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3 years ago

Identify how the graph is shifted from that of the parent function.

Mathematics

2 answers:

morpeh [17]3 years ago

7 0

Answer:

1. 4 units left

2. 4 units down

Step-by-step explanation:

Semenov [28]3 years ago

3 0

Answer:

4 units left

Step-by-step explanation:

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There is a dining room table with an area of 28 square feet. The length is 3 feet longer than the width. What is the width of th

Ivahew [28]

The width is 4 ft and the length is 7 feet

3 0

2 years ago

sofia has to walk 1 2/25 miles to school. she has already walk 2/3 of a mile. how much farther dose she need to walk ? help me p

love history [14]

Answer:

She need to walk 31/75 miles to school.

Step-by-step explanation:

It is given that,

Sofia has walk $1\dfrac{2}{25}$ miles to school. She has already walk $\dfrac{2}{3}$ of a mile.

We need to find how much farther does she need to walk.

Total distance = $1\dfrac{2}{25}$ $=\dfrac{27}{25}$

Let she has to walk x distance to school.

$x=\dfrac{27}{25}-\dfrac{2}{3}\\\\=\dfrac{31}{75}$

Hence, she need to walk 31/75 miles to school.

7 0

2 years ago

Find all possible values of α+

const2013 [10]

Answer:

$\rm\displaystyle 0,\pm\pi$

Step-by-step explanation:

please note that to find but α+β+γ in other words the sum of α,β and γ not α,β and γ individually so it's not an equation

===========================

we want to find all possible values of α+β+γ when tanα+tanβ+tanγ = tanαtanβtanγ to do so we can use algebra and trigonometric skills first

cancel tanγ from both sides which yields:

$\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \alpha ) \tan( \beta ) \tan( \gamma ) - \tan( \gamma )$

factor out tanγ:

$\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \gamma ) (\tan( \alpha ) \tan( \beta ) - 1)$

divide both sides by tanαtanβ-1 and that yields:

$\rm\displaystyle \tan( \gamma ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{ \tan( \alpha ) \tan( \beta ) - 1}$

multiply both numerator and denominator by-1 which yields:

$\rm\displaystyle \tan( \gamma ) = - \bigg(\frac{ \tan( \alpha ) + \tan( \beta ) }{ 1 - \tan( \alpha ) \tan( \beta ) } \bigg)$

recall angle sum indentity of tan:

$\rm\displaystyle \tan( \gamma ) = - \tan( \alpha + \beta )$

let α+β be t and transform:

$\rm\displaystyle \tan( \gamma ) = - \tan( t)$

remember that tan(t)=tan(t±kπ) so

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm k\pi )$

therefore when k is 1 we obtain:

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm \pi )$

remember Opposite Angle identity of tan function i.e -tan(x)=tan(-x) thus

$\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm \pi )$

recall that if we have common trigonometric function in both sides then the angle must equal which yields:

$\rm\displaystyle \gamma = - \alpha - \beta \pm \pi$

isolate -α-β to left hand side and change its sign:

$\rm\displaystyle \alpha + \beta + \gamma = \boxed{ \pm \pi }$

when is 0:

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta \pm 0 )$

likewise by Opposite Angle Identity we obtain:

$\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm 0 )$

recall that if we have common trigonometric function in both sides then the angle must equal therefore:

$\rm\displaystyle \gamma = - \alpha - \beta \pm 0$

isolate -α-β to left hand side and change its sign:

$\rm\displaystyle \alpha + \beta + \gamma = \boxed{ 0 }$

and we're done!

8 0

2 years ago

Read 2 more answers

Provide an example of a function that does not have an inverse function. How do you prove that it is not a function?

SOVA2 [1]

Answer:

f(x) = x^2 is a classic example

f( 3 ) = 9 and

f( -3 ) = 9, but

f^(-1)[9] is undefined because the result can be 3 and -3

6 0

2 years ago

The length of a rectangle is 4 less than 2 times the width. The perimeter is 40 units.

bezimeni [28]

Answer:

Let l be length and w be width.

First equation:

l = 2w-4

Second equation:

perimeter = 40 units

Perimeter of a rectangle: 2(l+w)

2(2w-4+w)=40

2(3w-4)=40

6w-8=40

6w=40+8

6w=48

w=48/6

w=8

Therefore the width=8;

length= 2w-4 = 2(8)-4 = 16-4 = 12

perimeter = 40 units

8 0

2 years ago