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3 years ago

The line x+ 2y = 9 intersects the curve xy + 18 = 0 at the points A and B. Find the coordinates of A and B.

Mathematics

1 answer:

victus00 [196]3 years ago

6 0

Subtracting the second equation by 18 on both sides, we have xy=-18. Next, we divide both sides by x to get y=-18/x Plugging that into the first equation, we have x+2(-18/x)=9. Multiplying both sides by x, we get x^2-36=9x. After that, we subtract both sides by 9x to get x^2-9x-36=0. Finding 2 numbers that add up to -9 but multiply to -36, we do a bit of guess and check to find the answers to be -12 and 3. Factoring it, we get
x^2-12x+3x-36=x(x-12)+3(x-12)=(x+3)(x-12). To find the x values, we have to find out when 0=(x+3)(x-12). This is simple as when you multiply 0 with anything, it is 0. Therefore, x=-3 and 12. Plugging those into x=-18/y, we get x=-18/y and by multiplying y to both sides, we get xy=-18 and then we can divide both sides by x to get -18/x=y. Plugging -3 in, we get -18/-3=6 and by plugging 12 in we get -18/12=-1.5. Therefore, our points are (-3,6) and (12, -1.5)

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Classify the triangle with 9, 15, 19 as an acute right obtuse or not a triangle

Novosadov [1.4K]

Answer:

Hence the correct option is the last one . The triangle is an obtuse angled triangle.

Step-by-step explanation:

i) the sum of any two sides added together is greater than the third side hence this is a triangle.

ii) it is<em><u> not</u></em> a right angled triangle as $\sqrt{9^{2} + 15^{2} } \neq 19$ and $\sqrt{9^{2} + 15^{2} } < 19$

iii) the triangle is not acute from ii) above

iv) the triangle is an obtuse triangle from ii) above.

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3 years ago

Hey do any of yall now what 65'6 x777

katrin2010 [14]

Answer:

If you mean 656, then the answer is 509,712.

Edit: If you're talking about measurements, then it would be 50,893 feet and 6 inches.

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1 year ago

a lawn is in the shape of a rectangle with a length of 100 feet and a width of 45 feet. how many whole bags of fertilizer must b

leva [86]

Answer:

3 bags

Step-by-step explanation:

$45 \times 100 = 4500 \\ 4500 \div 2000 = 2.25$

you cant have 0.25 of a bag so you round up to 3.

8 0

3 years ago

Plz help!!

garri49 [273]

Answer:

150 ft^3

.1 ton or 200 lbs

Step-by-step explanation:

The volume is given by

V = l*w*h

V = 5*5*6

V = 150 ft^3

To find how much 1 ft^3 weighed take the weight and divide by the volume

15 tons / 150 ft^3

.1 ton / 1 ft^3

1 ft^3 weights .1 ton

We know that 1 ton = 2000 pounds

.1 ton = 200 pounds

4 0

3 years ago

Read 2 more answers

Find equation of set of points pieces that its distance from the point 3, 4, -5 and -2, 1, 4 are equal.

Gnesinka [82]

Answer:

Step-by-step explanation:

Suppose we a point $P(x,y,z)$ such that its distance from either the point $A(3,4,-5)$ or $B(-2,1,4)$ is the same.

Using this information we can formula:

distance AP = distance BP

first, let's find the distance from AP, using the distance formula.

$r = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2 + (z_1 - z_2)^2}$

$AP = \sqrt{(3 - x_2)^2 + (4 - y_2)^2 + (-5 - z_2)^2}$

similarly, we can find the distance BP

$BP = \sqrt{(-2 - x_2)^2 + (1 - y_2)^2 + (4 - z_2)^2}$

since both distances are exactly the same we can equate them

$AP = BP$

$\sqrt{(3 - x_2)^2 + (4 - y_2)^2 + (-5 - z_2)^2} = \sqrt{(-2 - x_2)^2 + (1 - y_2)^2 + (4 - z_2)^2}$

we can simplify it a bit squaring both sides, and getting rid of the subscripts.

$(3 - x)^2 + (4 - y)^2 + (-5 - z)^2 = (-2 - x)^2 + (1 - y)^2 + (4 - z)^2$

what we have done here is formulated an equation which consists of any point P that will have the same distance from (3,4,-5) and (-2,1,4).

To put it more concretely,

This is the equation of the the plane from that consists of all points (P) from which the distance from both (3,4,-5) and (-2,1,4) are equal.

3 0

2 years ago