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2 years ago

Prove that the difference between squares of consecutive even numbers is always a multiple of 4

Mathematics

2 answers:

jasenka [17]2 years ago

5 0

Answer:

Answer: Proved: the difference between squares of consecutive even numbers is always a multiple of 4. ... From the results above, we can see that 12, 20, and 28 are multiples of 4. Therefore, the difference between squares of consecutive even numbers is always a multiple of 4.

Step-by-step explanation:

svp [43]2 years ago

4 0

Answer:

Step-by-step explanation:

Let's call the numbers n and n + 2.

(n + 2)² - n²

= n² + 4n + 4 - n²

= 4n - 4

= 4(n - 1)

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Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning.

natka813 [3]

Suppose that the height (in centimeters) of a candle is a linear function of

the amount of time (in hours) it has been burning.

Let x be the amount of time in hours

Let y be the heoght of a candle in centimeters

The two points are then as (9,24.5) and (23,17.5).

$\mathrm{Find\:the\:line\:}\mathbf{y=mx+b}\mathrm{\:passing\:through\:}\left(9,\:24.5\right)\mathrm{,\:}\left(23,\:17.5\right)$

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(9,\:24.5\right),\:\left(x_2,\:y_2\right)=\left(23,\:17.5\right)$

$m=\frac{17.5-24.5}{23-9}$

$m=-0.5$

$\mathrm{Plug\:the\:slope\:}-0.5\mathrm{\:into\:}y=mx+b$

$y=\left(-0.5\right)x+b$

$\mathrm{Plug\:in\:}\left(9,\:24.5\right)\mathrm{:\:}\quad \:x=9,\:y=24.5$

$24.5=\left(-0.5\right)\cdot \:9+b$

$-4.5+b=24.5$

$b=29$

$\mathrm{Construct\:the\:line\:equation\:}\mathbf{y=mx+b}\mathrm{\:where\:}\mathbf{m}=-0.5\mathrm{\:and\:}\mathbf{b}=29$

$y=-0.5x+29$

Now plug in x=21, we get

$y=-0.5*21+29=18.5$

Thus the height of the candle after 21 hours is 18.5 centimeters.

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3 years ago

What is the solution to this equation? 3(4x + 3) = 2x - 5(3 - x) + 2 A. B. C. D.

RideAnS [48]

Answer:

Exact form - x= - 22/5

Decimal form - x=-4.4

Mixed Number form - x= -4 2/5

Step-by-step explanation: Isolate the variable by dividing each side by your factors that don't contain variables.

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2 years ago

A rectangle has vertices (r,t) , (r,s) and (t,t). find the fourth vertex

Andrej [43]

Answer:

(t,s)

Step-by-step explanation:

this point has the x value t and the y value s that is missing.

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2 years ago

A company advertises that its cans of caviar each contain 100 g of their product. A consumer advocacy group doubts this claim, a

Blizzard [7]

Answer:

The value of the test statistic is -3.14.

Step-by-step explanation:

Test statistic:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the expected value, $\sigma$ is the standard deviation and n is the size of the sample.

A company advertises that its cans of caviar each contain 100 g of their product.

This means that $\mu = 100$

They calculate a sample mean weight of 99 g and a sample standard deviation of 0.9 g. Sample of 8 cans.

This means that $X = 99, \sigma = 0.9, n = 8$

So the test statistic will be given by:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$t = \frac{99 - 100}{\frac{0.9}{\sqrt{8}}}$

$t = -3.14$

The value of the test statistic is -3.14.

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2 years ago

Select all of the following that are quadratic equations.

kifflom [539]

A quadratic equation is one in which the highest exponent of x is 2.
$7x^2+14x=0$ is quadratic; the highest exponent is 2.
x³-3x²+1=0 is NOT quadratic. The highest exponent of x is 3, not 2.
5x-7=0 is NOT quadratic. The highest exponent of x is 1, not 2.
x²+3x-5=0 is quadratic; the highest exponent of x is 2.
x-5=9x+7 is NOT quadratic. The highest exponent of x is 1, not 2.
x²-x=3x+7 is quadratic; the highest exponent of x is 2.

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3 years ago