Volume of a cylinder = πr²h

r= radius h= height

diameter = 2*radius

diameter = 2* 4cm= 8cm

Volume = π × 4² × 11

= 553.14cm³

Answer:

Center → (1, -3)

Radius → 5 units

Step-by-step explanation:

Equation of the given circle is,

x² + y² - 2x + 6y - 15 = 0

Now convert this equation into the standard equation of the circle

x² - 2x + y² + 6y - 15 = 0

x² -2x + 1 - 1 + y² + 2(3)(y) + 9 - 9 - 15 = 0

(x² - 2x + 1) - 1 + (y² + 2(3y) + 9) - 9 - 15 = 0

(x - 1)² + (y + 3)² - 10 - 15 = 0

(x - 1)² + (y + 3)² = 25

(x - 1)² + (y + 3)² = 5²

By comparing this equation with the standard equation of the circle,

(x - h)²+ (y - k)² = r²

Where (h, k) is the center and r is the radius of the circle.

Center of the circle → (1, -3)

Radius of the circle → 5 units

answer is 2.

x is divided by 28 and 7 is divided by x

after that cut 28 by 7

and the anwer will be x square = 4

and the square will go to 4

and four will be root 4

and the answer will be x = 2

Answer:

The answer is 6x^2+9x-15

Answer:

6x^2 + 9x -15x

Step-by-step explanation:

This may seem hard, but it is actually very simple.

When you think of area, you think of multiplying.

The equation for this rectangle is: 3(2x^2+3x-5)

Why is 3(2x^2+3x-5) the equation?

You are basically multiplying the height (3) and all the widths (2x^2, 3x, and -5)

3 x 2x^2 is 6x^2.

3 x 3x is 9x (3 x 3 = 9)

-5 x 3x is -15x (5 x 3 = 15, plus the negative sign)

Now, you will combine the answers and get 6x^2 + 9x -15x

Answer:

Step-by-step explanation:

3m^2(5m+8) + 5(5m +8)

(3m^2+5)(5m+8)

Answer:

Step-by-step explanation:

let K be ken's number of marbles

K<10

Ken's number of marbles are fewer than Joe's number of marbles

Answer:

x <10

Step-by-step explanation:

Ken = x

Joe = 10

because  Ken has fewer marbles than Joe and Joe has 10

x <10

Answer:if you are looking for the hypotenuse use Pythagoras theorem 17.2047

Step-by-step explanation:square both the base and height .Add their total then find the square root

Answer: C

Step-by-step explanation:

Reflection in the x -axis:

A reflection of a point over the x -axis is shown. The rule for a reflection over the x -axis is (x,y)→(x,−y) .