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2 years ago

Which statement correctly compares the angles?

Mathematics

2 answers:

Masja [62]2 years ago

5 0

The answer would be Angle G is congruent to angle P.

ivann1987 [24]2 years ago

5 0

Answer:

Step-by-step explanation:

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I am confused on this , I’ve tried twice and got it wrong.

babunello [35]

Answer:

$f^-^1(x)=-x^2+6x-5 \ \text{for the domain}\ [3, \infty)$

Step-by-step explanation:

Consider the function $f(x)=\sqrt{4-x}+3$ for the domain $(- \infty, 4]$ .

Find $f^-^1(x)$ , where f^(-1) is the inverse of f.

Also state the domain of f^(-1) in interval notation.

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We can start solving this problem by finding the inverse of f(x). This is done by switching the x- and y- variables, and solving for y.

$y=\sqrt{4-x}+3 \rightarrow x=\sqrt{4-y}+3$
$x=\sqrt{4-y}+3$

We can start solving for y by subtracting 3 from both sides of the equation.

$x-3=\sqrt{4-y}$

Get rid of the radical by squaring both sides of the equation.

$(x-3)^2=(\sqrt{4-y})^2$
$(x-3)(x-3)=4-y$

Use FOIL to multiply the binomial (x-3) together.

$x^2-3x-3x+9=4-y$

Combine like terms.

$x^2-6x+9=4-y$

Subtract 4 from both sides of the equation.

$x^2-6x+5=-y$

Divide both sides of the equation by -1.

$-x^2+6x-5=y$
$f^-^1(x)=-x^2+6x-5$

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The domain and range of a function are flipped for its inverse, meaning that to find the domain of the inverse function, you can find the range of the original function f(x), and that will be your inverse function's domain.

The range of $f(x)=\sqrt{4-x} +3$ is $y \geq 3$ , since the vertical shift of the graph is at k = 3. You can also graph this function on a calculator to see that the graph does indeed start at y = 3.

Now that we know the domain and range of the original function, we know that these are flipped for the inverse function.

Original function:

Domain: $x\leq 4$
Range: $y\geq 3$

Inverse function:

Domain: $x\geq 3$
Range: $y\leq 4$

The final answer is:

The inverse $f^-^1(x)=-x^2+6x-5 \ \text{for the domain}\ [3, \infty)$ .

You can also write the domain as: $x\geq 3$ .

4 0

2 years ago

Two numbers have a sum of 33. The same two numbers have a difference of 13. What are the two numbers?

padilas [110]

Answer:

x = 23

y = 10

Step-by-step explanation:

Let the two numbers be x and y where x>y

x + y = 33

<u>x - y = 13</u> Add

2x = 46 Divide by 2

2x/2=46/2 Do the division

x = 23

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

Solve for y

x + y = 33 Substitute for x

23 + y = 33 Subtract 23 from both sides.

23-23+y = 33 - 23

y = 10

3 0

2 years ago

Find the lcd of 2/3 and 1/3

wariber [46]

Hello!

The least common denominator is like the least common multiple. As you can see, these numbers already have the same denominators, and cannot be divided any further as they are prime.

Therefore, our answer is 3.

I hope this helps!

4 0

2 years ago

Read 2 more answers

Find the product of (-8) and (-13)

KiRa [710]

To find this you can always use a calculator, if your teacher allows you to. Just remember to punch in the negative signs correctly and don't mistake them for subtraction signs. Also if you don't know what product means, that means the answer of a multiplication problem so for example 9 is the product of 3x3 or 5 is the product of 5x1. The answer to your question is 104. Maybe next time you can solve it on your own! :)

4 0

2 years ago

You need a loan of $135,000 to buy a home. Calculate your monthly payment and total closing costs for each choice below. Briefly

Ahat [919]

You need to multiply the four numbers and then takeway

6 0

3 years ago