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riadik2000 [5.3K]
2 years ago
6

Solve each system by using substitution. 3x - y = 4 x + 5y = -4

Mathematics
1 answer:
babunello [35]2 years ago
5 0

Answer:

from \: last \: equation : \\ x =  - 4 - 5y -  -  - (a) \\ substitute \: in \: first \: equation \\ 3( - 4 - 5y) - y = 4 \\  - 12 - 15y - y = 4 \\  - 16y = 16 \\ y =  - 1 \\  \\ therefore \: from \: (a) \\ x =  - 4 - 5( - 1) \\ x = 1

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F(x)=2x^2-x-10 part a: what are the X intercepts of the graph of f(x)? Show your work
Genrish500 [490]
A. x intercepts are where the graph hits the x axis or where f(x)=0
0=2x^2-x-10
solve
hmm
we can use the ac method
multiply 2 and -10 to get -20
what 2 numbers muliply to get -20 and add to get -1 (the coefint of the x term)
-5 and 4
split the midd into that
0=2x^2+4x-5x-10
group
0=(2x^2+4x)+(-5x-10)
factor
0=2x(x+2)-5(x+2)
undistribute
0=(x+2)(2x-5)
set each to 0
0=x+2
0=-2

0=2x-5
5=2x
5/2=x

x intercepts are at x=-2 and 5/2 or the points (-2,0) and (5/2,0)


B. ok, so for f(x)=ax^2+bx+c
if a>0, then the parabola opens up and the vertex is a minimum
if a<0 then the parabola opens down and the vertex is a max

f(x)=2x^2-x-10
2>0
opoens up
vertex is minimum

ok, the vertex

the x value of  the vertex in f(x)=ax^2+bx+c= is -b/(2a)
the y value of the vertex is f(-b/(2a)) so
given
f(x)=2x^2-x-10
a=2
b=-1
-b/2a=-(-1)/(2*2)=1/4
f(1/4)=2(1/4)^2-(1/4)-10
f(1/4)=2(1/16)-1/4-10
f(1/4)=1/8-1/4-10
f(1/4)=1/8-2/8-80/8
f(1/4)=-81/8
so the vertex is (1/4,-81/8) or (0.25,-10.125)


C. graph the x intercepts and the vertex
the vertex is min and the graph goes through the x intercepts
4 0
3 years ago
What the answer to this?
Alex787 [66]

Out of the four choices, it would be A

8 0
3 years ago
Read 2 more answers
Are you all trying to torture me. i might get kicked from brainly, but people do NOT answer this .. please XD.
diamong [38]

one more person has to answer now lol

8 0
3 years ago
Read 2 more answers
How many solutions does the equation - 8x + 5 = - 8x + 4 have
KiRa [710]

- 8x + 5 =  - 8x + 4 \\   - 8x =  - 8x + 4 - 5 \\  - 8x =  - 8x - 1 \\  0 =  - 1(false)

we don't have solutions !!

3 0
3 years ago
The cost of a car rental is ​$30 per day plus 18c per mile. You are on a daily budget of ​$75. Write and solve an inequality to
Tanzania [10]

Answer:

2. 5 miles

Step-by-step explanation:

Given that:

Rental cost = $30

Cost per mile driven = 18 cent

Daily budget = $75

Greatest distance you can drive each day while staying within budget :

Rental cost + (cost per mile driven * distance) ≤ daily budget

$30 + 18d ≤ $75

18d ≤ 75 - 30

18d ≤ 45

d ≤ 45 / 18

d ≤ 2.5

Greatest distance you can drive each day while staying within budget is 2.5 miles.

8 0
3 years ago
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