MATHEMATICS HIGH SCHOOL

What is the area, in square meters, of the shaded part of the rectangle below?6 m
14 m
13 m

Answers

Answer 1

Answer:

Answer:

130 square metres

Step-by-step explanation:

The shaded area is a trapezium.

Therefore, the rule for its area is base1+base2/2xh

base1=6

base2=14

height = 13

Therefore, 6+14/2 x 13

= 130

Hope that helped!!! k

Answer 2

Answer:

Answer:

130 meters squared

Step-by-step explanation:

14-6=8

8*13/2=52

14*13=182

182-52=130 meters

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Evaluate the log without a calculator ( Show your work )

$log_(25) (1)/(5)$

Answers

Answer:

$\log_(25)((1)/(5))=-(1)/(2)$

Step-by-step explanation:

Let

$\log_(25)((1)/(5))=x$

We rewrite as an exponential equation to obtain;

$(1)/(5)=25^x$

We rewrite both sides of the equation as an index number to base 5.

$5^(-1)=5^(2x)$

Since the bases are the same, we equate the exponents to obtain;

$-1=2x$

Divide both sides by 2;

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25^x=1/5
thinking of number that satisfy it
it is =-1/2

If A(7,9) and B(3,12) find AB (remember: AB means "the distance between points A and B")

Answers

The length of segments ab is 24

Find the distance between (11, 10) and (1,3). Round your answer to
the nearest tenth.

Answers

Answer:

12.2

Step-by-step explanation:

$d=√((x_2-x_1)^2+(y_2-y_1)^2)\n\nd=√((1-11)^2+(3-10)^2)=√((-10)^2+(-7)^2)=√(149)\n\nd=12.2065...\approx12.2$

Solve by completing the square: x^2-2x-1=0

Answers

$(a-b)^2=a^2-2ab+b^2\ (*)\n------------------------------\n\nx^2-2x-1=0\n\nx^2-2x\cdot1=1\n\n\underbrace{x^2-2x\cdot1+1^2}_((*))-1^2=1\n\n(x-1)^2-1=1\n\n(x-1)^2=1+1\n\n(x-1)^2=2\Rightarrow x-1=-\sqrt2\ \vee\ x-1=\sqrt2\n\n\underline{\underline{x=1-\sqrt2\ \vee\ x=1+\sqrt2}}$