For number 4, the midpoint is M, so the lengths of the 2 segments are half of the whole. PM and MQ are 11.

For number 5, TM and MS are 7.5.

Have an amazing day :)

8 0

3 years ago

What is the inverse of f(x)=x^4+7 for x>0 where function g is the inverse of function f?<br> -

Ann [662]

Answer:

$g(x) = \sqrt[4]{x-7},~ x\geq 7$

Step by step explanation:

$y= f(x) = x^4+7\\\\\text{Replace x with y and solve for y:}\\\\~~~~~~~x = y^4 +7\\\\\implies y^4 = x-7\\\\\implies y = \pm\sqrt[4]{x-7}\\\\ \implies f^{-1}(x) = \pm\sqrt[4]{x-7}$

7 0

2 years ago

√180 can be expressed in the form p√q. where p and q are integers. Find the smallest value of p + q.

frutty [35]

Answer:

The smallest value of p+q is 11

It happens when p = 6 and q = 5.

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

Explanation:

Let's factor 180 in such a way that exactly one factor is a perfect square.

I'll ignore the trivial factor of 1.

Here are the possible factorizations we could go with:

180 = 4*45

180 = 9*20

180 = 36*5

Those factorizations then lead to the following

$\sqrt{180} = \sqrt{4*45} = \sqrt{4}*\sqrt{45}= 2\sqrt{45}\\\\\sqrt{180} = \sqrt{9*20} = \sqrt{9}*\sqrt{20}= 3\sqrt{20}\\\\\sqrt{180} = \sqrt{36*5} = \sqrt{36}*\sqrt{5}= 6\sqrt{5}\\\\$

Then we have

p+q = 2+45 = 47

p+q = 3+20 = 23

p+q = 6+5 = 11

The smallest value of p+q is 11 and it happens when p = 6 and q = 5.

Side note: p+q is smallest when we go with the largest perfect square factor.

6 0

2 years ago

Pls help me solve this

melamori03 [73]

Answer:

See below.

Step-by-step explanation:

1.) False - It contains 6 sig figs, not 2.

2.) False - It goes up to 2 decimal places, not 3.

3.) True

4.) False - It goes up to 1 sig fig, not 4.

8 0

3 years ago