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schepotkina [342]
3 years ago
14

Solve algebraically y=x^2 + 2x y=3x+20

Mathematics
2 answers:
Zina [86]3 years ago
5 0
This one looks very tricky but ill try it out
hodyreva [135]3 years ago
5 0

Answer:

x = 5 and y = 35

OR

x = -4 and y = 8.

Step-by-step explanation:

Equate the right-hand side of the two equations:

x² + 2 x = y = 3 x + 20.

x² + 2 x - 3 x - 20 = 0.

x² - x - 20 = 0.

Quadratic discriminant

Δ = b² - 4 a · c

= (-1)² - 4 × 1 × (-20)

= 81.

There are two roots:

x₁ = (-b + \sqrt{\Delta}) / (2 a)

= (- (-1) + \sqrt{81}) / (2 × 1)

= (1 + 9) / 2

= 10 / 2

= 5

and

x₂ = (-b - \sqrt{\Delta}) / (2 a)

= (1 - 9) / 2

= -4.

Find the value of y in both case.

y₁ = 3 × 5 + 20 = 35.

y₂ = 3 × (-4) + 20 = 8.

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ΔABC is dilated by a scale factor of 0.25 with the origin as the center of dilation, resulting in the image ΔA′B′C′. If A = (-1,
Leni [432]

Answer:

5

Step-by-step explanation:

To find B and C prime, you must multiply them by .25, or 1/4.


B' =  

(-2 x .25),(1 x .25)


I did mine in fraction form, because it will prove to be more useful in future mathematics.


B' = (1/2  ,  1/4)


Repeat the process with C.


C' =

(14 x .25),(17 x .25)


C' =

(7/2  ,  17/4)




You only need to focus on B and C because you are finding the length of B'C'.


The formula for distance is the square root of x to the sub of 2 minus x to the sub of 1 squared minus y to the sub of 2 minus y to the sub of 1 square.


x2 -  x1 =  7/2  -  1/2  =  6/2  =  3 squared  =  9


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8 0
3 years ago
What is the probability that a junior non-Nutrition major and then a sophomore Nutrition major are chosen at random? Express you
aleksandr82 [10.1K]

Answer:

0.0032

The complete question as seen in other website:

There are 111 students in a nutrition class. The instructor must choose two students at random Students in a Nutrition Class Nutrition majors Academic Year Freshmen non-Nutrition majors 17 18 Sophomores Juniors 13 Seniors 18 Copy Data. What is the probability that a senior Nutrition major and then a junior Nutrition major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places.

Step-by-step explanation:

Total number of in a nutrition class = 111 students

To determine the probability that the two students chosen at random is a junior non-Nutrition major and then a sophomore Nutrition major, we would find the probability of each of them.

Let the probability of choosing a junior non-Nutrition major = Pr (j non-N)

Pr (j non-N) = (number of junior non-Nutrition major)/(total number students in nutrition class)

There are 13 number of junior non-Nutrition major

Pr (j non-N) = 13/111

Let the probability of choosing a sophomore Nutrition major = Pr (S N-major)

Pr (S N-major)= (number of sophomore Nutrition major)/(total number students in nutrition class)

There are 3 number of sophomore Nutrition major

Pr (S N-major) = 3/111

The probability that the two students chosen at random is a junior non-Nutrition major and then a sophomore Nutrition major = 13/111 × 3/111

= 39/12321

= 0.0032

7 0
3 years ago
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A student claims that 3√80 is in the simplest radical form. Which statement is true?
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The answer i think is C
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