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3 years ago

How far apart are cities A and B in the new map?

Mathematics

1 answer:

Lubov Fominskaja [6]3 years ago

5 0

Answer:

22.5 miles

Step-by-step explanation:

If 2 inches equal 15 miles then 1 mile equals 7.5 miles. 15/2=7.5

7.5 x 3=22.5 miles.

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Please help me on this problem I don't know how to do it.

quester [9]

1: establish the angles, basically label one x (the small one) and the other y (the bigger one)

2. supplementary angles add up to 180, so therefore you have the equation x + y = 180.

3. so y (the bigger one) is 8 less than 3 times the smaller one (x) therefore you come up with the equation y = 3x - 8

4. plug in the equation of the bigger one into the other equation

x + 3x - 8 = 180
(combine like terms)
4x - 8 = 180

5. solve the equation by adding 8 to 180, then by dividing by 4.
x should equal 47

6. plug in 47 into the x + y = 180 equation, subtract 47 from 180 and you end up with 133

i hope i explained it alright

7 0

3 years ago

Three cell phones towers can be modeled by the points X(6,0), Y(8,4), and Z(3,9). Determine the location of another cell phone t

Marat540 [252]

Answer:

The location of the new cell phone tower is $(h,k) = (3,4)$ , and the equation of the circle is $x^{2}+y^{2} -6\cdot x - 8\cdot y = 0$ .

Step-by-step explanation:

The location of the cell phone tower coincides with the location of a circunference passing through the three cell phone towers. By Analytical Geometry, the equation of the circle is represented by the following general formula:

$x^{2} + y^{2}+A\cdot x + B\cdot y +C = 0$ (1)

Where:

$x$ - Independent variable.

$y$ - Dependent variable.

$A$ , $B$ , $C$ - Circunference constants.

Given the number of variable, we need the location of three distinct points:

$(x_{1},y_{1}) = (6,0)$

$36 +6\cdot A + C = 0$

$(x_{2},y_{2}) = (8,4)$

$80 + 8\cdot A + 4\cdot B + C = 0$

$(x_{3},y_{3}) = (3,9)$

$90 + 3\cdot A + 9\cdot B + C = 0$

Then, we have the following system of linear equations:

$6\cdot A + C = -36$ (2)

$8\cdot A +4\cdot B + C = -80$ (3)

$3\cdot A + 9\cdot B + C = -90$ (4)

The solution of this system is:

$A = -6$ , $B = -8$ , $C = 0$

By comparing the general form with the standard form of the equation of the circunference is:

$A = -2\cdot h$ (5)

$B = -2\cdot k$ (6)

$C = h^{2}+k^{2}-r^{2}$ (7)

Where:

$h$ , $k$ - Coordinates of the center of the circle.

$r$ - Radius of the circle.

If we know that $A = -6$ , $B = -8$ and $C = 0$ , then coordinates of the center of the circle and its radius are, respectively:

$h = -\frac{A}{2}$

$k = -\frac{B}{2}$

$r = \sqrt{h^{2}+k^{2}-C}$

$h = 3$ , $k = 4$ , $r = 5$

The location of the new cell phone tower is $(h,k) = (3,4)$ , and the equation of the circle is $x^{2}+y^{2} -6\cdot x - 8\cdot y = 0$ .

3 0

2 years ago

5x - 6y = 0 y = x solve the system by substitution. a. no solution b. coincident c. (0, 0)

tatiyna

Answer:

Step-by-step explanation:

$\left\{\begin{array}{ccc}5x-6y=0&(1)\\y=x&(2)\end{array}\right\\\\\text{Put (2) to (1):}\\\\5x-6x=0\\-x=0\to x=0\\\\\text{Put it to (2):}\\\\y=0$

8 0

3 years ago

The absolute value of a negative fraction is always greater than 1, true of false?!

Fantom [35]

Answer: False

Step-by-step explanation: False because zero is negative or positive. The absolute value of any number could also include the absolute value of 0, which would be 0. Thus, the absolute value of any rational number is not always greater than zero, it can be zero as well. However, it is true that the absolute value of any rational number can never be negative.

Rational Number definition: Rationals contain whole numbers, integers, decimals, fractions, basically most numbers or any numbers.

6 0

2 years ago

A positive integer is 47 more than 9 times another. Their product is 1860. Find the two integers.

svlad2 [7]

X = 47 + 9y
xy = 1860

y(47 + 9y) = 1860
47y + 9y² = 1860
9y² + 47y - 1860 = 0

> using a quadratic equation solver on a calculator but you can also use the quadratic equation = [-b+/- √(b²-4ac)]/(2a)
> only integer solution is x = 12

12y = 1860
y = 155

integers are 12 and 155

8 0

3 years ago