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3 years ago

The pair (-1, 1) is a solution to the equation 2y - 3x = 5. Find another (x, y) pair that is a

Mathematics

1 answer:

morpeh [17]3 years ago

6 0

Answer: (1,4)

Step-by-step explanation:

Given

Equation of line is $2y-3x=5$

(-1,1) is the solution of the equation

Take x=1 and substitute it in the above equation

$\Rightarrow 2y-3(1)=5\\\Rightarrow 2y=5+3\\\Rightarrow y=4$

So, another pair of the solution is (1,4)

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Solve the problem.A plane flying a straight course observes a mountain at a bearing of 35° to the right of its course. At that t

Mice21 [21]

Given:

A plane flying a straight course observes a mountain at a bearing of 35° to the right of its course.

The distance between plan and mountain is 10 km.

A short time later, the bearing to the mountain becomes 45°.

Here NM is the distance between the plane from the mountain when the second bearing is taken.

We need to find the measure of NM.

$We\text{ know that }\angle INM\text{ and }\angle\text{XNM are supplementary angles.}$

The sum of the supplementary angles is 180 degrees.

$\angle INM+\angle XNM=180^o$ $\text{Substitute }\angle XNM=45^o\text{ in the equation.}$

$\angle INM+45^o=180^o$

$\angle INM=180^o-45^o$

$\angle INM=135^o$

We know that the sum of all three angles of the triangle is 180 degrees.

$\angle INM+\angle NIM+\angle INM=180^o$ $\text{Substitute }\angle INM=135^o\text{ and }\angle NIM=35^o\text{ in the equation.}$

$135^o+35^o+\angle INM=180^o$

$170^o+\angle INM=180^o$

$\angle INM=180^o-170^o$

$\angle INM=10^o$

Consider the sine law.

$\frac{\sin N}{IM}=\frac{\sin M}{IN}=\frac{\sin I}{NM}$

Take the equation to find the measure of NM.

$\frac{\sin N}{IM}=\frac{\sin I}{NM}$ $\text{Substitute }\angle N=135^o,\angle I=35^o,\text{ and IM=10 in the equation.}$

$\frac{\sin 135^o}{10}=\frac{\sin35^o}{NM}$

$NM=\frac{\sin 35^o}{\sin 135^o}\times10$ $NM=8.11$

Hence the measure of NM is 8.1 km.

The plane is 8.1 km far from the mountain when the second bearing is taken.

5 0

1 year ago

Help please, I need it

OlgaM077 [116]

Answer:

2) c) (x-3)² + (y+2)² = 25

5) x^2 +y^2 -8x -16y +54 = 0

6) x^2 +y^2 -10x -12y +36 = 0

Step-by-step explanation:

2) The standard form equation for a circle is ...

(x -h)^2 +(y -k)^2 = r^2

You are given the center: (h, k) = (3, -2) and a point on the circle. So, the equation will be ...

(x -3)^2 +(y +2)^2 = r^2

Since we know a point on the circle we know that ...

(7 -3)^2 +(1 +2)^2 = r^2 = 16 +9 = 25

So, the circle's equation is ...

(x -3)^2 +(y +2)^2 = 25 . . . . . matches choice C

5) As in the previous problem, the standard form equation is ...

(x -4)^2 +(y -8)^2 = (-1-4)^2 +(7-8)^2 = 25+1 = 26

To put this in general form, we need to subtract 26 and eliminate parentheses.

x^2 -8x +16 +y^2 -16y +64 -26 = 0

x^2 +y^2 -8x -16y +54 = 0

6) A circle tangent to the y-axis will have a radius equal to the x-value of the center point.

(x -5)^2 +(y -6)^2 = 5^2

x^2 -10x +25 +y^2 -12y +36 = 25

x^2 +y^2 -10x -12y +36 = 0

8 0

4 years ago

A circle with a circumference of 40.82 centimeters what is the area of the circle is 3.14 for pi

s2008m [1.1K]

You need two formulas for this:

C = πd or C = 2πr ( d = 2r ) Where C is circumference and d is diameter, r is radius

A = πr² Where A is area, and r is radius

First you get the diameter and radius by substituting the value of pi and circumference. With that, you can calculate the Area of the circle with the second formula. square² the radius then multiply it to 3.14. Remember that radius is half of diameter.

5 0

3 years ago

Read 2 more answers

382.993 is the nearest hundredth

julsineya [31]

382.99 is rounded to the nearest hundredth

8 0

3 years ago

Read 2 more answers

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Neko [114]

Answer: