12. The square and rectangle shown below have the same perimeter length Show that the length of the rectangle (3x + 1) centimetres
12. The square and rectangle shown below have the same - 1

Answers

Answer 1
Answer: Lets call the perimeter P and the length of the rectangle l.  The first figure is a square with side length 2x + 2 so P = 4(2x + 2) = 8x + 8.  For the rectangle, P = 2l + 2(x + 3) = 2l + 2x + 6.  These values both equal P so they must equal each other.  8x + 8 = 2l + 2x + 6.  Now we have to solve for l.  

8x + 8 = 2l + 2x + 6  
8x + 2 = 2l + 2x
6x + 2 = 2l
3x + 1 = l

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Find the 4th term of (x+2)^10

Answers

(x + 2)¹⁰

Would take the terms in reducing powers of x, and increasing powers of 2.


1st term =        ¹⁰C₀ x¹⁰(2)⁰        = x¹⁰

Second term =  ¹⁰C₁ x¹⁰⁻¹(2)¹      =  ¹⁰C₁ x⁹(2)¹

Third term =    ¹⁰C₂ x¹⁰⁻²(2)²        =  ¹⁰C₂ x⁸(2)² 

Fourth term =  ¹⁰C₃ x¹⁰⁻³(2)³        =  ¹⁰C₃ x⁷(2)³


So we shall now simplify the fourth term which is = ¹⁰C₃ x⁷(2)³

ⁿCr = n! /( r!(n -r)! )

¹⁰C₃ = 10! /( 3!(10 -3)! ) = 10! / (3!*7!) =  (10 *9 * 8* 7!) / (3!*7!)

        =     10*9*8 / 3! = (10*9*8) / (3*2*1) = 120  


4th term = ¹⁰C₃ x⁷(2)³ = 120 *x⁷*(2)³ = 120*2³*x⁷

             = 120*8x⁷

             = 960x⁷

So the fourth term in reducing powers of x = 960x⁷

I hope this helped.

During the Age of Exploration, stretching from the 1400s to the 1900s, which of the following regions was the focal point for global trade and exchange of culture? A Option A: Pacific B Option B: Atlantic C Option C: African D Option D: Asian

Answers

Answer:

The correct answer is Option B: Atlantic

Step-by-step explanation:

During the Age of Exploration, stretching from the 1400s to the 1900s, the Atlantic region was the focal point for global trade and exchange of culture.

During the Age of Exploration, the European ships traveled extensively overseas around the world to search new trading routes.

Which set of ordered pairs represents a function?{(0, 1), (1, 3), (1, 5), (2, 8)}
{(0, 0), (1, 2), (2, 6), (2, 8)}
{(0, 0), (0, 2), (2, 0), (2, 4)}
{(0, 2), (1, 4), (2, 6), (3, 6)}

Please explain why.

Answers

The very last set
{(0, 2), (1, 4), (2, 6), (3, 6)}.

The reason why is because of the vertical line test. If there are two y-coordinates on a x-coordinate then it is not a function. A function is that each x-coordinate has a y-coordinate with the x-coordinates being different.

Example is above. If you have any questions then leave a comment. Good luck!

Answer:

last one

Step-by-step explanation:

How to solve -5/7-11/7x=-y
2y=7+5x

Answers

\left\{\begin{array}{ccc}-(5)/(7)-(11)/(7)x=-y&/\cdot(-1)\n2y=7+5x\end{array}\right\n\left\{\begin{array}{ccc}(5)/(7)+(11)/(7)x=y\n2y=7+5x\end{array}\right\n\nsubstitute\n\n2\cdot\left((5)/(7)+(11)/(7)x\right)=7+5x\n\n(10)/(7)+(22)/(7)x=7+5x\ \ \ /\cdot7\n\n10+22x=49+35x\n\n22x-35x=49-10\n\n-13x=39\ \ \ /:(-13)\n\nx=-3

\left\{\begin{array}{ccc}x=-3\ny=(5)/(7)+(11)/(7)x\end{array}\right\n\left\{\begin{array}{ccc}x=-3\ny=(5)/(7)+(11)/(7)\cdot(-3)\end{array}\right\n\left\{\begin{array}{ccc}x=-3\ny=(5)/(7)-(33)/(7)\end{array}\right\n\left\{\begin{array}{ccc}x=-3\ny=-(28)/(7)\end{array}\right\n\left\{\begin{array}{ccc}x=-3\ny=-4\end{array}\right

PLZ HELP! MATH >__<What is the lateral area of the rectangular prism with a base length of 14 m, a base width of 9 m, and a height of 6 m?
A. 264 m2
B. 276 m2
C. 528 m2
D. 756 m2

Answers

Lateral area = surface area not including the bases.

To find this area we just need to add up the area of all of those sides.

The 2 bases are the same area and defined by the length and width.

That leaves the 2 sides defined by length and height,
plus the 2 defined by width and height.

Of course, to find the area of a rectangle, we just multiply together its two dimensions.
length × height = 14 × 6 = 84
width × height = 9 × 6 = 54

2 × 84 + 2 × 54 = 276 m²
My answer would be 276m2 
k12

Solve the inequality. 42 < –6d
A. d < –7
B. d < 36
C. d > –7
D. d < –48

Answers

42 < -6d

divide 6 by both sides,

7 < -d

(C) d > -7 is the answer.