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3 years ago

Which of the following is a counterexample to "the sum of two numbers is always greater than either of the numbers"?

Mathematics

1 answer:

Butoxors [25]3 years ago

8 0

Which of what following?

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On a map, the distance from Happy Hill Park to Rainbow Valley Park is 4/1/2 inches. The scale is 1/2 inch: 3 miles. What is the

Studentka2010 [4]

we are given

The scale is

$\frac{1}{2} inch=3miles$

the distance from Happy Hill Park to Rainbow Valley Park is 4 1/2 inches

we can change it into rational form

and we get

$=\frac{9}{2}inch$

so, we can multiply both sides by 9

$9*\frac{1}{2} inch=9*3miles$

now, we can simplify it

$\frac{9}{2} inch=27 miles$

so, the actual distance between the two parks is 27 miles........Answer

6 0

3 years ago

What will be the sum of an integer and its additive inverse

klemol [59]

Answer:

Step-by-step explanation:

4 is an integer

-4is its additive inverse

4+-4=0

5 1

3 years ago

A circle has the order pairs (-1, 2) (0, 1) (-2, -1) what is the equation . Show your work.

olga55 [171]

We know that:

$(x-a)^2+(y-b)^2=r^2$

is an equation of a circle.

When we substitute x and y (from the pairs we have), we'll get a system of equations:

$\begin{cases}(-1-a)^2+(2-b)^2=r^2\\(0-a)^2+(1-b)^2=r^2\\(-2-a)^2+(-1-b)^2=r^2\end{cases}$

and all we have to do is solve it for a, b and r.

There will be:

$\begin{cases}(-1-a)^2+(2-b)^2=r^2\\(0-a)^2+(1-b)^2=r^2\\(-2-a)^2+(-1-b)^2=r^2\end{cases}\\\\\\
\begin{cases}1+2a+a^2+4-4b+b^2=r^2\\a^2+1-2b+b^2=r^2\\4+4a+a^2+1+2b+b^2=r^2\end{cases}\\\\\\
\begin{cases}a^2+b^2+2a-4b+5=r^2\\a^2+b^2-2b+1=r^2\\a^2+b^2+4a+2b+5=r^2\end{cases}\\\\\\
$

From equations (II) and (III) we have:

$\begin{cases}a^2+b^2-2b+1=r^2\\a^2+b^2+4a+2b+5=r^2\end{cases}\\--------------(-)\\\\a^2+b^2-2b+1-a^2-b^2-4a-2b-5=r^2-r^2\\\\-4a-4b-4=0\qquad|:(-4)\\\\\boxed{-a-b-1=0}$

and from (I) and (II):

$\begin{cases}a^2+b^2+2a-4b+5=r^2\\a^2+b^2-2b+1=r^2\end{cases}\\--------------(-)\\\\a^2+b^2+2a-4b+5-a^2-b^2+2b-1=r^2-r^2\\\\2a-2b+4=0\qquad|:2\\\\\boxed{a-b+2=0}$

Now we can easly calculate a and b:

$\begin{cases}-a-b-1=0\\a-b+2=0\end{cases}\\--------(+)\\\\-a-b-1+a-b+2=0+0\\\\-2b+1=0\\\\-2b=-1\qquad|:(-2)\\\\\boxed{b=\frac{1}{2}}\\\\\\\\a-b+2=0\\\\\\a-\dfrac{1}{2}+2=0\\\\\\a+\dfrac{3}{2}=0\\\\\\\boxed{a=-\frac{3}{2}}$

Finally we calculate $r^2$ :

$a^2+b^2-2b+1=r^2\\\\\\\left(-\dfrac{3}{2}\right)^2+\left(\dfrac{1}{2}\right)^2-2\cdot\dfrac{1}{2}+1=r^2\\\\\\\dfrac{9}{4}+\dfrac{1}{4}-1+1=r^2\\\\\\\dfrac{10}{4}=r^2\\\\\\\boxed{r^2=\frac{5}{2}}$

And the equation of the circle is:

$(x-a)^2+(y-b)^2=r^2\\\\\\\left(x-\left(-\dfrac{3}{2}\right)\right)^2+\left(y-\dfrac{1}{2}\right)^2=\dfrac{5}{2}\\\\\\\boxed{\left(x+\dfrac{3}{2}\right)^2+\left(y-\dfrac{1}{2}\right)^2=\dfrac{5}{2}}$

7 0

3 years ago

The measure of the vertex angle of an isoceles triangle is one- fourth that of a base angle

horsena [70]

Answer:

Base angle = 72

Vertex angle = 18

Step-by-step explanation:

Measure of the base angle = x. But there are two of them. (Definition of isosceles). Keep that in mind.

The vertex angle is 1/4 of one of the base angles. That means that the vertex is 1/4 x

All three angles = 180 degrees.

So we have x + x + x/4 = 180 degrees.

change 1/4x to 0.25x x since 1/4 = 0.25

Equation

x + x + 0.25 = 180

2.5x = 180

Solution

2.5x = 180 Divide by 2.5 on both sides

2.5x/2.5 = 180/2.5

x = 72

Answer

That means that each base angle = 72 degrees

The Vertex Angle = 72/4 = 18

8 0

3 years ago

PLEASE HELP FAST!!!!!

Anit [1.1K]

The answer to the first question is 7(3.14)/6.

the answer to the second question is quadrant 2

8 0

3 years ago