Which will result in a difference of squares? (–7x + 4)(–7x + 4) (–7x + 4)(4 – 7x) (–7x + 4)(–7x – 4) (–7x + 4)(7x – 4)

Answers

Answer 1

Answer:
You can simply expand each product and see whether it gives you a difference of squares.

•   $\mathsf{(-7x+4)\cdot (-7x+4)}$

That's actually $\mathsf{(-7x+4)^2:}$

$\mathsf{(-7x+4)^2}\n\n \mathsf{=(-7x+4)\cdot (-7x+4)}\n\n \mathsf{=(-7x+4)\cdot (-7x)+(-7x+4)\cdot 4}\n\n \mathsf{=49x^2-28x-28x+16}$

$\mathsf{=49x^2-56x+16}$   ✖

which is not a difference of squares.

—————

•   $\mathsf{(-7x+4)\cdot (4-7x)}$

$\mathsf{=(-7x+4)\cdot 4-(-7x+4)\cdot 7x}\n\n \mathsf{=-28x+16-(-49x^2+28x)}\n\n \mathsf{=-28x+16+49x^2-28x}$

$\mathsf{=49x^2-56x+16}$ ✖

which is not a difference of squares.

—————

•   $\mathsf{(-7x+4)\cdot (-7x-4)}$

$\mathsf{=(-7x+4)\cdot (-7x)-(-7x+4)\cdot 4}\n\n \mathsf{=49x^2-28x-(-28x+16)}\n\n \mathsf{=49x^2-\diagup\!\!\!\!\! 28x+\diagup\!\!\!\!\! 28x-16}\n\n \mathsf{=49x^2-16}$

$\mathsf{=(7x)^2-4^2}$   ✔

That is a difference of two squares.

—————

•   $\mathsf{(-7x+4)\cdot (7x-4)}$

$\mathsf{=(-7x+4)\cdot 7x-(-7x+4)\cdot 4)}\n\n \mathsf{=-49x^2+28x-(-28x+16)}\n\n \mathsf{=-49x^2+28x+28x-16}$

$\mathsf{=-49x^2+56x-16}$   ✖

which is not a difference of squares.

—————

Only the third option will result in a difference of squares.

Answer: (− 7x + 4) · (− 7x − 4).

I hope this helps. =)

Answer 2

Answer:

Answer:

The expression which will result in difference of two squares is:

(–7x + 4)·(–7x – 4)

Step-by-step explanation:

We know that the formula of the type:

$(a-b).(a+b)=a^2-b^2$

i.e. it is a difference of two square quantities. (a^2 and b^2)

Hence the option which satisfies the following expression is:

(-7x + 4)·(-7x-4)

since,

here $a=-7x$ and $b=4$ and

$(-7x+4).(-7x-4)=(-7x)^2-(4)^2=(7x)^2-4^2$

so the expression is a difference of two square quantities:

$(7x)^2$ and $4^2$

Hence, the correct answer is:

(-7x + 4)·(-7x-4)

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The sum of two integers is 44. The difference of the two integers is 8.What is the smaller integer?

Answers

Answer:

Step-by-step explanation:

44/2=22

the difference between the two numbers= 8

8/2=4

(22-4) + (22+4) = 18+26 = 44

the smaller number = 18

Answer:

The smaller integer is 18.

Step-by-step explanation:

x is the larger integer, and y is the smaller integer.

x + y = 44

x - y = 8

For x - y = 8, add y to both sides and get x = 8 + y.

Change x in x + y = 44 for 8 + y.

8 + y + y = 44

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A boat leaves the harbor entrance and travels 28 miles in the direction N 43° E. The captain then turns the boat 90° and travels another 15 miles in the direction S 47° E. At that time, how far is the boat from the harbor entrance, and what is the bearing of the boat from the harbor entrance?

Answers

Answer:

Step-by-step explanation:

A boat leaves the harbor entrance and travels 28 miles in the direction N 43° E.

Displacement in vector form

= 28 cos43 i + 28sin43j

= 20.47 i + 19.1 j

The captain then turns the boat 90° and travels another 15 miles in the direction S 47° E

Displacement

= 15 cos47 i - 15 sin47 j

= 10.22 i - 10.97 j

Total displacement

= 20.47 i + 19.1 j + 10.22 i - 10.97 j

= 30.69 i - 8.13 j

Magnitude of displacement

= 31.75 miles

Angle with east direction

TanФ = - 8.13 / 30.69

Ф = 15 degree south of east.

Pls help me with this and show any work

Answers

Answer: 9.5 (D.)

Step-by-step explanation:

SOCAHTOA

the sin of an angle is equal to the opposite side over the hypotenuse.

angle: 32

opposite side: x

hypotenuse: 18 m

1. sin32 = x/18

2. 18(sin32) = x

3. 9.5 = x

if you are confused with how it went from 18(sin32) to 9.5, you can plug 18(sin32) into your calculator.

Urgent can you help right away! Please help with these math questions!!!!
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Answers

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Answers

Answer:

30 - Acute

249 - Obtuse

126 - Obtuse

Step-by-step explanation:

Less than 90 - Acute

90 - Right

More than 90 - Obtuse

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