I need some help on this. Not sure how to solve.

Mathematics

1 answer:

andreyandreev [35.5K]2 years ago

5 0

Answer:

x = 9

Step-by-step explanation:

This shape is a 30-60-90 triangle, which means that the angles of the triangle are each 30°, 60° and 90°. Given that the measures of the angles of the triangle are known, as well as one side, we can find the measures of all the other sides (example attached). A 30-60-90 triangle is special because of the relationship of its sides. The hypotenuse (directly across from the 90° angle) is equal to twice the length (2x) of the shorter leg, in this case labeled 'x' and directly across from the 30° angle. The longer leg, across from the 60° angle, is equal to multiplying the shorter leg (x) by √3 or x√3.

Since the measure of the hypotenuse is given at 18, we can set the expression of that side equal to 18 and solve for x:

2x = 18 or x = 9

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Andrew is paid $4 per hour for the first 30 hours he works each week. He makes $5 per hour for each hour he works over 30 hours

klasskru [66]

Answer:

If Andrew works for 30 for $4 he will have a total wage of 30×4=$120

And gets additional $5for every hr worked beyond 30hrs in that week

So he gets a total of 5(x-30)

So if he works for 40hrs he gets a total wage of

5(40-30)=50

120+50=$170

If he works for 50 hours he gets Total wage of

5(50-30)=100

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4 0

3 years ago

The condition_______?proves that ∆ABC and ∆EFG are congruent by the SAS criterion.

snow_lady [41]

Answer:

(1) D.Angle C is congruent to to Angle F. (2) C. SSS. (3) C. cannot be congruent to.

Step-by-step explanation:

From the given figure it is noticed that

$AC=EG$

$CB=GF$

According to SAS postulate, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then both triangles are congruent.

The included angles of congruent sides are angle C and angle G.

So, condition "Angle C is congruent to to Angle F" will prove that the ∆ABC and ∆EFG are congruent by the SAS criterion.

If $AB\neq EF$

According to SSS postulate, if all three sides in one triangle are congruent to the corresponding sides in the other.

Since two corresponding sides are congruent but third sides of triangles are not congruent, therefore SSS criterion for congruence is violated.

Since two corresponding sides are congruent but third sides of triangles are not congruent, therefore the included angle of congruent sides are different.

$\angle C\neq \angle G$