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3 years ago

PLEASE HELP!! (QUESTION 1)

Mathematics

1 answer:

postnew [5]3 years ago

3 0

9514 1404 393

Answer:

a. reflection over the x-axis

b. vertical expansion by a factor of 2

c. right shift 3 units

d. shift upward 4 units

Step-by-step explanation:

It is a good idea to become familiar with what these various factors do. You will see them repeatedly.

a. Multiplying a function by a negative value reflects its graph over the x-axis.

b. A multiplier of 2 will expand the graph vertically by a factor of 2.

c. Subtracting 3 from each x-value will shift the graph right 3 units.

d. Adding 4 to each function value will shift the graph up 4 units.

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Please help!! Please give step by step so i can understand

miss Akunina [59]

Answer:

p = - 14

Step-by-step explanation:

Using the rules of exponents

$a^{m}$ ÷ $a^{n}$ = $a^{(m-n)}$

$(a^{m}) ^{n}$ = $a^{mn}$

Note 81 = 9² and 729 = 9³

Given

$(81)^{-4}$ ÷ $(729)^{2-p}$

= $(9^{2}) ^{-4}$ ÷ $(9^{3}) ^{2-p}$

= $9^{-8}$ ÷ $9^{6-3p}$

= $9^{-8-(6-3p)}$

= $9^{-8-6+3p}$

= $9^{3p-14}$

Thus

$9^{3p-14}$ = $9^{4p}$

Since bases on both sides are equal then equate the exponents

4p = 3p - 14 ( subtract 3p from both sides )

p = - 14

6 0

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

Jon has y stickers. He uses 20 stickers and divided the remainder equally between his two sisters. find the number of stickers e

ale4655 [162]

Jon has y stickers and uses 20
jon=y-20
the sisters share y-20 between 2 of them
therefore each sister receives

(y-20) divided by 2 -- (y-20)/2

6 0

3 years ago

F(x) = x + 2 g(x) = x - 4 (f9)(x) =

san4es73 [151]

Answer:

(fºg)(x) = x -2

Step-by-step explanation:

f(x) = x + 2

g(x) = x - 4

(fºg)(x) = ( x - 4) + 2

(fºg)(x) = x -2

3 0

3 years ago

What is the y-intercept of the line shown? -1 0 1

Hatshy [7]

Answer:

-1

Step-by-step explanation:

The y-intercept is where the line crosses the y-axis.

7 0

2 years ago

Read 2 more answers