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3 years ago

2x squared - 3x = 2x - 2

Mathematics

2 answers:

elena-s [515]3 years ago

4 0

Answer: x=1/2 or x=2

FinnZ [79.3K]3 years ago

4 0

2x^2 - 3x = 2x - 2
2x^2 -5x + 2

Factoring:
1. find the two numbers that multiply to equal ac (2 • 2) and add to equal b (-5)
The numbers = -4, -1

2. Extend the b term into these two numbers.
2x^2 -4x - x + 2

3. Group the first two terms and the last two terms to each other.
(2x^2 - 4x)(-x + 2)

4. Take out the GCF's in the parentheses sections. Note: the terms inside both of the parentheses should be equal, or you have done something wrong.
2x(x - 2) - 1(x - 2)

5. Group the GCF's together alongside the equivalent parentheses sections.
(2x - 1)(x - 2)

You're done here, but IF you want to find the solutions, you have to set each of the new parentheses sections to zero and solve for x.
2x - 1 = 0 >> 2x = 1 >> x = 1/2
x - 2= 0 >> x = 2

In conclusion, your solutions are x = 1/2 and x = 2, and your factored equation is (2x - 1)(x - 2)

Hope this helps!!

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The graph represents two complex numbers, z1 and z2, as solid line vectors. Which points represent their complex conjugates?

REY [17]

Point A represents the complex conjugate z₁ and point L represents the complex conjugate of z₂ respectively

The complex conjugate of a complex number is a complex number that having equal magnitude in the real and imaginary part as the complex number to which it is a conjugate, but the imaginary part of the complex conjugate has an opposite sign to the original complex number

Therefore, graphically, the complex conjugate is a reflection of the original complex number across the x-axis because the transformation for a reflection of the point (x, y) across the x-axis is given as follows;

Preimage (x, y) reflected across the x axis give the image (x, -y)

Where in a complex number, we have;

x = The real part

y = The imaginary part

The reflection of z₁ across the x-axis gives the point A, while the reflection of z₂ across the x-axis gives the point L

Therefore;

Point A represents the complex conjugate z₁ and point L represents the complex conjugate of z₂

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3 years ago

1. A new brand of hot dog claims to have a lower sodium content than the leading brand.

kherson [118]

Answer:

(a) Population mean = 314.5mg

(b) Margin of error = 21.281mg

The new brand of hot dog has a lower sodium content on average than the leading brand

(d) Yes

Step-by-step explanation:

(a) Population mean = (370+326+322+297+326+289+293+264+327+331)/10 = 3145/10 = 314.5mg

(b) Margin of error = t×sd/√n

sd = 29.73, n = 10, degree of freedom = n-1 = 10-1 = 9

Assuming 95% confidence level

t-value corresponding to 9 degrees of freedom and 95% confidence level is 2.262

Margin of error = 2.262×29.73/√10 = 21.281mg

Lower limit of new brand = 314.5 - 21.281 = 293.219mg

Upper limit = 314.5 + 21.281 = 335.781mg

The range of sodium content for the new brand of hot dog is between 293.219mg and 335.781mg which is lower than the leading brand (350mg)

(d) Margin of error = t×sd/√n

From the formula above, margin of error varies inversely as the square root of sample size

The smaller the sample size (n = 10) the larger the margin of error and the less accurate is the population mean

The larger the sample size (n = 40) the smaller the margin of error and the more accurate is the population mean

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