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4 years ago

Write this in y=ax^2+b form: y=(x-5)^2 - 2

Mathematics

2 answers:

erma4kov [3.2K]4 years ago

5 0

$y=(x-5)^2-2\\
y=x^2-10x+25-2\\
y=x^2-10x+23
$

MrMuchimi4 years ago

3 0

Expand (x - 5)^2

(x - 5)^2 = (x - 5)(x - 5)

Multiply all the terms in the first parenthesis to all the terms in the 2nd:

x * x = x^2
x * -5 = -5x
-5 * x = -5x
-5 * -5 = 25

So we have:

x^2 - 5x - 5x + 25

Combine like terms:

x^2 - 10x + 25

Plug it back in:

y = (x - 5)^2 - 2

y = x^2 - 10x + 25 - 2

Combine like terms:

y = x^2 - 10x + 23

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2 years ago

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The correlation coefficient of the health research institute data measures the relationship between the age and the years of the smokers

The correlation coefficient is 0.53

<h3>How to calculate the correlation coefficient</h3>

The correlation coefficient (r) is calculated as:

$r = \frac{n(\sum xy) - \sum x \sum y}{\sqrt{[n \sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2}}$

Using the given parameters, we have:

$r = \frac{20 *8249 - 1257* 116}{\sqrt{[20 * 98823 - 1257^2][20 * 836 - 116^2}}$

Evaluate the exponents

$r = \frac{20 *8249 - 1257* 116}{\sqrt{[20 * 98823 - 1580049][20 * 836 - 13456}}$

Evaluate the products

$r = \frac{164980 - 145812}{\sqrt{[1976460 - 1580049][16720 - 13456}}$

Evaluate the differences

$r = \frac{19168}{\sqrt{[396411*3264}}$

Evaluate the product

$r = \frac{19168}{\sqrt{1293885504}}$

Evaluate the root

$r = \frac{19168}{35970.6}$

Evaluate the quotient

$r = 0.53$

Hence, the correlation coefficient is 0.53

Read more about correlation coefficient at:

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2 years ago

Which expression is equivalent to b^m•b^n A. b^m-n B. b^m•n C. b^m÷n D. b^m+n

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$\displaystyle\\ 
\bold{b^m \times b^n = b^{m + n}~~~(D)}\\\\ 
\bold{\frac{b^m}{b^n}= b^{m - n}~~~~~~~~~(A)}\\\\ 
\bold{\Big(b^m \Big)^n = b^{m\times n}~~~~(B)}\\\\ 
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3 years ago

A marketing firm tracks data on grocery store visits. In one study, it finds that the probability that a shopper buys bread duri

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Answer:

Option B.

Step-by-step explanation:

Two events are said to be independent of each other, if the probability of one event ocurrin in not way affects the probability of the other event occurring.

The interception of two independent events P(A ∩ B) = P(A) × P(B), where:

P(A) = 0.70

P(B) = 0.20

P(A ∩ B) = P(A) × P(B) = 0.70x0.20 = 0.14

The two events are independent if the probability of buying Bread AND cheese equals: 0.14, which is Option B.

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3 years ago

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What is the greatest common factor of 44c^5, 22c^3 and 11c^4

Alexxandr [17]

$\text{ GCF of } 44c^5, 22c^3 , 11c^4 \text{ is } 11c^3$

Solution:

Given that, we have to find the greatest common factor of $44c^5, 22c^3 , 11c^4$

The greatest number that is a factor of two (or more) other numbers.

When we find all the factors of two or more numbers, and some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor

$\underline{\text{ GCF of } 44c^5, 22c^3 , 11c^4 :}$