What's the numerator for the following rational expression? G/h + 8/h = ?/h

The answer is: true.

Here's why:

A slope of 0 indicates a horizontal line, meaning there's no change in y-value as x changes.

A y-intercept of 6 means the line intersects the y-axis at the point (0, 6).

The equation y = 6 represents a constant y-value for any x, which indeed depicts a horizontal line that intersects the y-axis at (0, 6).

Therefore, both the slope and the equation confirm that the line is horizontal.

The 38th power, [tex]i^{38[/tex] simplifies to -1.

To simplify [tex]\( i^{38 \),[/tex] you can start by recognizing the pattern that powers of i repeat every four terms. This means that [tex]\( i^{4\),[/tex]  equals 1, [tex]\( i^{8 \),[/tex]  also equals 1, and so on. Therefore,  [tex]\( i^{38 \),[/tex]can be simplified as follows:

[tex]\[ i^{38} = i^{4 \cdot 9 + 2} \][/tex]

Since [tex]\( i^4 \)[/tex] is equal to 1, we have:

[tex]\[ i^{38} = (i^4)^9 \cdot i^2 = 1^9 \cdot (-1) = -1 \][/tex]

So,[tex]\( i^{38} \)[/tex] simplifies to -1.

Complete question is:

Simplify i³⁸. [i=√(-1)]

Answer:

The correct answer is: 60°  

Step-by-step explanation:

Rotational symmetry is a type of symmetry, in which an object returns back to its original shape after rotation at an angle of 360°/n about a fixed point.

A hexagon is a regular polygon that has six edges and vertices. It has six internal angles, 120° each.

Since there are 6 equal edges, therefore, the hexagon will rotate onto itself after every rotation at an angle of: 360°/n = 360°/6 = 60°

Answer: x+2. The answer is C.

Step-by-step explanation:

Answer:

[tex]\text{The value of }f^{-1}(8)\text{ is }\frac{3}{2}[/tex]        

Step-by-step explanation:

Given the function

[tex]f(x)=2x+5[/tex]

[tex]\text{we have to find the value of }f^{-1}(8)[/tex]

First we have to find the inverse

Step 1: Put f(x)=y, the equation becomes

[tex]y=2x+5[/tex]

Step 2: Replace x to y and y to x, we get

[tex]x=2y+5[/tex]

Step 3: Solve for y and then replace it with [tex]f^{-1}x[/tex]

[tex]x-5=2y[/tex]

[tex]y=\frac{x-5}{2}[/tex]

[tex]f^{-1}(x)=\frac{x-5}{2}[/tex]

Now substitute x=8, we get

[tex]f^{-1}(8)=\frac{8-5}{2}=\frac{3}{2}[/tex]

[tex]\text{hence, the value of }f^{-1}(8)\text{ is }\frac{3}{2}[/tex]

The simultaneous equations 3x-3y=3 and y=-5x-17 can be solved using substitution, resulting in the solution x = -8/3 and y = -11/3.

To solve the simultaneous equations 3x-3y=3 and y=-5x-17, we can use substitution or elimination. Substitution is straightforward since we already have y expressed in terms of x in the second equation. We can substitute y=-5x-17 into the first equation:

Now, plug x back into y=-5x-17 to find y:

The solution to the system of equations is x = -8/3 and y = -11/3.

Answer:

Eight cups of yogurt will be used.

Step-by-step explanation:

Let cups of yogurt used in 12 cups of smoothies be x

Cups of juice  used in 12 cups of smoothies = 12- x

The ratio of yogurt to juice is 2 cups to 1 cup that is:

[tex]\frac{Yogurt}{Juice}=\frac{2}{1}[/tex]

Ratio will be maintained through out 12 cups of smoothies:

[tex]\frac{Yogurt}{Juice}=\frac{2}{1}=\frac{x}{12-x}[/tex]

[tex]2(12-x)=1(x)[/tex]

[tex]24-2x=x[/tex]

[tex]24=3x[/tex]

x = 8

Eight cups of yogurt will be used.

The correct equation for the line that passes through the point (2, 4) with a slope of 3 is 'y - 4 = 3(x - 2)' using the point-slope form of a linear equation.

The equation that represents the line passing through the point (2, 4) with a slope of 3 is y - 4 = 3(x - 2). To find the equation of a line given a point and a slope, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope of the line.

Since the line must pass through (2, 4) and the slope (m) is 3, we plug these values into the point-slope form to get the correct equation.

Answer: A. AB=QR,BC=RS

Step-by-step explanation:

The congruence property of congruence triangle CPCTC says that the corresponding parts of congruent triangles are congruent.

From the given figure, we have

[tex]\angle{A}\cong\angle{Q}\\\angle{C}\cong\angle{S}[/tex]

[tex]\overline{AC}=\overline{QS}[/tex]

The other congruent parts in the triangle.

[tex]\overlien{AB}\cong\overlien{QR}[/tex] [∵ AB corresponds QR]

[tex]\\\\\overlien{BC}\cong\overlien{RS}[/tex]  [∵BC corresponds RS]

Answer:

[tex]\frac{1}{5} ;\frac{2}{10} ;\frac{3}{15}[/tex]

Step-by-step explanation:

To find the three ratios we only have to find the most simple ratio of [tex]\frac{7}{35}[/tex], and then find the other ratios that are equal to it.

So, [tex]\frac{7}{35} = \frac{1}{5}[/tex]

Also, [tex]\frac{1}{5} =\frac{2}{10}[/tex], by multiplying by two each part of the fraction.

Similarly, [tex]\frac{3}{15} = \frac{1}{5}[/tex], by multiplying by three.

Therefore, comparing all these ratios, all are the same, they are equal to [tex]\frac{1}{5}[/tex]. So, the option that correctly has these choices is D.

Answer:

A

Step-by-step explanation:

other guy said it and I got it right.

From the attached diagram you can see that regression that best fits given data is quadratic (not linear).

Answer: correct choice is B.

The graph of the given values is required.

Option B is correct.

The points are

[tex](1,97)[tex]

[tex](2,168)[/tex]

[tex](3,259)[/tex]

[tex](4,375)[/tex]

Let us find if the points are in the form of a line by finding the slope.

[tex]\dfrac{168-97}{2-1}=71[/tex]

[tex]\dfrac{259-168}{3-2}=91[/tex]

[tex]71\neq 91[/tex]

So, the function is not linear.

Therefore, A and C are incorrect.

Also the function is not decreasing so option D is also eliminated.

Hence, option B is correct.

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The correct two-way table for comparing the car color choices of eight surveyed individuals by gender is Option D, which shows 2 females choosing green and 2 blue, while 1 male chose green and 3 chose blue.

The question is about analyzing a two-way table that compares categorical data: gender and car color preferences. To find the correct table, we need to tally the choices made by each person based on the information given and compare it to the options provided in the answer choices. By counting the number of times each gender chose each color, we can determine the accurate representation of the data.

For females, 2 chose green and 2 chose blue.

For males, 1 chose green and 3 chose blue.

Given this information, the correct two-way table that compares the categorical data is:

Option D.

            Green Blue

Female   2        2

Male        1         3

This table correctly captures the car color preferences by gender among the eight people surveyed.

The original price of the shoes can be found by dividing the current price, $52, by 0.85, which yields an original price of approximately $61.18.

The current price of a pair of shoes is $52, which is 15% lower than it was last week. To find the original price, you can set up an equation where the original price minus 15% of the original price equals the current price of $52.

Let x represent the original price. The equation is then x - 0.15x = $52. Simplify this to 0.85x = $52. Divide both sides by 0.85 to solve for x.

x = $52 / 0.85

x = $61.18

Therefore, the price of the shoes last week was approximately $61.18.

If y is directly proportional to x^2, when x is halved, y becomes 0.25 times its original value. Given the original value of y is 10, when x is halved, the new y is 2.5.

When we say that y is directly proportional to x^2, it means there exists a constant of proportionality (let's call this 'k') such that the equation y = k*(x^2) always holds. From the problem, we know that y=10 for a certain x, let's square this x sometimes referred as x2 (we could say [tex]x2 = (x^1.5)^2).[/tex]

If x is halved, the new x which we can call [tex]x1 = 0.5*x2[/tex], then substitute x1 in the equation of direct proportion we get [tex]y1 = k*(0.5 *2)^2 = y*0.25[/tex], this is because (0.5)^2 is 0.25. So, the new y when x is halved (y1) will be 0.25 as much as the original y. Therefore, if your initial y was 10, your new y would be y1 = 10*0.25 which equals 2.5.

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Answer: There can be made 40 smallest game boards.

Step-by-step explanation:

Since we have given that

Number of rows = 8

Number of spaces in each row = 10

we need to find the smallest game board that can be made.

As we know that For Smallest we always find "L.C.M" because L.C.M. stands for least common multiple.

So, L.C.M. of 8 and 10 = 40

Hence, there can be made 40 smallest game boards.