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4 years ago

The questions are below:

Mathematics

1 answer:

forsale [732]4 years ago

8 0

Answer:

See below in BOLD.

Step-by-step explanation:

The first part:

Applying the Pythagoras theorem to both triangles.

The one on the left:

13^2 = 12^2 + x^2

x^2 = 169 - 144 = 25

x = 5 units.

The one on the right:

x^2 = 5^2 + 12^2 = 169

x = 13 units.

(a) So the 2 shorter sides in the triangles have the same length.

(b) The 3 sides of each triangle have the same length so they are congruent by SSS.

The Second Part.

(a) F. They could be congruent because the angles are all equal but we don't know anything about the lengths of the sides.

(b). C. Congruent. by ASA. The angles at each side of the line of length 9.2 are equal in measure.

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A rectangle with sides 12 cm and 14 cm has the same diagonal as a square.

umka2103 [35]

Answer:

$a=\sqrt{170}$

Step-by-step explanation:

Diagonal of a Square

Given a square of length side a, the length of the diagonal is

$D=\sqrt{2}a$

The diagonal of a rectangle of sides x and y is

$D=\sqrt{x^2+y^2}$

The sides have lengths 12 cm and 14 cm, the diagonal is

$D=\sqrt{12^2+14^2}$

$D=\sqrt{340}$

Since this value is the same of the diagonal of certain square, we can say

$\sqrt{2}a=\sqrt{340}$

Dividing by $\sqrt{2}$

$\boxed{a=\sqrt{170}}$

6 0

3 years ago

find three consecutive odd integers such that the sum of the first and the third equals the sum of the second and 13

andreyandreev [35.5K]

Answer: The three odd integers are 11, 13 and 15.

Step-by-step explanation: The first point to note is that the three unknown numbers are consecutive, which means they follow one after the other. Also we are told that the numbers are consecutive “odd integers.” This also means there is a two-digit interval between one number and the next. Hence, if the first number is A, the next number will be A + 2, and the third number will be A + 2 + 2 (that is, A + 4)

At this point we can now derive the following expressions based on the information we have been given, which is;

The sum of the first and third (A + {A + 4} )equals the sum of the second and 13 ({A + 2} + 13). Therefore we can write this out as follows;

A + {A + 4} = {A + 2} + 13

After removing brackets we now have

A + A + 4 = A + 2 + 13

2A + 4 = A + 15

By collecting like terms we now have

2A - A = 15 - 4

(Remember that when a positive value crosses to the other side of the equation it becomes negative, and vice versa)

2A - A = 15 - 4

A = 11

Hence, the three consecutive integers are 11, 13 and 15.

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3 years ago

Write an expression in simplest form for the area of a rectangle with length 6c meters and width 2 meters.

zloy xaker [14]

Answer:

12c square meters

Step-by-step explanation:

We know that

Area of a rectangle = length (L)× width(w)

Here it is given that length ,and width of the rectangle is 6c meters and 2 meters respectively.

Therefore, required area of the rectangle = 6c × 2 = 12c square meters.

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3 years ago

A cake recipe needs to be baked at 350 degrees Fahrenheit (°F). A pizza recipe needs to be baked at a higher temperature.

Art [367]

400 bc it
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3 years ago

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2+2=20? free coins have a good day

eimsori [14]

Answer:

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Step-by-step explanation:

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3 years ago

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