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Black_prince [1.1K]
3 years ago
6

What epuation correctly shows how to determine the distance between points 9,-2 6,3

Mathematics
1 answer:
Masteriza [31]3 years ago
8 0

d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}

This is the distance formula. To find the distance, solve as shown:

d=\sqrt{(6-9)^{2}+(3-(-2))^{2} } \\d=\sqrt{(6-9)^{2}+(3+2)^{2} } \\d=\sqrt{(-3)^{2}+(5)^{2} } \\d=\sqrt{9 +25 } \\d=\sqrt{34 }

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If the function f (x) has a domain of (a,b] and a range of [c,d), then what is the domain and range of g (x) = m × f (x) + n?
xz_007 [3.2K]
<h3>Answer: Choice A</h3>

Domain = (a,b]

Range = [mc + n,md + n)

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

Explanation:

The domain stays the same because we still have to go through f(x) as our first hurdle in order to get g(x).

Think of it like having 2 doors. The first door is f(x) and the second is g(x). The fact g(x) is dependent on f(x) means that whatever input restrictions are on f, also apply on g as well. So going back to the "2 doors" example, we could have a problem like trying to move a piece of furniture through them and we'd have to be concerned about the f(x) door.

-------------------

The range will be different however. The smallest value in the range of f(x) is y = c as it is the left endpoint. So the smallest f(x) can be is c. This means the smallest g(x) can be is...

g(x) = m*f(x) + n

g(x) = m*c + n

All we're doing is replacing f with c.

So that means mc+n is the starting point of the range for g(x).

The ending point of the range is md+n for similar reasons. Instead of 'c', we're dealing with 'd' this time. The curved parenthesis says we don't actually include this value in the range. A square bracket means include that value.

6 0
3 years ago
Sorry for the bother help plz
Zepler [3.9K]

(6a^2)^3

6^3(a^2)^3

216(a^2)^3

216a^6

Answer: 216a^6

3 0
3 years ago
Read 2 more answers
Refer to the variable on the number of miles driven. the mean is 830.11 and the standard deviation is 42.19 miles. estimate the
Alex787 [66]
The proportion of buses traveling more than 900 miles would be 0.0485; multiply this by the total number of buses and you will have your answer.

We find the z-score associated with 900 miles:

z = (X - μ)/σ = (900-830.11)/42.19 = 1.66

Using a z-table (http://www.z-table.com) we see that the area under the curve to the left of this, less than this, is 0.9515.  This means that the area under the curve to the right of this, greater than this, would be 1-0.9515 = 0.0485.
8 0
3 years ago
The volume of a sphere can be found using the formula V = πr . If the sphere has a diameter of 10x y z mm, what is the volume of
viva [34]

Answer:

<em>500πx³y³z³ </em>

Step-by-step explanation:

Volume of a sphere = 4πr³

r is the radius of the sphere

Given

Diameter of the sphere = 10xyz mm

Radius = diameter/2

Radius = 10xyz/2

Radius = 5xyz

Substitute the radius into the formula

Volume of the sphere = 4π(5xyz)³

Volume of the sphere = = 4π(125)x³y³z³

Volume of the sphere = 500πx³y³z³

<em>Hence the volume of the sphere is 500πx³y³z³ mm³</em>

8 0
3 years ago
In right triangle ∆ABC, ∠A=36°. Find the measure of the other acute angle: ∠B. 54° 64° 24° 36°
vlabodo [156]
(36+90)+C=180
126+C=180
C=180-126
=54
Answer=54
6 0
4 years ago
Read 2 more answers
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