A new movie was released over the weekend with 8 show times. 124 people saw the movie during the first 2 show times. If people come to the movie at the same rate, how many saw it over the weekend?

(x+a)(x+3a)= x²+bx+75

x²+4a+3a²=x²+bx+75

by comparing 3a²=75 and b= 4a

a= ±5

possible values of b= ±20

Two possible values of b are 20 and -20.

What is Mathematical expression?

The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.

Given that;

The mathematical expression as;

(x + a)(x + 3a) = x² + bx + 75​

Now,

The mathematical expression is;

(x + a)(x + 3a) = x² + bx + 75​

Solve the expression as;

(x + a)(x + 3a) = x² + bx + 75​

x² + 3ax + ax + 3a² = x² + bx + 75

x² + 4ax + 3a² = x² + bx + 75

After comparison we get;

4a = b  ... (i)

And, 3a² = 75  .. (ii)

Solve the second equation for a as;

3a² = 75

Divide by 3;

a² = 25

Take square root both side, we get;

a = ± 5

So, By equation (i) we get;

b = 4a

Substitute a = 5;

b = 4 x 5

b = 20

And, Substitute b = -5;

b = 4 x -5

b = -20

Thus, Two possible values of b are 20 and -20.

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The information shows that:

It should be noted that the mean is the average of the numbers that are given.

The median is the number in the middle when they are arranged in ascending or descending order. The mode is the number that appears most.

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Answer:

45 degrees

Step-by-step explanation:

A reference angle can be found by identifying its terminal side and see by what angle the terminal side is close to the x-axis.

To do this, we can subtract this given angle by the nearest 90° angle.

270° is the closest.

[tex]\textsf {Solving :}[/tex]

[tex]\implies \textsf{Reference angle = 270 - 225}[/tex]

[tex]\implies \textsf {45 degrees}[/tex]

The reference angle is the angle from the x-axis thus 45 degrees will be the reference angle to θ = 225°.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

As per the given angle,

θ = 225°

It is going to the third quadrant as shown below,

The reference angle is the angle from x-axis.

The angle from the negative x-axis will be as,

180° + x = 225°

x = 225° - 180° = 45°

Hence "The reference angle is the angle from the x-axis thus 45 degrees will be the reference angle to θ = 225°".

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The ordered pair that is 5 units away is (-1, -3)

What is a line?

A line is a distance between two points.

Analysis:

see attached file.

In conclusion, the ordered pair is (-1, -3)

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Answer:

The actual width would be 9.75 feet. (I think).

Step-by-step explanation:

If two inches represents three feet, then two inches also represents thirty-six inches. You would then have to set up the proportion [tex]\frac{2}{36} = \frac{6.5}{x}[/tex]. Solving that proportion would get you an answer of 117 inches, equal to 9.75 feet. I hope this helps! :)

Work Shown:

[tex]\displaystyle \lim_{x \to c}f(x) = -4\\\\\\\lim_{x \to c}g(x) = 1/5\\\\\\L = \lim_{x \to c}\frac{g(x)}{f(x)}\\\\\\L = \frac{\displaystyle \lim_{x \to c}(g(x))}{\displaystyle \lim_{x \to c}(f(x))}\\\\\\L = \frac{1/5}{-4}\\\\\\L = (1/5)*(-1/4)\\\\\\L = -1/20\\\\[/tex]

Put simply, we divide the two given values g(x) = 1/5 over f(x) = -4 to end up with -1/20

Answer:

y=x+4

Step-by-step explanation:

pretty sure

The sum of the cubes of first 15 natural numbers.

[tex]( \frac{(15 \times 16)}{2} {)}^{2} [/tex]

[tex] = (15 \times 8 {)}^{2} [/tex]

=14400

Hence, the sum of the cubes of first 15 natural numbers is 14400

Equation of the new function -3(x+1)².

The correct option is (B)

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given function:

f(x) = x²

The given condition are shift one unit right+ 1.

i.e., x+1

Vertically stretch 3 units= -3

i.e., -3(x+1)

So, reflect over x- axis = square the function'

So, new function= -3(x+1)²

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Answer:

hope you can understand

A function assigns the values. The function will be 8cos(2x-π)+4.

A function assigns the value of each element of one set to the other specific element of another set.

Given the maximum value is 12, while the minimum value is -4, therefore,

A = (Max-Min)/2 = 12-(-4)/2 = 8

D = (Max+Min)/2 = (12-4)/2 = 4

Period=π, but since x =-4 at 0 or π, therefore,

(2π/B) = π

B = 2π/π = 2

C/B = π/2, {∴At π/2 maximum}

C=π

Hence, the function will be 8cos(2x-π)+4.

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Answer:

24 is the length of segment XZ

The value of x in the triangle using the cosine rule is 22.1 degrees.

An equation is an expression that shows the relationship between two or more numbers and variables.

Cosine rule is used to show the relationship between the sides and angles of a triangle. It is given by:

c² = a² + b² - 2ab cos C

Where a, b, c are the sides and C is the angle opposite side c.

Using cosine rule:

8² = 14² + 19² - 2(14)(19) * cos(x)

cos(x) = 0.9267

x = 22.1°

The value of x in the triangle using the cosine rule is 22.1 degrees.

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Using the law of Cosines, the value of x to the nearest tenth is 77.8

From the question, we are to determine the value of x

Using the law of Cosines

c² = a² + b² - 2ab cos C

c is the unknown side length  

a and b are the given side lengths

and C is the included angle

From the given information,

a = 63

b = 62

C = 142°

Then,

x² = 63² + 61² -2×63×61 cos 142°

x² = 3969 + 3721 -7686(-0.788)

x² = 7690 + 6056.568

x² = 13746.569

x = √13746.569

x = 77.8

Hence, the value of x to the nearest tenth is 77.8

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Answer:

[tex]m=\dfrac{-n+p}{10}[/tex]

Solve for 'm'

To solve for 'm', we have to isolate 'm'.

          10m - p = -n

                  10m = -n + p

                   [tex]\sf\dfrac{10m}{m}=\dfrac{-n+p}{10}\\[/tex]

                    [tex]\sf \boxed{\bf m = \dfrac{-n+p}{10}}[/tex]

After considering the given data we come to the conclusion that the two other cards are 6 and 10, under the condition that Neyha has six number cards. Here are four of Neyha's cards. 8;8;8;8.

Let us assume that the other two cards x and y.
The given mean of all six cards is 8. Then, the sum of all six cards is 48 (8×6). We have that four of the cards are 8s.
So, the summation of these four cards is 32 (8×4).
The dedicated range of all six cards is 4. Therefore, the difference between the largest and smallest card is 4.
Furthermore, we know that four of the cards are 8s, the other two cards must be different from 8.
Hence, we can consider that x and y are the smallest and largest numbers in the set.
Here we have to apply basic algebraic expression
We can perform the setting up two equations:
x + y = 48 - 32 = 16 (the summation of x and y is equivalent to the summation of all six cards minus the summation of the four 8s)
y - x = 4 (the difference considering y and x is equal to the range of all six cards)
Evaluating these equations simultaneously gives us:
y = 10
x = 6
Therefore, the other two cards are 6 and 10.
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Answer:

See below ~

Step-by-step explanation:

P (first red) :

⇒ Original number of red balls / Total

⇒ 4 / 10

⇒ 0.4

⇒ 40%

===============================================================

Remember the first ball drawn is NOT replaced.

P (second red) :

⇒ Original number of red - 1 / Total - 1

⇒ 4 - 1 / 10 - 1

⇒ 3/9

⇒ 33%

Answer:

2x+4/ x-1 C

Step-by-step explanation:

Because the y-intercept is -4

The number of ways for the jobs to be ordered in the queue so that job A is the first to finish or the last to finish is; 2 * 9!

We are told that;

There is a set of 10 jobs in the printer queue.

One of the jobs is job A. Thus, there are 9 other identified jobs.

Number of ways to order this nine jobs = 9!

Since the job A has to be ordered first or last, then;

Number of ways to order job A = 2 ways.

Thus;

Total number of ways to order the jobs in the given order = 2 * 9!

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The average rate of change for this function for the interval from x = 1

to x = 3 will be 8. Therefore option B is correct.

Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:

[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

where when

[tex]x = x_1, y = y_1\\and \\x = x_2, y = y_2[/tex]

The average rate of change can be calculated as;

From x=1 to x=3,

y = 2 and y = 18

Therefore, based on the table, when:

[tex]x_1 = 1 y_1 = 2 \\and \\x_2 = 3, y_2 = 18[/tex]

Then:

[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]\text{Average rate} = \dfrac{18 - 2}{3-1}\\\\\text{Average rate} = \dfrac{16}{2}\\\\\text{Average rate} = 8[/tex]

Therefore option B is correct.

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The principal value of Arccsc (1.607) to the nearest minute is 38°29'

To answer the question, we need to know what arccsc is

Arccsc is the inverse of the cosec of an angle.

Let x =  arccsc(1.607)

So, taking the inverse, we have

csc(x) = 1.607

Since csc(x) = 1/sinx, we have

1/sinx = 1.607

sinx = 1/1.607

sinx = 0.6223

Taking inverse, we have

x = arcsin(0.6223)

x = 38.483°

Since 60' = 1°, we have

x = 38 + 0.483° × 60'/1°

x = 38° + 28.98'

x = 38°28.98'

x ≅ 38°29'

So, the principal value of Arccsc (1.607) to the nearest minute is 38°29'

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The measure of central tendency that is most affected by the lowest score is; A: The mean.

The points table is missing and so I have attached it.

The 3 main measures of central tendency are called mean, median and mode.

Now, from the table attached, if we find the average which is the mean, we will get 56.6.

Now, the mode is the number that occurs the most times. In this case, there is no mode because no number appears more than the other.

For the median, if we arrange in ascending order, we have;

42, 48, 49, 53, 55, 56, 58, 66, 68, 71.

The median = (55 + 56)/2 = 55.5

Now, if we remove the lowest score, the measure that will be most affected will be the mean as the median will only change by 0.5 to 56.

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Answer:

B

Step-by-step explanation:

The equivalent expression of [tex]\frac{(5ab)^3}{30ab^{-7}}[/tex] is [tex]\frac{25a^{2}b^{10}}{6}[/tex]

The expression is given as:

[tex]\frac{(5ab)^3}{30ab^{-7}}[/tex]

Expand the numerator

[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{125a^3b^3}{30ab^{-7}}[/tex]

Divide 125 and 30 by 5

[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^3b^3}{6ab^{-7}}[/tex]

Apply the law of indices

[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^{3-1}b^{3+7}}{6}[/tex]

Evaluate the exponent

[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^{2}b^{10}}{6}[/tex]

Hence, the equivalent expression of [tex]\frac{(5ab)^3}{30ab^{-7}}[/tex] is [tex]\frac{25a^{2}b^{10}}{6}[/tex]

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Answer:

As x approaches infinity, f(x) approaches negative infinity

As x approaches negative infinity, f(x) approaches negative infinity

Step-by-step explanation:

Because the function goes in the downward direction on both sides, it would be negative infinity for both.

It's basically saying, as the x values go towards the positives, the y values go towards the negatives

and as the x values go towards the negatives, the y values go towards the negatives.

Answer:

Your answers are:

A, B and C

Step-by-step explanation:

So 12 over 3 is equal to 4 which is a Whole number. meaning Not a fraction, an Integer is a whole number (not a fractional number) that can be positive, negative, or zero. Rational numbers would include this example as well

Hope this helped have a wonderful day/night/afternoon

Answer:

11,676 M&M's

Step-by-step explanation:

A dozen is 12

the problem is saying that in the jar, there are 973 (12-M&M's)

973 * 12 is 11676

There are 11,676 M&M's in the jar

Answer:

they are 11,676

Step-by-step explanation:

A dozen is 12 so since there are 973 dozen, we multiply by 12.

Answer: rhombus

Step-by-step explanation:

By inspection, we can tell that there are no right angles, so we can determine it is not a square or a rectangle.

From the options, it is implied that it is a parallelogram, so to determine if it is a rhombus, we can determine if there is a pair of consecutive congruent sides.

By the distance formula,

[tex]AB=\sqrt{(-1-3)^{2}+(-1-1)^{2}}=\sqrt{16+4}=2\sqrt{5}\\BC=\sqrt{(-1-1)^{2}+(-1-3)^{2}}=\sqrt{4+16}=2\sqrt{5}[/tex]

As AB=BC, there is indeed a pair of consecutive congruent sides, and thus the most specific classification is a rhombus