Consider the equation 3p – 7 + p = 13. What is the resulting equation after the first step in the solution?

A quadratic polynomial can have 0, 1, or 2 real roots, including repeated roots. The roots are determined by the discriminant. Numbers 4, 5, or 6 are not possible numbers of real roots for a quadratic polynomial.

In Mathematics, specifically in Algebra, a quadratic polynomial with real coefficients can have either 0, 1, or 2 real roots, including any repeated roots. The number of roots is determined by the discriminant (the value under the square root in the quadratic formula). If the discriminant is greater than 0, the quadratic has 2 real roots. If it equals 0, there is 1 real root (a repeated root), and if it is less than 0, there are no real roots (there are 2 complex roots instead). Consequently, the possible number of real roots for a quadratic polynomial is not 4, 5, or 6.

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A quadratic polynomial with real coefficients can have 0, 1, or 2 real roots. Only '0 real roots' is a valid choice. This is determined based on the discriminant of the quadratic equation.

A quadratic polynomial with real coefficients is of the form [tex]\( ax^2 + bx + c = 0 \)[/tex], where ( a, b, ) and ( c ) are real numbers.

The number of real roots of a quadratic polynomial can be determined by its discriminant, [tex]\( \Delta = b^2 - 4ac \)[/tex]:

1. If [tex]\( \Delta[/tex] > 0, the polynomial has two distinct real roots.

2. If [tex]\( \Delta[/tex] = 0, the polynomial has one real root (a repeated root).

3. If [tex]\( \Delta[/tex] < 0, the polynomial has no real roots (it has two complex conjugate roots).

Based on this, the possible number of real roots, including repeated roots, for a quadratic polynomial with real coefficients are:

- ( 0 ) (when the discriminant is negative, there are no real roots)

- ( 1 ) (when the discriminant is zero, there is one repeated real root)

- ( 2 ) (when the discriminant is positive, there are two distinct real roots)

Given the options:

- 0

- 4

- 5

- 6

The only valid number of real roots for a quadratic polynomial with real coefficients from the provided options is: 0

The number of possible outcomes for the two remaining games is 9.

The number of possible outcomes for the two remaining games can be found by multiplying the number of outcomes for each game. Since each game can have three possible outcomes (win, lose, or tie), there are a total of 3 outcomes for each game. Therefore, the number of possible outcomes for the two games is 3 x 3 = 9.

The cost of the car after an 8% reduction on the initial price of £15,400 is £14,168. This is found by calculating 8% of the original price and subtracting that amount from the initial price.

The initial price of the car is £15,400. To calculate the price after an 8% reduction, we first find the value of the discount and then subtract it from the original price. An 8% reduction on £15,400 is calculated as follows:

Therefore, as per the above explaination, the cost of the car after the reduction is £14,168.

Answer:

6 movies

Step-by-step explanation:

You pay each month for satellite TV = $30

and for every movie you purchase = $2.50

Let the number of the movies you purchase be x

The equation will be

30 + 2.50x = 45

2.50x = 45 - 30

2.50x = 15

x = [tex]\frac{15}{2.5}[/tex]

x = 6

You purchased 6 movies during the month.

Slope = 4/3, y intercept = -5/3

 see attached picture:

we have

[tex]y=\frac{1}{2}x+3[/tex]

we know that

the slope m of the line is equal to

[tex]m=\frac{1}{2}[/tex]

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

so

For [tex]y=0[/tex] find the value of x

[tex]0=\frac{1}{2}x+3[/tex]

[tex]x=-6[/tex]

The x-intercept is the point [tex](-6,0)[/tex]

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

so

For [tex]x=0[/tex] find the value of y

[tex]y=\frac{1}{2}*0+3[/tex]

[tex]y=3[/tex]

The y-intercept is the point [tex](0,3)[/tex]

therefore

the answer is the option

B. Plot the Y-intercept (0,3) and use the slope of 1/2 to find a second point

Final answer:

To graph the line y = 1/2x + 3, plot the y-intercept (0,3) and use the slope of 1/2 to find another point on the line.

Explanation:

The correct procedure to graph the line represented by the equation y = ½x + 3 is to start by plotting the y-intercept and then using the slope to find a second point. The y-intercept is the point where the line crosses the y-axis. In this equation, the y-intercept is (0, 3) because when x is 0, y is 3. The slope of the line is ½, which means that for every 1 unit increase in x, y increases by ½ a unit. Therefore, starting at the y-intercept (0, 3), you can go up ½ unit and right 1 unit to find another point on the line.

The correct answer to the multiple-choice question is:

B. Plot the Y-intercept (0,3) and use the slope of 1/2 to find a second point

Final answer:

The graph of g(x)=⌊x⌋-3 is the same as the graph of f(x)=⌊x⌋ but shifted downward by 3 units because of the subtraction of 3, resulting in each step being 3 units lower.

Explanation:

The student has asked how the graph of g(x)=⌊x⌋-3 differs from the graph of f(x)=⌊x⌋. The function ⌊x⌋ represents the greatest integer function or floor function, which maps a real number to the largest integer less than or equal to it. The graph of f(x) is a step function that jumps up by 1 at each integer value of x. The graph of g(x) will be exactly the same as f(x) but will be shifted downward by 3 units due to the -3 in the function. This means that each step on the graph of g(x) will occur at an integer value of y that is 3 less than the corresponding step on the graph of f(x). For example, where f(x) has a step at y=0, g(x) will have a step at y=-3.

Answer:

Step-by-step explanation:

In the given image you can observe two triangles with congruent sides,

[tex]PQ \cong SQ\\PN \cong SN\\QN \cong QN[/tex]

Notice that all three corresponding sides are congruent. That means,

[tex]\triangle PQN \cong \triangle SQN[/tex], by SSS postulate.

The SSS postulate states that if two triangles have all three corresponding sides congruent, then those triangles are congruent.

Therefore, the right answer is D) SSS.

A function is a relationship between inputs where each input is related to exactly one output.

The function that is used to determine how much money he has left over after x rides is

f(x) = -1.25x + 64.

A function is a relationship between inputs where each input is related to exactly one output.

f(x) = 2x + 2 is a function.

f(x) = 3x + 6 is a function.

We have,

Total amount = $80

Cost of entering the fair = $4

Cost on food = $12

Cost per ride = $1.25

The money left after x rides.

= 80 - (1.25x + 12 + 4)

= 80 - 1.25x - 12 - 4

= 80 - 1.25x - 16

= 64 - 1.25x

= -1.25 + 64

The function to determine money left can be represented as:

f(x) = -1.25x + 64

Thus,

The function that is used to determine how much money he has left over after x rides is

f(x) = -1.25x + 64.

Learn more about functions here:

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Answer:

3 x 10^8

Step-by-step explanation:

I got it right on Kahn Academy :D

(g *f)(x) = (2x+8)^4

replace x with -3

(2(-3)+4)^4 =

(-6+4)^4 =

= (-2)^4

= 16

f(x) = 3x+2

f(5) = 3(5) +2 = 15 +2 =17

 Answer is D. 17

a. [tex]\( P(X = 66) \approx 0.014 \)[/tex]

b. [tex]\( P(X = 77) \approx 0 \)[/tex]

c. [tex]\( P(X \geq 66) \approx 0.015 \)[/tex]

d. Option C: Yes, 66 is significantly high; probability [tex]\( < 0.05 \).[/tex]

To solve this problem, we'll use the binomial probability formula:

[tex]\[ P(X = k) = \binom{n}{k} \cdot p^k \cdot (1 - p)^{n - k} \][/tex]

Where:

[tex]- \( n \) is the number of trials (77 adults in this case)\\- \( k \) is the number of successes (the number of adults believing in reincarnation)\\- \( p \) is the probability of success (the proportion of adults believing in reincarnation, which is 0.40 in this case)\\- \( \binom{n}{k} \) is the binomial coefficient, which represents the number of ways to choose \( k \) successes out of \( n \) trials.[/tex]

Now let's calculate the probabilities:

a. Probability that exactly 66 of the selected adults believe in reincarnation:

[tex]\[ P(X = 66) = \binom{77}{66} \cdot (0.40)^{66} \cdot (1 - 0.40)^{77 - 66} \][/tex]

b. Probability that all of the selected adults believe in reincarnation:

[tex]\[ P(X = 77) = \binom{77}{77} \cdot (0.40)^{77} \cdot (1 - 0.40)^{77 - 77} \][/tex]

c. Probability that at least 66 of the selected adults believe in reincarnation:

This is the sum of probabilities from 66 to 77.

[tex]\[ P(X \geq 66) = \sum_{k=66}^{77} \binom{77}{k} \cdot (0.40)^{k} \cdot (1 - 0.40)^{77 - k} \][/tex]

Let's calculate these probabilities.

a. Probability that exactly 66 of the selected adults believe in reincarnation:

[tex]\[ P(X = 66) = \binom{77}{66} \cdot (0.40)^{66} \cdot (0.60)^{11} \]\[ = \frac{77!}{66!(77-66)!} \cdot (0.40)^{66} \cdot (0.60)^{11} \]\[ \approx 0.014 \][/tex]

b. Probability that all of the selected adults believe in reincarnation:

[tex]\[ P(X = 77) = \binom{77}{77} \cdot (0.40)^{77} \cdot (0.60)^{0} \]\[ = (0.40)^{77} \]\[ \approx 0 \][/tex]

c. Probability that at least 66 of the selected adults believe in reincarnation:

[tex]\[ P(X \geq 66) = \sum_{k=66}^{77} \binom{77}{k} \cdot (0.40)^{k} \cdot (0.60)^{77 - k} \]\[ \approx 0.015 \][/tex]

So, for the options:

d. If 77 adults are randomly​ selected, is 66 a significantly high number who believe in​ reincarnation?

C. Yes, because the probability that 66 or more of the selected adults believe in reincarnation is less than 0.05.