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4 years ago

Which expressions simplify to a rational number? Select each correct answer

Mathematics

2 answers:

Westkost [7]4 years ago

6 0

a rational number is a number that can be written in form a/b where a and b are integers (integers are like -5,-4,-3,-2,-1,0,1,2,3,4, etc)

remember that (√a)(√b)=√(ab)

and √(a^2)=a

do each

√3 · √16=√3·√(4^2)=√3·4=4√3 which is irrational

2√9·√4=2√(3^2)·√(2^2)=2(3)·2=6·2=12 which is rational

7√3·√3=7√(3·3)=7√(3^2)=7(3)=21 which is rational

√5·√5=√(5·5)=√(5^2)=5 which is rational

rational expressions:

2√9·√4

7√3·√4

√5·√5

Nataly [62]4 years ago

3 0

sqrt (3) * sqrt(16) = 4sqrt(3) = irrational

2sqrt(9) *sqrt(4) = 6*2 = 12 rational

7 sqrt(3)* sqrt(3) = 7*3 =21 rational

sqrt(5) * sqrt(5) = 5 rational

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Dafna11 [192]

The answer would be D. This is because the perimeter of the first one 6+6=12 and 9+9=18 then add those together to get 30. Now we have the first perimeter you take 30 then subtract 3 twice to get 24. Now take 24 and divide it by 2 to get the length which is 12 aka D

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2 years ago

1. A MAP SCALE READS 1CM:5KM. IF A DISTANCE ON THE MAP MEASURES 7CM, THE ACTUAL DISTANCE WILL BE?. 2. A SCHOOL DINING HALL IS 35

Agata [3.3K]

Answer:

1. 35 km

2. 1 cm to 5m

3. 6 cm

4. $42^\circ$

5. 16.73 m

Step-by-step explanation:

Solution 1.

Reading of map scale = 1cm:5km

i.e. 1 cm is equivalent to 5 km

Measurement of map = 7 cm

Actual distance = Measurement of map $\times 5$

Actual distance = 7 $\times 5$ = 35 km

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Solution 2.

Length of dining hall = 35 m

Measurement of map = 7 cm

Scale = Measurement of map : Length of dining hall (i.e. ratio)

Scale = 7 cm :35 m = 1 cm : 5 m

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Solution 3.

Length of building = 30 m

Scale = 1 cm to 5m

5 m is equivalent to 1 cm on scale

1 m is equivalent to $\frac{1}{5}$ cm on scale

30m is equivalent to $\frac{1}{5} \times 30$ = 6 cm on scale

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Solution 4.

Angle of elevation of A from B = $42^\circ$

Angle of depression of B from A = ?

Please refer to the image attached, we can clearly observe that both the angles (i.e. angle of elevation from A to B and angle of depression from B to A )will be equal.

Angle of depression of B from A = $42^\circ$

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

Solution 5.

Given that:

String length, or hypotenuse of triangle BC= 25 m

Angle of string with horizontal, $\angle B = 42^\circ$