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3 years ago

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A girl starts to walk to her school, which is 20 miles away, at 6:50 and at a rate of 3 miles per hour. After a while, her dad p

icks her up and drives her through the remainder of the way at 30 miles per hour. If they arrived at school at 9:00, how far did she walk?

2 answers:

harina [27]3 years ago

7 0

Answer:

She walked 5 mi

Alinara [238K]3 years ago

4 0

The girl walked 5 miles.

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2 years ago

Order from least to greatest 0.6 4/5 0.75

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Because the majority is in decimal form, you'll have to change the fraction to a decimal too so that it would be easier to solve this problem. 4/5 in decimal form is 0.8

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2 years ago

raj and his sister zia are both at secondary school. Raj is three years older than zia. the sum of the squares of their ages is

steposvetlana [31]

Let's assume

Raj's age is x years

Zia's age is y years

we are given

Raj is three years older than zia

so, we get

$x=y+3$

now, we can solve for y

$y=x-3$

the sum of the squares of their ages is 369

so, we get

$x^2+y^2=369$

now, we can plug back y

$x^2+(x-3)^2=369$

now, we can solve for x

$2x^2-6x+9=369$

$2x^2-6x-360=0$

$x^2-3x-180=0$

$(x+12)(x-15)=0$

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Since, age can not be negative

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3 years ago

Equilateral triangle ABC has an area of \sqrt{3}√ 3 . If the shaded region has an area of \piπK − \sqrt{3}√ 3 , what

Liono4ka [1.6K]

Answer:

The value of k = 4/3

Step-by-step explanation:

* Lets explain how to solve the problem

- An equilateral triangle ABC is inscribed in a circle N

- The area of the triangle is √3

- The shaded area is the difference between the area of the circle

and the area of the equilateral triangle ABC

- The shaded are = k π - √3

- We need to find the value of k

* <u><em>At first lets find the length of the side of the Δ ABC</em></u>

∵ Δ ABC is an equilateral triangle

∴ Its area = √3/4 s² , where s is the length of its sides

∵ The area of the triangle = √3

∴ √3/4 s² = √3

- divide both sides by √3

∴ 1/4 s² = 1

- Multiply both sides by 4

∴ s² = 4 ⇒ take √ for both sides

∴ s = 2

∴ The length of the side of the equilateral triangle is 2

* <u><em>Now lets find the radius of the circle</em></u>

- In the triangle whose vertices are A , B and N the center of the circle

∵ AN and BN are radii

∴ AN = BN = r , where r is the radius of the circle

∵ The sides of the equilateral angles divides the circle into 3 equal

arcs in measure where each arc has measure 360°/3 = 120°

∵ The measure of the central angle in a circle equal the measure

of the its subtended arc arc

∵ ∠ANB is an central angle subtended by arc AB

∵ The measure of arc AB is 120°

∴ m∠ANB = 120°

- By using the cosine rule in Δ ANB

∵ AB = 2 , AN = BN = r , m∠ANB = 120°

∴ $(2)^{2}=r^{2}+r^{2}-2(r)(r)cos(120)$

∴ $4=r^{2}+r^{2}-2(r)(r)(-0.5)$

∴ $4=r^{2}+r^{2}-(-r^{2})$

∴ $4=r^{2}+r^{2}+r^{2}$

∴ $4=3r^{2}$

- Divide both sides by 3

∴ $r^{2}=\frac{4}{3}$

- Take square root for both sides

∴ r = 2/√3

* <u><em>Lets find the value of k</em></u>

∵ Area circle = πr²

∵ r = 2/√3

∴ Area circle = π(2/√3)² = (4/3)π

∵ Area shaded = area circle - area triangle

∵ Area triangle = √3

∴ Area shaded = (4/3) π - √3

∵ Area of the shaded part is π k - √3

- Equate the two expressions

∴ π k - √3 = (4/3) π - √3

∴ k = 4/3

* The value of k = 4/3

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2 years ago

I need help thank you

balandron [24]

Answer:

Question 4 is B

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2 years ago