HELP PLEASE

use the coordinates of the vertex and the point to write the quadratic equation in standard form (-2, -2) point (-1, 1)

kogti [31]

Answer:

Step-by-step explanation:

vertex form of quadratic: y = a ( x − h ) ^ 2 + k

h= -2 , k = -2

y=a(x+2)^2-2

Substitute (-1,1)

1=a(-1+2)^2-2

a=3

y=3(x+2)^2-2

Expanding and give

y=3x^2+12x+10

5 0

3 years ago

Find the lowest common denominator for the following rational expressions

SCORPION-xisa [38]

Answer:

Hi i think that the correct answer is B

3 0

3 years ago

The coordinates of polygon ABCD are A(-4,-1), B(-2,3), C(2,2), and D(4,-3). Use these coordinates to complete the sentences belo

oee [108]

Answer:

The perimeter of polygon ABCD, to the nearest thousandth units is

22.227 units

The perimeter of polygon ABCD', to the nearest thousandth, would be 20.980 units

The area of polygon ABCD' is 19.5 units²

Step-by-step explanation:

The coordinates forming the polygon are

A (-4,-1), B(-2,3), C(2,2), and D(4,-3)

The perimeter then is given by the sum of the length of the sides as follows;

Length of line between two X and Y points distance, xi and yj apart is

length XY = $\sqrt{x^2+y^2}$

Therefore, the length between points AB is

length AB = $\sqrt{(-4 - (-2))^2+(-1-3)^2}$

= $\sqrt{(-4 +2)^2+(-4)^2} = \sqrt{-2^2+-4^2} = \sqrt{20}$ = 4.472 units

Similarly, length BC is given by

Length BC = $\sqrt{(-4)^2+1^2} = \sqrt{17}$ = 4.123 units

Length CD = $\sqrt{(-2)^2+5^2} = \sqrt{29}$ = 5.385 units

Length DA = $\sqrt{(8)^2+(-2)^2} = \sqrt{68}$ = 8.246 units

The perimeter is equal to;

length AB + Length BC + Length CD + Length DA

= 4.472 + 4.123 + 5.385 + 8.246 = 22.227 units

If the point D is moved up 2 units and left 1 unit we have

D' = x-1, y+2 where x and y are the coordinates of point D

D(4, -3) → D'((4-1), (-3+2)) = D'(3, -1)

The length D'A = $\sqrt{(7)^2+(0)^2} = \sqrt{49}$ =7 units

The perimeter of polygon ABCD'

length AB + Length BC + Length CD + Length D'A

= 4.472 + 4.123 + 5.385 + 7 = 20.980 units.

The area is given by the determinant of the 3 by 3 matrix using Cramer's Rule as follows

$S_{\bigtriangleup}$ = $(\frac{1}{2})|x_1y_2+x_2y_3+x_3y_1-x_1y_3-x_2y_1-x_3y_2|$

= $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

Triangle ABC we have

A(-4,-1)

B(-2,3)

C(2,2)

$S_{{\bigtriangleup}ABC}$ = $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

$=(\frac{1}{2})|(-4)(3-2)+(-2)(2-(-1)) +2((-1)-3)|$

= $=(\frac{1}{2})|-4-6 -8|= 9 units^2$

Triangle ACD'

A(-4,-1)

C(2,2)

D'(3, -1)

$S_{{\bigtriangleup}ACD'}$ = $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

$=(\frac{1}{2})|(-4)(2+1)+(2)(-1+1) +3((-1)-2)| = \frac{21}{2}$ = 10.5 units²

Area of polygon = $S_{{\bigtriangleup}ABCD'}$ = $S_{{\bigtriangleup}ABC}$ + $S_{{\bigtriangleup}ACD'}$ = (9 + 10.5) units²

Area of polygon ABCD' = 19.5 units².

7 0

3 years ago

A spinner divided into four equal parts, A, B, C, and D, is spun, then is followed by a roll of a standard six-sided die.

gavmur [86]

Answer: 24

Step-by-step explanation:

Total Possible Outcomes given A, B, C, D and 1, 2, 3, 4, 5, 6

= 4 x 6

= 24

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Answer: 3

Step-by-step explanation:

Total outcomes for an A and and odd number

= A and (1 or 3 or 5)

= 1 x 3

= 3

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Answer: $\bold{\dfrac{1}{4,}\qquad \dfrac{1}{2,}\qquad \dfrac{1}{8}}$

Step-by-step explanation:

Probability of an A out of A, B, C, D is: $\dfrac{1}{4}$

Probability of an odd (1, 3, 5) out of 1, 2, 3, 4, 5, 6 is: $\dfrac{3}{6}=\dfrac{1}{2}$

Probability of an A and an odd is: $\dfrac{1}{4}\times\dfrac{1}{2}=\dfrac{1}{8}$

*******************************************************************************

Answer: $\bold{\dfrac{1}{2}}$

Step-by-step explanation:

Probability of an odd (1, 3, 5) out of 1, 2, 3, 4, 5, 6 is: $\dfrac{3}{6}=\dfrac{1}{2}$

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Answer: $\bold{\dfrac{3}{4}}$

Step-by-step explanation:

Probability of an A or an odd is: $\dfrac{1}{4}+\dfrac{1}{2}=\dfrac{1}{4}+\dfrac{2}{4}=\dfrac{3}{4}$

6 0

3 years ago

3/5 of a number is 60. what is 45% of the number

lisabon 2012 [21]

The present of 45 Is 45.0 present

4 0

3 years ago