Name a pair of angles that are a linear pair

Choose the correct answer below.
A. B. C. D.

Answer:

The value of x that minimizes the total area of the two squares is x = 5.

Step-by-step explanation:

A wire 10 centimeters long is cut into two pieces, with one piece measuring x centimeters and the other (10 - x) centimeters.

Each piece is bend into the shape of a square, and we want to find the value of x that minimizes the total area of the two squares.

If x is bend into a square with four equivalent sides, then each side measure:

[tex]\displaystyle A = \frac{x}{4}[/tex]

Likewise, each side of the second square will measure:

[tex]\displaystyle A = \frac{10-x}{4}[/tex]

The area of a square is its side squared. Hence, the area of both squares will be given by:

[tex]\displaystyle T = \left( \frac{x}{4}\right) ^2 + \left(\frac{10-x}{4}\right)^2[/tex]

Simplify:

[tex]\displaystyle \begin{aligned} T &= \frac{x^2}{16} + \frac{x^2 - 20x + 100}{16} \\ \\ &=\frac{2x^2-20x+100}{16}\\ \\ &= \frac{1}{8}x^2-\frac{5}{4}x+\frac{25}{4} \end{aligned}[/tex]

Since this is a quadratic with a positive leading coefficient, the minimum value will occur at the vertex point.

Recall that the x-coordinate of the vertex is given by:

[tex]\displaystyle x = -\frac{b}{2a}[/tex]

In this case, a = 1/8 and b = - 5/4. Hence:

[tex]\displaystyle x = -\frac{\left(-\dfrac{5}{4}\right)}{2\left(\dfrac{1}{8}\right)} = 5[/tex]

In conclusion, the value of x that minimizes the total area of the two squares is x = 5.

Answer:

5(14-2)^2÷2=360

Step-by-step explanation:

Further explanation

We at present undergo the following operations: addition, subtraction, multiplication, and division. When given an expression sometimes we confuse operations which must take precedence.

In the 1500s the rules of the order of operation were issued. The "order" of these operations states which processes take precedence (as a priority) before which other operations.

The priority of operations is:

Brackets (simplify in it)

Exponent

Multiplication and Division (from left to right)

Addition and Reduction (from left to right)

Answer:

-2

Step-by-step explanation:

brackets first

12 - 9 = 3

Then square it

3^2 = 9

Now multiply by 2

9*2 = 18

finally get - 5 * 4 = - 20

and put them both together

18 - 20 = - 2

Answer:

Translation:

1. Movement of furniture

2. Airplane positioning within a taxiway

3. The position of the mouse cursor on your computer

Reflection:

1. A mirror

2. A double-door exit at school

3. Chairs facing each other at school

Rotation:

1. The Earth's rotation

2. Hands on a clock

3. A carousel

Dilation/Stretch:

1. A balloon expanding

2. A balloon deflating

3. Biological growth

Transformation involves changing the position and/or size of a shape. Some real world examples of transformation are:

Translation: Mouse cursor

Reflection: Mirror

Rotation: The clock

Dilation: Magnifying lenses

Translation

When an object is moved away from its original position, then the object has been translated. Real world examples include:

Reflection

When an object is flipped from its original position, then the object has been reflected. Real world examples include:

Rotation

When an object is turned around a center, then the object has been rotated. Real world examples include:

Dilation

When the size of an object is changed in equivalent proportions, then the object has been dilated. Real world examples include:

See attachment for examples of each transformation

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Answer:

780 kg

Step-by-step explanation:

If 1 weights 60 kg then 13 of them should weight 780 kg

1 60 kg

13 ↗️ ?

(13 × 60) ÷ 1

Answer:

yes the number is divisible by 4 in which we get 171143 without any decimal but if we try to divide it by 8 then we get

85571.5 with decimal include

Answer:

LOVE and CARING for each other

Step-by-step explanation:

Answer:

A. x^6

Step-by-step explanation:

[tex]z = {y}^{2} = {( {x}^{3} )}^{2} = {x}^{3 \times 2} = {x}^{6} [/tex]

Answer:

the awnser is 20 bc 4 x 5 = 20

The total number of tokens needed for v video games is 4v.

Number of tokens needed per game = 4 tokens

Number of video games = v

Total number of tokens needed = Number of tokens needed per game × Number of video games

= 4 × v

= 4v

Therefore, if the 6 video games are played;

Total number of tokens needed = 4v

= 4 × 6

= 24 tokens

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El volumen de material requerido para la construcción de la escultura es:

[tex]V_{tot}=122,26\: m^{3}[/tex]

Esta escultura esta compuesta de dos volúmenes, un prisma de base hexagonal y una pirámide de base hexagonal. Calculemos el volumen de cada figura por separado, para luego sumarlos.

Prisma

La ecuacion del área de un hexágono está dada por:

[tex]A_{hex}=\frac{P*a}{2}[/tex]

Donde:

Entonces el área será:

[tex]A_{hex}=\frac{24*3,4}{2}[/tex]

[tex]A_{hex}=40,8\: m^{2}[/tex]

Ahara, el volumen de un prisma de base hexagonal está dada por:

[tex]V_{prisma}=A_{hex}*h[/tex]

h es la altura del prisma, en nuestro caso h = 2 m.

Entonces:

[tex]V_{prisma}=40,8*2[/tex]

[tex]V_{prisma}=81,6\: m^{3}[/tex]

Pirámide

El volumen de una pirámide de base hexagonal está dado por:

[tex]V_{piramide}=\frac{A_{hex}*H}{3}[/tex]

Donde:

Nosotros tenemos la apotema del volumen 4,53 m, por lo tanto podremos calcular H usadon el teorema de pitagoras.

[tex]4,53^{2}=a^{2}+H^{2}[/tex]

[tex]4,53^{2}=3,4^{2}+H^{2}[/tex]

[tex]H=2,99\: m[/tex]

Por lo tanto el volumen de la pirámide será:

[tex]V_{piramide}=\frac{40,8*2,99}{3}[/tex]

[tex]V_{piramide}=40,66\: m^{3}[/tex]

El volumen total del material necesario será:

[tex]V_{tot}=V_{prisma}+V_{piramide}[/tex]

[tex]V_{tot}=81,6+40,7=122,26\: m^{3}[/tex]

Puedes aprender más de volúmenes aquí:

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Espero te haya sido de ayuda!

Hi ;-)

¾ + √64 = ¾ + 8 = 8¾

√64 = 8, because 8 · 8 = 64

Answer:

C

Step-by-step explanation:

all whole numbers can be written as fractions that is over 1

Answer:

A. 6^-12

Step-by-step explanation:

This is a "power of a power"--so we multiply the exponents

(6^4)^-3 = 6^(4*-3) = 6^-12

Answer:

5!

Step-by-step explanation:

2x+260=mB50

= 2(5)+260

=310

sq=5

Answer:

how did the "X" on the right get to the left...

to remove it you have to SUBTRACT ...

you added "X" to both sides that was/is the error in your attempt

Step-by-step explanation:

-2x + 5(x-1) = -11 + x

-2x + 5x - 5 = -11 +x

3x - 5 = -11 + x

2x - 5 = -11

2x = -6

x = -3

Answer:

P: 4x+10

A: [tex]x^{2}[/tex]+5x+4

Step-by-step explanation:

Perimeter: 2*(length+width) =

2*(2x+5) = 4x+10

Area: (x+4)*(x+1) = [tex]x^{2}[/tex]+5x+4

Answer:

Machine A is 5, machine B is 6, and machine c is 3. Therefore C is the fastest.

Step-by-step explanation:

Answer:

B - 18

Step-by-step explanation:

Area of a right triangle

1/2 * b * h

1/2 * 9 * 4

1/2 * 36

18

Answer:

D 150 ft is the length of 5 ft

Answer:

Step-by-step explanation:

The ground level is zero, then we have the following equations.

2 levels below ground level:

5 levels up:

Answer:

[tex]here \: elevator \: is \: at \: below \: ground \: \\ level \: by \: two \: floors \\ so \: take \: it \: as \: 1 \: so \: then \: ground \: level = 3 \\ \\ then \: the \:upper \: floor \: is \: 5 \\ \\ then \: upper \: - ground = 5 - 2 = 23\ so \: answer \: is3 \\ thank \: you[/tex]

Answer:

x = 3

Step-by-step explanation:

3х/2+5/2= 7

(3x+5)/2 = 7

3x+5 = 14

3x = 9

x = 3

Step-by-step explanation:

m∠RSU + m∠UST = 90° (as complementary angles)

(7x + 3)° + (11x − 21)° =90°

18x -18° = 90°

18x = 108°

x = 6

so, m∠RSU = (7x + 3)° = 7(6)+3 = 45°

and m∠UST = (11x − 21)° = 11(6) -21 = 45°

The required measures of the angles ∠RSU and ∠UST are 31° and 23° respectively.

The angle can be defined as the one line inclined over another line. Also the angles are measured in radian or degrees.

The sum of the complementary angles is 90.
So,
∠RSU + ∠UST = 90
7x +3 + 11x - 21 = 90
18x - 18 = 90
18 (x - 1) = 90
x - 1 = 90 / 18
x - 1 = 5
x = 4

Required measures of the angles,|

1) m∠RSU = (7x + 3)°
m∠RSU = (7 * 4+ 3)°|

m∠RSU = 31°

2)  m∠UST = (11x − 21)°.
    m∠UST = (11 * 4 − 21)°
    m∠UST = (44 − 21)°
     m∠UST =  23°

Thus, the required measures of the angles ∠RSU and ∠UST are 31° and 23° respectively.

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Answer:

the class started a new one

Answer:

$48.

Step-by-step explanation:

60% off

= 120 - 0.60*120

= 120 - 72

= $48.

Answer:

25 - (6 x y) + (3 x y) = -56, y = 3.44

Step-by-step explanation:

-56 + 25 = 31, 6y + 3y = 9y, 31 = 9y, 31 / 9 = 3.44

it's a repeating number so uh yeah

y = 3.44

Answer:

Slope: 7/5

y intercept: (0,3)

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

If we need to find the distance between two points on a number line, we subtract one of the points from the other. We then take the absoulte value of the difference. You done this right.

Answer:

B

Step-by-step explanation:

The correct statement is, the graph of g(x) is the graph of f(x) shifted 5 units up.

In geometry, a vertical shift otherwise known as vertical translation, is a translation of a geometric object in a direction parallel to the vertical axis of the Cartesian coordinate system. In simpler terms, it is a shift in which a plane figure moves vertically.

Given that g(x) = f(x) + 5. We need to find that which statement best compares the graph of g(x) with the graph of f(x),

So,

If f is any function of x, then the graph of the function f(x) + c, may be obtained by a vertical translation of the graph of f(x) by distance c.

For this reason, the function f(x) + c is sometimes called a vertical translate of f(x).

Hence, the correct statement is, the graph of g(x) is the graph of f(x) shifted 5 units up.

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