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Readme [11.4K]
3 years ago
11

_________ is the ratio of the vertical change to the horizontal change between any two points on a line.

Mathematics
1 answer:
leva [86]3 years ago
4 0
Rate of change or slope. Hope it helps. 
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Divide 24xy²z³ by 6yz²​
liberstina [14]

Answer: 4xyz

Step-by-step explanation:

24xy²z³ / 6yz² =4xy²⁻¹z³⁻² = 4xyz

3 0
3 years ago
James is working out and has decided that for every 10 sit-ups he does, he needs to do 4 push-ups. If he does 120 sit-ups, how m
mario62 [17]

Answer:

480 is the answer

Step-by-step explanation:

120x4 is 480

4 0
2 years ago
Write the equation of the line perpendicular to 2x+3y=9 that passes through (-2,5). Write your answer in slope-intercept form. S
Harman [31]
ANSWER

y =  \frac{3}{2} x + 8



EXPLANATION

The line given to us has equation,

2x + 3y = 9

We need to write this equation in the slope intercept form to obtain,


3y =  - 2x + 9



\Rightarrow \: y =  -  \frac{2}{3}x + 3


The slope of this line is

m_1 =  -  \frac{2}{3}
Let the slope of the perpendicular line be

m_2

Then
m_1 \times m_2 =  - 1


-  \frac{2}{3} m_2=  - 1

This implies that,

m_2 =  - 1 \times  -  \frac{3}{2}


m_2 =  \frac{3}{2}



Let the equation of the perpendicular line be,

y = mx + b

We substitute the slope to get,


y =  \frac{3}{2} x + b

Since this line passes through
(-2,5)
it must satisfy its equation.


This means that,

5=  \frac{3}{2} ( - 2)+ b


5 =  - 3 + b



5 + 3 = b


b = 8

Wherefore the slope-intercept form is

y =  \frac{3}{2} x + 8
6 0
3 years ago
Arrange the parabolas represented by the equations in increasing order with respect to the y-values of their directrixes.
Alexus [3.1K]
(x-h)^2=4P(y-k), vertex is (h,k)
P is distance from vertex to directix
remember to subtract P from the y value of the vertex (p-k) and that y value is the directix, y=p-k

nut
ok so one way is to just graph them on a graphing utility
remember if the graph opens up, then the directix is below that
or we can convert to 4P(y-k)=(x-h)^2 form where P is distance from directix

I will only convert the 1st one fully, you should be able to do the rest

1. y=-x^2+3x+8
multiply both sides by -1 since we don't like the x^2 term negative
-y=x^2-3x-8
add8 to both sides
-y+8=x^2-3x
take 1/2 of linear coeficient and square it and add to both sides
-3/2=-1.5
 (-1.5)^2=2.25
-y+10.25=x^2-3x+2.25
factor perfect square
-y+10.25=(x-1.5)^2
force undistribute -1 in left side
(-1)(y-10.25)=something, we don't care anymore for now
factor out a 4 in -1
4(-1/4)(y-10.25)

k=10.25
p=-1/4=-0.25
directix=k-p=10.25-(-0.25)=10.5
directix is y=10.5

basically completee the square with x and find P by force factoring a 4 out

2.  directix: y=-1.75

3. directix: y=1.5

4. directix: y=17.25

5. d: -37.5

6. d: 9.25

7. d=2.625

order them yourself

7 0
3 years ago
Answers fast please. 1.) y=x−63x+2y=8 Use the substitution method. A.) (4, −2) B.) (14, 8) C.) (0, −6) D.) (3, −3) 2.) What is t
GrogVix [38]

<u>QUESTION 1</u>

The given system of equation is

y=x-6...eqn1

and


3x+2y=8...eqn2


Let us substitute equation (1) into equation (2) to get,

3x+2(x-6)=8


We expand the bracket to get,

3x+2x-12=8


We simplify to get.

5x-12=8


We group like terms to get

5x=8+12

\Rightarrow 5x=20

\Rightarrow x=4


We now substitute x=4 in to equation (1) to obtain,


y=4-6=-2


The correct answer is option A.


<u>QUESTION 2</u>

The given system of equations is

y-x=9...eqn1


and

10+2x=-2y...eqn2

We make y the subject in equation (2) to get,

y=-x-5..eqn3


We put equation (3) into equation (1) to obtain,


-x-5-x=9


We group like terms to get,

-x-x=9+5


This implies that,

-2x=14


We divide through by -2 to get,

x=-7


Hence the x-coordinate is -7



<u>QUESTION 3</u>

The given system is

y=3x-1..eqn1


and


x-y=-9...eqn2

We make x the subject in equation (2) to get,

x=y-9...eqn3


We put equation (3) into equation (1) to obtain,


y=3(y-9)-1


We expand the bracket to get,


y=3y-27-1


Group like terms to get,


y-3y=-27-1


We simplify to get;

-2y=-28


This implies that,

y=14


Therefore the y-coordinate is 14.

4 0
3 years ago
Read 2 more answers
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