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2 years ago

Please help me with this

Mathematics

1 answer:

N76 [4]2 years ago

4 0

Answer:

ASA

Step-by-step explanation:

One pair of corresponding angles (in the bottom left/right) are already marked for us, and we're also given a pair of corresponding sides (the 8cm ones on the left and right). The two triangles have one more angle in common too - the one they're overlapping on the top corner. So, we have:

- Two pairs of congruent corresponding angles, and

- A pair of congruent corresponding sides between them,

which is enough information to call the triangles congruent by Angle-Side-Angle (ASA).

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Please help thanks!

Kryger [21]

Answer:

All except irrational-

Step-by-step explanation:

100/100 is 1. This makes it real, an integer, whole,natural, and rational.

4 0

3 years ago

Input in stand form the equation of the given line.

Daniel [21]

Answer:

3x +8y = -17

Step-by-step explanation:

The point-slope equation is a good place to start.

y -k = m(x -h) . . . . . equation through (h, k) with slope m

Filling in your numbers gives ...

y +4 = -3/8(x -5)

Multiplying by 8, we get

8y + 32 = -3x + 15

Adding 3x-32 puts this in standard form.

3x + 8y = -17

_____

Standard form is ...

ax +by = c

where a, b, c are mutually-prime integers and the leading coefficient is positive. (If a=0, the leading coefficient is b.)

8 0

3 years ago

Find the area of these two rectangles, show your work.

ratelena [41]

Answer:

1. 4.5

Step-by-step explanation:

3 x 1.5 = 3 x 1 1/5 = 4.5

3 0

2 years ago

a. Determine all bijections from the {1,2,3} into {a,b,c}. b. Determine all bijections from {1, 2, 3} into {a,b,c,d}.

avanturin [10]

Part A

There are 6 bijections from {1,2,3} to {a,b,c}. This is effectively the same as asking the question "how many ways are there to arrange {a,b,c} where order matters?" We use a factorial to answer this question.

3 factorial = 3! = 3*2*1 = 6

You can also use a permutation, which is composed of factorials, to get the same answer.

======================================================

Part B

There are no bijections from {1,2,3} to {a,b,c,d}. Why is this? Because a bijection has two properties: it must be one-to-one, and it must be onto. The term "onto" in mathematics means "every value in the range is targeted". In the case of the range {a,b,c,d} it is not possible for each value to show up. This is because there are only three items in the domain {1,2,3}. You'll always be one letter short.

As you can probably guess, a bijection is only possible if and only if n(D) = n(R), where D and R are the domain and range respectively. The notation n(D) represents the count or number of items in set D.

3 0

3 years ago

Twice the sum of a number and 3 is equal to three times the difference of the number and 7. Find the number

Agata [3.3K]

Answer:

The number is 27

Step-by-step explanation:

Let us change the word statement to an algebraic equation

→ Assume that the number is x

→ Twice the sum of a number and 3, means add x by 3, then multiply the sum by 2

→ The algebraic expression is 2(x + 3)

→ Three times the difference of the number and 7, means subtract x and 7, then multiply the difference by 3

→ The algebraic expression is 3(x - 7)

→ Equate the two expressions

∴ 2(x + 3) = 3(x - 7)

→ Simplify each side

∵ 2(x + 3) = 2(x) + 2(3) = 2x + 6

∵ 3(x - 7) = 3(x) - 3(7) = 3x - 21

∴ 2x + 6 = 3x - 21

Let us solve the equation to find x

→ Subtract 6 from both sides

∴ 2x + 6 - 6 = 3x -21 - 6

∴ 2x = 3x - 21

→ Subtract 3x from both sides

∴ 2x - 3x = 3x - 3x - 27

∴ -x = -27

→ Divide both sides by -1

∴ x = 27

The number is 27

6 0

3 years ago