Melany wants to hang a canvas, which is 8 feet wide, on his wall. Where on the
canvas should Melany mark the location of the hangers if the canvas requires a
hanger every 1/5 of its length, excluding the edges? Justify your answer.

Answer:

___-5___is 3 units left from -2 on a number line.

___1___- is 3 units right from -2 on a number line

Hey there! I'm happy to help!

We want to get all of the variables on the left side and all of the numbers on the right side. This will allow our variable to be isolated so we can see what it is equal to.

1/4x - 1/8 = 7/8 + 1/2x

We add 1/8 to both sides.

1/4x=1+1/2x

We subtract 1/2x from both sides.

-1/4x=1

We divide both sides by -1/4 (same thing as multiplying -4).

B. x=-4

Have a wonderful day and keep on learning! :D

Answer:

10+15i/13

Step-by-step explanation:

This question is about complex numbers.

so,

in this type of questions we have to multiply this fraction by the conjugate of the denominator

   conjugate of the denominator is  3-2i

    1)    5i(3-2i)/(3+2i)(3-2i)

    2) 15i-10i^2/9-4i^2   ( we know that i^2 = -1 )

    3) 15i+10/9+4

     4) 15i+10  / 13

Number combination can be used to find the number of selecting n  items from m items

The known parameters are;

Number of days the six friends play a game of tennis = Every day = 7 days

Number of weeks the six friends the friends play for = 7 weeks

Therefore the total number of days = 7 × 7 days = 49 days

Required:

(a) The number of ways the friends can play with each other once is given as follows;

[tex]The \ number \ of \ 2 \ combinations \ in \ 6 \ options, C_6^2 = \dfrac{6!}{2!\times (6-2)!} = 15[/tex]

The number of ways the six friends can play with each other once is 15 ways

Therefore, minimum number of singles games that will be between the same friends playing each other is given as follows;

[tex]\mathbf{Number \ of \ games = \dfrac{7 \times 7}{C_6^2} }=3.2\overline 6[/tex]

Therefore, more than 3 of the games or four games will be between pairs playing the game more than four times together, and when at least four of the games of singles are counted it will be between friends playing each other for the fourth time

(b) The number of ways the friends can play game of doubles is given as follows;

[tex]C_6^4 = \dfrac{6!}{4! \times (6 - 4)!} = 15[/tex]

The number of pairs = ₆C₂ = 15

The number of games of doubles = 49

In 49 games, we have;

The number of times the same opposing  will play a game of doubles where a member of the pair can be on either side of the court will given as follows;

[tex]\mathbf{Number \ of \ games \ of \ doubles \ between \ same \ pair} = \dfrac{7 \times 7}{15 } =3.2\overline 6[/tex]

Therefore, at least four of the of the games of doubles will be between the same set of four friends playing for the 4th time, which gives; at least four games of doubles between the same set of four friends, two of which are playing (as a pair) the same opposing pair for the 4/2 = second time

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Step-by-step explanation:

Infinitely many solutions are there....

hope it helps

Answer:

C. 8/17

Step-by-step explanation:

PM = 16+14 = 30 cm

KP= LN = 16×tan45° = 16×1 = 16cm

by using pythagorean theorem, we find :

KM² = PM²+KP²

= 30²+16²

= 900+256

= 1156

=> KM =√1156 = 34cm

so, cos theta = KP/KM = 16/34 = 8/17

Density is mass per unit volume,

ρ = m/v

Solving for mass gives

m = ρv

so that a gas with density 0.824 g/L that occupies 3.00 L has a mass of

m = (0.824 g/L) (3.00 L) = 2.47 g

Answer:

not proportional

Step-by-step explanation:

We can check using cross products

18/73  = 4/16

18*16 = 73*4

288=292

Since this is not equal, this is not proportional

Answer:

= sin x

1

−

cos

x

(

1

+

cos

x

1

+

cos

x

)

-multiply by the conjugate

=

sin

x

+

sin

x

cos

x

1

−

cos

2

x

-distribute

=

sin

x

sin

2

x

+

sin

x

cos

x

sin

2

x

-use property  

sin

2

x

+

cos

2

x

=

1

=

1

sin

x

+

cos

x

sin

x

-simply

=

csc

x

+

cot

x

=

Right Hand Side

Step-by-step explanation:

Answer:

1/9 probability

Step-by-step explanation:

The total cookies are 36 and the new flavors are 4, if you simplify 4/36, it equals 1/9

Answer:

Step-by-step explanation:t55

An octagon has 8 sides. If each of them has a length of x, then the perimeter is 8x which is twice the perimeter of the square. (The square has a perimeter of 4x)

A dodecagon is a 12 sided regular polygon. It will have 12 sides all of which are equal to x. Since the square has a perimeter of 4x and the dodecagon has a perimeter of 12x the perimeter of the dodecagon is 3 times that of the given square.

Answer:

a horizontal translation 3 units to the right because-3 has been added to the exponent

The length of the shorter piece is 45 inches.

Let's represent the length of the shorter piece as "x" inches.

According to the information given, the length of the longer piece would be three times the length of the shorter piece, which means it's 3x inches.

Since the total length of the pipe is 180 inches, we can set up an equation:

x (shorter piece) + 3x (longer piece) = 180

Now solve for x:

4x = 180

x = 45

Therefore, the length of the shorter piece is 45 inches.

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Answer:

O Natural, whole, integer, rational, real

Step-by-step explanation:

it can be expressed as a fraction of 45/3, which means that it is rational.

it is a whole number because it does not contain a fraction or decimal.

it is a real number because it is a number we normally use such as 1, -0.1, 3/4, etc

it is a natural number because it is a positive integer.

and it is an integer because it does not contain a decimal.

Answer: Natural, whole, integer, rational, real

Answer:

a)

There are 6 planes - 5 faces of the pyramid and one base, which overlaps with the plane X.

b)

Collinear points are the points on the same line:

c)

The intersection of planes X and HGD is the line section HG.

a:-

This is a pentagonal pyramid

B:-

C:-

HG is the intersection line

Answer:

No solutions for n

Step-by-step explanation:

Distribute the 4 to the -8 and the 2n

-4 + 4*-8 + 4*2n = -37 + 8n

Multiply

-4 - 32 + 8n = -37 + 8n

Subtract 8n on both sides

-4 - 32 = -37

Subtract on the left

-36 = -37

No solutions because -36 does not equal -37

Answer:

No solution

Step-by-step explanation:

-4 + 4(-8 + 2n) = -37 + 8n

-4 - 32 + 8n = -37 + 8n

-36 + 8n = -37 + 8n

8n - 8n = -37 + 36

0 = -1

Since 0 does not equal 1, this is a “No Solution”

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Given

- [tex]\frac{1}{4}[/tex] × - [tex]\frac{4}{3}[/tex] ( negative times negative = positive )

= [tex]\frac{1}{4}[/tex] × [tex]\frac{4}{3}[/tex] ( cancel the 4 on the numerator and denominator )

= [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

72° and a° is the angle of a straight line so

a+72°=180

a=180-72

a=108°

By using alternate exterior angle definition:

7x+24=180

7x=108-24

7x=84

x=84/7

x=12

Answer:

35/100 if I remembered correctly, XD

Answer:

[tex]\frac{35}{100}[/tex]

Step-by-step explanation:

if you want to convert decimal to fraction you first have to observe the decimal point

here the decimal point is after 2 numbers so

u will take 100 to be divided with

[tex]\frac{35}{100}[/tex]

Answer:

[tex]3(x-1)^2 +6[/tex]

Step-by-step explanation:

Write [tex]3x^2-6x+9[/tex] in the form: [tex]x^2 + 2ax + a^2[/tex].

Factor out 3.

[tex]3(x^2 -2x+3)[/tex]

Add and subtract [tex]\left(-1\right)^2\:[/tex].

[tex]3\left(x^2-2x+3+\left(-1\right)^2-\left(-1\right)^2\right)[/tex]

You dont have to write this section down but its for notes:

[tex]x^2+2ax+a^2=\left(x+a\right)^2[/tex]

[tex]x^2-2x+\left(-1\right)^2=\left(x-1\right)^2[/tex]

Continue writing this down to show work:

Complete the square

[tex]3\left(\left(x-1\right)^2+3-\left(-1\right)^2\right)[/tex]

Simplify

[tex]3\left(x-1\right)^2+6[/tex]

Answer:

first angle is 20, 2nd is 120, 3rd is 40.

Step-by-step explanation:

with these words, "20 less than a number, Three

times the number, is the number." We can set up the equation x-20+3x+x = 180. combine like terms and we get 5x-20=180. add 20 to both sides to get 5x=200 then divide 200 by 5x to get x = 40. We can then plug 40 into each of the expressions, x-20, 3x, x, to get our angles.

Answer:

123/1

Step-by-step explanation:

-135- (-258)

123

123/1

brainliest is appreciated

Answer:

-7

Step-by-step explanation:

Equation: 2x - 4 = -18

First, add 4 to both sides:

2x = -14

Finally, divide both sides by 2:

x = -7

Check (optional):

2(-7) - 4 = -18

-14 - 4 = -18

-18 = -18 so this is correct

If you're confused about any of these steps, just let me know and I'll try to clear it up for you! :)

Answer:

It is being multiplied by 6 each time.

Step-by-step explanation:4x6, 24x6

The coordinate of E will be (1, -3) if the coordinates of E if E divides CH three -fourths of the way from C to H

Midpoint of a line is a point that divides a line into two equal parts.

If the line is divided in the ratio a:b, then the midpoint formula will be expressed as:

[tex]M(X,Y) =(\frac{ax_1+bx_2}{a+b}, \frac{ay_1+by_2}{a+b})\\[/tex]

Given the coordinate points, C(2, 1) and H(-2, 15) divided in the ratio of 3:4

[tex]X = \frac{3(2)+1(-2)}{3+1}\\X= \frac{6-2}{4}\\X=\frac{4}{4}\\X = 1[/tex]

Get the coordinates Y:

[tex]Y = \frac{3(1)+1(-15)}{3+1}\\Y= \frac{3-15}{7}\\Y=\frac{-12}{4}\\Y= -3[/tex]

This shows that the coordinate of E will be (1, -3)

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Answer:

Step-by-step explanation:

[tex]\alpha+\beta=\dfrac{5}{2} \\\\\alpha*\beta=\dfrac{1}{2} \\\\\alpha^2+\beta^2=\dfrac{21}{4} \ (see\ previous\ post)\\\\(\alpha+\beta)^4=\dfrac{625}{16} \\\\=\alpha^4+\beta^4+4*\alpha^3*\beta+6*\alpha^2*\beta^2+4*\alpha*\beta^3\\\\=\alpha^4+\beta^4+4*(\alpha*\beta)(\alpha^2+\beta^2)+6*\alpha^2*\beta^2\\\\\alpha^4+\beta^4=(\alpha+\beta)^4-4*(\alpha*\beta)(\alpha^2+\beta^2)-6*\alpha^2*\beta^2\\\\= \dfrac{625}{16} -4*\dfrac{1}{2} *\dfrac{21}{4} -6*(\dfrac{1}{2})^2 \\\\[/tex]

[tex]= \dfrac{625}{16}- \dfrac{168}{16}-\dfrac{24}{16}\\\\\\= \dfrac{433}{16}[/tex]