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3 years ago

There are 25 towns in a certain country, and every pair of them is connected by a train route. How many train routes are there?

Mathematics

1 answer:

7nadin3 [17]3 years ago

5 0

Answer:

Step-by-step explanation:

a pair=2

so 25/each pair of towns

25/2=12+1=13

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What is the distance between points (9,-7) and (9,4) on a coordinate plane

hichkok12 [17]

Answer:

Step-by-step explanation:

-7 to 4 is 11 Hoped that helped

4 0

3 years ago

The difference in the x-coordinates of two points is 3, and the difference in the y-coordinates of the two points is 6. Wha

Yanka [14]

Answer:

to find the slope you get the rise which is the difference between the y coordinates over the run which is the difference between the x coordinates. so 6/3=2

3 0

3 years ago

the base of a triangle is five less than twice it’s height, if the area of the triangle is 6 cm^2, find the length of the base

sammy [17]

Answer:

Base = 3 cm

Step-by-step explanation:

Area of a triangle = $\frac{1}{2} bh$

Let h = height

base = 2 times the height - 5; b = 2h-5

Area = 6 cm²

A = $\frac{1}{2}bh$

$6 =\frac{1}{2}(2h - 5)(h)$ Multiply 2h(h) -5(h)

$6 (2) = 2(\frac{1}{2})(2h^{2} - 5h$ Multiply both sides by 2 to remove the fraction

12 = 2h²- 5h

2h ² - 5h - 12 = 0 Set the equation = 0 and factor

(2h + 3)(h - 4) = 0

2h + 3 = 0 or h - 4 = 0

2h = -3 h = 4

h = -3/2 or h = 4 Answer can not be negative so h = 4cm

The base is 2(4) - 5; The base = 8 - 5; base = 3 cm

7 0

2 years ago

1a.) Write an expression that represents the area of a circle with a radius of 7 units? (1 point)

Tresset [83]

Answer:

1. a.) A = $\pi r^{2}$ where the value of r = 7 units

b.) A = $\pi \times 7^{2} = \pi \times 49 = 49\pi = 49\times 3.1414 = 153.93 units^2$

Step-by-step explanation:

1.) a.) the area of a circle with a radius of 7 units

is given by Area, A = $\pi r^{2}$ where the value of r = 7 units

b) $\therefore$ A = $\pi \times 7^{2} = \pi \times 49 = 49\pi = 49\times 3.1414 = 153.93 units^2$

6 0

3 years ago

Which is the equation of a hyperbola with directrices at y = ±2 and foci at (0, 6) and (0, −6)?

klasskru [66]

Given:

Hyperbola with directrices at y = ±2 and foci at (0, 6) and (0, −6).

To find:

The equation of hyperbola.

Solution:

We have, directrices at y = ±2 so this hyparabola is along the y-axis.

The standard form of hyperbola is

$\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1$ ...(i)

where, (h,k) is center, foci are $(h,k\pm c)$ and directrix are $y=k\pm \dfrac{a^2}{c}$ .

On comparing foci, we get

$(h,k\pm c)=(0,\pm 6)$

$h=0,k=0,c=6$

On comparing directrix we get

$k\pm \dfrac{a^2}{c}=\pm 2$

$\dfrac{a^2}{c}=2$

$\dfrac{a^2}{6}=2$

$a^2=12$

Now,

$a^2+b^2=c^2$

$12+b^2=(6)^2$

$b^2=36-12$

$b^2=24$

Putting $h=0,k=0,a^2=12,b^2=24$ , we get

$\dfrac{(y-0)^2}{12}-\dfrac{(x-0)^2}{24}=1$

$\dfrac{y^2}{12}-\dfrac{x^2}{24}=1$

Therefore, the equation of hyperbola is $\dfrac{y^2}{12}-\dfrac{x^2}{24}=1$ .

7 0

3 years ago