giovanni justifies what is expression -4x - 8 is equivalent to -2( x + 1) - 2 ( x + 3 ) by letting x equal 3 in both expressions what is the value of each expression when x equals 3

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: Option B

(B) 12

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 probability that X is greater than 10.52 for a normal distribution with a mean of 5 and a standard deviation of 2 is found by calculating the z-score of 10.52. The z-score is 2.76, and the area to the right under the normal curve represents a very small probability, typically less than 0.003.

Explanation:

To find the probability that X is greater than 10.52, when X is a normally distributed random variable with a mean of 5 and a standard deviation of 2, we first need to calculate the z-score for 10.52. Using the formula:

Z = (X - mean) / standard deviation

Substitute the given values into the formula:

Z = (10.52 - 5) / 2 = 5.52 / 2 = 2.76

This z-score tells us how many standard deviations above the mean our value lies. In this case, X = 10.52 is 2.76 standard deviations above the mean.

The probability of X being greater than 10.52 corresponds to the area under the standard normal distribution curve to the right of the z-score 2.76. Using standard normal distribution tables or software, we can find this probability to be very small, typically less than 0.003.

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. your welcome

Answer:

720

Step-by-step explanation:

Given : A church has 10 bells in its bell tower.

          Before each church service 3 bells are rung in sequence.

To Find: How many sequences are there?

Solution:

Since we are given that 3 bells are rung in sequence. no bell is rung more than once.

So, we will use permutation.

Formula :[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]

Since A church has 10 bells in its bell tower.

So, n =10

We are also given that Before each church service 3 bells are rung in sequence . So, r =3

So, the number of possible sequence = [tex]^{10}P_3[/tex]

                                                               = [tex]\frac{10!}{(10-3)!}[/tex]

                                                               = [tex]\frac{10!}{(7)!}[/tex]

                                                               = [tex]\frac{10 \times 9 \times 8 \times 7!}{(7)!}[/tex]

                                                               = [tex]10 \times 9 \times 8[/tex]

                                                               = [tex]720[/tex]

Hence there are 720 sequences.

There are 120 different sequences in which the 3 bells can be rung in sequence before each church service without any bell being rung more than once.

To find the number of sequences in which the 3 bells can be rung in sequence out of 10 bells without any bell being rung more than once, you can use the concept of combinations.

The number of ways to choose 3 distinct bells out of 10 is given by the binomial coefficient "10 choose 3," which is denoted as C(10, 3) and calculated as follows:

C(10, 3) = 10! / (3!(10 - 3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120

So, there are 120 different sequences in which the 3 bells can be rung in sequence before each church service without any bell being rung more than once.

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The car needs 14 gallons of gas for the 714 mile trip.

To determine the amount of gas required for a 714-mile trip, we can set up a proportion based on the given information:

We know that the car travels 204 miles on 4 gallons of gas. We need to find the amount of gas needed for 714 miles. Let the gas required for 714 miles be X gallons

First, let us set up the proportion:

Next, we solve for x (the amount of gas required for 714 miles):

Therefore, the car requires 14 gallons of gas for a 714-mile trip.

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.

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:

mary sue: 359, betty; 244

Step-by-step explanation:

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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.