In your English class you are given a list of 12 books you want to choose three books to read over the summer how many groups of three books are available from the list of 12

Answer:

α² + β² = 5

Step-by-step explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 ( a≠ 0 ) , then

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

product of roots = [tex]\frac{c}{a}[/tex]

x² - x - 2 = 0 ← is in standard form

with a = 1, b = - 1, c = - 2 , then

α + β = - [tex]\frac{-1}{1}[/tex] = 1

αβ = [tex]\frac{-2}{1}[/tex] = - 2

Using the identity

(α + β)² = α² + β² + 2αβ , then

α² + β² = (α + β)² - 2αβ = 1² - 2(- 2) = 1 + 4 = 5

[tex] \large \boxed{ \boxed{\mathrm{ \alpha }^{2} + { \beta }^{2} = 5}}[/tex]

let's solve for :

let's plug the values,

[tex] \mathfrak{best \: \: of \: \: luck \: \: for \: \: your \: \: assignment}[/tex]

Answer:

10 and 40

Step-by-step explanation:

Find the prime factorization of 10

10 = 2 × 5

Find the prime factorization of 40

40 = 2 × 2 × 2 × 5

Multiply each factor the greater number of times it occurs to find the LCM:

LCM = 2 × 2 × 2 × 5

LCM=40

Answer: Check out the diagram below

The reflected image is shown in red.

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

Explanation:

Draw a vertical line through -2 on the x axis. This is the mirror line.

Now focus on the upper right corner of the figure, which is at (-3, -1). Notice how the horizontal distance from this corner point to the mirror line is exactly 1 unit. If we move another 1 unit to the right, then we'll arrive at (-1,-1) which is where the reflected point lands or ends up.

In short, the upper right corner point (-3,-1) reflects over x = -2 to land on (-1,-1)

----------------------

As another example, the upper left corner point (-5, -1) will move exactly 4 spaces to the right to get to the mirror line. Then we move another 4 spaces to the right to get to (2,-1).

So the upper left corner (-5,-1) will ultimately move to (2,-1) after the reflection over x = -2.

Apply these steps to the other corner points and you'll end up with what is shown below.

Take note that a point like A(-5,-1) moves to A'(1,-1), and similar to the other points as well. Also, notice that when going from A to B to C, etc we are moving clockwise. We move counterclockwise when going from A' to B' to C' etc. Reflections always swap the orientation.

Transformation involves changing the position of a shape.

The coordinates of the image are:

[tex]\mathbf{A '= (1,1)}[/tex]      [tex]\mathbf{B' = (-1,-1)}[/tex]     [tex]\mathbf{C' = (-1,-4)}[/tex]     [tex]\mathbf{D' = (0,-4)}[/tex]

[tex]\mathbf{E' = (0,-3)}[/tex]      [tex]\mathbf{F = (1,-3)}[/tex]

The vertices of the shape are:

[tex]\mathbf{A = (-5,-1)}[/tex]

[tex]\mathbf{B = (-3,-1)}[/tex]

[tex]\mathbf{C = (-3,-4)}[/tex]

[tex]\mathbf{D = (-4,-4)}[/tex]

[tex]\mathbf{E = (-4,-3)}[/tex]

[tex]\mathbf{F = (-5,-3)}[/tex]

The rule of reflection across line x =-2 is:

[tex]\mathbf{(x,y)=(-x -4,y)}[/tex]

So, we have:

[tex]\mathbf{A '= (5 - 4,-1) = (1,-1)}[/tex]

[tex]\mathbf{B' = (3-4,-1) = (-1,-1)}[/tex]

[tex]\mathbf{C' = (3-4,-4) = (-1,-4)}[/tex]

[tex]\mathbf{D' = (4-4,-4) = (0,-4)}[/tex]

[tex]\mathbf{E' = (4-4,-3) = (0,-3)}[/tex]

[tex]\mathbf{F = (5-4,-3) = (1,-3)}[/tex]

So, the coordinates of the image are:

[tex]\mathbf{A '= (1,-1)}[/tex]

[tex]\mathbf{B' = (-1,-1)}[/tex]

[tex]\mathbf{C' = (-1,-4)}[/tex]

[tex]\mathbf{D' = (0,-4)}[/tex]

[tex]\mathbf{E' = (0,-3)}[/tex]

[tex]\mathbf{F = (1,-3)}[/tex]

See attachment for the image of the transformations

Read more about transformations at:

https://brainly.com/question/11709244

Answer:

[tex]\sqrt{68}[/tex]

Step-by-step explanation:

(7 , -1) = (x1 , y1)

(9 , -9) = (x2 , y2)

distance formula = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]

=[tex]\sqrt{(9 - 7)^2 + (-9 - (-1))^2}[/tex]

=[tex]\sqrt{2^2 + (-9 + 1)^2}[/tex]

=[tex]\sqrt{4 + (-8)^2}[/tex]

=[tex]\sqrt{4 + 64}[/tex]

=[tex]\sqrt{68}[/tex]

Answer:

[tex]Distance = \sqrt{ 68 } \\\\or \\\\Distance =2 \sqrt{17}[/tex]

Step-by-step explanation:

[tex]Let \ (x_1 , y_1) = ( 7 , - 1 ) \ and \ (x_2, y _ 2 ) = ( 9 , - 9 )\\\\\\Distance = \sqrt{(x_2 - x_ 1)^2 + (y_ 2 - y_ 1)^2}\\\\[/tex]

               [tex]= \sqrt{(9 - 7)^2 + ( -9 --1)^2} \\\\=\sqrt{2^2 + ( -9 + 1)^2 }\\\\=\sqrt {4 + (-8)^2 }\\\\=\sqrt{ 4 + 64 }\\\\=\sqrt{68}\\\\= \sqrt { 4 \times 17}\\\\=\sqrt{2^2 \times 17}\\\\=2 \sqrt{17}[/tex]

Answer:

€270

Step-by-step explanation:

If a fruit vendor has bought 165kg of apples at € 2 per kilo, the total amount spent is expressed as;

Cost price = 165 * 2 = €330

If 15kg spoilt, the amount of fruit remaining will be 165 - 15 = 150kg

If he rests he sells for € 4 per kilo, then;

Selling price = 150 * 4 = €600

Amount earned = €600 - €330

Amount earned = €270

Answer: The "?" would equal 1.

Step-by-step explanation: This is simply a line with a slope of 1 and a y-intercept of zero.

Answer:

radical

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

f(-7) = 5-(-7)=5+7=12

Answer:

452.16 ft²

Step-by-step explanation:

Use the circle area formula, A = [tex]\pi[/tex]r²

Plug in 3.14 as pi and 12 as the radius, then solve:

A = (3.14)(12)²

A = (3.14)(144)

A = 452.16

So, the area of the circle is 452.16 ft²

Answer and Step-by-step explanation:

Convert the numbers into improper fractions.

[tex]\frac{25}{6} ,\frac{28}{5}[/tex]

Now, multiply the numbers.

[tex]\frac{700}{30}[/tex]

Finally, simplify.

[tex]\frac{70}{3}[/tex] is the answer.

#teamtrees #PAW (Plant And Water)

Answer:

There are no choices but in order to qudratic equation not to have real roots the discriminant must be negative.

If d < 0, we get:

or

or

Answer:

2n +11

Step-by-step explanation:

4n+11−2n

Combine like terms

4n -2n +11

2n +11

Answer:

2n+11

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

To check, the squared values of the two smaller lengths must equal the squared value of the biggest length (Pythagorean Theorem)

40² + 75² = 85²

1600 + 5625 = or ≠ 7225

7225 = 7225

It is equivalent so it is correct.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

1st one is 9

2nd one is 6

3rd one is 2

Step-by-step explanation:

Answer:

79/300 mm

Step-by-step explanation:

We can use Ratio and Proportion to answer this question,

We know,

12 sheets of paper = 3.16mm

So,

1 = 3.16/12 mm

So, the thickness of 1 sheet of paper is => 3.16 / 12

=> 79/300

Hope it helps :)

Answer:

Step-by-step explanation:

Thickness of  1 sheet = thickness of 12 sheets ÷ number of sheets

                                  = 3.16 ÷ 12

                                  = 0.26 mm

Answer: D

Step-by-step explanation:

Answer:

the final price is $ 163 can be wrong

Profit: $78.60

Revenue: $340.60

Answer:

gdfhddfdhgbg

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

it's right cause I took the quix

Answer:

(a) 1.5 inches

(b) 2.5 inches

(c) 5 inches

Step-by-step explanation:

speed of first turtle = 4 1/2 inches per  minute = 9/2 inches per minute

speed of the second turtle = 5inches per minute

distance = speed x time

(a) Distance traveled by first turtle in 3 minutes

s = 9/2 x 3 = 13.5 inches

distance traveled by second turtle in 3 minutes

s' = 5 x 3 = 15 inches

So, the gap is

s'- s = 15 - 13.5 = 1.5 inches

(b) Distance traveled by first turtle in 5 minutes

s = 9/2 x 5 = 22.5 inches

distance traveled by second turtle in 5 minutes

s' = 5 x 5 = 25 inches

So, the gap is

s'- s = 25 - 22.5 = 2.5 inches

(c) Distance traveled by first turtle in 10 minutes

s = 9/2 x 10 = 45 inches

distance traveled by second turtle in 10 minutes

s' = 5 x 10 = 50 inches

So, the gap is

s'- s = 50 - 45 = 5 inches

Answer:

A≈1075.21

d Diameter

37

d

r

r

r

d

d

C

A

Using the formulas

A=

π

r

2

d=

2

r

Solving forA

A=

1

4

π

d

2

=

1

4

π

37

2

≈

1075.21009

Step-by-step explanation:

Answer:

La torre tiene 543.78 pies de altura.

Step-by-step explanation:

Podemos pensar en esta situación como si fuera un triángulo rectángulo, donde el cable es la hipotenusa y la torre es uno de los catetos. (Abajo se puede ver un dibujo de esta situación).

Nosotros queremos encontrar el valor de H, que es el cateto opuesto al ángulo conocido de 65°.

Entonces simplemente podemos usar la relación:

Sin(θ) = (cateto opuesto)/(hipotenusa)

donde:

cateto opuesto = H

θ = 65°

hipotenusa = 600 ft

sin(65°)  = H/600ft

sin(65°)*600ft = H = 543.78 ft

La torre tiene 543.78 pies de altura.

Answer:

y = 2/3x - 5

Step-by-step explanation:

y = 2/3x + b

-1 = 2/3(6) + b

-1 = 4 + b

-5 = b

Answer:

For the first one it is 8, and the second one is 19

Step-by-step explanation:

Answer:

20 cents

Step-by-step explanation:

Divide 3 dollars by 15 caterpillars.

3/15 = 0.2

20 cents

Answer:

Area of ​​its base = 12cm²

Step-by-step explanation:

The Area of ​​its base = 1/2 of its surface area - 1/2 of its lateral area

Its surface area = 64, then 1/2 X 64 = 32cm²

Its lateral area = 40, then 1/2 X 40 = 20cm²

So, Area of ​​its base = 32 - 20 = 12cm²

Answer:

C. There are two solutions: 2 and –2.

Step-by-step explanation:

Answer:

Step-by-step explanation:

we have

we know that

The solution of the function is equivalent to solve the following system of equations

 ------> equation A

 ------> equation B

The x-coordinate of the intersection point both graphs is the solution of the given function

Using a graphing tool

see the attached figure

The intersection points are  and  

therefore

The solution of the given function are

Solve x2 + 2 = 6 by graphing the related function. x^2 + 2 is a parabola with a vertex at the point (0, 2). When x = -1 or x = 1, then x^2 + 2 = 3, so we should put the points (-1,3) and (1,3) on the graph. When x = -2 or x = 2, then x^2 + 2 = 6, so we should put the points (-2,6) and (2,6) on the graph. We could continue adding points to the graph if we want, but we already have our two solutions. x^2 + 2 = 6 when x = -2 or x = 2. Therefore, x = -2, and x = 2 are the two solutions to this equation.

Answer: option C.

Step-by-step explanation:

Given  a quadratic function of the form , if the coefficient a is less than zero, then the function is opened upward.

The options A is not opened upwards, then it is not the answer.

Then the given equation  can be written as:

This function is equal to the parent function, shifted 4 units down.

Therefore, the graph that you are looking for must be a parabola that is opened upwards and has its vertex in the point (0,-4).

Then, the correct option is C. And the solution is:

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

Explanation:

Plot the two points on the same xy grid (refer to the diagram below). Once this is done, the answer probably will become apparent. We should move point B 11 units to the right so that we move directly over top point B'. Count out the spaces to see why this is the case, or you can subtract the x coordinates and apply absolute value

|x1-x2| = |-5 - 6| = 11

Then we need to move 3 units down to finally arrive at point B'

---------------------------

A non-visual or non-graph approach could look like this:

B is at (-5,-2) while B' is at (6,-5)

Focus on the x coordinates for now. Like before, we subtract the x coordinates and apply absolute value to get |x1-x2| = |-5 - 6| = 11. This is the "11 units to the right" motion.

Do the same for the y coordinates to get |y1-y2| = |-2-(-5)| = 3. We move down because the y coordinate of B' is further away from 0 compared to the y coordinate of B.

In short, we apply the translation rule [tex](x,y) \to (x+11, y-3)[/tex] to describe the motion of right 11, down 3.