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2 years ago

Write the rules for factoring. x method, difference of squares

Mathematics

1 answer:

ch4aika [34]2 years ago

6 0

Difference-of-Squares Formula:

For a difference of squares a2 – b2, the factorization is:

(a – b)(a + b)

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Evaluate f(x)=-4x-5 for x = -1

Lubov Fominskaja [6]

F(x)=-4(-1)-5
f(x)=4-5
f(x)= -1
-1 is your answer

5 0

3 years ago

What number must you add to complete the square?<br> x^2 + 2x = -1

Andru [333]

$\large\begin{array}{l} \textsf{You must add 1 to complete the square.}\\\\ \textsf{There is a very common special product: (square of a sum)}\\\\ \mathsf{(a+b)^2=a^2+2ab+b^2}\\\\\\ \textsf{Take the given equation:}\\\\ \mathsf{x^2+2x=-1\qquad(i)}\\\\\\ \textsf{The first term is a square (x squared)}\\\\ \textsf{The second term is a product of 2, x and 1.} \end{array}$

$\large\begin{array}{l}\\\\\\ \textsf{We need to find a proper value for b, so that if we add it to}\\\textsf{the left side of the equation, we get a perfect square.}\\\\ \textsf{So,}\\\\ \begin{array}{cccccccccc} \mathsf{a^2}&\!\!\!+\!\!\!&\mathsf{2}&\!\!\!\cdot\!\!\!&\mathsf{a}&\!\!\!\cdot\!\!\!&\mathsf{b}&\!\!\!+\!\!\!&\mathsf{b^2}&=\mathsf{(a+b)^2}\\\\ \mathsf{\downarrow}&&&\!\!\!\!\!&\downarrow&\!\!\!\!\!&\downarrow&&\downarrow\\\\ \mathsf{x^2}&\!\!\!+\!\!\!&\mathsf{2}&\!\!\!\cdot\!\!\!&\mathsf{x}&\!\!\!\cdot\!\!\!&\mathsf{1}&\!\!\!+\!\!\!&\mathsf{1^2}&=\mathsf{(x+1)^2} \end{array}\\\\\\ \textsf{Just by comparing the expressions above, we can conclude that}\\\textsf{b must be equal to 1, so we get a perfect square:}\\\\ \mathsf{(x+1)^2=x^2+2x+1} \end{array}$

$\large\begin{array}{l}\\\\\\ \textsf{Back to (i), adding 1 to both sides:}\\\\ \mathsf{x^2+2x+1=-1+1}\\\\ \boxed{\begin{array}{c} \mathsf{(x+1)^2=0} \end{array}} \end{array}$

$\large\begin{array}{l}\\\\\\ \textsf{If you want to solve this equation for x, you will find}\\\\ \mathsf{x+1=0}\\\\ \mathsf{x=-1}\quad\longleftarrow\quad\textsf{(solution)} \end{array}$

If you're having problems understanding the answer, try seeing it through your browser: brainly.com/question/2112248

$\large\begin{array}{l} \textsf{Any doubt? Please, comment below.}\\\\\\ \textsf{Best regards! :-)} \end{array}$

6 0

3 years ago

Read 2 more answers

in the circle, m∠S=33°, mRS=120, and RU is a tangent. the diagram is not drawn to scale. what is m∠U? Please help!

SIZIF [17.4K]

Answer:

27°

Step-by-step explanation:

arc RT = 66

1/2(120 - 66) = 27

8 0

3 years ago

Read 2 more answers

Evaluate the function at the given value and simplify.

Licemer1 [7]

Answer:

The correct option is b.

Step-by-step explanation:

The given function is

$f(x)=-5x+1$

We need to find the value of f(-2). It means we have to find the value of given function at x=-2.

Substitute x=-2 in the given function to find the value of f(-2).

$f(-2)=-5(-2)+1$

On simplification we get

$f(-2)=10+1$

$f(-2)=11$

The value of f(-2) is 11. Therefore the correct option is b.

8 0

3 years ago

Compare and contrast prisms and pyramids

iogann1982 [59]

Answer:

A prism has 5 sides, pyramids have 4 sides, the shapes of the sides of a pyramid are squares and triangles, the sides of a prism are rectangles and triangles, both are 3D

I hope this helps u pls give a brainliest and a thx ;)

3 0

2 years ago