All categories

3 years ago

Suzie simplified the following expression. What mistake did she make? 2(3 + 9x) - 2x 6 + 9x - 2x 6 + 7x

Mathematics

1 answer:

Levart [38]3 years ago

3 0

2(3 + 9x) - 2x

= 6 + 9x - 2x <----------------mistake right here

= 6 + 7x

Correct:

Expanding by using distributive property

2(3 + 9x) - 2x

= 2* 3 + 2 * 9x - 2x

= 6 + 18x - 2x

= 6 + 16x

You might be interested in

How do you solve his with working

AlexFokin [52]

Check the picture below.

a)

so the perimeter will include "part" of the circumference of the green circle, and it will include "part" of the red encircled section, plus the endpoints where the pathway ends.

the endpoints, are just 2 meters long, as you can see 2+15+2 is 19, or the radius of the "outer radius".

let's find the circumference of the green circle, and then subtract the arc of that sector that's not part of the perimeter.

and then let's get the circumference of the red encircled section, and also subtract the arc of that sector, and then we add the endpoints and that's the perimeter.

$\bf \begin{array}{cllll}
\textit{circumference of a circle}\\\\ 
2\pi r
\end{array}\qquad \qquad \qquad \qquad 
\begin{array}{cllll}
\textit{arc's length}\\\\
s=\cfrac{\theta r\pi }{180}
\end{array}\\\\
-------------------------------$

$\bf \stackrel{\stackrel{green~circle}{perimeter}}{2\pi(7.5) }~-~\stackrel{\stackrel{green~circle}{arc}}{\cfrac{(135)(7.5)\pi }{180}}~+
\stackrel{\stackrel{red~section}{perimeter}}{2\pi(9.5) }~-~\stackrel{\stackrel{red~section}{arc}}{\cfrac{(135)(9.5)\pi }{180}}+\stackrel{endpoints}{2+2}
\\\\\\
15\pi -\cfrac{45\pi }{8}+19\pi -\cfrac{57\pi }{8}+4\implies \cfrac{85\pi }{4}+4\quad \approx \quad 70.7588438888$

b)

we do about the same here as well, we get the full area of the red encircled area, and then subtract the sector with 135°, and then subtract the sector of the green circle that is 360° - 135°, or 225°, the part that wasn't included in the previous subtraction.

$\bf \begin{array}{cllll}
\textit{area of a circle}\\\\ 
\pi r^2
\end{array}\qquad \qquad \qquad \qquad 
\begin{array}{cllll}
\textit{area of a sector of a circle}\\\\
s=\cfrac{\theta r^2\pi }{360}
\end{array}\\\\
-------------------------------$

$\bf \stackrel{\stackrel{red~section}{area}}{\pi(9.5^2) }~-~\stackrel{\stackrel{red~section}{sector}}{\cfrac{(135)(9.5^2)\pi }{360}}-\stackrel{\stackrel{green~circle}{sector}}{\cfrac{(225)(7.5^2)\pi }{360}}
\\\\\\
90.25\pi -\cfrac{1083\pi }{32}-\cfrac{1125\pi }{32}\implies \cfrac{85\pi }{4}\quad \approx\quad 66.75884$

7 0

3 years ago

Find the slope of the line that goes through the points (0,2) and (-1,-4)

loris [4]

The formula foh slope is y1-y2/x1-x2 , therefore , the slope is 6

3 0

2 years ago

Read 2 more answers

What is the answer for 3x=x+8

liraira [26]

Answer:

X = 4 pls mark me brainliest

7 0

3 years ago

Read 2 more answers

A wallet contains $460 in $5, $10, and $20 bills. The number of $5 bills exceeds twice the number of $10 bills by 4, and the num

Butoxors [25]

Answer:

Number of $5 bills = 32

Number of $10 bills = 14

Number of $20 bills = 8

Step-by-step explanation:

Let x number of $5, y number of $10 and z number of $20

The number of $5 bills exceeds twice the number of $10 bills by 4.

Therefore, x = 2y + 4

The number of $20 bills is 6 fewer than the number of $10 bills.

Therefore, z = y - 6

A wallet contains $460 in $5, $10, and $20 bills.

Therefore,

5x + 10y + 20z = 460

Substitute x and y into equation

5(2y+4) + 10y + 20(y-6) = 460

10y + 20 + 10y + 20y - 120 = 460

40y - 100 = 460

40y = 460 + 100

40y = 560

y = 14

Put the value of y into x = 2y + 4 and solve for x

x = 2(14) + 4

x = 32

Put the value of y into z = y - 6 and solve for z

z = 14 - 6

z = 8

Hence, the each type of bills,

Number of $5 bills = 32

Number of $10 bills = 14

Number of $20 bills = 8

3 0

3 years ago

Read 2 more answers

?? So lost with this

labwork [276]

Answer:

$A)\ 1,\ -1,\ -3\\\\B)\ d=-2\\\\C)\ \left\{\begin{array}{ccc}a_1=11\\a_n=a_{n-1}-2\end{array}\right\\\\D)\ f(n)=-2n+13$

Step-by-step explanation:

It's an arithmetic sequence.

9 = 11 - 2

7 = 9 - 2

5 = 7 - 2

3 = 5 - 2

A) next three terms: 3 - 2 = 1, 1 - 2 = -1, -1 - 2 = -3

B) Common difference = -2

C) Recursive Function:

$\left\{\begin{array}{ccc}a_1=11\\a_n=a_{n-1}-2\end{array}\right$

D) Explicit Function:

$f(n)=a_1+(n-1)d$

a₁ - first term

d - common difference

Substitute a₁ = 11 and d = -2:

$f(n)=11+(n-1)(-2)=11-2n+2=-2n+13$

4 0

3 years ago