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3 years ago

A shelf is built on a wall, as shown below. What is the value of x?

Mathematics

1 answer:

sp2606 [1]3 years ago

8 0

Answer:

Step-by-step explanation:

Given:

A shelf is built on a wall. The angles of the triangle are given as (x + 3)°, (2x - 18)° and 90°

We need to determine the value of x.

Value of x:

By triangle sum property, the angles in a triangle always add up to 180°

Thus, we have;

Simplifying, we get;

Subtracting both sides by 75, we get;

Dividing both sides of the equation by 3, we get;

Thus, the value of x is 35.

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VERNON TOSED A COIN 20 TIMES THE RESULTS WERE8 HEADS AND 12 TAILS

Oxana [17]

Answer:

8+12=20

Step-by-step explanation:

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2 years ago

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Write the quadratic equation in standard form: x^2+x=-4x^2+16

Rainbow [258]

Answer

-3 $x^{2}$ + $x$ +16=0

Step-by-step explanation:

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3 years ago

PLEASE HELP WILL MARK AND 5 STARS I BEG OF U

jek_recluse [69]

Answer:

X=120

X=54

Step-by-step explanation:

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3 years ago

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The hypotenuse of a right angled triangle is 2√13 cm . If the smaller side is increased by 2 cm and the larger side is increased

White raven [17]

Statement:

The hypotenuse of a right angled triangle is 2√13 cm. If the smaller side is increased by 2 cm and the larger side is increased by 3 cm, the new hypotenuse will be √117 cm.

To find out:

The length of the larger side of the right angled triangle.

Solution:

Let us consider x as the smaller side and y as the larger side.

Then, in the right angled triangle,

x² + y² = (2√13)² ...(I) [By Pythagoras Theorem]

Now, if the smaller side is increased by 2 cm, then the smaller side will be (x + 2).

And if the larger side is increased by 3 cm, then the larger side will be (y + 3).

Then, in the new right angled triangle,

(x + 2)² + (y + 3)² = (√117)² [By Pythagoras Theorem]

or, x² + 2 × 2 × x + 2² + y² + 2 × 3 × y + 3² = (√117)²

or, x² + 4x + 4 + y² + 6y + 9 = (√117)²

or, x² + y² + 4x + 6y + 13 = (√117)²

Now, put the value of x² + y² from equation (I),

or, (2√13)² + 4x + 6y + 13 = (√117)²

or, (2 × 2 × √13 × √13) + 4x + 6y + 13 = (√117 × √117)

or, 52 + 4x + 6y + 13 = 117

or, 4x + 6y = 117 - 52 - 13

or, 4x + 6y = 52

or, 4x = 52 - 6y

or, x = $\frac {(52 - 6y)}{4}$ ...(II)

Now, put the value of x of equation (II) in (I),

x² + y² = (2√13)²

or, $\frac {(2704-624y +36y²)}{16}$ + y² = 52

or, $\frac {(2704-624y +36y² + 16y²)}{16}$ = 52

or, 52y²-624y + 2704 = 52 × 16

or, 52y² - 624y + 2704 - 832 = 0

or, 52y² - 624y + 1872 = 0

or, 52(y² - 12y + 36) = 0

or, y²-12y +36 = 0 ÷ 52

or, y²-12y +36 = 0

or, (y)² - 2 × 6 × y + (6)² = 0

or, (y - 6)² = 0

or, y - 6=0

or, y = 6

We have taken y as the length of the larger side of the right angled triangle.

So, the length of the larger side is 6 cm.

Answer:

6 cm

Hope you could understand.

If you have any query, feel free to ask.

6 0

2 years ago

A semicircle has an area of 76.97 squared km. Find it’s radius

shtirl [24]

Answer:

7 km

Step-by-step explanation:

Substitute:

The equation for area of a semi-circle is $\frac{r^{2}\pi }{2}$

A = $\frac{r^{2}\pi }{2}$

76.97 = $\frac{r^{2}\pi }{2}$

Multiply by 2 on both sides:

2(76.97) = ( $\frac{r^{2}\pi }{2}$ )2

153.94 = $r^{2} \pi$

Divide by pi on both sides:

153.94 = $r^{2} \pi$

/pi /pi

49.03 ≈ $r^{2}$

Find the square root:

$\sqrt{49.03} =\sqrt{r^{2} }$

7 = r

7 0

3 years ago