Mathematics, 21.07.2019 16:20, hadilalhjajih

Which expressions simplify to a rational answer? select each correct answer.

Answers: 2

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Answers

answered: Spuddle4403

1. 5 (yes)
2. 4 \sqrt{3} (no)
3. 12 (yes)
4. 21 (yes)

answered: carswellml

Answer

The expression that simplify to a rational answer are:

$\sqrt{5} *\sqrt{5}$

$2\sqrt{9} *\sqrt{4}$

$7\sqrt{3} *\sqrt{3}$

Explanation

Remember that to multiply radicals/roots of the same index, we just need to multiply the radicans (the numbers inside the radical/root) and simplify. Let's simplify each of our expressions.

1. $\sqrt{5} *\sqrt{5}=\sqrt{5*5} =\sqrt{5^2} =5$

Since 5 is rational, our expression simplifies to a rational answer.

2. $\sqrt{3} *\sqrt{16} =\sqrt{3*16} =\sqrt{48}=4\sqrt{3}$

Since $4\sqrt{3}$ is irrational, our expression doesn't simplifies to a rational answer.

3. $2\sqrt{9} *\sqrt{4} =2\sqrt{9*4}=2 \sqrt{36} =2\sqrt{6^2} =2*6=12$

Since 12 is rational, our expression simplifies to a rational answer.

4. $7\sqrt{3} *\sqrt{3} =7\sqrt{3*3} =7\sqrt{3^2} =7*3=21$

Since 21 is rational, our expression simplifies to a rational answer.

answered: Guest

wholesale price is the initial price before markup. retail price comes after the markup.

a price of 8 bucks that's marked up by 100% is

formula: initial price + (percent markup in fraction/decimal)(initial price)

8+(1)(8)

8+8

retail price is $16.

answered: Guest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.