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3 years ago

ADHE - ADGF below. Find the value of 'x'. X H н E 8 2. 12

Mathematics

1 answer:

Vlad1618 [11]3 years ago

8 0

Given:

$\Delta DHE\sim \Delta DGF$

To find:

The value of x.

Solution:

We know that, corresponding sides of similar triangles are proportional.

Since, $\Delta DHE\sim \Delta DGF$ , therefore

$\dfrac{HE}{GF}=\dfrac{DE}{DF}$

On substituting the values from the figure, we get

$\dfrac{8}{12}=\dfrac{x}{x+2}$

$\dfrac{2}{3}=\dfrac{x}{x+2}$

On cross multiplication, we get

$2(x+2)=3x$

$2x+4=3x$

$4=3x-2x$

$4=x$

Therefore, the value of x is 4.

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X = ? y = ? 16 45 degrees

mezya [45]

Let's put more details in the figure to better understand the problem:

Let's first recall the three main trigonometric functions:

$\text{ Sine }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Hypotenuse}}$ $\text{ Cosine }\theta\text{ = }\frac{\text{ Adjacent Side}}{\text{ Hypotenuse}}$ $\text{ Tangent }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Adjacent Side}}$

For x, we will be using the Cosine Function:

$\text{ Cosine }\theta\text{ = }\frac{\text{ Adjacent Side}}{\text{ Hypotenuse}}$ $Cosine(45^{\circ})\text{ = }\frac{\text{ x}}{\text{ 1}6}$ $(16)Cosine(45^{\circ})\text{ = x}$ $(16)(\frac{1}{\sqrt[]{2}})\text{ = x}$ $\text{ }\frac{16}{\sqrt[]{2}}\text{ x }\frac{\sqrt[]{2}}{\sqrt[]{2}}\text{ = }\frac{16\sqrt[]{2}}{2}$ $\text{ 8}\sqrt[]{2}\text{ = x}$

Therefore, x = 8√2.

For y, we will be using the Sine Function.

$\text{ Sine }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Hypotenuse}}$ $\text{ Sine }(45^{\circ})\text{ = }\frac{\text{ y}}{\text{ 1}6}$ $\text{ (16)Sine }(45^{\circ})\text{ = y}$ $\text{ (16)(}\frac{1}{\sqrt[]{2}})\text{ = y}$ $\text{ }\frac{16}{\sqrt[]{2}}\text{ x }\frac{\sqrt[]{2}}{\sqrt[]{2}}\text{ = }\frac{16\sqrt[]{2}}{2}$ $\text{ 8}\sqrt[]{2}\text{ = y}$

Therefore, y = 8√2.

5 0

1 year ago

The numerator of the given fraction is 4 less than the denominator. If 5 is added to both numerator and denominator, the resulti

Sholpan [36]

Answer:

5/9

Step-by-step explanation:

Let the denominator be x and numerator be y.

Given, numerator is 4 less than denominator

=> y = x - 4 ...(1)

When 5 is added to both:

Numerator = y + 5 , and, denominator = x + 5

Now their ratio is 5/7.

=> (y + 5)/(x + 5) = 5/7

=> 7(y + 5) = 5(x + 5)

=> 7y + 35 = 5x + 25

=> 7y - 5x = 25 - 35

=> 7(x - 4) - 5x = -10 {y=x-4}

=> 7x - 28 - 5x = -10

=> 2x = 18

=> x = 9

Thus,

Fraction is y/x = (x-4)/x = (9-4)/9 = 5/9

4 0

3 years ago

2nd question this is still confusing even after getting the formula

Nana76 [90]

Check the picture below.

so the figure is really just 3 rectangles and two triangles.

simply get the area of all 5, sum them up, and that's the area of the figure.

recall that area of a triangle A = ½bh.

3 0

3 years ago

What is the point of intersection of the x-axis and the y-axis called

tester [92]

That is called the Origin , where the number 0 is.

6 0

3 years ago

Read 2 more answers

What’s the Value of x?

denpristay [2]

X will be 8.49
the other side is 6 too

6 0

3 years ago