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3 years ago

How do I find angle CAE?

Mathematics

1 answer:

Tju [1.3M]3 years ago

7 0

<h3>Answer: 28 degrees</h3>

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

Explanation:

Angle DAB and angle ABC are congruent angles due to the parallel lines (note they are alternate interior angles).

So angle DAB = 47 since angle ABC = 47.

Let angle CAE be equal to x for now.

The three angles DAB, CAB, and CAE all add up and combine to form a straight angle which is 180 degrees.

We'll use this fact to find x

(angle DAB) + (angle CAB) + (angle CAE) = 180

(47) + (105) + (x) = 180

x + 152 = 180

x + 152-152 = 180-152 .... subtract 152 from both sides

x = 28

angle CAE = 28 degrees

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What is the value of the expression 12(m−23n) when m=32 and n=12 ?

Verizon [17]

are those the options? something is wrong here and I'm not sure what. I'm sorry if this is wrong, I tried my best

Answer:

-2,928

Step-by-step explanation:

12 ( 32 - [ 23 • 12 ] )

order of operations PEMDAS ( parenthesis, exponents, multiplication/division, addition/subtraction )

23 • 12 = 276

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3 years ago

The perimeters of square region S and rectangular region R are equal. If the sides of R are in the ratio 2 : 3, what is the rati

Ksivusya [100]

<h2>Answer:</h2>

The ratio of the area of region R to the area of region S is:

$\dfrac{24}{25}$

<h2>Step-by-step explanation:</h2>

The sides of R are in the ratio : 2:3

Let the length of R be: 2x

and the width of R be: 3x

i.e. The perimeter of R is given by:

$Perimeter\ of\ R=2(2x+3x)$

( Since, the perimeter of a rectangle with length L and breadth or width B is given by:

$Perimeter=2(L+B)$ )

Hence, we get:

$Perimeter\ of\ R=2(5x)$

i.e.

$Perimeter\ of\ R=10x$

Also, let " s " denote the side of the square region.

We know that the perimeter of a square with side " s " is given by:

$\text{Perimeter\ of\ square}=4s$

Now, it is given that:

The perimeters of square region S and rectangular region R are equal.

i.e.

$4s=10x\\\\i.e.\\\\s=\dfrac{10x}{4}\\\\s=\dfrac{5x}{2}$

Now, we know that the area of a square is given by:

$\text{Area\ of\ square}=s^2$

and

$\text{Area\ of\ Rectangle}=L\times B$

Hence, we get:

$\text{Area\ of\ square}=(\dfrac{5x}{2})^2=\dfrac{25x^2}{4}$

and

$\text{Area\ of\ Rectangle}=2x\times 3x$

i.e.

$\text{Area\ of\ Rectangle}=6x^2$

Hence,

Ratio of the area of region R to the area of region S is:

$=\dfrac{6x^2}{\dfrac{25x^2}{4}}\\\\=\dfrac{6x^2\times 4}{25x^2}\\\\=\dfrac{24}{25}$

6 0

3 years ago

Read 2 more answers

Does anyone know how to solve this?

masya89 [10]

Answer:

b = -125/9

Step-by-step explanation:

1 + log5 ( -9b) = 4

Subtract 1 from each side

1 -1+ log5 ( -9b) = 4-1

log5 ( -9b) = 3

Raise each side to the base 5

5^ log5 ( -9b) = 5^3

This will cancel the log5

-9b = 125

Divide each side by 9

-9b/-9 = 125/-9

b = -125/9

3 0

3 years ago

Point K is rotated 90°. The coordinate of the pre-image point K was (2, –6) and its image K’ is at the coordinate (−6, −2). Find

umka21 [38]

Answer:

Hello! The answer to your question will be below.

Step-by-step explanation:

The answer would be clockwise.

So point k was rotated 90 degrees clockwise.....

Review.....

Question:

Point K is rotated 90 degrees. The coordinate of the pre-image point K was (2,-6) and it’s image K’ is at the coordinate (-6,-2).Find the direction of the rotation.

THE DIRECTION OF THE ROTATION WAS CLOCKWISE.

Hope this helps! :)

⭐️Have a wonderful day!⭐️

8 0

3 years ago

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kozerog [31]

A is the answer. Hope this helps!

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3 years ago

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