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2 years ago

Determine whether test point (-6,4) is a solution to the linear inequality x+y_<1

Mathematics

1 answer:

tamaranim1 [39]2 years ago

7 0

$\bf \begin{array}{llll}
-6&,&4\\
\uparrow &&\uparrow \\
x&&y
\end{array}\qquad x+y\le 1\implies -6+4\le 1\implies -2\le 1$

now, is it true that -2 is lesser than 1? if it's true, is a solution, if is false, is not then

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Please help. Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact valu

o-na [289]

Answer:

Area = (18 + 4.5π) cm²

Perimeter = (6√2 + 12 + 3π) cm

Step-by-step explanation:

The shaded region given is made up of triangle ABC and a semicircle

AB = BC = 6 cm (note that the triangle is a portion of a square)

Diameter of semi-circle (d) = BC = 6cm

Radius (r) = ½*6 = 3 cm

==>Area of the shaded region in terms of π

Area of shaded region = area of triangle + area of semicircle

Area = ½*a*b + ½*πr²

Area = ½*6*6 + ½*π3²

Area = 18 + ½*π9

Area = 18 + 4.5π

Area of the shaded portion = (18 + 4.5π) cm²

==>Perimeter of shaded region in terms of π

Perimeter of shaded region = perimeter of triangle + perimeter of semicircle

= Sum of all sides of the triangle + ½πd

Sides of triangles are AB = 6 cm, BC = 6 cm

Use Pythagorean theorem to find side AC:

AC² = AB² + BC²

AC² = 6² + 6² = 36 + 36 = 72

AC = √72 cm

Perimeter of shaded triangle = √72 + 6 + 6 = √72 + 12 = (6√2 + 12) cm

Perimeter of semicircle = ½*πd = ½π6

= 3π

Perimeter of the whole shaded region in terms of π = (6√2 + 12 + 3π) cm

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2 years ago

Read 2 more answers

How to slove A=10,000(1+.08/2)*12

suter [353]

This is basically the form of a compounded interest. Honestly the best answer i can give is: plug it into your calculator.
I'll give you a few "do it by hand" tips. Simplify 0.08/2 into 0.04. Now you do 1.04 to the 12th power in your calculator. Multiply that buy 10,000 is your answer. 16010.32 is your answer. This means that
You put $10,000 into some sort of savings account that gave 0.04 interest rate. You leave it there to be compounded each year for 12 years. And now you have 16010 dollars instead of 10k. Not bad at all if you're patient. :)

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2 years ago

Please help me with numbers #2-5?

trasher [3.6K]

Just keep doing what you did in 1. I'll show you how easy it is.

a) g(9) = 9 - 5 / 2 = 4 / 2 = 2.

b) g(0) = 0 - 5 / 2 = 5 / 2 = 2 1 / 2.

c) g(3) = 3 - 5 / 2 = 2 / 2 = 1.

d) g(17) = 17 - 5 / 2 = 12 / 2 = 6.

a) f(3) = 3^2 - 4 = 9 - 5 = 4.

b) f(-4) = -4^2 - 4 = 16 - 4 = 12.

c) f(0) = 0^2 - 4 = 0 - 4 = -4.

d) f(-2) = -2^2 - 4 = 4 - 4 = 0.

a) f(10) = 10 / 2 - 6 = 5 - 6 = -1; -1 is the solution.

a) I'll test one after another.

1. f(0) = 2(0) - 3 = 0 - 3 = -3 > g(0) = 3(0) / 2 + 1 = 0 + 1 = 1; this is incorrect.

2. f(2) = 2(2) - 3 = 4 - 3 = 1 = g(2) = 3(2) / 2 + 1 = 6 / 2 + 1 = 3 + 1 = 4; this is incorrect.

3. f(8) = 2(8) - 3 = 16 - 3 = 13 = g(8) = 3(8) / 2 + 1 = 24 / 2 + 1 = 12 + 1 = 13; this is correct.

4. g(4) = 3(4) / 2 + 1 = 12 / 2 + 1 = 6 + 1 = 7 < f(4) = 2(4) - 3 = 8 - 3 = 5; this is incorrect.

Hope this helps :)

7 0

2 years ago