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3 years ago

Rewrite the equation in standard form : y=2x=7

Mathematics

1 answer:

e-lub [12.9K]3 years ago

6 0

Answer:

2x - y = -7

Step-by-step explanation:

The equation y = 2x+7 needs to be written in standard form $Ax+By=C$ where A must be positive.

To convert to standard form, subtract 2x from both sides.

-2x + y = 7

Multiply each term by -1.

-1(-2x + y =7)

2x - y = -7

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stira [4]

Angle CFE is an alternate interior angle with angle FCD

5 0

3 years ago

What is the answer to -8(-1)•1(-4)

horsena [70]

The answer is -32. This is because when you multiply to negatives it becomes a positive. So its 8*-4 making the answer be -32.

3 0

3 years ago

A soccer ball was kicked in the air and follows the path h(x)=−2x2+1x+6, where x is the time in seconds and h is the height of t

madam [21]

The ball will hit the ground at 2 seconds.

Step-by-step explanation:

Given that,

The path of the ball = h(x)=−2x2+1x+6

Here,

x is the time while h is the height of ball.

When the ball will hit the ground, the height will become zero. Therefore,

h(x)=−2x2+1x+6

0 =−2x2+1x+6

2x2 -1x - 6 = 0

This is a quadratic equation, hence by applying quadratic equation formula:

$x = \frac{-b +- \sqrt{b^{2} - 4ac } }{2a}$

here,

a = 2

b = -1

c = -6

Putting these values in formula, we get

$x = \frac{-(-1) +- \sqrt{-1^{2} - 4.2.-6 } }{2.2}$

$x = \frac{1 +- \sqrt{1 + 48 } }{4}$

$x = \frac{1 +- \sqrt{49 } }{4}$

$x = \frac{1 +- 7 }{4}$

x = 2, -3/2

As the time cannot be negative. Therefore, the ball will hit the ground at 2 seconds.

6 0

4 years ago

Read 2 more answers

Lim (n/3n-1)^(n-1) n → ∞

n200080 [17]

Looks like the given limit is

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1}$

With some simple algebra, we can rewrite

$\dfrac n{3n-1} = \dfrac13 \cdot \dfrac n{n-9} = \dfrac13 \cdot \dfrac{(n-9)+9}{n-9} = \dfrac13 \cdot \left(1 + \dfrac9{n-9}\right)$

then distribute the limit over the product,

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \lim_{n\to\infty}\left(\dfrac13\right)^{n-1} \cdot \lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}$

The first limit is 0, since 1/3ⁿ is a positive, decreasing sequence. But before claiming the overall limit is also 0, we need to show that the second limit is also finite.

For the second limit, recall the definition of the constant, e :

$\displaystyle e = \lim_{n\to\infty} \left(1+\frac1n\right)^n$

To make our limit resemble this one more closely, make a substitution; replace 9/(n - 9) with 1/m, so that

$\dfrac{9}{n-9} = \dfrac1m \implies 9m = n-9 \implies 9m+8 = n-1$

From the relation 9m = n - 9, we see that m also approaches infinity as n approaches infinity. So, the second limit is rewritten as

$\displaystyle\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8}$

Now we apply some more properties of multiplication and limits:

$\displaystyle \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m} \cdot \lim_{m\to\infty}\left(1+\dfrac1m\right)^8 \\\\ = \lim_{m\to\infty}\left(\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = e^9 \cdot 1^8 = e^9$

So, the overall limit is indeed 0:

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \underbrace{\lim_{n\to\infty}\left(\dfrac13\right)^{n-1}}_0 \cdot \underbrace{\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}}_{e^9} = \boxed{0}$

7 0

3 years ago

Chad ran a red light and hit another car. He decided to file a claim for damage

pochemuha

Answer:

Comprehensive deductible

Step-by-step explanation:

There is nothing called Premium deductible rather deductible determines how higher of lower a premium on a subject matter of insurance can be. Deductible is the amount with the insured have to bear at loss and any excess above the loss will be compensated by the insurance company.

Comprehensive deductible is the application to only to comprehensive insurance which was what Chad had on his motor vehicle. Comprehensive insurance covers majority of peril that happens to the insured vehicle. Therefore, comprehensive deductible is the deductible Chad has to bear himself before the insurance company take other losses upon theirself..

If he had $500 deductible on his car and total repair cost $700, then he will bear the $500 while the insurance company is entitled to pay only $200 as per policy statement.

6 0

3 years ago

Read 2 more answers