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3 years ago

Show that (4p^2-3q)^2+48p^2q =(4p^2+3q^2)

Mathematics

1 answer:

Brut [27]3 years ago

5 0

Given:

The statement is

$(4p^2-3q)^2+48p^2q=(4p^2+3q^2)$

To prove:

The given statement.

Solution:

We have,

$(4p^2-3q)^2+48p^2q=(4p^2+3q^2)$

Now,

$LHS=(4p^2-3q)^2+48p^2q$

Using $(a-b)^2=a^2+b^2-2ab$ , we get

$LHS=(4p^2)^2+(3q)^2-2(4p^2)(3q)+48p^2q$

$LHS=(4p^2)^2+(3q)^2-24p^2q+48p^2q$

$LHS=(4p^2)^2+(3q)^2+24p^2q$

It can be rewritten as

$LHS=(4p^2)^2+(3q)^2+2(4p^2)(3q)$

Using $(a+b)^2=a^2+b^2+2ab$ , we get

$LHS=(4p^2+3q^2)$

$LHS=RHS$

Hence proved.

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What is the area, in square units, of the parallelogram shown below? A parallelogram ABCD is shown with height 7 units and base

Goshia [24]

Answer: The correct answer is: [B]:

____________________________________________

→ " 35 square units " .

____________________________________________

{or; write as: " 35 sq units " ; or; " 35 units² " .}.

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Step-by-step explanation:

____________________________________________

Note that the area, "A" ; of a "parallelogram" ;

→ {for which we wish to solve} ;

→ can be calculated by using the formula:

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→ " A = b * h " ;

→ { that is: " Area = base * height " } ;

→ in which:

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→ "A" is the "area" [of the parallelogram] ;

in: [ "square units" ; or: "sq units" ; or: "units² " ] ;

____________________________________________

→ "b" is the "base length" (of one of the bases of the parallelogram) ;

{Note that both bases of a parallelogram have equal lengths.

— Refer to "image attached" for additional information.}.

____________________________________________

→ "h" is the "perpendicular height" [of the parallelogram] ;

____________________________________________

Note:

All rectangles are parallelograms, but not all parallelograms are rectangles.

All squares are rectangles, but not all rectangles are squares.

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So, let us consider a "rectangle" that is not a square;

→ but has 4 (four) right angles; as follows:

____________________________________________

Rough sketch:

base (b)

---------------------------

| | height (h)

|_____________ |

____________________________________________

The formula (equation) for the area, "A" ; of a rectangle is:

→ " A = b * h " ;

→ { that is: " Area = base * height " .} .

→ Since a rectangle is a parallelogram;

→ The formula (equation) for the area, "A" ;

for Any parallelogram is the same :

→ " A = b * h " ;

→ { that is: " Area = base * height " .} .

____________________________________________

→ However, it is important to remember that the formula/equation for the "area, "A" ; for any parallelogram — [including All rectangles] — is actually:

→ " A = b * h " ; that is: " Area = base * [perpendicular] height " .

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Note that we are Not Given Any "image attached" that represents the: "parallelogram" —

Note: Refer to the text within "this very Brainly question being asked" ; that is; the following text:

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"the parallelogram ABCD" that is "shown below" {sic} ; as stated within the question.

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Nonetheless:

We are given:

h (height) = 7 units ; And:

b (base) = 5 units. ;

For our purposes, let us assume that the given "height, "h" = 7 units" ;

→ refers to the "perpendicular height " ;

Now, we can calculate the "Area; A" ; in "square units" ; as follows:

___________________________________________

→ " A = b * h " ; Solve for: "A" ;

Plug in our given values for "b" and "h" ; to solve for "A" ;

→ " A = (5 units) * (7 units) " ;

= 5 * 7 * units * units " ;

" A = 35 units² ;

or: " 35 square units " ;

→ which is:

___________________________________________

Answer choice: [B]: " 35 square units " .

___________________________________________

Note: Refer to "image attached" ; to refer to: "perpendicular height " — as regards to many "traditional" types of " parallelograms " .

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Hope this helps!

Best wishes to you in your academic pursuits

— and within the "Brainly" community, as well!

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3 years ago

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Answer:

It will take 9 weeks

Step-by-step explanation:

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8x $\geq$ 67

x $\geq$ 8.375

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3 years ago

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nirvana33 [79]

Answer:

$5.976\times10^{24}$

Step-by-step explanation:

Standard form, also called scientific notation, is a more compact way of writing very big or very small numbers. All numbers in scientific notation have the form

$m\times10^b$

where m is a number between 1 and 10, and b is an integer that represents how we've shifted the decimal point from the original number. For example, the number 23,000 in standard form would be written as 2.3 × 10⁴, since we have to shift the decimal point 4 places to the right to get back our original number.

We can turn 5,976,000,000,000,000,000,000,000 into a number between 1 and 10 by shifting the decimal 24 places to the left, giving us 5.976. We'll save that 24 as the exponent for our 10, giving us the final form

$5.976\times10^{24}$

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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If (x-2)(y-1)=3 and (x+2)(2y-5)=15,

daser333 [38]

Answer:

Equation 1, Multiplied by 2: 2x + 4y = 10

Equation 1, Multiplied by 2: 2x + 4y - 10 = 10 - 10

Equation 1, Multiplied by 2: 2x + 4y - 10 = 0

Equation 1, Multiplied by 2: 2x - 2x + 4y - 10 = 0 - 2x

Equation 1, Multiplied by 2: 4y - 10 = - 2x

Equation 1, Multiplied by 2: - 10 + 4y = - 2x

Notice that Equation 1 = Equation 2

One Solution

Equation 1: x - y = -10

Equation 2: 2x + 3y = 15

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3 years ago

Show that (4p^2-3q)^2+48p^2q =(4p^2+3q^2)​

Show that (4p^2-3q)^2+48p^2q =(4p^2+3q^2)