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3 years ago

9

Use Special Triangle Shortcuts to find the values of x and y in the first figure. Explain how you determined the length of segme

nts x and y using 2-3 sentences or explain your steps used to find the values.

1 answer:

ivann1987 [24]3 years ago

7 0

Answer:

Solution given:

short cut to find x

Tan 30°=P/B

Tan30°=x/22√3

x=tan 30×22√3

x=22

and

for y

cos 30=B/H

cos30×y=22√3

y=22√3/cos30

y=44

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A rectangle has a length of 34 inches less than 5 times it’s width. If the area of the rectangle is 867 square inches, find the

pshichka [43]

Length of the rectangle is 51 inches

<u>Solution:</u>

Given that

Length of the rectangle in 34 miles less than 5 times its width

Area of rectangle = 867 square inches

Need to determine length of the rectangle.

Let assume width of the rectangle be represented by variable x.

So 5 times width of the rectangle =5x

34 inches less than 5 times width of the rectangle = 5x – 34

As Length of the rectangle in 34 miles less than 5 times its width

=> Length of the rectangle = 5x – 34

<em><u>The formula for rectangle is given as:</u></em>

$\text { area of rectangle }=length \times width$

As given that Area of rectangle = 867 square inches

$\begin{array}{l}{=>867=(5 x-34) \times(x)} \\\\ {=>5 x^{2}-34 x-867=0}\end{array}$

On solving quadratic equation by using quadratic formula

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

In our case a = 5, b = -34 and c = -867

On substituting value of a, b and c in quadratic formula we get

$\begin{array}{l}{x=\frac{-(-34) \pm \sqrt{(-34)^{2}-4 \times 5 \times(-867)}}{2 \times 5}} \\\\ {=>x=\frac{34 \pm \sqrt{18496}}{10}=\frac{34+136}{10}} \\\\ {=>x=\frac{34+136}{10}=17 \text { or } x=\frac{34-136}{10}=-10.2}\end{array}$

Since x represents width, it cannot be negative, so x = 17

Length of the rectangle = 5x – 34 = 5(17) – 34 = 51

Hence length of the rectangle is 51 inches

5 0

3 years ago

What is 1.10 fraction of 6000

katrin2010 [14]

In my calculation is divide it 0.00018333333
and if multiply it well be 6600

5 0

3 years ago

AfilCa [17]

Answer:

a.) P(HH|C)=2/5

Explanation:

Given following:

P(HH) = 7

P(C) = 10

P(HH ∩ C) = 4

P(HH ∪ C) = 13

Solving steps:

$\sf P(HH|C) = \dfrac{P(HH \cap C) }{P(C)}$

$\sf P(HH|C) = \dfrac{4 }{10}$

$\sf P(HH|C) = \dfrac{2 }{5}$

8 0

1 year ago

Find the equation of the line that is perpendicular to the line 4x+2y=1 and passes through the point (-4,3)

serious [3.7K]

First find the slope of the given line:

4x +2y = 1

Subtract 4x from each side:

2y = -4x + 1

Divide both sides by 2:

y = -2x +1/2

The slope is -2.

Now use the slope to find the y-intercept. Because the line is perpendicular, you need to use the negative inverse of the slope.

The negative inverse of -2 is 1/2

Now using the point-slope form y - y1 = m(x-x1)

Use the inverse slope for m, and the given point(-4,3) to get:

y - 3 = 1/2(x+4)

Simplify:

y - 3 = x/2 +2

Add 3 to each side:

y = x/2 + 5

Reorder the terms to get y = 1/2x +5

The answer is D.

5 0

3 years ago

Si un rectángulo con perímetro de 74 pulgadas tiene un largo de 5 pies más que el ancho,

baherus [9]

Perímetro del rectángulo = 74 pulgadas

Deje que el ancho del rectángulo sea 'x'.

Entonces, la longitud de este rectángulo = x + 5

We know that :

$\color{hotpink}\tt \: Perímetro \: del \: rectángulo =\color{plum} 2 × (l + b)$

Lo que significa :

$=\tt 2(x + x + 5) = 74$

$=\tt 2(2x + 5) = 74$

$=\tt 4x +10 = 74$

$=\tt 4x = 74 - 10$

$=\tt 4x = 64$

$=\tt x = \frac{64}{4}$

$\color{plum} =\tt x = 16$

Por lo tanto, el ancho de este rectángulo = 16 pulgadas

Entonces, la longitud de este rectángulo :

$=\tt x + 5$

$= \tt16 + 5$

$\color{plum} =\tt 21 \: pulgadas$

La longitud de este rectángulo = 21 pulgadas

<h2>Por lo tanto :</h2>

● Longitud del rectángulo = <em>21 pulgadas</em>

● Ancho del rectángulo = <em>16 pulgadas</em>

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2 years ago