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3 years ago

Please help solve this problem

Mathematics

2 answers:

Yuri [45]3 years ago

7 0

Answer: OPTION C

Step-by-step explanation:

By definition you know that:

$\sqrt[n]{a^n}=a$

and by the exponents properties you also know that:

$a^n*a^m=a^{(n+m)}$

Now, descompose 18 into its prime factors:

18=2*3*3=2*3²

Rewrite the expression and simplify (Keep on mind that: $\sqrt{x^4}=x^{(\frac{4}{2})}=x^{2}$ ). Then, you obtain:

$\sqrt{2*3^2*x^4*y*y^2}=3x^2y\sqrt{2y}$

Licemer1 [7]3 years ago

4 0

Answer:

C. $3x^2y\sqrt{2y}$ .

Step-by-step explanation:

The given radical expression is $\sqrt{18x^4y^3}$ .

We can rewrite this radical expression to obtain;

$\sqrt{2\times9 \times (x^2)^2\times y^2\times y}$ .

This will give us;

$\sqrt{2y} \times \sqrt{9(x^2)^2 y^2}$ .

$3x^2y\sqrt{2y}$ .

The correct choice is C

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Step-by-step explanation:

Q1-5.

1. Plane parallel to WXT is ZYU.

2. Segments parallel to $\overline {VU}$ are $\overline {ZY}, \overline {WX}$ and $\overline {ST}$

3. Segments parallel to $\overline {SW}$ are $\overline {VZ}, \overline {YU}$ and $\overline {XT}$

4. Segments skew to $\overline {}$ $\overline {XY}$ are $\overline {SV}$ and $\overline {VZ}$ (not lie in the same plane and not parallel)

5. Segments skew to $\overline {}$ $\overline {VZ}$ are $\overline {WX}$ and $\overline {XT}$ (not lie in the same plane and not parallel)

Q6.

a. $\angle 4$ and $\angle 10$ are the same-side interior angles, transversal k

b. $\angle 8$ and $\angle 11$ are alternate exterior angles, transversal m

c. $\angle 1$ and $\angle 4$ do not form any pair of angles

d. $\angle 2$ and $\angle 12$ are the same-side exterior angles, transversal k

e. $\angle 5$ and $\angle 7$ are corresponding angles, transversal j

f. $\angle 2$ and $\angle 13$ are alternate interior angles, transversal l

Q7.

$m\angle 1=m\angle 7=131^{\circ}$ (as vertical angle with angle 7)

$m\angle 2=180^{\circ}-131^{\circ}=49^{\circ}$ (as supplementary angle with angle 1)

$m\angle 8=49^{\circ}$ (as vertical angle with angle 2)

$m\angle 3=m\angle 1=131^{\circ}$ (as corresponding angles when parallel lines p and q are cut by transversal r)

$m\angle 4=m\angle 2=49^{\circ}$ (as corresponding angles when parallel lines p and q are cut by transversal r)

$m\angle 5=m\angle 7=131^{\circ}$ (as corresponding angles when parallel lines p and q are cut by transversal r)

$m\angle 6=m\angle 8=49^{\circ}$ (as corresponding angles when parallel lines p and q are cut by transversal r)

$m\angle 10=m\angle 16=88^{\circ}$ (as vertical angle with angle 16)

$m\angle 9=180^{\circ}-88^{\circ}=92^{\circ}$ (as supplementary angle with angle 16)

$m\angle 15=92^{\circ}$ (as vertical angle with angle 9)

$m\angle 14=m\angle 16=88^{\circ}$ (as corresponding angles when parallel lines p and q are cut by transversal s)

$m\angle 13=m\angle 15=92^{\circ}$ (as corresponding angles when parallel lines p and q are cut by transversal s)

$m\angle 12=m\angle 10=88^{\circ}$ (as corresponding angles when parallel lines p and q are cut by transversal s)

$m\angle 11=m\angle 9=92^{\circ}$ (as corresponding angles when parallel lines p and q are cut by transversal s)

Q8.

$m\angle 7=m\angle 9=105^{\circ}$ (as vertical angles)

$m\angle 8=180^{\circ}-105^{\circ}=75^{\circ}$ (as supplementary angle with angle 9)

$m\angle 10=m\angle 8=75^{\circ}$ (as vertical angles)

$m\angle 6=m\angle 8=75^{\circ}$ (as alternate interior angles when parallel lines a and b are cut by transversal c)

$m\angle 1=180^{\circ}-75^{\circ}-63^{\circ}=42^{\circ}$ (by angle addition postulate)

$m\angle 3=180^{\circ}-42^{\circ}-63^{\circ}=75^{\circ}$ (by angle addition postulate)

$m\angle 4=m\angle 1=42^{\circ}$ (as vertical angles)

$m\angle 5=m\angle 2=63^{\circ}$ (as vertical angles)

$m\angle 11=m\angle 4=42^{\circ}$ (as alternate interior angles when parallel lines a and b are cut by transversal d)

$m\angle 12=180^{\circ}-42^{\circ}=138^{\circ}$ (as supplementary angles)

$m\angle 13=m\angle 11=42^{\circ}$ (as vertical angles)

$m\angle 14=m\angle 12=138^{\circ}$ (as vertical angles)

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