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3 years ago

Please answer to receive ten points. I'll vote who answers first the brainliest if its correct.

Mathematics

1 answer:

beks73 [17]3 years ago

3 0

The distance between points $P_1(x_1,y_1)$ and $P_2(x_2,y_2)$ can be calculated using formula

$P_1P_2=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.$

$AB=\sqrt{(-7-(-11))^2+(8-4)^2}=\sqrt{16+16}=\sqrt{32}=4\sqrt{2}\approx 5.657.$

$AC=\sqrt{(-4-(-11))^2+(4-4)^2}=\sqrt{49+0}=\sqrt{49}=7.$

$CB=\sqrt{(-7-(-4))^2+(8-4)^2}=\sqrt{9+16}=\sqrt{25}=5.$

Then

$P_{ABC}=5.657+7+5=17.657\approx 17.7$

Answer: correct choice is C.

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What is the functions average rate of change over each interval?

telo118 [61]

we can use average rate of change formula

$\frac{f(b)-f(a)}{b-a}$

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Firstly, we will find points

(-2,2) and (1,-4)

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$=\frac{-4-2}{1+2}$

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Firstly, we will find points

(0,-3) and (1,-4)

now, we can plug these values into formula

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Firstly, we will find points

(1,-4) and (2,0)

now, we can plug these values into formula

and we get

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Firstly, we will find points

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3 0

3 years ago

How can I break apart the dividend to find the quotient for 224 divided by 7

lianna [129]

Answer:

see the explanation

Step-by-step explanation:

we have

$\frac{224}{7}$

decompose the number 224 in prime factors

$224=2^{5}7$

substitute

$\frac{2^{5}7}{7}$

Simplify

$\frac{2^{5}7}{7}=2^{5}=32$

3 0

3 years ago

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

Margaret [11]

Answer:

Step-by-step explanation:

8 0

3 years ago

BRAINLIESSTTTT ASAP !!!!!!!!!! 20 pointssss

Mars2501 [29]

Answers:
_____________________________________________________
Part A) " (3x + 4) " units .
_____________________________________________________
Part B) "The dimensions of the rectangle are:

" (4x + 5y) " units ; <u>AND</u>: " (4x − 5y)" units."
_____________________________________________________

Explanation for Part A):
_____________________________________________________

Since each side length of a square is the same;

Area = Length * width = L * w ; L = w = s = s ;

in which: " s = side length" ;

So, the Area of a square, "A" = L * w = s * s = s² ;

{<u>Note</u>: A "square" is a rectangle with 4 (four) equal sides.}.

→ Each side length, "s", of a square is equal.

Given: s² = "(9x² + 24x + 16)" square units ;

Find "s" by factoring: "(9x² + 24x + 16)" completely:

→ " 9x² + 24x + 16 ";

Factor by "breaking into groups" :

"(9x² + 24x + 16)" =

  → "(9x² + 12x) (12x + 16)" ;
_______________________________________________________

Given: " (9x² + 24x + 16) " ;
_______________________________________________________
Let us start with the term:
_______________________________________________________

" (9x² + 12x) " ;

  → Factor out a "3x" ; → as follows:
_______________________________________

  → " 3x (3x + 4) " ;

Then, take the term:
_______________________________________
→ " (12x + 16) " ;

And factor out a "4" ;   → as follows:
_______________________________________

→ " 4 (3x + 4) "
_______________________________________
We have:

" 9x² + 24x + 16 " ;

= " 3x (3x + 4) + 4(3x + 4) " ;
_______________________________________
Now, notice the term: "(3x + 4)" ;

We can "factor out" this term:

3x (3x + 4) + 4(3x + 4) =

→ " (3x + 4) (3x + 4) " . → which is the fully factored form of:

" 9x² + 24x + 16 " ;
____________________________________________________
→ Or; write: "  (3x + 4) (3x + 4)" ; as: " (3x + 4)² " .
____________________________________________________
→ So, "s² = 9x² + 24x + 16 " ;

Rewrite as: " s² = (3x + 4)² " .

→ Solve for the "positive value of "s" ;

→ {since the "side length of a square" cannot be a "negative" value.}.
____________________________________________________
→ Take the "positive square root of EACH SIDE of the equation;
to isolate "s" on one side of the equation; & to solve for "s" ;

→ ⁺√(s²) = ⁺√[(3x + 4)²] '

To get:

→ s = " (3x + 4)" units .
_______________________________________________________

Part A): The answer is: "(3x + 4)" units.
____________________________________________________

Explanation for Part B):
_________________________________________________________<span>

The area, "A" of a rectangle is:

A = L * w ;

in which "A" is the "area" of the rectangle;
"L" is the "length" of the rectangle;
"w" is the "width" of the rectangle;
_______________________________________________________
Given: " A = </span>(16x² − 25y²) square units" ;

→ We are asked to find the dimensions, "L" & "w" ;
→ by factoring the given "area" expression completely:
____________________________________________________
→ Factor: " (16x² − 25y²) square units " completely '

Note that: "16" and: "25" are both "perfect squares" ;

We can rewrite: " (16x² − 25y²) " ; as:

= " (4²x²) − (5²y²) " ; and further rewrite the expression:
________________________________________________________
Note:
________________________________________________________
" (16x²) " ; can be written as: "(4x)² " ;

↔ " (4x)² = "(4²)(x²)" = 16x² "

Note: The following property of exponents:

→ (xy)ⁿ = xⁿ yⁿ ; → As such: " 16x² = (4²x²) = (4x)² " .
_______________________________________________________
Note:
_______________________________________________________

→ " (25x²) " ; can be written as: " (5x)² " ;

↔ "( 5x)² = "(5²)(x²)" = 25x² " ;

Note: The following property of exponents:

→ (xy)ⁿ = xⁿ yⁿ ; →  As such: " 25x² = (5²x²) = (5x)² " .
______________________________________________________

→ So, we can rewrite: " (16x² − 25y²) " ;

as: " (4x)² − (5y)² " ;

→ {Note: We substitute: "(4x)² " for "(16x²)" ; & "(5y)² " for "(25y²)" .} . ;
_______________________________________________________
→ We have: " (4x)² − (5y)² " ;

→ Note that we are asked to "factor completely" ;

→ Note that: " x² − y² = (x + y) (x − y) " ;

→ {This property is known as the "<u>difference of squares</u>".}.

→ As such: " (4x)² − (5y)² " = " (4x + 5y) (4x − 5y) " .
_______________________________________________________
Part B): The answer is: "The dimensions of the rectangle are:

" (4x + 5y) " units ; AND: " (4x − 5y)" units."
_______________________________________________________

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