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Anuta_ua [19.1K]
3 years ago
9

Two points are given: (-4,3) and (2,-5). Find the distance between the two points. (The numerical value simplified as much as po

ssible thanks)
Mathematics
1 answer:
natulia [17]3 years ago
4 0

Answer:

distance is 11.3137 units

Step-by-step explanation:

\sqrt{( - 4 -2) ^{2}  + (3 -  - 5) ^{2}  }  \\  \sqrt{64 + 64}  \\  \sqrt{128 } \\  \sqrt{2 \times 64}  \\  \sqrt{2}  \times  \sqrt{64}   \\ 8 \sqrt{2} \: units \\ 11.3137 \: units

hopefully it makes sense

:)

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For what values of x is x2 + 2x = 24 true?<br><br> –6 and –4<br> –4 and 6<br> 4 and –6<br> 6 and 4
kolezko [41]
You can solve this 2 ways: plug in all of the options or solve for x.
i going to solve for x.

given: x^2+2x=24     (subtract 24 on both sides to get make it look like x^2+x+1)

x^2+2x-24=0    (now factor x^2+2x-24 out)

<span>x^2+2x-24 --> (x-4)(x+6)
</span>
new equation: <span>(x-4)(x+6)=0   (now make them both equl zero)

new equaions:    </span>x-4=0      x+6=0    <span> (now solve for x for both)

x-4=0        x+6=0
   x=4            x=-6
your <span>answer is 4 and -6.
if you were not taught how to do what i just did then i can message you how to plug those numbers into </span></span><span> x^2+2x=24 to find the answer.</span>
5 0
4 years ago
Read 2 more answers
In a recent survey of monetary donations made by college graduates, the following information was obtained: 91 graduates had don
vodka [1.7K]

Answer: a) 11.26% and b) 50.23%

Step-by-step explanation:

Number of graduates donated to a political campaign n(A) = 91

Number of graduates donated to assist medical research n(B) = 76

Number of graduated to help preserve the environment n(C) = 131

Number of graduated donated to all n(A∩B∩C) = 27

Number of graduates donated to none = 24

Number of graduated donated to political campaign and to medical research n(A∩B) = 32

Number of graduates donated to medical research and to preserve the environment n(B∩C) = 48

Number of graduates  donated to a political campaign and to preserve the environment n(C∩A) = 56

Now,

n(U)=n(A)+n(B)+n(C)-n(A∩B)-n(B∩C) -n(C∩A)+n(A∩B∩C)+n(none)

n(U)=91+76+131-32-48-56+27+24=213

So, What percent of the college graduates donated to none of the three listed causes?

Percentage would be

\dfrac{24}{213}\times 100\\\\=11.26\%

(b) What percent of the college graduates donated to exactly one of the three listed causes?

Exactly one = 91+76+131-2(32-56-48)+3(27)=107

Percentage would be

\dfrac{107}{213}\times 100\\\\=50.23\%

Hence, a) 11.26% and b) 50.23%

4 0
3 years ago
The statement "a&gt;2 and a &lt;5" is true when a is equal to what?
iris [78.8K]

Answer:

A

Step-by-step explanation:

As 2 < a < 5, only option A suffices this condition, because 2 < 3 < 5.

6 0
3 years ago
Identify the system of equations that is not satisfied by the given ordered pair.
andreev551 [17]
Cccccccccccccccccccccccccccccccccccccccc
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3 years ago
In the app you are creating, a duck is going to fly from the coordinates (1, 3) then go 3 units right. And 6 units down. Write a
nevsk [136]

Answer:

The rule of the translation is  (x,y) ----> (x+3,y-6)

The coordinates of the duck’s final position are (4,-3)

Step-by-step explanation:

we know that

A duck is going to fly from the coordinates (1, 3) then go 3 units right. And 6 units down

That means -----> The rule of the translation is

3 units right ----> x+3

6 units down ---> y-6

so

(x,y) ----> (x+3,y-6)

To find out the the coordinates of the duck’s final position, apply the rule of the translation to the duck’s original position

so

(1,3) ------> (1+3,3-6)

(1,3) ------> (4,-3)

8 0
3 years ago
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