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3 years ago

Y=x+3 and y=x-y help me

Mathematics

1 answer:

Nuetrik [128]3 years ago

4 0

Step-by-step explanation:

Given

y = x + 3.....equation 1

y = x - y

or y + y = x

or 2y = x

or y = x / 2......equation 2

Now

Putting equation 2 in equation 1

x / 2 = x + 3

x - x/2 = - 3

2x - x  = - 3

x / 2 = -3

x = - 6

Now

y = x/ 2

= - 6/2

= - 3

Hope this helps

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Find the exact value of the expression. tan( sin−1 (2/3)− cos−1(1/7))

Sonja [21]

Answer:

$\tan(a-b)=\frac{2\sqrt{5}-20\sqrt{3}}{5+8\sqrt{15}}$

Step-by-step explanation:

I'm going to use the following identity to help with the difference inside the tangent function there:

$\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}$

Let $a=\sin^{-1}(\frac{2}{3})$ .

With some restriction on $a$ this means:

$\sin(a)=\frac{2}{3}$

We need to find $\tan(a)$ .

$\sin^2(a)+\cos^2(a)=1$ is a Pythagorean Identity I will use to find the cosine value and then I will use that the tangent function is the ratio of sine to cosine.

$(\frac{2}{3})^2+\cos^2(a)=1$

$\frac{4}{9}+\cos^2(a)=1$

Subtract 4/9 on both sides:

$\cos^2(a)=\frac{5}{9}$

Take the square root of both sides:

$\cos(a)=\pm \sqrt{\frac{5}{9}}$

$\cos(a)=\pm \frac{\sqrt{5}}{3}$

The cosine value is positive because $a$ is a number between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$ because that is the restriction on sine inverse.

So we have $\cos(a)=\frac{\sqrt{5}}{3}$ .

This means that $\tan(a)=\frac{\frac{2}{3}}{\frac{\sqrt{5}}{3}}$ .

Multiplying numerator and denominator by 3 gives us:

$\tan(a)=\frac{2}{\sqrt{5}}$

Rationalizing the denominator by multiplying top and bottom by square root of 5 gives us:

$\tan(a)=\frac{2\sqrt{5}}{5}$

Let's continue on to letting $b=\cos^{-1}(\frac{1}{7})$ .

Let's go ahead and say what the restrictions on $b$ are.

$b$ is a number in between 0 and $\pi$ .

So anyways $b=\cos^{-1}(\frac{1}{7})$ implies $\cos(b)=\frac{1}{7}$ .

Let's use the Pythagorean Identity again I mentioned from before to find the sine value of $b$ .

$\cos^2(b)+\sin^2(b)=1$

$(\frac{1}{7})^2+\sin^2(b)=1$

$\frac{1}{49}+\sin^2(b)=1$

Subtract 1/49 on both sides:

$\sin^2(b)=\frac{48}{49}$

Take the square root of both sides:

$\sin(b)=\pm \sqrt{\frac{48}{49}$

$\sin(b)=\pm \frac{\sqrt{48}}{7}$

$\sin(b)=\pm \frac{\sqrt{16}\sqrt{3}}{7}$

$\sin(b)=\pm \frac{4\sqrt{3}}{7}$

So since $b$ is a number between $0$ and $\pi$ , then sine of this value is positive.

This implies:

$\sin(b)=\frac{4\sqrt{3}}{7}$

So $\tan(b)=\frac{\sin(b)}{\cos(b)}=\frac{\frac{4\sqrt{3}}{7}}{\frac{1}{7}}$ .

Multiplying both top and bottom by 7 gives:

$\frac{4\sqrt{3}}{1}= 4\sqrt{3}$ .

Let's put everything back into the first mentioned identity.

$\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}$

$\tan(a-b)=\frac{\frac{2\sqrt{5}}{5}-4\sqrt{3}}{1+\frac{2\sqrt{5}}{5}\cdot 4\sqrt{3}}$

Let's clear the mini-fractions by multiply top and bottom by the least common multiple of the denominators of these mini-fractions. That is, we are multiplying top and bottom by 5:

$\tan(a-b)=\frac{2 \sqrt{5}-20\sqrt{3}}{5+2\sqrt{5}\cdot 4\sqrt{3}}$

$\tan(a-b)=\frac{2\sqrt{5}-20\sqrt{3}}{5+8\sqrt{15}}$

4 0

3 years ago

Sarafina and Katie have between $105 and $420 dollars to spend on jewelry for Christmas presents for their friends. If they buy

algol13

Answer:

Step-by-step explanation:

105+420=525 (Total Money)

7x3.25=22.75 (Cost of all bracelets)

8x11.74=93.92 (Cost of all necklaces)

93.92+22.75=116.67 (Cost of all Christmas presents)

525-116.67=408.33 (Total money - Cost of all Christmas presents)

408.33/6.15=66.39... (Amount of necklaces)

since in real life you can only buy a whole number of things, you would round down 66.39 to 66. I hope this helped!

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2 years ago

Tourists from a tour bus were asked about places they visited during their stay in a city. The results are shown in the table.

nlexa [21]

Given:

visited museum didn't visit museum Total

visited zoo 9 14 23

didn't visit zoo 5 2 7

Total 14 16 30

Simply look at the table and check the number that corresponds to visitors who visited the museum but did not visit the zoo. The number is 5.
Divide it by the total number of people surveyed. Total is 30.

Probability visited the museum but did not visit the zoo = 5/30 = 0.16666 or 16.67%

7 0

3 years ago

Factor completely 4x^5-20x^3

nikdorinn [45]

Answer:

4x^3(x^2 - 5)

Step-by-step explanation:

First, try to factor a common factor.

GCF of 4 and -20 is 4.

GCF of x^5 and x^3 is x^3.

Factor out 4x^3.

4x^5 - 20x^3 =

= 4x^3(x^2 - 5)

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3 years ago

Determine values of a, b,c, d, e for the cubic spline

Aleonysh [2.5K]

There is not enough information

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3 years ago

Y=x+3 and y=x-y help me ​

Y=x+3 and y=x-y help me