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Dovator [93]
3 years ago
11

Scott sets up a volleyball net in his backyard. One of the poles, which forms a right angle with the ground, is 12 feet high. To

secure the pole, he attached a rope from the top of the pole to a stake 10 feet from the bottom of the pole. Find the length of the rope, rounded to the nearest tenth.

Mathematics
1 answer:
Assoli18 [71]3 years ago
6 0

Answer:

Length of the rope = 15.6 ft.

Step-by-step explanation:

Given:

Height of the pole from the ground = 12 ft

Adjacent distance from the pole = 10 ft

We have to find the length of the rope attached by Scott to secure the pole.

According to the question :

In forma  right angled triangle as shown in the figure.

We have to find the measure of the hypotenuse.

Length of rope = Hypotenuse measure

Let the length of the rope = "h" ft

Using Pythagoras formula.

⇒ (hypotenuse)=\sqrt{opposite^2+ adjacent^2}

⇒ Plugging the values.

⇒ h=\sqrt{12^2 + 10^2}

⇒ h=\sqrt{144 + 100}

⇒ h=\sqrt{244}

⇒ h=15.62 ft

The length of the rope, rounded to the nearest tenth is 15.6 ft.

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Answer:

Point R is at (−20, 10), a distance of 30 units from point Q

Step-by-step explanation:

Q has coordinates (-20,-20).

P has coordinates (10,-20)

Since point R is vertically above point Q, it will have the same x-coordinate as Q.

Let R have coordinates (-20,y).

It was given that;

|RQ|=|PQ|

\Rightarrow |y--20|=|10--20|

\Rightarrow y+20=10+20

\Rightarrow y=10+20-20

\Rightarrow y=10.

The coordinates of R are (-20,10).

The dstance from Q is 30 units.

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2 years ago
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Answer:

Step-by-step explanation:

9) PQR Is an isosceles triangle

=> ∠PRQ = (180° - x)/2

PRS is an isosceles right triangle

=> ∠PRS = 45°

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=> \frac{180-x}{2}+45=115 \\

=> 180 - x = (115 - 45).2 = 140

<=> x = 180 - 140 = 40

10) ABD is an isosceles right triangle => ∠ABD = 45°

BCD is an equilateral triangle => ∠CBD = 60°

have: x = ∠ABD + ∠CBD = 45° + 60° = 105°

11) have: x = y (2)

PQT is an isosceles triangle => ∠PQT = 180 - 70.2 = 40

QTS   is an isosceles triangle => ∠TQS = 180 -2x

QRS   is an isosceles triangle => ∠RSQ = y

have: 40 + 180 - 2x + y = 180 => 2x - y = 40 (1)

(1)(2) => \left \{ {{y=x} \atop {2x-y=40}} \right.\\\\=> \left \{ {{x=40} \atop {y=40}} \right.

=> x + y = 80

12) EFJ Is an equilateral  triangle => ∠FJE = 60

∠FJE is the outer angle of the triangle FHJ but FHJ is an isosceles triangle

=> 60 = 2.∠JHF => ∠JHF = 30°

∠JHF is the outer angle of the triangle FHG

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2 years ago
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Answer:

972 x^16 y^24

Step-by-step explanation:

Simplify the following:

(-2 x^3 y^7)^2 (3 x^2 y^2)^5

Multiply each exponent in -2 x^3 y^7 by 2:

(-2)^2 x^(2×3) y^(2×7) (3 x^2 y^2)^5

2×7 = 14:

(-2)^2 x^(2×3) y^14 (3 x^2 y^2)^5

2×3 = 6:

(-2)^2 x^6 y^14 (3 x^2 y^2)^5

(-2)^2 = 4:

4 x^6 y^14 (3 x^2 y^2)^5

Multiply each exponent in 3 x^2 y^2 by 5:

4 x^6 y^14×3^5 x^(5×2) y^(5×2)

5×2 = 10:

4×3^5 x^6 y^14 x^(5×2) y^10

5×2 = 10:

4×3^5 x^6 y^14 x^10 y^10

3^5 = 3×3^4 = 3 (3^2)^2:

4×3 (3^2)^2 x^6 y^14 x^10 y^10

3^2 = 9:

4×3×9^2 x^6 y^14 x^10 y^10

9^2 = 81:

4×3×81 x^6 y^14 x^10 y^10

3×81 = 243:

4×243 x^6 y^14 x^10 y^10

4 x^6 y^14×243 x^10 y^10 = 4 x^(6 + 10) y^(14 + 10)×243:

4×243 x^(6 + 10) y^(14 + 10)

14 + 10 = 24:

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6 + 10 = 16:

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4×243 = 972:

Answer: 972 x^16 y^24

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