Help please! i need get answers to 3 and 4 :)

Solve for x in the diagram below.

Zielflug [23.3K]

Answer:

3x+45=180

3x=180-45

3x=135

x=45

Step-by-step explanation:

8 0

3 years ago

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A 9.85 m ladder is placed against a wall. The height to the top of the ladder is 5 m more than the distance between the wall and

Dafna1 [17]

Given:

Length of the ladder = 9.85 m

The height to the top of the ladder is 5 m more than the distance between the wall and the foot of the ladder.

To find:

The height to the top and the distance between the wall and the foot of the ladder.

Solution:

let x be the distance between the wall and the foot of the ladder. Then the height to the top of the ladder is (x+5).

Pythagoras theorem: In a right angle triangle,

$Hypotenuse^2=Base^2+Perpendicular^2$

In the given situation, hypotenuse is the length of ladder, i.e., 9.85 m. The base is x m and the height is (x+5) m.

Using the Pythagoras theorem, we get

$(9.85)^2=x^2+(x+5)^2$

$97.0225=x^2+x^2+10x+25$

$0=2x^2+10x+25-97.0225$

$0=2x^2+10x-72.0225$

Here, $a=2, b=10,c=-72.0225$ . Using the quadratic formula, we get

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\dfrac{-10\pm \sqrt{(10)^2-4(2)(-72.0225)}}{2(2)}$

$x=\dfrac{-10\pm \sqrt{676.18}}{4}$

Approximating the value, we get

$x=\dfrac{-10\pm 26}{4}$

$x=\dfrac{-10+26}{4},\dfrac{-10-26}{4}$

$x=\dfrac{16}{4},\dfrac{-36}{4}$

$x=4,-9$

Distance cannot be negative so $x\neq -9.$

Now we have $x=4$

$x+5=4+5$

$x+5=9$

Therefore, the base is 4 m and the height is 9 m.

5 0

3 years ago

Which is closest to the value of w in the triangle below?

mr Goodwill [35]

Answer: B. 2.5 in

Step-by-step explanation:

From the given right angle triangle,

the hypotenuse of the right angle triangle is the unknown side.

With m∠32 as the reference angle,

the adjacent side of the right angle triangle is 4 in

the opposite side of the right angle triangle is w

To determine w, we would apply

the tangent trigonometric ratio which is expressed as

Tan θ = opposite side/adjacent side. Therefore,

Tan 32 = w/4

w = 4tan32 = 4 × 0.625

w = 2.5 in

8 0

3 years ago

Rachel earned $85.25 for working 6 1 4 hours. How much does Rachel earn per hour?

GaryK [48]

Answer:

Rachel earns per hour is $ 13.64 .

Step-by-step explanation:

As given

Rachel earned $85.25 for working $6 \frac{1}{4}$ hours.

i.e

Rachel earned $85.25 for working $\frac{25}{4}$ hours.

Now calculate earning of Rachel for 1 hour .

$Rachel\ earning\ for\ one\ hour = \frac{Total\ earning}{Total\ time}$

$Rachel\ earning\ for\ one\ hour = \frac{85.25}{\frac{25}{4}}$

$Rachel\ earning\ for\ one\ hour = \frac{85.25\times 4}{25}$

$Rachel\ earning\ for\ one\ hour = \frac{341}{25}$

$Rachel\ earning\ for\ one\ hour = \$ 13.64$

Therefore Rachel earns per hour is $ 13.64 .

7 0

3 years ago

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Chase has been playing a game where he can create towns and help his empire expand. Each town he has allows him to create 1.13 t

riadik2000 [5.3K]

Well the way I see it is he started with 4 villager so I would see the equation to be

1.13x times 17+4 would equal the amount of villagers he could have which would be 23.21 as for the equation it would be 1.13x times 17 plus four equals the number of villagers total

7 0

3 years ago