Please help, im super late on my work :((

Prove the following using a direct proof:

hodyreva [135]

Answer:

Step-by-step explanation:

Prove: That the sum of the squares of 4 consecutive integers is an even integer.

An integer is a any directed number that has no decimal part or indivisible fractional part. Examples are: 4, 100, 0, -20,-100 etc.

Selecting 4 consecutive positive integers: 5, 6, 7, 8. Then;

$5^{2}$ = 25

$6^{2}$ = 36

$7^{2}$ = 49

$8^{2}$ = 64

The sum of the squares = 25 + 36 + 49 + 64

= 174

Also,

Selecting 4 consecutive negative integers: -10, -11, -12, -13. Then;

$-10^{2}$ = 100

$-11^{2}$ = 121

$-12^{2}$ = 144

$-13^{2}$ = 169

The sum of the squares = 100 + 121 + 144 + 169

= 534

Therefore, the sum of the squares of 4 consecutive integers is an even integer.

8 0

3 years ago

Just number 7 would be fine but if you could also number 8 would help a lot

BlackZzzverrR [31]

Answer:

7. r = -5

8. x = -1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define

r + 2 - 8r = -3 - 8r

Step 2: Solve for r

Combine like terms: -7r + 2 = -3 - 8r
Add 8r to both sides: r + 2 = -3
Subtract 2 on both sides: r = -5

Step 3: Check

Plug in r into the original equation to verify it's a solution.

Substitute in r: -5 + 2 - 8(-5) = -3 - 8(-5)
Multiply: -5 + 2 + 40 = -3 + 40
Add: -3 + 40 = -3 + 40
Add: 37 = 37

Here we see that 37 does indeed equal 37.

∴ r = -5 is a solution of the equation.

Step 4: Define equation

-4x = x + 5

Step 5: Solve for x

Subtract x on both sides: -5x = 5
Divide -5 on both sides: x = -1

Step 6: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x: -4(-1) = -1 + 5
Multiply: 4 = -1 + 5
Add: 4 = 4

Here we see that 4 does indeed equal 4.

∴ x = -1 is a solution of the equation.

8 0

3 years ago

Read 2 more answers

Define geometric relationship

blagie [28]

Answer:

Geometric relationships control the orientation of an element with respect to another element or reference plane. For example, you can define a tangent relationship between a line and an arc. ... For example, a connect relationship and a tangent relationship can be used where an arc meets a line. (make me brainliest)

7 0

3 years ago

Mr Bryce planted a garden in his backyard the length and width of the garden are shown below. what is the area, in square meters

VashaNatasha [74]

Answer:

A. Area = 5/9 sq.meters

Step-by-step explanation:

Area = (lenght × widht)

$A=(\frac{5}{6} )(\frac{2}{3}) =\frac{(5)(2)}{(6)(3)} =\frac{10}{18}$