Which quadratic function has a leading coefficient of 2 and a constant term of –3? f(x) = 2x3 – 3 f(x) = –3x2 – 3x 2 f(x) = –3x3 2 f(x) = 2x2 3x – 3

Answers

Answer 1

Answer: The standard form of quadratic function is:
f(x) = a x² + b x + c
where: a - a leading coefficient, c- constant term:
a = 2, c = -3
Answer: D) f( x ) = 2 x² + 3 x - 3

Answer 2

Answer:

Answer:

tHE ANSWER IS d

Step-by-step explanation:

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Compare the mean and standard deviation of Set A and Set B.Set A: 7, 3, 4, 9, 2
Set B: 5, 8, 7, 6, 4

Answers

Set A: {7, 3, 4, 9, 2}
Finding the Mean of Set A: $\bar{x} = (7 + 3 + 4 + 9 + 2)/(5)$
   $\bar{x} = (25)/(5)$
   $\bar{x} = 5$

Finding the Standard of Set A: $\sigma = \sqrt{\frac{(\bar{x} - x_(1))^(2) + (\bar{x} - x_(2))^(2) + (\bar{x} - x_(3))^(2) + (\bar{x} - x_(4))^(2) + (\bar{x} - x_(5))^(2)}{n}}$
   $\sigma = \sqrt{((5 - 7)^(2) + (5 - 3)^(2) + (5 - 4)^(2) + (5 - 9)^(2) + (5 - 2)^(2))/(5)}$
   $\sigma = \sqrt{((-2)^(2) + (2)^(2) + (1)^(2) + (-4)^(2) + (3)^(2))/(5)}$
   $\sigma = \sqrt{(4 + 4 + 1 + 16 + 9)/(5)}$
   $\sigma = \sqrt{(34)/(5)}$
   $\sigma = √(6.8)$
   $\sigma \approx 2.6$

Finding the Mean of Set B: $\bar{x} = (5 + 8 + 7 + 6 + 4)/(5)$
   $\bar{x} = (30)/(5)$
   $\bar{x} = 6$

Finding the Standard Deviation of Set B: $\sigma = \sqrt{\frac{(\bar{x} - x_(1))^(2) + (bar{x} - x_(2))^(2) + (\bar{x} - x_(3))^(2) + (\bar{x} - x_(4))^(2) + (\bar{x} - x_(5))}{n}}$
$\sigma = \sqrt{((6 - 5)^(2) + (6 - 8)^(2) + (6 - 7)^(2) + (6 - 6)^(2) + (6 - 4)^(2))/(5)}$
$\sigma = \sqrt{((1)^(2) + (-2)^(2) + (-1)^(2) + (0)^(2) + (2)^(2))/(5)}$
$\sigma = \sqrt{(1 + 4 + 1 + 0 + 4)/(5)}$
$\sigma = \sqrt{(10)/(2)}$
$\sigma = √(5)$
$\sigma \approx 2.236$

The mean and standard deviation of Sets A and B are different.

Final answer:

Mean of Set A is 5 and Set B is 6. Standard deviation of Set A is approximately 2.83, and for Set B, it's approximately 1.67. This indicates that values in Set B are generally closer to their mean than values in Set A to their mean.

Explanation:

To compare the mean and standard deviation of Set A and Set B, we first need to calculate these for each set. Mean is the average of the numbers and standard deviation is a measure of the amount of variation or dispersion of a set of values.

First, calculate the mean by adding the numbers in each set and dividing by the total number of values. For Set A, the mean is (7+3+4+9+2)/5 = 5. For Set B, the mean is (5+8+7+6+4)/5 = 6.

The standard deviation is a bit more complex, as it involves subtracting the mean from each value, squaring the result, finding the mean of these squares, and then taking the square root of that mean. For Set A, these steps result in a standard deviation of approximately 2.83. For Set B, these steps result in a standard deviation of approximately 1.67.

In conclusion, Set B has a higher mean and a lower standard deviation compared to Set A which means values in Set B are generally closer to the mean of Set B than values in Set A are to the mean of Set A.

Learn more about Mean and Standard Deviation here:

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joannna baked some cookies. She tried to divide them evenly between two plates,then three plates and finally four plate. Each time, she had one cookie left over. How many cookies did Joanna bake? (A)10 ( B) 13 (C) 11 (D) 9 (E) 12

Answers

Answer: 13 cookies

Step-by-step explanation: 13 divided by 2 is 6 with a remainder of 1. 13 divided by 3 is 4 with a remainder of 1. 13 divided by 4 is 3 with a remainder of 1.

Answer:

Step-by-step explanation:

Divide each option by 4.

13/4= 3.25

.25 x 4 =1(whole cookie)

AA, BBB, and CCC are collinear, and BBB is between AAA and CCC. The ratio of ABABA, B to BCBCB, C is 1:21:21, colon, 2. If AAA is at (7,-1)(7,−1)left parenthesis, 7, comma, minus, 1, right parenthesis and BBB is at (2,1)(2,1)left parenthesis, 2, comma, 1, right parenthesis, what are the coordinates of point CCC?

Answers

Answer:

The coordinates of point C are (-8,5).

Step-by-step explanation:

It is given that A, B and C collinear and B is between A and C.

The ratio of AB to BC is 1:2. It means Point divided the line segments AC in 1:2.

Section formula:

$((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n))$

The given points are A(7,-1) and B(2,1).

Let the coordinates of C are (a,b).

Using section formula the coordinates of B are

$B=(((1)(a)+(2)(7))/(1+2),((1)(b)+(2)(-1))/(1+2))$

$B=((a+14)/(3),(b-2)/(3))$

We know that point B(2,1).

$(2,1)=((a+14)/(3),(b-2)/(3))$

On comparing both sides we get

$2=(a+14)/(3)$

$6=a+14$

$6-14=a$

$-8=a$

The value of a is -8.

$1=(b-2)/(3)$

$3=b-2$

$3+2=b$

$5=b$

The value of b is 5.

Therefore, the coordinates of point C are (-8,5).

The coordinates of the pointC such that pointsA and B are (7, -1) and (2, 1) and the ratioAB to BC is 1 : 2 is (-8, 5).

How to determine the location of a point within a line segment

According to the Euclidean geometry, a line is formed by two points on a plane and three points are collinear if all the three points go through a single line.

By definitions of vector and ratio we derive an expression to determine the coordinates of the point B:

$\overrightarrow{AB} = (1)/(1+2)\cdot \overrightarrow{AC}$

$\vec B - \vec A = (1)/(3)\cdot \vec C -(1)/(3)\cdot \vec A$

$(1)/(3)\cdot \vec C = \vec B - (2)/(3)\cdot \vec A$

$\vec C = 3 \cdot \vec B - 2\cdot \vec A$

If we know that A(x,y) = (7, -1) and B(x,y) = (2, 1), then the coordinates of point C is:

C(x, y) = 3 · (2, 1) - 2 · (7, -1)

C(x, y) = (6, 3) + (- 14, 2)

C(x,y) = (- 8, 5)

The coordinates of the pointC such that pointsA and B are (7, -1) and (2, 1) and the ratioAB to BC is 1 : 2 is (-8, 5).

Remark

The statement is poorly formatted and reports mistakes. Correct form is shown below:

A, B and C are collinear and B is between A and C. The ratio of AB to BC is 1 : 2. If A is A(x, y) = (7, -1) and B(x, y) = (2, 1), what are the coordinates of point C?

To learn more on line segments, we kindly invite to check this verified question: brainly.com/question/25727583

If ∠BGC = 16x - 4 and ∠CGD = 2x + 13, find the value of x so that ∠BGD is a right angle.