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3 years ago

Please help me with this

Mathematics

1 answer:

pogonyaev3 years ago

7 0

Answer:

$x = 1, \: \: x = \frac{2}{3}$

Step-by-step explanation:

$\sqrt{3x + 1} - \sqrt{2 - x} = \sqrt{2x - 1} \\ \\ squaring \: both \: sides \\ \\ ( \sqrt{3x + 1} - \sqrt{2 - x})^{2} = ( \sqrt{2x - 1} ) ^{2} \\ \\ 3x + 1 + 2 - x - 2( \sqrt{3x + 1} ) ( \sqrt{2 - x} ) = 2x - 1 \\ \\ \cancel{ 2x} + 3 - 2( \sqrt{3x + 1} ) ( \sqrt{2 - x} ) = \cancel{ 2x} - 1 \\ \\ 3 - 2( \sqrt{3x + 1} ) ( \sqrt{2 - x} ) = - 1 \\ \\ - 2( \sqrt{3x + 1} ) ( \sqrt{2 - x} ) = - 1 - 3 \\ \\ - 2( \sqrt{3x + 1} ) ( \sqrt{2 - x} ) = - 4 \\ \\ ( \sqrt{3x + 1} ) ( \sqrt{2 - x} ) = 2 \\ \\ squaring \: both \: sides \: again \\ { [( \sqrt{3x + 1} ) ( \sqrt{2 - x} )] }^{2} = {2}^{2} \\ \\ (3x + 1)(2 - x) = 4 \\ \\ 6x - 3 {x}^{2} + 2 - x = 4 \\ \\ - 3 {x}^{2} + 5x - 2 = 0 \\ \\ 3 {x}^{2} - 5x + 2 = 0 \\ \\ 3 {x}^{2} - 3x - 2x + 2 = 0 \\ \\ 3x(x - 1) - 2(x - 1) = 0 \\ \\ (x - 1)(3x - 2) = 0 \\ \\ x - 1 = 0, \: \: 3x - 2 = 0 \\ \\ x = 1, \: \: x = \frac{2}{3}$

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There are 10 Superscript 9 bytes in a gigabyte. There are 10 Superscript 6 bytes in a megabyte. How many times greater is the st

ohaa [14]

To find the how many times greater is the storage capacity of a 1-gigabyte flash drive than a 1-megabyte flash drive we have to apply exponent operation.

The storage capacity of a 1-gigabyte is 1000 greater than 1-megabyte flash drive.

Given:

The given exponent for gigabyte is,

$10^9$

The given exponent of megabyte is,

$10^6$

<h3>What is exponent rule?</h3>

The power rule of exponent rule is defined as if raise the a number with exponent to power then we will mulitply exponent to the power times.
to change the negative exponent into a positive we have to invert the base.

Calculate the storage capacity.

$\dfrac{10^9}{ 10^6}=10^9-6}\\
\dfrac{10^9}{ 10^6}=10^3\\
\dfrac{10^9}{ 10^6}=1000$

Thus, the storage capacity of a 1-gigabyte is 1000 greater than 1-megabyte flash drive.

Learn more about exponent rule here:

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8 0

3 years ago

15. Rewrite the given functions in

Lisa [10]

15. The vertex form of f(x) = x² + 8x - 10 is f(x) = (x + 4)² - 26

17. The standard form of g(x) = (x + 3)² - 4 is g(x) = x² + 6x + 5

Step-by-step explanation:

Any quadratic function has:

1. A vertex form form f(x) = a(x - h)² + k, where (h , k) are the

coordinates of its vertex point

2. A standard form g(x) = ax² + bx + c, where a , b , c are constant and

a is the coefficient of x², b is the coefficient of x and c is the

y-intercept

3. the x-coordinate of the vertex point h = $\frac{-b}{2a}$ and

k = f(h)

15.

∵ f(x) = x² + 8x - 10

∴ a = 1 and b = 8

∵ h = $\frac{-b}{2a}$

∴ h = $\frac{-8}{2(1)}=-4$

∴ h = -4

∵ k = f(h)

∴ k = f(-4)

- Substitute x by -4 in f(x)

∴ k = (-4)² + 8(-4) - 10

∴ k = 16 - 32 - 10

∴ k = -26

∴ f(x) = (x - -4)² + (-26)

∴ f(x) = (x + 4)² - 26

The vertex form of f(x) = x² + 8x - 10 is f(x) = (x + 4)² - 26

17.

∵ g(x) = (x + 3)² - 4

- Lets solve the power 2 of the bracket:

(1st + 2nd)² = (1st)(1st) + 2(1st)(2nd) + (2nd)(2nd)

∵ (x + 3)² = (x)(x) + 2(x)(3) + (3)(3)

∴ (x + 3)² = x² + 6x + 9

∴ (x + 3)² - 4 = (x² + 6x + 9) - 4

∵ 9 - 4 = 5

∴ (x + 3)² - 4 = x² + 6x + 5

The standard form of g(x) = (x + 3)² - 4 is g(x) = x² + 6x + 5

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You can learn more about the vertex form of quadratic function in brainly.com/question/9390381

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4 0

4 years ago

Between what two integers is √95?

andrey2020 [161]

Answer:

Between 9 and 10.

Step-by-step explanation:

We know that √81 = 9 and that √100 = 10.

Since √95 is between √81 and √100, we know it will be between 9 and 10.

√95 = 9.74679

4 0

4 years ago

Plz answer it’s an iready

Dafna11 [192]

Answer:

6(6x + 4y), 12(3x + 2y), 4(9x + 6y)

Step-by-step explanation:

The expressions are equivalent to 36x + 24 y

Hope this helps! :)

5 0

3 years ago

Write the slope-intercept form of the equation that passes through the point (4,-6) and is parallel to the line y = -3/4x - 5

Karolina [17]

The equation that runs through the location (4,-6) has the slope-intercept form, $y=-\frac{3}{4}x-3$ .

<h2>Formation of the equation</h2>

A line's equation written in the slope-intercept form:

y=mx+b

where m= slope & b= y-intercept

The slope of two parallel lines is equal.

Currently, we know the line's equation:

$y=-\frac{3}{4} x-5$

here, slope, m= $-\frac{3}{4}$

A line equation is created by adding the slope's value and the point's coordinates (4, -6):

$-6=-\frac{3}{4}(4)+b$

⇒ -6=-3 +b [adding 3 to both sides]

⇒-3=b

⇒b= -3

Hence the solution is $y=-\frac{3}{4}x-3$ .

Learn more about slope-intercept form here:

brainly.com/question/9682526

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5 0

2 years ago