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3 years ago

1. What should be added to 2p - q + r to make it p + q - 2r? -

Mathematics

1 answer:

ASHA 777 [7]3 years ago

6 0

Answer:

-p + 2q - 3r

Step-by-step explanation:

(p + q - 2r) - (2p - q + r)

= p + q - 2r - 2p + q - r

= -p + 2q - 3r

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Hello, I am currently very stuck with this problem and I am unsure as to how I would solve it.

borishaifa [10]

We have the equation

$20y=x^2-10-15$

Let's complete the square, to do it let's add and subtract 25 on the right side

$\begin{gathered} 20y=x^2-10-15+25-25 \\ \\ 20y=(x-5)^2-15-25_{} \\ \\ 20y=(x-5)^2-40 \\ \\ \end{gathered}$

Now we can have y in function of x

$\begin{gathered} y=\frac{1}{20}(x-5)^2-2 \\ \\ \end{gathered}$

Now we can already identify the vertex because it's in the vertex form:

$y=a(x-h)+k$

Where the vertex is

$(h,k)$

As we can see, h = 5 and k = -2, then the vertex is

$(5,-2)$

Now we can continue and find the focus, the focus is

$\mleft(h,k+\frac{1}{4a}\mright)$

We have a = 1/20, therefore

$\begin{gathered} \mleft(5,-2+5\mright) \\ \\ (5,3) \end{gathered}$

The focus is

$(5,3)$

And the last one, the directrix, it's

$y=k-\frac{1}{4a}$

Then

$\begin{gathered} y=-2-5 \\ \\ y=-7 \end{gathered}$

Hence the correct answer is: vertex (5, -2); focus (5, 3); directrix y = -7

5 0

1 year ago

Put in standard form; identify degree and leading coefficient of polynomial: -4x + 3x2 - 2 + 4x3

Fofino [41]

Answer:

-4 (x-4)

Step-by-step explanation:

simplify the expression

-4x + 16

4 0

3 years ago

In the United States, 7% of all registered voters belong to the Green party. A random sample of 50 registered voters is taken. U

Maksim231197 [3]

Answer:

The expected value of the sample proportion is of 0.07.

1. P(p < .02) = 0.0823

2. P(p > .15) = 0.0132

3. P(.05 < p < .09) = 0.4176

Step-by-step explanation:

This question is solved using the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$