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3 years ago

Solve the system by substitution. y=2x^2-3x-1 y=x-3

2 answers:

6 0

The answer is B(1,-2). This is the only point where the two lines intercept. & if you plug the numbers into the equations they fit.

vekshin13 years ago

4 0

Answer: The correct option is (B) (1, -2).

Step-by-step explanation: We are given to solve the following system of equations by substitution method :

$y=2x^2-3x-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x-3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Substituting the value of y from equation (ii) in equation (i), we get

$x-3=2x^2-3x-1\\\\\Rightarrow 2x^2-4x+2=0\\\\\Rightarrow x^2-2x+1=0\\\\\Rightarrow (x-1)^2=0\\\\\Rightarrow x-1=0,~~~x-1=0\\\\\Rightarrow x=1,1.$

Substituting x = 1 in equation (ii), we get

$y=1-3=-2.$

Thus, the required solution is (x, y) = (1, -2).

Option (B) is correct.

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Which statement is true of the determinant of a matrix? A. It can be either positive or zero, but never negative. B. It can have

Andre45 [30]

Answer: D

Step-by-step explanation:

A. Det can be negative.

B. Is gobbledygook

C. All components of the matrix are included.

D. The others have been eliminated, and it's true.

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3 years ago

Identify the function that contains the data in the following table: x -2 0 2 3 5 f(x)

Veseljchak [2.6K]

Answer:

f(x) = |x - 2| + 1

Step-by-step explanation:

When x = -2, then f(-2) = 5

The first function gives the relation equation as f(x) = |x| + 1

So, f(-2) = |-2| + 1 = 2 + 1 = 3 ≠ 5

{Since the definition of |x| is given by

|x| = x, when x ≥ 0 and |x| = - x, when x < 0}

Again, the second function gives the relation equation as f(x) = |x - 2|.

So, f(-2) = |-2 - 2| = |-4| = 4 ≠ 5

Now, the third function gives the relation equation as f(x) = |x - 2| - 1.

So, f(-2) = |-2 - 2| - 1 = |-4| - 1 = 4 - 1 = 3 ≠5

Again, the fourth function gives the relation equation as f(x) = |x - 2| + 1.

Hence, f(-2) = |-2 - 2| + 1 = |-4| + 1 = 4 + 1 = 5

Therefore, the fourth function f(x) = |x - 2| + 1 contains the given data table.

For further clarity we can check f(0) = 3, f(2) = 1, f(3) = 2 and f(5) = 4. (Answer)

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4 years ago

Read 2 more answers

Something divided by 6 = 7 8 3

Karo-lina-s [1.5K]

The answer is going to be 4698

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3 years ago

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How would you solve x + 3y = 18 -3x - 12y = -75 showing all of the work

VikaD [51]

Answer:

x = -3, y = 7.

Step-by-step explanation:

x + 3y = 18

-3x - 12y = -75

Multiply the first equation by 3:

3x + 9y = 54

Adding the last 2 equations to eliminate x:

-3y = -21

y = 7.

Substitute y = 7 into the first equation:

x + 3(7) = 18

x + 21 = 18

x = 18 - 21

x = -3.

3 0

3 years ago

In a given year, the average annual salary of a NFL football player was $189,000 with a standard deviation of $20,500. If a samp

nika2105 [10]

Answer:

15.15% probability that the sample mean will be $192,000 or more.

Step-by-step explanation:

To solve this problem, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$