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faltersainse [42]
3 years ago
9

Determine the x-intercept and the y-intercept for the graph of this equation: 2x - 3y + 36 = 0

Mathematics
1 answer:
natali 33 [55]3 years ago
7 0

QUESTION:- DETERMINE THE X-INTERCEPT AND THE Y-INTERCEPT FOR THE GRAPH OF THE EQUATION.

EQUATION:- 2x - 3y + 36 = 0

STANDARD EQUATION:- y=mx+c

where

  1. m-> slope.
  2. c-> Y-INTERCEPT
  3. x&y are the coordinates.

SO GIVEN EQUATION:- 2x - 3y + 36 = 0

WE CAN SOLVE THIS TO CHANGE IN FORMAT OF STANDARD EQUATION

2x - 3y + 36 = 0 \\ 2x + 36 =3y \\ y =  \frac{2}{3} x +  \frac{36}{3}  \\ y =  \frac{2}{3} x +  \frac{ \cancel{36}^{ \:  \: 12} }{ \cancel3}  \\ y =  \frac{2}{3} x +  12 \\

SO :-

m =  \frac{2}{3}  \\ y - intercept = 12 \: ans

slope =  \frac{y2 - y1}{x2 - x1}  \\  \frac{2}{3}  =  \frac{0  - 12}{x  - 0}  \\ 2x = ( - 12) \times 3 \\ x =  \frac{ -  \cancel{12}^{ \:  \: 6} \times 3 }{ \cancel{2}} \\  x =  - 18 \:  \: ans

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Find the inverse of f(x)= -x + 3
inna [77]
Let g the inverse function of f.

The most important property of g and f being inverses of each other, is that 

g(f(x))=x,      also f(g(x))=x

so, what one function 'does' to x, the other 'undoes' it.



Thus, we have:

f(g(x))=x      and alos   f(g(x))= -g(x)+3, from the rule


thus : 

-g(x)+3=x

-g(x)=x-3

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3 years ago
I DONT KNOW THESE! HELP!
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Answer:

20. x = 5, y = -2

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22. x = 22, y = 11

23. x = 11, y = 10

Step-by-step explanation:

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2y+18=3x-1\\ \\6x-3=17-5y

Solve this system of two equations:

\left\{\begin{array}{l}2y-3x=-19\\ \\6x+5y=20\end{array}\right.

Multiply the first equation by 2 and add two equations:

2(2y-3x)+6x+5y=2\cdot (-19)+20\\ \\4y-6x+6x+5y=-38+20\\ \\9y=-18\\ \\y=-2

Substitute it into the first equation:

2\cdot (-2)-3x=-19\\ \\-3x=-19+4\\ \\-3x=-15\\ \\x=5

21. Opposite angles in the parallelogram are congruent, so

11x+5=10y+6

Consecutive angles are supplementary, so

6x-y+11x+5=180^{\circ}

Solve this system of two equations:

\left\{\begin{array}{l}11x-10y=1\\ \\17x-y=175\end{array}\right.

From the second equation

y=17x-175

Substitute it into the first equation:

11x-10(17x-175)=1\\ \\11x-170x+1750=1\\ \\-159x=-1749\\ \\x=11\\ \\y=17\cdot 11-175=187-175=12

22. Opposite angles in the parallelogram are congruent, so

2x-5=3y-12

Consecutive angles are supplementary, so

2x-5+7y+x=180^{\circ}

Solve this system of two equations:

\left\{\begin{array}{l}2x-3y=-7\\ \\3x+7y=185\end{array}\right.

From the first equation

x=-3.5+1.5y

Substitute it into the second equation:

3(-3.5+1.5y)+7y=185\\ \\-10.5+4.5y+7y=185\\ \\-105+45y+70y=1,850\\ \\115y=1,850+105\\ \\115y=1,955\\ \\y=17\\ \\x=-3.5+1.5\cdot 17=22

23. Opposite sides in the parallelogram are congruent, so

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\left\{\begin{array}{l}2x-4y=-18\\ \\3x-2y=13\end{array}\right.

Multiply the second equation by 2 and subtract it from the first equation:

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Substitute it into the first equation:

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SVEN [57.7K]

The given function is

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According to this function, the starting height of the rocket is 20 feet because that's the initial condition of the problem stated by the independent term.

Additionally, we find the maximum height by calculating the vertex of the function V(h,k).

h=-\frac{b}{2a}

Where a = -16 and b = 300.

\begin{gathered} h=-\frac{300}{2(-16)}=\frac{300}{32}=\frac{150}{16}=\frac{75}{8} \\ h=9.375 \end{gathered}

Then, we find k by evaluating the function

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Hence, the maximum height is 1426.25 feet.

At last, to know the time need to hit the ground, we just use h=9.375 and we multiply it by 2

t=2\cdot9.375=18.75

Hence, the rocket hits the ground after 18.75 seconds.

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1 year ago
The two trapezoids shown are similar. If the area of the larger trapezoid is 96 square centimeters, what is the area of the smal
Tasya [4]
Similar, so the dimentions and thus the area should be in proprotion
bigger one is 4 times of smaller one

96=4 times smaller
divide b 4
24=smaller

smaller=24 square cm
7 0
3 years ago
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