MATHEMATICS HIGH SCHOOL

If ABCD is a rectangle, calculate x as a function of α

Answers

Answer 1

Answer:

Answer:

x = 90 - 2α

Step-by-step explanation:

Solution:-

- Consider the right angled triangle " ABD ". The sum of angles of an triangle is always "180°".

< BAD > + < ADB > + < ABD > = 180°

< ABD > = 180 - 90° - α

< ABD > = 90° - α

- Then we look at the figure for the triangle "ABE". Where " E " is the midpoint and intersection point of two diagonals " AC and BD ".

- We name the foot of the perpendicular bisector as " F ": " BF " would be the perpendicular bisector. The angle < BAE > is equal to < ABD >.

< ABD > = < BAE > = 90° - α ... ( Isosceles triangle " BEA " )

Where, sides ( BE = AE ).

- Use the law of sum of angles in a triangle and consider the triangle " BFA " as follows:

< ABF> + < BFA > + < BAF > = 180°

< ABF > = 180 - (90° - α) - 90°

< ABF > = α

Where, < BAF > = < BAE >

- The angle < ABD > = < ABE > is comprised of two angles namely, < ABF > and < FBE > = x.

< ABD > = < ABE > = < ABF > + x

90° - α = α + x

x = 90 - 2α ... Answer

Answer 2

Answer:

Step-by-step explanation:

The length of this triangle is 10 squares

and the width is 4 squares

The diagonals divide the rectangle into four triangles

These traingles are isoceles

Each two triangles facing each others are identical

<B = 90 degree

B = alpha + Beta

Let Beta be the angle next alpha

The segment that is crossing Beta is its bisector since it perpendicular to the diagonals wich means that:

Beta = 2x

Then B = alpha + 2x

90 = alpha +2x

90-alpha = 2x

x = (90-alpha)/2

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What is the volume of a rectangular prism with a length of 812 cm, width of 913 cm and a height of 1225 cm?

Answers

812*913*1225 = 908161100cm^3
or 8.12*9.13*12.25 = 908.1611 m^3

Volume is Length X width X height. They already give you the values, so you'd multiply 812 by 913 and 1225, which would give you;

908161100

It is known that a certain function is an inverse proportion. Find the formula for this function if it is known that the function is equal to 12 when the independent variable is equal to 2.

Answers

Answer:

$y=(24)/(x)$

Step-by-step explanation:

We have been given that a certain function is an inverse proportion. We are asked to find the formula for the function if it is known that the function is equal to 12 when the independent variable is equal to 2.

We know that two inversely proportional quantities are in form $y=(k)/(x)$ , where y is inversely proportional to x and k is constant of variation.

Upon substituting $y=12$ and $x=2$ in above equation, we will get:

$12=(k)/(2)$

Let us solve for constant of variation.

$12\cdot 2=(k)/(2)\cdot 2$

$24=k$

Now, we will substitute $k=12$ in inversely proportion equation as:

$y=(24)/(x)$

Therefore, the formula for the given scenario would be $y=(24)/(x)$ .

Isolating variables abx=cy the variable is x. [please show me how)

Answers

abx = cy

We want to get rid of 'ab', and it is being multiplied to 'x', so we divide it to both sides.

x = (cy)/(ab)

$abx=cy\nx=(cy)/(ab)$

What is the y- intercept of the line 6y+12x=18
A. 18
B.-18
C.3
D.-3

Answers

The answer would be C. which is 3.

answer is sea. positive three

BRAINLIEST The price of a leather coat is $256. The store will cut this price in half each day until the price drops below $20. How much will it cost on the day the price drops below $20?

Answers

Okay, the price before was $256, then it goes down to below 20. I think the answer is $12.80, because I said 256 ÷ 20 = 12.8, which can be turned into $12.80

Brainliest if it is correct!

price drop is following this pattern

256, 128, 64, 32, 16 . . . .

so you can see 16 is the price which is less than 20 $. you can also solve it by using GP

What is the range and domain of the function : y= sqrt(x) -5 ... Can you please explain? Thanks btw the square root is only over the x

Answers

Domain of $√(x)$ - 5 : x ≥ 25 .

Range of √x - 5 : y ≥ -5 .

Given,

f(x) = √x - 5

Here,

To find the domain,

√x - 5 ≥ 0

√x ≥ 5

Squaring both sides ,

x ≥ 25 .

Thus domain of √x - 5 is x ≥ 25 .

Range of √x - 5,

To define the range of the function the value of x can not be negative as it will make the function complex .

So,

Range will be ,

y ≥ -5 .

Know more about domain and range,

brainly.com/question/30133157

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okay so basically domain =input and range =output. you can never have a negative number underneath the square root sign because it will make the answer imaginary (i), unless you are on that concept. Therefore the range is any number greater than 0. -> all real numbers greater than or = 0

for the range if you input 0 as x you will get -5, so any number you input after 0 will be greater than -5. so range is all real numbers greater than or equal to -5.