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Leni [432]
4 years ago
9

Express (x + 9)2 as a trinomial in standard form.

Mathematics
2 answers:
DENIUS [597]4 years ago
6 0

Answer:

{x}^{2}  + 18x + 81

Step-by-step explanation:

(x + 9) {}^{2}

Apply foil method.

(x + 9) {}^{2}  = (x + 9)(x + 9)

Multiply the first terms, X

x \times x =  {x}^{2}

Multiply outer terms, 9 and x.

x \times 9 = 9x

Multiply inner terms,

9 \times x = 9x

Multiply outer terms.

9 \times 9 = 81

Add the inner and outer terms

9x + 9x = 18x

Write in standard form

{x}^{2}  + 18x + 81

ivann1987 [24]4 years ago
3 0

Answer:

Step-by-step explanation:

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Isha, a super excited Khan Academy user, has increased
HACTEHA [7]

Answer:  8000 points last week.

Step-by-step explanation:

If she has increased by 75% in a week to get 14000 points then  we can say that 175% times a number has to equal 14,000 , where the number of points she had last week.

175% * x = 14000

1.75x =14000     Divide both sides by 1.75

x= 8000

So she had 8000 points last week.

Check:

175% * 8000= 14000

1.75 * 8000 = 14000

  14000 = 14000

5 0
3 years ago
Find the flaw with the following "proof" that every postage of 3 cents or more can be formed using just 3-cent and 4-cent stamps
Reika [66]

Answer:

The main flaw of this  proof is that it did not take into consideration the fact a 4 cent postage must be made with a 4 cent stamp  and a 3 cent postage  must be made with a 3 cent stamp but only looked at allocating the stamps based on the total amount of postage

Step-by-step explanation:

From the question we are told that

   The  proof is

Every postage stamp of three cents or more can be formed using just 3 cent and 4 cent stamps.  

 Basic Step : We can form postage of 3 cents with a single 3 cent stamp and we can form postage of 4 cents using a single four cents tamp

Inductive Step: Assume that we can form postage of j cents for all non negative integers j with j <= k using just 3 cent and 4-cent stamps. We can then form postage of k+1 cents by replacing one 3 cent stamp with a 4-cent or two 4-cent stamps with three 3-cent stamps

  FLAW IDENTIFICATION

Looking the inductive step, the statement ''by replacing one 3 cent stamp with a 4-cent or two 4-cent stamps with three 3-cent stamps '' means that it is possible to use a 3-cent stamp for postage that requires a 4 -cent stamp  and this is not correct according the statement in the basic step

Generally the main flaw of this  proof is that it did not take into  consideration the fact a 4 cent postage must be made with a 4 cent stamp  and a 3 cent postage  must be made with a 3 cent stamp but only looked at allocating the stamps based on the total amount of postage

4 0
3 years ago
Math help please sighh &gt;.&lt; (4 options included)
Elena-2011 [213]
The answer is the third option with 2/3 as the slope.

Hope I didn't mess up for your sake!
4 0
4 years ago
Rina is 6x+3/8 feet tall and Ryan is 5x+1/8 feet tall. How much taller is Rina than Ryan
worty [1.4K]

Answer:

Rina is 1/4 feet taller than Ryan

Step-by-step explanation:

(height of Rina)-(height of Ryan)

6x+3/8-(5x+1/8)

6x+3/8-5x-1/8

x+3-1/8

x+2/8

x+1/4

8 0
4 years ago
What is the slope of a line perpendicular to the line whose equation is 2x+3y=21. Fully simplify your answer.
erastova [34]

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

2x+3y=21\implies 3y=-2x+21\implies y=\cfrac{-2x+21}{3} \\\\\\ y=\cfrac{-2x}{3}+\cfrac{21}{3}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{3}}x+7\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}

therefore then

\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-2}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-2}\implies \cfrac{3}{2}}}

3 0
2 years ago
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