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4 years ago

Which describes the effect of the transformations on the graph of ƒ(x) = x2 when changed to ƒ(x) = −

Mathematics

1 answer:

storchak [24]4 years ago

4 0

Answer:

B) reflected over x-axis, compressed vertically, shifted right 2 units, and shifted up 3 units

Step-by-step explanation:

ƒ(x) = −⅛(x − 2)² + 3

- minus indicates reflection along the x-axis

⅛ indicates a vertical compression

x - 2 indicates 2 units towards right

+3 indicates 3 units upwards

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Two problems here I need solved! I need every step, so please have that with your answers!!

Free_Kalibri [48]

QUESTION 1

We want to solve,

$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x^{2}-6x+8}$

We factor the denominator of the fraction on the right hand side to get,

$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x^{2}-4x - 2x+8}.$

This implies
$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x(x-4) - 2(x - 4)}.$

$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{(x-4)(x - 2)}$

We multiply through by LCM of
$(x-4)(x - 2)$

$(x - 2) + x(x-4) = 2$

We expand to get,

$x - 2 + {x}^{2} - 4x= 2$

We group like terms and equate everything to zero,

${x}^{2} + x - 4x - 2 - 2 = 0$

We split the middle term,

${x}^{2} + - 3x - 4 = 0$

We factor to get,

${x}^{2} + x - 4x- 4 = 0$

$x(x + 1) - 4(x + 1) = 0$

$(x + 1)(x - 4) = 0$

$x + 1 = 0 \: or \: x - 4 = 0$

$x = - 1 \: or \: x = 4$

But
$x = 4$
is not in the domain of the given equation.

It is an extraneous solution.

$\therefore \: x = - 1$
is the only solution.

QUESTION 2

$\sqrt{x+11} -x=-1$

We add x to both sides,

$\sqrt{x+11} =x-1$

We square both sides,

$x + 11 = (x - 1)^{2}$

We expand to get,

$x + 11 = {x}^{2} - 2x + 1$

This implies,

${x}^{2} - 3x - 10 = 0$

We solve this quadratic equation by factorization,

${x}^{2} - 5x + 2x - 10 = 0$

$x(x - 5) + 2(x - 5) = 0$

$(x + 2)(x - 5) = 0$

$x + 2 = 0 \: or \: x - 5 = 0$

$x = - 2 \: or \: x = 5$

But
$x = - 2$
is an extraneous solution

$\therefore \: x = 5$

7 0

4 years ago

If you have a vertical angle and the side angles are 83 and 83 whats the other one?

Hoochie [10]

Answer:

97°

Step-by-step explanation:

you do $83*2=166$ and then $360-166=194$ which is the total sum of the two unknown vertical angles. once you have that, divide it by 2 to get $194/2=97°$ as the measure of each individual unknow vertical angle

7 0

3 years ago

Read 2 more answers

A pile of 42 coins worth $4.90, consisting of nickels and quarters. How many nickels are there?

Ymorist [56]

Answer:14

Step-by-step explanation:

A nickel is 5 cents (20% of dollar)

and a quarter is 25 cents (25% of dollar)

We have given a pile of 42 coins worth of $4.90

Let x be the no nickels and

y be the no of quarter

therefore

x+y=42 -----1

$\frac{x}{4}$ + $\frac{y}{20}$ =4.90 ---2

Solving $\left ( 1\right )&\left ( 2\right )$ we get

x=14 & y=28

Therefore no of nickels is 14 & no of quarters is 28

6 0

3 years ago

Which is the dependent variable when 3x = y?

Andrej [43]

Answer:

A dependent variable is a variable (often denoted by y ) whose value depends on that of another. so it is the variable that changes depending on the numbers beside it.

I hope this helps if not check out Khan academy

https://www.khanacademy.org/math/algebra/introduction-to-algebra/alg1-dependent-independent/v/dependent-and-independent-variables-exercise-example-3

7 0

3 years ago

Holly and Jimmy went shopping. For every $2

laila [671]

You can write the amount that they spent individually in a ratio where:

Holly : Jimmy

2 : 5

The total of this ratio would be 2+5 = $7.

To find the scale factor multiplier for the base ratio of 2:5:

35/7 = 5

Multiply both sides of the ratio by 5.

Holly : Jimmy

2 x5 : 5 x5

10 : 25

You can see that the total of this ratio is now $35, where Jimmy spent $25.

5 0

2 years ago

Read 2 more answers