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klasskru [66]
2 years ago
12

Solve the following system of equations. Show all work and solutions.

Mathematics
1 answer:
Hitman42 [59]2 years ago
4 0
  • y=2x²+6x+1
  • y=-4x²+1

Make the equations equal and solve for x

  • 2x²+6x+1=-4x²+1
  • 6x²+6x=0
  • 6x(x+1)=0
  • 6x=0 or x+1=0
  • x=0 or x=-1

For x=0

  • y=-4(0)+1=1

For x=-1

  • y=-4(1)+1=-3

The solutions are

  • (0,1) and (-1,-3)

Graph attached

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Determine the discriminant for the given equation x^2+4x+5=0. Then describe the roots(how many and what type).
Fed [463]

Discriminant = b^2 - 4ac, where a, b and c come from the form of the quadratic equation as ax^2 + bx + c

Discriminant = (4)^2 - 4(1)(5)
= 16 - 20
= -4

-4 < 0, therefor there are no roots

(If the discriminant = 0, then there is one root
If the discriminant > 0, there are two roots, and if it is a perfect square (eg. 4, 9, 16, etc.) then there are two rational roots
If the discriminant < 0, there are no roots)
3 0
3 years ago
2. Write an equation of the line in<br> slope-intercept form.<br> (5, 3)<br> 2<br> f(0, -1)
Leona [35]

Answer:

We need to use

Step-by-step explanation:

We have to use the equation for passing through the points known as

y2-y1/x2-x1

-1-3/0-5= -4/-5

the answer is 4/5

decimal: 0.8

7 0
2 years ago
T(x) = -2(-x - 3)' + 1
Anna [14]

Answer:

2

Step-by-step explanation:

3 0
2 years ago
In 1995, Hazel was 25 years older than her son Gary. In 2022, Hazel's age will be 150% of Gary's age. How old were they in 1995?
Kitty [74]
So find the difference between 1995 and 2022 to make it easier
2022-1995=27

so the rephrased question is
when hazel was x years old, she was 25 years older than son gary who was y old at that time (equation is x is 25 more than y or x=25+y)
in 27 years, (this means x+27 and y+27) hazel's age will be 150% of gary's age (x+27= 150% of y+27)
percent means parts out of 100  so 150%=150/100=15/10=1.5
'of' in math means multiply so
the equations are
x=25+y
x+27=1.5(y+27)
subsitute 25+y for x in second euation
25+y+27=1.5(y+27)
add like terms
y+52=1.5(y+27)
I personally dislike decimals to multiply both sides by 2 to make 2 0.5's or 1 (you are technically supposed to distribute or divide both sides by 1.5) so
2y+104=3(y+27)
distribute
2y+104=3y+81
subtract 2y from both sides
104=y+81
subtract 81 from both sides
23=y
subsitute
x=25+y
x=25+23
x=48


Hazel was 48 and Gary was 23 in the year of 1995
5 0
3 years ago
PLS HURRY I WILL GIVE BRAINLIEST Which statement describes the locations of the two numbers in the inequality fraction negative
mariarad [96]

Answer:

fraction negative 4 over 5 is to the left of −0.4 and to the left of 0

Step-by-step explanation:

-4/5

-0.4 = -4/10 = -2/5

4 0
3 years ago
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