MATHEMATICS MIDDLE SCHOOL

!!!!10 points!!! The triangles shown below must be congruent.
!!!!10 points!!! The triangles shown below must be congruent. - 1

Answers

Answer 1
Answer:

Answer:

True

Step-by-step explanation:

RHS congruence proves that these two triangles are congruent.
Answer 2
Answer:

Answer:

B. False

Step-by-step explanation:

Without knowing at least one side,we cannot be sure if two triangles are congruent.

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A hospital has a large fish tank with the dimensions shown. The tank does NOT have a cover. What is the surface area of the fish tank? Math item stem image CLEAR CHECK 25 square feet 332 square feet 392 square feet 480 square feet

Answers

Answer:8300

Step-by-step explanation:

A number increase by 7 is greater than 30

Answers

Answer:

x > 23

Step-by-step explanation:

Subtract 7 on both sides in the equation: x + 7 > 30

You will get x > 23

Explain whether the shapes are similar

Answers

All 3 angles are the same, the sides are just shorter as the object has been made smaller

What is 11*1/4 for math

Answers

2.75 is the answer the your question
first, make 11 a fraction like 1/4
11 becomes 11/1
then multiply the numerators 11*1 = 11
then multiply the denominators 1*4
So, your answer would be

11/4 which simplifies to 2 3/4

Helen has 4 jogging outfits and three pairs of shoes. How many different outfits can she make?

Answers

she can wear 12 different outfits. 
She can make 12 different outfits

Which expressions are equal to a real number?

Answers

Answer:

Option B

Option C

Step-by-step explanation:

$ i = √(-1) $

⇒ $ i^2 = (√(-1))^2 = -1 $, which is a real number.

Similarly, $ i^3 = i^2.i = -1 * i = -i $

And we also know that $ i^4 = 1 $

So, we see that odd powers of $ i $ is a complex number and even powers renders us a real number.

Using this we solve the problem.

Option A:$ (-4i)^(11) $ 11 is an odd power. This would be a complex number and not a real number.

Option B:$ (-3i)^(12) $ Even power of i. So, this should give us a real number.

Option C:$ (2 + 3i)^2 $

                            (a + bi)² = a² - b² + 2abi

So, (2 + 3i)² would be a complex number because of the 2bi term.

Option D: (4 + 5i)(4 - 5i)

                         (a + ib)(a - ib) = a² + b²

So, (4 + 5i)(4 - 5i) = 4² + 5² = 41, a real number.

Option E: (6 + 8i)(8 + 6i)

                     (a + ib)(c + id) = ac - bd + (ad + bc)i

This would be a complex number because of the (ad + bc) term.

So, Options B and D are real numbers.
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