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3 years ago

Please help

Mathematics

1 answer:

ElenaW [278]3 years ago

5 0

Answer: 3.61km or √13

Step-by-step explanation:

Given Data:

Sides of hexagon = 2km each

Distance walked by Ama = 5km

Therefore;

Let Ama starting position be the origin.

With this She would travel along two edges and then go halfway along a third.

Her new x- coordinate would be

= 1 + 2 + 1/2 = 7/2

Because she travels a distance of 5km which translates to 2 and half side of the Hexagon

= 2*1/2

= 1km. On her x-coordinates

For her y-coordinate we use same principles as x-coordinates

= √3 + 0 - √3/2

= √3/2

Therefore her distance walked

= √ ( (7/2)^2 + (√ 3/2)^2 )

= √ ( 49/4 + 3/4 )

= √ 13

= 3.61km

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In yoga class, all of the students are lined up according to height. Andy notices that the number of students who are taller tha

hichkok12 [17]

Answer:

The number of students in the class is 21

Step-by-step explanation:

The first thing to consider is Andy.

Let x be the number of students who are taller than Andy.

Then the number of the rest students, excluding Andy, is 4x, according to the condition.

So, the total number of students in the class is (x + 4x + 1), or 5x+1.

Next, consider Violetta.

Let y be the number of students who are shorter than Violetta.

Then the number of the rest students, excluding her, is 3y, according to the condition.

So, the total number of students in the class is (y + 3y + 1), or 4y+1.

We see, that the number of students in the class MINUS one is a multiple of 4 (four) and of 5 (five), at the same time.

So, the number of students in the class is EITHER 20+1 = 21 OR 40+1 = 41, if consider couple of minimal values.

But 41 is excluded by the condition, leaving a UNIQUE ANSWER:

The number of students in the class is 21.

6 0

3 years ago

Please help me with these questions

Mars2501 [29]

Slope of a Line Passing through two points (x₁ , y₁) and (x₂ , y₂) is given by :

$\spadesuit\; Slope(m) = \frac{y_1 - y_2}{x_1 - x_2}$

Given Points are (8 , 30) and (18 , 60)

here x₁ = 8 and x₂ = 18 and y₁ = 30 and y₂ = 60

$\spadesuit\; Slope(m) = \frac{30 - 60}{8 - 18} = \frac{-30}{-10} = 3$

We know that the form of line passing through point (x₀ , y₀) and having slope m is : y - y₀ = m(x - x₀)

Here the line passes through the point (8 , 30)

⇒ x₀ = 8 and y₀ = 30

We found Slope(m) = 3

Substituting all the values in the standard form, We get :

Equation of the line : y - 30 = 3(x - 8)

Let d be the x-intercept of this line

⇒ The line passes through the point (d , 0) as at x-intercept, y-coordinate is zero.

⇒ 0 - 30 = 3(d - 8)

⇒ 3d - 24 = -30

⇒ 3d = -30 + 24

⇒ 3d = -6

⇒ d = -2

⇒ The x - coordinate of the x-intercept of the line is -2

6 0

4 years ago

2x+5y=12

anastassius [24]

Y = -3x - 1......so we sub in -3x - 1 in for y in the other equation

2x + 5y = 12
2x + 5(-3x - 1) = 12....now distribute the 5 through the parenthesis
2x - 15x - 5 = 12...add 5 to both sides
2x - 15x = 12 + 5..combine like terms
-13x = 17...divide both sides by -13
x = -17/13
now sub in -17/13 for x in the other equation
y = -3x - 1
y = -3(-17/13) - 1
y = 51/13 - 1
y = 51/13 - 13/13
y = 38/13

so the solution is (-17/13, 38/13)

8 0

3 years ago

1/4 times the sum of a number and −3.2 is 1.8. What is the number?

joja [24]

Answer:

10.4

Step-by-step explanation:

Let the number be x

Sum of x and -3.2 : x + (-3.2) = x - 3.2

1/4 times the sum of a number and −3.2 = (1/4) * (x - 3.2)

$\dfrac{1}{4}* \left( x - 3.2 \right) = 1.8\\\\\Multiply \ the \ whole \ equation \ by \ 4 \\\\4*\dfrac{1}{4} *(x - 3.2) = 1.8*4\\\\\\x - 3.2 = 7.2\\\\Add \ 3.2 \ to \ both \ sides\\\\\\x = 7.2 + 3.2\\$