Are the two triangles similar? How do you know?

Mathematics

1 answer:

Bess [88]3 years ago

7 0

There are several conditions where triangles can be proved similar:

AA - where two of the angles are same.

SAS - where two sides of a triangle compare to the corresponding sides in the other are in same proportion, and the angle in the middle are equal.

SSS - Where all sides in a triangle and the corresponding sides are in the same proportion.

In the case above, we can only use the method of SAS, as only two sides of the triangles are given.

<HMG = <JMK (vertically opposite angles)

HM/MK = 8/12 = 2/3

GM/MJ = 6/9 = 2/3

As the two sides of a triangle comparing to the corresponding sides in the other are in same proportion, and the angle in the middle are equal, the above triangles are similar, with the prove of SAS.

Therefore, the answer is C.yes by SAS.

Hope it helps!

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Carmen has a $350 gift card to spent at Modell's. She wants to buy 2 pairs of sneakers that cost $100 each. She wants to find th

tatyana61 [14]

Answer:

The inequality is $200 + x*$8≤ $350

Step-by-step explanation:

An inequality is an inequality between letters (unknowns) and numbers related by arithmetic operations. Its solution set is the set of real numbers that satisfy it. In other words, an algebraic inequality in which its members are linked by the signs <(less than), ≤ (less than or equal to),> (greater than) or ≥ (greater than or equal to) is called an inequality.

Solving an inequality is to find the values of the unknown for which the inequality holds. The solution of an inequality is an interval or a union of intervals of real numbers.

In this case, you know that Carmen wants to buy 2 pairs of sneakers that cost $ 100 each.So the 2 pairs of sneakers will cost Carmen:

2 * $ 100 = $ 200

On the other hand, Carmen wants to find the possible amount of socks that she can buy, knowing that a pair costs $ 8. Being x the amount of socks that she can buy, then Carmen spends on socks:

x*$8

Knowing that Carmen has a $ 350 gift card to spend at Modell's, then what she spent on sneakers and socks cannot be more than $ 350. That is to say, the sum of what was spent on sneakers and socks must be less than or equal to $ 350, because Carmen cannot spend more than she has. This is expressed by the following inequality:

Solving for x:

x*$8 ≤ $350 - $200

x*$8≤ $150

x≤ $\frac{150}{8}$