Which of the following is an example of the identity property of 1?
O 0+2 = 24
O 3 - 2 = 1
O (1) = 1
1.11(0) = 0

Answer:

[tex] \alpha = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} \\ \beta= \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \alpha +\beta = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} + \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} \\ = \frac{ - 2b + 0}{2a} = \frac{ - 2b}{2a} \\ \therefore \: \alpha +\beta = - \frac{b}{a} \\ \alpha \times \beta = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} \times \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} \\ = \frac{ {b}^{2} - ( {b}^{2} - 4ac) }{4 {a}^{2} } \\ = \frac{4ac}{4 {a}^{2} } \\ \therefore \alpha \times \beta = \frac{c}{a} \\ (x - \alpha)(x - \beta) = 0 \\ {x }^{2} + (\alpha + \beta)x + \alpha\beta = 0\\\\Let \:D =\sqrt{ {b}^{2} - 4ac}\\ If \:D >0 \Rightarrow \alpha, \beta \in \mathbb R\:(2 \: real \:roots)\\ If D =0 \Rightarrow \alpha= \beta \in \mathbb R\: (one \:real\: root) \\ If D <0 \Rightarrow \alpha, \beta \in \mathbb C\:(complex\: roots)\\At least 4examples\\{(x-1)}^{2}=0\\{x}^{2}-x-1=0 \\{x}^{2}-2x+13=0\\7{x}^{2}-49x-7=0\\ Applications\\ut+g{t}^{2}=s\\a=g\\u=-\frac{b}{a}\\s=\frac{c}{a}[/tex]

Answer:

Step-by-step explanation:

1) Determining the nature of roots:

Quadratic equation: ax² + bx +c = 0

Find D (Discriminant) using the  D = b² - 4ac

If D = 0 , then the two roots are equal.

If D > 0, then the equation has two distinct real roots.

If D < 0, then the roots are complex/ imaginary.

One can find the sum and product of the roots using the below mentioned formula.

1) sum of roots = [tex]\frac{-b}{a}[/tex]

2) Product of roots = [tex]\frac{c}{a}[/tex]

If sum and product of the roots are given, one can frame the quadratic equation by   x² - (sum of roots)*x + product of roots = 0

2) i) x² - 6x + 9 = 0

a = 1 ; b = -6  and c = 9

D = (-6)² - 4 * 1 * 9 = 36 - 36 = 0

D = 0. So, two equal roots

ii) x² - 4x + 3 = 0

a = 1 ; b = -4 ; c = 3

D = (-4)² - 4 * 1 * 3 = 16 - 12 = 4

D > 0. So, two distinct real roots.

iii) x² - 4x - 3 = 0

a = 1 ; b = -4 ; c = -3

D = (-4)² - 4*1*(-3) = 16 + 12 = 28 > 0

D > 0. So, two distinct real roots.

iv) x² - 4x + 7 = 0

a = 1 ; b = -4 ; c = 7

D =(-4)² - 4 *1 *7 = 16 - 28 = - 12

D< 0. So, two imaginary/ complex roots.

Answer:

no you cant be certain but you can.

Step-by-step explanation:

Answer:

Step-by-step explanation:

54/5=10 4/5

The polynomial [tex]x^3+ px^{2}-x-2[/tex] contains x - 1 as a factor.

The value of p = 2.

Given:

The polynomial [tex]x^3+ px^{2}-x-2[/tex] contains x - 1 as a factor.

Comparing x - 1 with x - a then

Substitute the value of x = 1, then we get

[tex]$1^3+p*1^2-1-2 = 0[/tex]

[tex]$1^{3}+p \cdot 1^{2}-1-2=0$$[/tex]

Apply rule [tex]$1^{a}=1$[/tex]

[tex]$&1^{3}=1,1^{2}=1 \\[/tex]

[tex]$&1+1 \cdot p-1-2=0[/tex]

Multiply: p-1 = p

1+p -1-2=0

Group like terms

p+1-1-2 = 0

Add/Subtract the numbers: 1-1-2 = -2

p-2 = 0

Add 2 to both sides

p-2+2 = 0+2

Simplify

p = 2

Therefore, the value of p = 2.

To learn more about polynomial function

https://brainly.com/question/11434122

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Answer:

w=-1

Step-by-step explanation:

Algebra.

Answer:

Step-by-step explanation:

Answer:

102.4

Step-by-step explanation:

8(19-6.2)

8(12.8)

102.4

Answer:

102.4

Step-by-step explanation:

I looked it up on mathaway there is no explanation

please mark this answer as brainlist

Answer:

x+5 > 4

Step-by-step explanation:

x+5 > 4 can be changed to

 -5 .   -5

x>-1

that is what is shown

Answer:

The answer is the first one. It's also in my picture that I included

Answer:

$38 for 2 sweaters

Step-by-step explanation:

$38 for 2 sweaters  ---> $38/2 = $19

$72 for 3 sweaters

$96 for 4 sweaters

$120 for 5 sweaters

Explanation:

Polynomials of degree 1, aka linear polynomials, are the highest allowed for the divisor when using synthetic division. If the divisor is degree 2 and larger, then you'll need to use polynomial long division instead.

An example divisor of degree 1 is something like [tex]x+5[/tex], which can be written as [tex]x^1+5[/tex]. That exponent of 1 determines the degree.

Answer:

1/4

Step-by-step explanation:

1. To find the slope, you can use the formula [tex]\frac{rise}{run}[/tex] to find it!

2. Rise means how many units you go up and down from point to point, and run means how far you go left or right from point to point.

3. Given the statement above, the rise would be 1, and the run would be 4.

4. Now, since slope is (rise)/(run), the slope is 1/4 because one divided by four is equal to one fourth.

what is happend here haha

Answer:

720 ways

Step-by-step explanation:

First place has 10 choices. First prize is chosen. So, 9 students are left.

Second place has 9 choices.

First and second prizes are chosen. Now 8 students are left

Third place has 8 choices.

Total ways = 10 * 9 * 8 = 720 ways

Answer:

3x +9 + 3x + 3x +8 = 3x + 3x + 4x + 6

9x + 17 = 10x + 6

x = 11

AB 42

BC 41

AC 33

PQ 33

QR 33

PR 50

Answer:

x = 11

Step-by-step explanation:

if the perimeters are equal then:

the perimeter of the first triangle : 3x + 9 + 3x + 3x + 8 = 9x + 17

the perimeter of the second triangle : 3x + 3x + 4x + 6 = 10x + 6 and

9x + 17 = 10x + 6 export like terms to the same side of the equation

17 - 6 = 10x - 9x

11 = x

we can find the lengths by replacing x with 11 in given expressions.

Answer:

C) Quadrant 4

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

[tex]618.75 cm^{3}[/tex]

Step-by-step explanation:

[tex]\frac{(11 cm)(7.5 cm)(15 cm)}{2} =618.75 cm^{3}[/tex]

The trapezoids are congruent if the corresponding sides of each trapezoid are equal

The option that gives the possible coordinates for the vertex I is the option;

[tex]\underline{(-4.5, -5)}[/tex]

Reason:

The given coordinates of the trapezoid TRAP = T(3, 5), P(3 2), R(6, 5), and A(7.5, 2)

The given coordinates of the trapezoid ZOID = Z(0, -2), and D(0, -5)

Required: The possible coordinates for a vertex on ZOID

Solution:

The given points of the trapezoid are the height of the trapezoid ZOID

The possible vertex of I, and O are;

Therefore;

The option that gives the possible coordinates (position) of a vertex I is the option [tex]\underline{(-4.5, -5)}[/tex]

Learn more here:

https://brainly.com/question/12871672

Answer:

The trapezoids are congruent if the corresponding sides of each trapezoid are equal

The option that gives the possible coordinates for the vertex I is the option;

(-4.5.-5)

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

I Think :D

Answer:

-x^4 + 6x^3 + 7x^2 -4x -4      

Step-by-step explanation:

1. Convert to decimal notation

The exponent is 11, making it 10 to the power of 11. As the exponent is positive, the solution is a number greater than the origin or base number. To find our answer, we move the decimal to the right 11 time(s):

Answer:

see explanation

Step-by-step explanation:

∠ A and ∠ FCE are corresponding angles and are congruent , then

∠ A = 150°

∠ FCE and ∠ C are vertically opposite angles and are congruent , then

∠ C = 150°

∠ FCE and ∠ ECB are adjacent angles on a straight line and sum to 180°

∠ ECB = 180° - ∠FCE = 180° - 150° = 30°

∠ E = 180° - (30 + 45)° ← sum of angles in a triangle

∠ E = 180° - 75° = 105°

∠ CBE and ∠ D are same- side interior angles and sum to 180° , then

∠ D = 180° - 45° = 135°

Answer:

7

Step-by-step explanation:

Pine Street in x miles long.

Maple street is 3 times as long as Pine Street, so Maple street is 3x miles long.

Maple street is 21 miles long.

3x = 21

x = 7

Maple Street is 7 miles long.

Answer:

fraction: 62/100=31/50

decimal: 0.62

percentage: 62%

Step-by-step explanation:

Answer: 13

Step-by-step explanation:

12 x 2 = 24 (because of the two sides)

50 - 24 = 26 (to find the remaining amount)

26 / 2 = 13 (to equally distribute the remaining amount.)

Answer:

a. 4

b. 1/4

c. 16

d. 1/9

e. 4/9

f. 9/16

Step-by-step explanation:

The ratio of the areas is the square of the ratio of the lengths of the sides.

a. Triangles G and F

Select a side in triangle G and the corresponding side in triangle F:

side in F: 10

corresponding side in G: 5

ratio of lengths of F to G = 10/5 = 2

ratio of areas of G to F: (2)^2 = 4

b. Triangles G and B

Select a side in triangle G and the corresponding side in triangle B:

side in G: 5

corresponding side in B: 5/2

ratio of lengths of B to G = (5/2)/5 = 1/2

ratio of areas of B to G: (1/2)^2 = 1/4

c. Triangles B and F

Select a side in triangle B and the corresponding side in triangle F:

side in B: 5/2

corresponding side in F: 10

ratio of lengths of F to B = 10/(5/2) = 4

ratio of areas of F to B: (4)^2 = 16

Do the same for the other 3 pairs of triangles.

The answers are:

d. 1/9

e. 4/9

f. 9/16

The ratio of the areas is the square of the ratio of the lengths of the sides.

Let's find the ratio of areas one by one:

A. Triangles G and F

Select a side in triangle G and the corresponding side in triangle F:

Side in F= 10

Corresponding side in G= 5

The ratio of lengths of F to G = 10/5 = 2

The ratio of areas of G to F= (2)^2 = 4

B. Triangles G and B

Select a side in triangle G and the corresponding side in triangle B:

Side in G= 5

Corresponding side in B= 5/2

The ratio of lengths of B to G = (5/2)/5 = 1/2

The ratio of areas of B to G: (1/2)^2 = 1/4

C. Triangles B and F

Select a side in triangle B and the corresponding side in triangle F:

Side in B= 5/2

Corresponding side in F= 10

The ratio of lengths of F to B = 10/(5/2) = 4

The ratio of areas of F to B: (4)^2 = 16

D. Triangles F and H

Select a side in triangle F and the corresponding side in triangle H:

Side in F= 10

Corresponding side in H= 10/3

The ratio of lengths of H to F = (10/3)/10 = 1/3

The ratio of areas of H to F: (1/3)^2 = 1/9

E. Triangles G and H

Select a side in triangle G and the corresponding side in triangle H:

Side in G= 5

Corresponding side in H=10/3

The ratio of lengths of H to G = (10/3)/5 = 2/3

The ratio of areas of H to G: (2/3)^2 = 4/9

F. Triangles H and B

Select a side in triangle H and the corresponding side in triangle B:

Side in H=10/3

Corresponding side in B= 5/2

The ratio of lengths of B to H = (5/2)/(10/3) = 3/4

The ratio of areas of H to G: (3/4)^2 = 9/16

The final answers are:

a. 4

b. 1/4

c. 16

d. 1/9

e. 4/9

f. 9/16

To learn more about the ratio of areas,

brainly.com/question/7071992

Answer:

-5/2

Step-by-step explanation:

5x+2y=6

First, put the equation in slope-intercept form

y = mx+b where m is the slope and b is the y intercept

Subtract 5x from each side

5x-5x+2y=-5x+6

2y = -5x+6

Divide each side by 2

2y/2 = -5/2x +6/2

y = -5/2 x +3

The slope is -5/2x

Lines that are parallel have the same slope

29.7°F + (1.23°F (2))

= 29.7°F + 2.46°F

= 32.16°F

#LearnWithEXO

Answer:

the 5 gallon

67.45 ÷ 5= $13.49