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Semmy [17]
3 years ago
13

Examine the expression.

Mathematics
2 answers:
shepuryov [24]3 years ago
8 0

Answer:

Step-by-step explanation:

kvasek [131]3 years ago
6 0

Answer:

17x(1-2y)

Step-by-step explanation:

Rewrite 34 as 2 · 17:

\implies 17x-2 \cdot 17 xy

Factor out common term 17x:

\implies 17x(1-2y)

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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
What are true bearings and how can they be calculated/read?
lubasha [3.4K]

Answer:

Compass bearings use the four directions on a compass in order to find the direction of one object from another. An example is N20°E. True bearings use the number of degrees measured clockwise from north an object is. An Example is 120°T.

Compass bearings use the four directions on a compass in order to find the direction of one object from another. An example is N20°E. True bearings use the number of degrees measured clockwise from north an object is. An Example is 120°T.

3 0
2 years ago
Read 2 more answers
To the nearest millimeter, a cell phone is 86 mm long and 40 mm wide. What is the ratio of the width to the length?
MAXImum [283]

Answer:

20 : 43

Step-by-step explanation:

width : length

40 mm : 86 mm

40 : 86

20 : 43

4 0
2 years ago
PLEASE HELP ! The total cost after tax to repair Kimber's cracked phone screen is represented by 0.04(30h)+30h where h represent
Ronch [10]

Answer: The term 0.040(30h) represents the amount of tax she must pay.


Explanation:


The functin 0.04(30h) + 30h, has two terms; the second term, 30h, represents cost due to h hours at at unit of 30, and the first term 0.04(30h) is the additional amount due to the taxes over h hours at the unit rate of 30.


When you add a tax rate of 4% to 30h, you get the the amount of taxes over the 30h.


The calcualtion is: (4/100)×(30h) = 0.04(30h). Hence, you conclude that 0.04(30h) is the amount of tax she must pay.

6 0
4 years ago
Read 2 more answers
Use geometry words to describe a way to separate triangles into other triangles
Masja [62]
Use a picture of an acute triangle a right triangle and a scalene, lastly a quadrilateral
5 0
3 years ago
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