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makkiz [27]
2 years ago
13

Given y varies inversely as x, and y = 5 when x = 9. *Write the inverse function

Mathematics
1 answer:
Ivahew [28]2 years ago
4 0

Answer:

y = 45/x

Step-by-step explanation:

Here, we want to write an inverse relationship

for an inverse relationship, the product of both variables will be equal to the constant term

Let us have the constant term as k

Thus, we have it that;

xy = k

9 * 5 = k

k = 45

So the inverse function is;

xy = 45

or y = 45/x

if y is a function of x, we can have it as;

f(x) = 45/x

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Find all points on the x-axis that are 14 units from the point (6,-7) All points on the x-axis that are 14 units from the point
Maksim231197 [3]

Answer: (6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0) are the required points.

or  (18.124,0) and ( -6.124,0) are the required points.

Step-by-step explanation:

Let (x,0) be the point on x -axis that are 14 units from the point (6,-7) .

Then by distance formula , we have

\sqrt{(x-6)^2+(0-(-7))^2}=14\ \ \ [\ \because distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}]

Taking square on both the sides , we get

(x-6)^2+7^2=14^2\\\\\Rightarrow\ x^2+6^2-2(6)x+49=196\\\\\Rightarrow\ x^2+36-12x=147\\\\\Rightarrow\ x^2-12x=111\\\\\Rightarrow\ x^2-12x-111=0

Using quadratic formula : x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

x=\dfrac{12\pm\sqrt{(-12)^2-4(1)(-111)}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{144+444}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{588}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{2^2\times7^2\times3}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm14\sqrt{3}}{2}\\\\\Rightarrow\ x=6\pm7\sqrt{3}

so, (6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0) are the required points.

since \sqrt{3}=1.732

so, (6+7(1.732),0)\text{ and }(6-7(1.732),0) are the required points.

i.e. (18.124,0) and ( -6.124,0) are the required points.

3 0
3 years ago
there are 245 students in 7th grade if 40% of them ride the bus to school how many 7th graders do not ride the bus to school? F
Ivenika [448]
Multiply 245 by .40 (which is 40%)
245 x (.40)= 98. When you get 98, you have to 245-98 and you get 147
3 0
3 years ago
Suppose M is the midpoint of FG. Find the missing measure.<br><br><br><br> FM=12x−4, MG=5x+10
Dmitrij [34]

Answer:

FG = 17x - 6

Step-by-step explanation:

FG = 12x + 5x + 10 - 4

5 0
3 years ago
Read 2 more answers
Find three consecutive integers whose sum is six times the greater integer
Zepler [3.9K]
3 times 6 18 and do that 6 times add

4 0
3 years ago
Problem #32 <br> I am not sure if I did this right can you check please and explain
Natasha2012 [34]

Answer:

Step-by-step explanation:

It seems you got the right answer, but didn’t do the problem correctly.

The square root of 2 times the square root of 2 is 2. And then 6 times the square root of two minus the product of 6 and the square root of two equals zero. And then obviously 6 and -6 equals -36. So 2+-36 is -34

6 0
3 years ago
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