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3 years ago

Hey mathematicians ! Can anyone help me with these problems please ! Will give brainly !

Mathematics

1 answer:

satela [25.4K]3 years ago

7 0

Answer:

77) YES , 78) YES , 79) NO , 80) YES

Step-by-step explanation:

77) 12/4=3 and 18/6=3 so YES

78) 30/6=5 and 40/8=5 so YES

79) 36/25=1.44 and 48/40=1.2 so NO

80) 15/5=3 and 13.8/4.6=3 so YES

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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

donte bought a computer that was 20% off the regular price of $1.080. If an 8% sales tax was added to the cost of the computer,

Oxana [17]

So 20% of $1,080 is 216.

1080 - 216 is 864

8% of 864 is 69.12

864 + 69.12 would be $933.12

4 0

3 years ago

Solve the equation 4(3y-1)-3(2y)=6

olga nikolaevna [1]

Answer:

$4(3y - 1) - 3(2y) = 6$

Remove backets

$12y - 4 - 6y = 6$

Group and Evaluate like terms

$12y - 6y = 6 + 4$

$6y = 10$

$y = 10 \div 6$

$y = 1.67$

$y = \frac{5}{3}$

6 0

4 years ago

The amount of money, in dollars, in an account after t years is given by A = 1000(1.03)t. The initial deposit into the account w

nadezda [96]

Given
A = 1000(1.03)t

With the above equation, the initial deposit is $1000 and the interest rate on said deposit is 3%.

I am assuming that the above equation is a compounding interest where t is an exponent. t represents time period in years.

Let us assume t is 5.

A = 1,000(1.03)^5 = 1,000(1.159) = 1,159.00

After 5 years, the $1,000 deposit will earn an interest of $159 for a total of $1,159.

4 0

3 years ago

Which of the following is equivalent to (ab)4? a4b a4b4 ab4 4ab

Dmitrij [34]

(ab)^4 means ab times itselv 4 times
multicplication is comutaive so
a^4b^4

2nd option is answer

5 0

3 years ago

Read 2 more answers