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valentina_108 [34]
3 years ago
6

Find the sum of \sqrt{4}√ ​4 ​ ​​ and 3\sqrt{9}3√ ​9 ​ ​​ in simplest form. also, determine whether the result is rational or ir

rational and explain your answer.
Mathematics
1 answer:
igomit [66]3 years ago
5 0
√​4 + <span>3√​9 = 2+3*3  = 11.

This is a rational number, since the answer can be express as a fraction (e.g., 11/1).

This does not hold for square roots in general. For example </span>√3 is irrational.
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What is 28.9-26.8 HELP ME PLEASE
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Mike can plow a field in 12 hours and his brother Phil can plow it in 15 hours. How long will it take them to plow it if they us
Korvikt [17]

Answer:

6.66 hours, that is, 6 hours and 40 minutes.

Step-by-step explanation:

If Mike can plow a field in 12 hours, we plows 1/12 of the field each hour.

If Phil can plow a field in 15 hours, we plows 1/15 of the field each hour.

So if they are working together, they can plow (1/12) + (1/15) of the field each hour, that is:

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5 0
3 years ago
Which of these points is the closest to the point (7, 1) ?
pantera1 [17]

Step-by-step explanation:

Solution

The general equation of the plane passing through (2,5,−3) is

a(x−2)+b(y−5)+c(z+3)=0 .........(1)

Now, this plane passes through B(−2,−3,5) and C(5,3,−3).Then we have

a(−2−2)+b(−3−5)+c(5+3)=0

⇒−4a−8b+8c=0

⇒−a−2b+2c=0 ..........(2)

a(5−2)+b(3−5)+c(−3+3)=0

⇒3a−2b=0 ..........(3)

Solving (2) and (3) we get

0+4

a

=

6−0

b

=

2+6

c

⇒

4

a

=

6

b

=

8

c

=λ(say)

⇒a=4λ,b=6λ,c=8λ

Substituting the values of a,b and c in (1), we get

4λ(x−2)+6λ(y−5)+8λ(z+3)=0

⇒4(x−2)+6(y−5)+8(z+3)=0

⇒4x+6y+8z−14=0

⇒2x+3y+4z−7=0

This is the equation of the plane determined by the points A(2,5,−3),B(−2,−3,5) and C(5,3,−3)

Now, the distance of this plane from the point (7,2,4) is

D=

2

2

+3

2

+4

2

∣(2×7+3×2+4×4)−7∣

=

4+9+16

∣(14+6+16)−7∣

=

4+9+16

∣36−7∣

=

29

29

=

29

29

×

29

29

=

29

units.

Thus, the distance between the point (7,2,4) and the plane 2x+3y+4z−7=0 is

29

units.

8 0
3 years ago
Angle BCA is congruent to angle DAC, and angle BAC is congruent to angle DCA by:
snow_tiger [21]
Answer is the alternate interior angles theorem
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3 years ago
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