identify the two rational numbers. A) √2 B) 1.01 C) 1.010010001... C) -2/5

The speed of the wind is 4 mph.

Let, the speed of the wind is W mph.

When Lupe rides with the wind, her effective speed is 20 + W mph, and when she rides against the wind, her effective speed is 20 - W mph.

We are given two pieces of information:

Lupe rode 2 miles against the wind, and it took her the same amount of time as riding 3 miles with the wind.

The time taken to cover a distance is equal to the distance divided by the speed.

Using this information, we can set up two equations:

Time taken against the wind = Time taken with the wind

2 / (20 - W) = 3 / (20 + W)

Now, let's solve for W:

2(20 + W) = 3(20 - W)

40 + 2W = 60 - 3W

5W = 20

W = 20 / 5

W = 4 mph

The speed of the wind is 4 mph.

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Answer:

C)square 37 - square root 26

Step-by-step explanation:

Answer:

Chart 2.

Step-by-step explanation:

In the figure Dan has constructed an angle at point Q.He wants to cinstruct an angle ar point R which is congruent to angle made at point Q.To construct the angle at point R Dan needs to draw an arc at point R .He will put the compass on point R and draw an arc .This is shown in the figure 2.

The figure is added below.

Final answer:

The total mass of Sandra's 5 toy cars is calculated by multiplying the mass of one toy car (8 grams) by the total number of cars, resulting in a total mass of 40 grams.

Explanation:

The question requires us to calculate the total mass of Sandra's toy cars. Since each toy car has a mass of 8 grams, we can find the total mass by multiplying the mass of one car by the number of cars, which is 5 in this case. Therefore, the calculation we need to perform is 8 grams times 5, which will give us the total mass of all the toy cars combined.

To solve: 8 grams/car × 5 cars = 40 grams.

Thus, the total mass of all 5 toy cars that Sandra has would be 40 grams.

Answer:

C. your welcome

Answer:

The graph for 12x-9y=36 is given below

Step-by-step explanation:

The graph for 12x-9y=36 is given below.

[tex]12x-9y=36\\\frac{12x}{36}+\frac{9y}{-36}=1\\\frac{x}{3}+\frac{y}{-4}=1[/tex]

So x intercept is 3 and y intercept is -4.

The required graph is shown below which represents the equation 12x - 9y = 36.

To graph the equation 12x-9y=36, we can rearrange it to slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept.

First, solve for y by subtracting 12x from both sides and then dividing by -9. This gives us y=-4/3x+4.

Now we can see that the slope is -4/3 and the y-intercept is 4.

To graph this line, we can start at the y-intercept of (0,4) and then use the slope to find another point.

Since the slope is negative, we can move down 4 units (which is the denominator of the slope) and then move to the right 3 units (which is the numerator of the slope) to get another point at (3,0).

We can then draw a straight line through these two points to graph the equation.

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Answer:92

Step-by-step explanation:

92

Answer:

mary sue: 359, betty; 244

Step-by-step explanation:

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The coordinates of the image after dilation with a scale factor of 2 are A'(-10, -14), B'(12, -6), C'(4, 14).

Your question involves geometry and specifically, dilation transformations. A dilation is a transformation that moves each point along the ray from the center of dilation to the point. The number given as the scale factor tells you how much to move. In this case, we are asked to dilate the given points with a scale factor of 2 centered at the origin (0,0).

So, each coordinate of the original triangle should be multiplied by 2. Let's find each coordinate after dilation:

So, the coordinates of the image after a dilation with a scale factor of 2 are A'(-10, -14), B'(12, -6), and C'(4, 14).

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Answer:

81

Step-by-step explanation:

To find the points of discontinuity and sketch the graph of the rational function (x^2-4)/(x+2)(x^2-49), we need to determine the values of x that make the denominator equal to zero. We find that x = -2, x = 7, and x = -7 are the points of discontinuity. We can then sketch the graph by plotting the vertical asymptotes at x = -2, x = 7, and x = -7, and determining the behavior of the function on each side of those points.

To find the points of discontinuity for the rational function (x^2-4)/(x+2)(x^2-49), we need to determine where the denominator is equal to zero. The denominator has two factors, (x+2) and (x^2-49). Setting each factor equal to zero, we find that x = -2, x = 7, and x = -7. These are the points where the function has vertical asymptotes or holes.

To sketch the graph, we can start by plotting the vertical asymptotes at x = -2, x = 7, and x = -7. Next, we can examine the sign of the function on each side of the vertical asymptotes to determine the behavior of the graph. Finally, we can plot any holes in the graph at the corresponding x-values.

Additionally, we should determine if there are any horizontal asymptotes. For rational functions, horizontal asymptotes occur when the degree of the numerator is less than or equal to the degree of the denominator. In this case, the degree of the numerator is 2 and the degree of the denominator is 3, so there is no horizontal asymptote.

Final answer:

The domain of the function h(x)=9x/x(x²-36) is all real numbers except 0, 6, and -6, because the function is undefined at these points.

In conclusion, the domain of h(x) is x ∈ ℝ, x ≠ 0, x ≠ 6, x ≠ -6.

Explanation:

The question asks to determine the domain of the function h(x) = 9x / x(x² - 36).

The domain of a function consists of all the real numbers x for which the function is defined. In this case, the function will be undefined when the denominator is zero because division by zero is not defined in mathematics.

To find these values, we set the denominator equal to zero and solve the resulting equation:

This can be factored further as x(x - 6)(x + 6) = 0, which gives us the zero points of x = 0, x = 6, and x = -6.

Therefore, the domain of h(x) is all real numbers except 0, 6, and -6.

In conclusion, the domain of h(x) is x ∈ ℝ, x ≠ 0, x ≠ 6, x ≠ -6.

To solve for the positive number when the sum of 5 and three times the number is subtracted from the square of the number to yield zero, set up and solve the quadratic equation x^2 - 3x - 5 = 0 using the quadratic formula.

The student has asked for help in finding a positive number when the sum of 5 and three times the number is subtracted from the square of the number, and the result is 0. This involves setting up a quadratic equation and solving for the number.

Let's denote this positive number as 'x'. According to the problem statement, the equation can be written as:

x2 - (5 + 3x) = 0.

We can then expand and simplify this equation:

x2 - 5 - 3x = 0

And, rearrange it into standard quadratic form:

x2 - 3x - 5 = 0

Next, we can either factorize this equation, if possible, or use the quadratic formula to find the value of 'x' that satisfies the equation. Since this equation does not factor neatly, we use the quadratic formula:

x = ∛2 - 4ac) / 2a

In this case, a = 1, b = -3, and c = -5. Plugging these into the quadratic formula, we find the two possible solutions for x. Only the positive solution is relevant since the problem states that the number is positive.