Solve 75=1/2(x−30).
1 answer:
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Answer:
Step-by-step explanation:
we have : lines 2 x + 4 y = 0 and 2 x + y = 10
Let ,
2 x + 4 y = 0............. (1)
2 x + y = 10...............(2)
solve these equations for x and y
Now subtract (2) from (1) ,we get
3y=-10
⇒y =
Put the value of y in (1) , we get
2x+4() = 0
⇒2x=
⇒x=
∴ Point of intersection is .
Hence,the x-coordinate of that point is .
Answer:
B' = (-4, -4)
Step-by-step explanation:
<u>Dilation</u>: A type of transformation that makes the pre-image larger or smaller without changing its shape.
<u>Center of a dilation</u>: a fixed point about which all points are dilated.
Given:
- A = (1, 2)
- B = (-1, -1)
- C = (0, -2)
- Scale factor = 4
For dilation when the <u>center of dilation</u> is the origin (0, 0), simply multiply the coordinates of the vertices of the pre-image by the given scale factor to find the image under dilation:
Therefore:
A' = (1 x 4, 2 x 4) = (4, 8)
B' = (-1 x 4, -1 x 4) = (-4, -4)
C' = (0 x 4, -2 x 4) = (0, -8)
The factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is:
6x³ - 11x² - 12x + 5 = (x + 1)(x - )(x -
)
For given question,
We have been given the cubic polynomial 6x³ - 11x² - 12x + 5
We need to factorize given cubic polynomial.
By the rational roots theorem, any rational zero of f(x) is expressible in the form ± for integers p, q with p a divisor of the constant term 5 and q a divisor of the coefficient 6 of the leading term.
Factors of p = 5: 1, 5
Factors of q = 6: 1, 2, 3, 6
That means that the only possible rational zeros are:
±{ }
= ±{ }
We need to find the exact zeros of given cubic polynomial.
For x = 1,
6(1)³ - 11(1)² - 12(1) + 5 = -12
This means, x = 1 is not a zero of given cubic polynomial.
For x = -1,
6(-1)³ - 11(-1)² - 12(-1) + 5 = 0
This means, x = -1 is a zero of given cubic polynomial and (x + 1) is a factor.
To factorize given cubic polynomial we use synthetic division.
The synthetic division (6x³ - 11x² - 12x + 5) ÷ (x + 1) is as shown in following image.
⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(6x² - 17x + 5)
The factors of above quadratic polynomial 6x² - 17x + 5 are:
⇒ 6x² - 17x + 5 = (x - )(x -
)
So, the factors of given cubic polynomial are:
⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(x - )(x -
)
Therefore, the factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is: 6x³ - 11x² - 12x + 5 = (x + 1)(x - )(x -
)
Learn more about the polynomial here:
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