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evablogger [386]
3 years ago
8

A tree is leaning toward the ground. How many degrees does the tree have to fall before hitting the ground?

Mathematics
2 answers:
Firdavs [7]3 years ago
6 0
Im not absolutely sure but i think its 14
Alborosie3 years ago
6 0
That is a straight angle, meaning the angle measure is 180 degrees. we know that 14x+22x=180, or 36x=180 by combining like terms. solving for x, we get x=5. plugging in, 14x5=70. the tree has to go 70 degrees before hitting the ground. looking at our diagram, this answer makes sense.
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Match the circle equations in general form with their corresponding equations in standard form. Not all will be used. 
Xelga [282]
<span>The standard form of the equation of a circumference is given by the following expression:

</span>(x-h)^{2}+(y-k)^{2}=r^{2} \\ \\ where \ (h, k) \ is \ the \ center \ of \ the \ circumference \ and \ r \ the \ radius
<span>
On the other hand, the general form is given as follows:

</span>x^{2}+y^{2}+Dx+Ey+F=0 \\ \\ where: \\ D=-2h, \ E=-2k, \ F=h^{2}+k^{2}-r^{2}<span>

In this way, we can order the mentioned equations as follows:

Equations in Standard Form:

</span>\bold{a)} \ (x-6)^{2}+(y-4)^{2}=56 \\ \bold{b)} \ (x-2)^{2} + (y+6)^{2}=60 \\ \bold{c)} \ (x+2)^{2}+(y+3)^{2}=18 \\ \bold{d)} \ (x+1)^{2}+(y-6)^{2}=46

Equations in General Form:

\bold{1)} \ x^{2}+y^{2}-4x+12y-20=0 \\ \bold{2)} \ x^{2}+y^{2}+6x-8y-10=0 \\ \bold{3)} \ 3x^{2}+3y^{2}+12x+18y-15=0 \\ \\ If \ we \ divide \ this \ equation \ by \ 3, \ the \ equation \ becomes: \\ x^{2}+y^{2}+4x+6y-5=0 \\ \\ \bold{4)} \ 5x^{2}+5y^{2}-10x+20y-30=0 \\ \\ If \ we \ divide \ this \ equation \ by \ 5, \ the \ equation \ becomes: \\ x^{2}+y^{2}-2x+4y-6=0 \\ \\ \bold{5)} \ 2x^{2}+2y^{2}-24x-16y-8=0 \\ \\ If \ we \ divide \ this \ equation \ by \ 2, \ the \ equation \ becomes: \\ x^{2}+y^{2}-12x-8y-4=0

\bold{6)} \ x^{2}+y^{2}+2x-12y

So let's match each equation:

\bold{From \ a)} \\ \\ (h,k)=(6,4),\ r=2\sqrt{14} \\ D=-12, \ E=-8 \\ F=-4

Then, its general form is:

x^{2}+y^{2}-12x-8y-4=0

<em><u>First. a) matches 5) </u></em>

\bold{From \ b)} \\ \\ (h,k)=(2,-6),\ r=2\sqrt{15} \\ D=-4, \ E=12 \\ F=-20

Then, its general form is:

x^{2}+y^{2}-4x+12y-20=0

<em><u>Second. b) matches 1) </u></em>

\bold{From \ c)} \\ \\ (h,k)=(-2,-3),\ r=3\sqrt{2} \\ D=4, \ E=6 \\ F=-5

Then, its general form is:

x^{2}+y^{2}+4x+6y-5=0

<em><u>Third. c) matches 3)</u></em>

\bold{From \ d)} \\ \\ (h,k)=(-1,6),\ r=\sqrt{46} \\ D=2, \ E=-12, \ F=-9

Then, its general form is: x^{2}+y^{2}+2x-12y-9=0

<em><u>Fourth. d) matches 6)</u></em>
6 0
3 years ago
Read 2 more answers
The students at Midtown Middle school sold flowers as a fundraiser in September and October. In October, they charged $1.50 for
lions [1.4K]

In the question it is given that,

The students at Midtown Middle school sold flowers as a fundraiser in September and October. In October, they charged $1.50 for each flower

And the October price was a 20% increase of the September price.

Let the price of the flower in October be $x

So we have

x+  \frac{20}{100}x = 1.50 \\ \frac{120x}{100} = 1.50 \\ x = \frac{1.50*100}{120} = 1.25

So the price of the flower in Septembet is $1.25 .

7 0
3 years ago
You can eliminate one of the variable terms in an ___ by adding or subtracting another equation
MakcuM [25]

Answer:

system of equations

Step-by-step explanation:

You can eliminate one of the variable terms in a <u>system of equations</u> by adding or subtracting another equation.

8 0
2 years ago
Is side “a” considered a leg or the hypotenuse in this right triangle?
skelet666 [1.2K]

Answer:

A leg.

Step-by-step explanation:

The hypotenuse is always the side that is across from the corner. In this triangle, the hypotenuse is 14.

6 0
3 years ago
Read 2 more answers
A car can travel 80 miles an hour. How many miles will the car travel in 6 3/4 hours?
Hoochie [10]
6 3/4= 6.75

80 mph * 6.75 hours = 540 miles total

Final answer: 540 miles
7 0
3 years ago
Read 2 more answers
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