Use technology to solve for x.
2^x -5 = 3x - 6
What are the solutions?

4/21 of the books in the library are both fiction and paperbacks.

To determine the fraction of books in the library that are both fiction and paperback, we need to multiply the fractions representing each condition.

Let's start with the fraction of books in the library that are fiction. If 4/7 of the books are fiction, then this fraction represents the number of fiction books.

Next, we want to find the fraction of fiction books that are also paperbacks. Since 1/3 of the fiction books are paperbacks, we multiply 4/7 (fiction books) by 1/3 (paperback fraction).

Multiplying fractions is done by multiplying the numerators together to get the new numerator and multiplying the denominators together to get the new denominator.

Thus, the fraction of books in the library that are both fiction and paperbacks is:

(4/7) * (1/3) = (4 * 1) / (7 * 3) = 4/21

Therefore, 4/21 of the books in the library are both fiction and paperbacks.

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The value of n is approximately -0.327.

To determine the value of n, we can substitute the given solution (x = 2.1) into the system of equations:

4x² - my = 10 ...(1)

mx² + ny = 20 ...(2)

Substituting x = 2.1 into equation (1), we get:

4(2.1)² - my = 10

8.4 - my = 10

-my = 10 - 8.4

-my = 1.6

Now, substituting x = 2.1 into equation (2), we get:

m(2.1)² + ny = 20

4.41m + ny = 20

Since we already have an expression for -my from equation (1), we can substitute it into equation (2):

4.41m + (-1.6) = 20

4.41m - 1.6 = 20

4.41m = 20 + 1.6

4.41m = 21.6

To solve for m, we divide both sides by 4.41:

m = 21.6 / 4.41

m ≈ 4.9

Now that we have the value of m, we can substitute it back into equation (1) to solve for n:

4(2.1)² - 4.9y = 10

8.4 - 4.9y = 10

-4.9y = 10 - 8.4

-4.9y = 1.6

Finally, to solve for y, we divide both sides by -4.9:

y = 1.6 / -4.9

y ≈ -0.327

Consequently, n has a value of roughly -0.327.

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The equation that represents the hyperbola shown in the graph is (y - 3)²/4 - (x + 2)²/25 = 1.

From the given options, the equation that represents the hyperbola shown in the graph is (y - 3)²/4 - (x + 2)²/25 = 1.

To determine the equation of a hyperbola, we examine the standard form:

For a hyperbola centered at (h, k), with vertical transverse axis, the standard form is:

(y - k)²/a² - (x - h)²/b² = 1

From the given graph, we can observe that the center of the hyperbola is (-2, 3). This corresponds to the values of (h, k) in the standard form.

Next, we need to determine the values of a and b, which are the lengths of the transverse and conjugate axes, respectively. Looking at the graph, we see that the transverse axis has a length of 2a = 4, so a = 2. The conjugate axis has a length of 2b = 10, so b = 5.

Plugging these values into the standard form, we obtain:

(y - 3)²/4 - (x + 2)²/25 = 1

The equation that represents the hyperbola shown in the graph is (y - 3)²/4 - (x + 2)²/25 = 1.

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The correct equation representing the hyperbola shown in the graph is:

(x + 2)²/25 - (y - 3)²/4 = 1.

The equation that represents the hyperbola shown in the graph is:

(x + 2)²/25 - (y - 3)²/4 = 1

Let's analyze the options provided:

(x - 2)²(v + 3)² = 1:

This equation is not a valid representation of a hyperbola because it contains a term (v + 3)², which is not consistent with the variable used in the graph.

(x + 2)²/25:

This equation represents a horizontal parabola, not a hyperbola.

(x - 2)²/25:

This equation represents a horizontal parabola, not a hyperbola.

(y - 3)²/1:

This equation represents a vertical line, not a hyperbola.

(y - 3)²/4:

This equation represents a hyperbola with a vertical transverse axis and a conjugate axis length of 2b = 4 (b = 2).

The equation is in the standard form for a hyperbola with a vertical transverse axis.

The equation is provided as a standard form assuming the given coordinates and graph match the standard form representation of a hyperbola.

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The extreme of the function is Absolute minimum

y = -2

x-intercept = 3

A discontinuous function is a mathematical function that has one or more points in its domain where the function fails to be continuous.

In other words, at these specific points, the function exhibits a discontinuity, indicating a break or jump in the graph.

In the graph, there was discontinuities at points

x = -2, and x = 2

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Answer:

3.34 * 10^-21 g

Step-by-step explanation:

1.67*10^-24 * 2000 = 1.67 * 10^-24 * 2 *10^3 = 3.34 * 10^-21 g

Answer:

A, C

Step-by-step explanation:

x² + 3x - 5 = 0

[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

[tex] x = \dfrac{-3 \pm \sqrt{3^2 - 4(1)(-5)}}{2(1)} [/tex]

[tex] x = \dfrac{-3 \pm \sqrt{29}}{2} [/tex]

Answer:

1 - 3√(5/35) = 1 - 3√(1/7) = 1 - 3*(1/sqrt(7)) ≈ 0.0755
0.0755 * 100 = 7.55%

Step-by-step explanation:

To find the percentage of 1 - 3√(5/35), we need to first evaluate the expression.

1 - 3√(5/35) = 1 - 3√(1/7) = 1 - 3*(1/sqrt(7)) ≈ 0.0755

To convert this decimal to a percentage, we simply multiply by 100:

0.0755 * 100 = 7.55%

Given the equation f(x) = a · bx where a and b are constants. So, the answer to the given problem is g(x) = a · bx + h, and the explanation of the trigonometric function.

To find the equation of transformed function g in terms of function f is explained below: If f(x) = a · bx, then the transformed function g(x) can be represented by g(x) = a · bx + h, where h is the vertical shift (if h > 0, the graph shifts upward, and if h < 0, the graph shifts downward).

Now, we have to replace the value of 'a' to complete the equation of g(x). But, we don't have any value of 'a' provided in the question. Hence, we can't determine the equation of transformed function g in terms of function f for the given information.

Next, let's move to the trigonometric function. It is given that: R S 9 sin cos tan sin cos tan-¹ /ASin, Cos, Tan, Cosec, Sec, and Cot are six trigonometric functions. Let's see their definitions and their corresponding inverse functions:

1. Sine: It is defined as the ratio of the length of the side opposite the given angle to the length of the hypotenuse in a right-angled triangle. Its corresponding inverse function is sin⁻¹.

2. Cosine: It is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle. Its corresponding inverse function is cos⁻¹.

3. Tangent: It is defined as the ratio of the length of the side opposite the given angle to the length of the adjacent side in a right-angled triangle. Its corresponding inverse function is tan⁻¹.

4. Cosecant: It is defined as the ratio of the length of the hypotenuse to the length of the side opposite the given angle in a right-angled triangle. Its corresponding inverse function is cosec⁻¹.

5. Secant: It is defined as the ratio of the length of the hypotenuse to the length of the adjacent side in a right-angled triangle. Its corresponding inverse function is sec⁻¹.

6. Cotangent: It is defined as the ratio of the length of the adjacent side to the length of the side opposite the given angle in a right-angled triangle. Its corresponding inverse function is cot⁻¹.

Hence, the answer to the given problem is g(x) = a · bx + h, and the explanation of the trigonometric function.

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Step-by-step explanation:

1. Answer is 2

2. Answer is -3

3. Answer is 4

Answer:

i) -5x + 3/2

ii) x = 11

iii) x + 9/2

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Answer:

(5, 3 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

D (5, - 3 ) → (5, - (- 3) ) → (5, 3 )

Answer:

(5,3)

Step-by-step explanation:

got it right on edg

Answer:

7

Step-by-step explanation:

In an 30-60-90 right triangle, the longer leg is the shorter leg multiplied by [tex]\sqrt{3}[/tex]

So [tex]7\sqrt{3} =x*\sqrt{3[/tex]

[tex]7=x[/tex]

x=7

Answer:

A. 21

Step-by-step explanation:

This is a 30-60-90 triangle, where you have one 30° angle, one 60°, and one 90° (aka right) angle.  

The sides of a 30-60-90 triangle adhere to the following rules:

Since 7√3 is the length of the side opposite the 30° angle, the entire expression represents x.

Since the length of the side opposite the 60° angle is given by x * √3, the length of this side is (7√3)(√3).

Simplifying gives us 7*3, which is 21.

Thus, the value of x in the triangle is 21 (answer choice A.)

The pixel resolution is 4.896 x 10^5 pixels; in megapixels, it's approximately 0.490; and the aspect ratio is 18:17.

First, let's calculate the resolution in pixels: Resolution is simply the width times the height of the sensor. Specifically for this question, multiply 720 by 680. This gives us 489600 pixels for the resolution - in scientific notation to 4 significant figures we have 4.896 x 10^5.

Next, to calculate the resolution in megapixels, we need to divide the resolution by 1 million (since one megapixel is equal to 1 million pixels). So, 489600/1,000,000 is approximately 0.490 megapixels when rounded to the nearest thousandth of a megapixel.

Finally, the aspect ratio is the relationship of the width to the height of an image or screen. For a 720 x 680 sensor, if we divide 720 by 680, the result would be approximately 1.0588. However, we want this ratio in its simplest form, so we should use the greatest common divisor (GCD). In this case, the GCD of 720 and 680 is 40, so by dividing both dimensions by 40, we get an aspect ratio of 18:17.

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