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2 years ago

11

What is the inverse function for h(x) =

{x+7} -1" alt="\sqrt{x+7} -1" align="absmiddle" class="latex-formula">

1 answer:

Blizzard [7]2 years ago

5 0

Step-by-step explanation:

$y = \sqrt{x + 7} - 1$

Replace x and y.

$x = \sqrt{y + 7} - 1$

Solve for y.

$x + 1 = \sqrt{y + 7}$

Square both sides.

$(x + 1) {}^{2} = y + 7$

$(x + 1) {}^{2} - 7 = y$

This is the inverse function or you can also say

${x}^{2} + 2x - 6 = y$

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An architect wants to draw a rectangle with a diagonal of 15 centimeters. The length of the rectangle is to be 6 centimeters mor

S_A_V [24]

Answer:

She should make a rectangle with dimensions 14.4 cm by 4.2 cm.

Step-by-step explanation:

The diagonal of a rectangle is represented by $\sqrt{length^2+width^2}$ .
Area of rectangle is = length×width
Perimeter of a rectangle = 2(length+width).

Assume x be the width of the rectangle.

The length of the rectangle is to be 6 cm more than twice the width.

The length of the rectangle is= (2x+6) cm

Then the diagonal of the rectangle is $\sqrt{length^2+width^2}$

$=\sqrt{(2x+6)^2+x^2}$

$=\sqrt{4x^2+24x+36+x^2}$

$=\sqrt{5x^2+24x+36}$ cm

According to the problem,

$\sqrt{5x^2+24x+36}=15$

Squaring both sides

$\Rightarrow{5x^2+24x+36}=15^2$

$\Rightarrow{5x^2+24x+36}=225$

$\Rightarrow{5x^2+24x+36-225=0$

$\Rightarrow{5x^2+24x-189=0$

⇒5x²+45x-21x-189=0

⇒5x(x+9)-21(x+9)=0

⇒(x+9)(5x-21)=0

⇒x+9=0 or, 5x-21=0

$\Rightarrow x=-9, \frac{21}5$

⇒x= -9, 4.2

Since the width of a rectangle can not negative.

So, x=4.2 cm

The width of rectangle is = 4.2 cm

The length of the rectangle is =(2×4.2+6)

=14.4 cm

She should make a rectangle with dimensions 14.4 cm by 4.2 cm.

8 0

3 years ago

F(x)=2x^2+4x-16<br> g(x)=4x^2-16<br> Find (f/g)(x).

Nastasia [14]

Answer:

Step-by-step explanation:

$(\frac{f}{g} )(x) = \frac{2x^{2} +4x-16}{4x^{2} -16}$

2x²+4x -16 = 2(x²+2x-8); factor 2

= 2(x+4)(x-2) ;factor the quadratic equation

4x²-16 = 4(x²-4) ; factor 4

=4(x²- 2²) ; rewrite 4 as 2²

= 4(x-2)(x+2); now use the difference of two squares a²-b²=(a-b)(a+b)

so now we have:

$(\frac{f}{g}) (x) = \frac{2(x+4)(x-2)}{4(x-2)(x+2)}$ ; simplify (x-2) from numerator and denominator

and 2/4 as 1/2

$(\frac{f}{g}) (x) = \frac{(x+4)}{2(x+2)}$

8 0

3 years ago

Last month, there were 4 sunny days for every rainy day. If there were 30 days in the month, how many days were rainy? Explain y

Alisiya [41]

Answer:

26 because 30-4=26

Step-by-step explanation:

6 0

3 years ago

A group of five friends are sharing 2 pounds of trail mix write a division problem and a fraction to represent this problem

KiRa [710]

2/5 or 2 divided by 5. 2 pounds are divided up by 5 friends.

3 0

3 years ago

Paid for $22 for for movie tickets how many would they have pay for for 16 tickets

bija089 [108]

Answer:

$352

Step-by-step explanation:

One ticket costs $22, so 16 tickets would be 22 times 16.

Final Answer: $352

5 0

2 years ago