Parallelogram Problem

Answer:

1/64

Step-by-step explanation:

Simplify the following:

1/(4^(11/3)×4^(-2/3))

Hint: | Simplify radicals.

1/4^(2/3) = 1/(4^2)^(1/3) = 1/(2^4)^(1/3) = (1/2^(1/3))/2:

1/(4^(11/3)×(1/2^(1/3))/2)

Hint: | Multiply numerator and denominator of 1/(2 2^(1/3)) by 2^(2/3).

Rationalize the denominator. 1/(2 2^(1/3)) = 1/(2 2^(1/3))×(2^(2/3))/(2^(2/3)) = (2^(2/3))/(2×2):

1/(4^(11/3)×(2^(2/3))/(2×2))

Hint: | Multiply 2 and 2 together.

2×2 = 4:

1/(4^(11/3)×(2^(2/3))/4)

Hint: | Separate the exponent of 4^(-11/3) into integer and fractional parts.

4^(-11/3) = 4^(1/3 - 12/3) = 4^(-12/3)×4^(1/3):

(4^(-12/3) 4^(1/3))/((2^(2/3))/4)

Hint: | Divide 12 by 3.

12/3 = (3 (-4))/3 = 4:

(4^(-4) 4^(1/3))/((2^(2/3))/4)

Hint: | Compute 4^4 by repeated squaring.

4^4 = (4^2)^2:

(4^(1/3))/((2^(2/3))/4) 1/(4^2)^2

Hint: | Evaluate 4^2.

4^2 = 16:

(4^(1/3))/(16^2×(2^(2/3))/4)

Hint: | Evaluate 16^2.

| 1 | 6

× | 1 | 6

| 9 | 6

1 | 6 | 0

2 | 5 | 6:

(4^(1/3))/(256×(2^(2/3))/4)

Hint: | Simplify radicals.

4^(1/3) = (2^2)^(1/3):

1/(256×(2^(2/3))/4) 2^(2/3)

Hint: | Write (2^(2/3))/(256×(2^(2/3))/4) as a single fraction.

Multiply the numerator by the reciprocal of the denominator, (2^(2/3))/(256×(2^(2/3))/4) = (2^(2/3))/256×4/2^(2/3):

(2^(2/3)×4)/(256×2^(2/3))

Hint: | Cancel common terms in the numerator and denominator of (2^(2/3)×4)/(256×2^(2/3)).

(2^(2/3)×4)/(256×2^(2/3)) = (2^(2/3))/(2^(2/3))×4/256 = 4/256:

4/256

Hint: | Reduce 4/256 to lowest terms. Start by finding the GCD of 4 and 256.

The gcd of 4 and 256 is 4, so 4/256 = (4×1)/(4×64) = 4/4×1/64 = 1/64:

Answer: 1/64

Answer:

I. 1 cup is $4.50

2 cups is $9.00

3 cups is $13.50

ll. 6 cups is $27.00

Step-by-step explanation:

Now since the number of cups is proportional to the total cost of frozen yoghurt,and the cost of 4 yoghurts cups where given .ie. $18.00

then 1 cup is $18/4 which is $4.50 per one cup, thus the other cost of cups are given.

therefore 6 cups is 6•18/4 which is $27.00.

hence 5 cups is 5•18/4 which is $22.50.

Answer:

-10

Step-by-step explanation:

4a-2b=10

-1(4a-2b)=-1*10

-4a+2b= - 10

2b - 4a = - 10

Answer:47.5

Step-by-step explanation:

Answer:x=3

Step-by-step explanation:

the 3 angles of a triangle equal 180

you add 105 and 46, which equals 151

you subtract 151 from 180 to see what the missing angle is (29)

you would make 6x+11 equal to 29

-subtract 11 from 29= 18

6x/6, 18/6

the answer is 3

hope this helps! :)

Answer:

SA = 480 cm²

Step-by-step explanation:

Surface area of the composite figure given in the picture = (Surface Area of the triangular prism on the top - area of the rectangular base) + (Surface area of the rectangular prism - Area of the rectangular base)

Surface area of the triangular prism = Area of the triangular bases + (perimeter of the base × Height)

= [tex]2(\frac{1}{2}\times 3\times 8)[/tex] + [(5 + 5 + 8)×12]

= 24 + 216

= 240 cm²

Area of the rectangular surface of the prism = 8 × 12 = 96 cm²

Surface area of the rectangular prism = 2(lb + bh + hl)

Here, l = Length, b = width and h = Height of the rectangular prism

                                                  = 2(8 × 12 + 12 × 6 + 6 ×8)

                                                  = 432 cm²

Surface area of the composite figure = (240 - 96) + (432 - 96)

                                                                = 144 + 336

                                                                = 480 cm²

Answer:

x = 8

Step-by-step explanation:

Use the direct variation equation, y = kx

Plug in the given values of x and y, and solve for k:

y = kx

-8 = k(-2)

4 = k

So, the equation is y = 4x

Using this, plug in 32 as y, and solve for x:

y = 4x

32 = 4x

8 = x

So, x = 8 when y = 32

Answer:

x = 48

Step-by-step explanation:

From the given diagram, the sum of the angles given is equal to 180 degrees as shown;

x+y+2x = 80

Since y = 36

x +36+2x = 180

3x = 180 - 36

3x = 144

x = 144/3

x = 48

Hence the value of x is 48

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Answer:

Step-by-step explanation:

Factorize the denominator

Sum = 4

Product = 3

Factors = 1 , 3    {1*3 = 3 and  1+3 = 4}

x² + 4x + 3 = x² + x    + 3x + 1*3

                 = x(x + 1) + 3(x + 1)

                 = (x + 1)(x + 3)

GCF of the numerator and denominator = (x + 3)

Answer:

(r + 20)t = r

Step-by-step explanation:

Distance is constant in the scenario above, distance from home to wedding and wedding back home is the same.

From wedding back home. :

Recall : Distance = speed * time

Distance = r * 1 hour

From home to wedding :

Speed = 20 mph more ; r + 20

Time = t

Distance = (r + 20)* t = (r +20)t

Since the distance are the same, we can equate both :

(r + 20)t = r * 1

= (r + 20)t = r

Step-by-step explanation:

This the answer in the photo

Answer:

Step-by-step explanation:

Rational numbers are numbers that can be expressed as a fraction or ratio of two integers. Rational numbers are denoted  Q

.

Since  −3  can be written as  −3/1

, it could be argued that  −3  is also a real number.

Answer:

yes

Step-by-step explanation:

Any rational number can be expressed in the form

[tex]\frac{a}{b}[/tex] ← a and b are integers , then

- 3 = [tex]\frac{-3}{1}[/tex] ← in rational form

Thus - 3 is a rational number

Answer:

72

Step-by-step explanation:

1/3 ft is 4 inches

24 feet is 288 inches

take 288 and divide it by 4

you get 72, which is the number of pieces of chain Andrew has

Answer:

1.39

Step-by-step explanation:

Given the quadratic equation :

2x^2+3x-8 = 0

We could apply the quadratic equation formula :

a = 2 ; b = 3, c = - 8

The formula is stated as :

-b±sqrt(b² - 4ac)/2a

To save computation tune, we could use a calculator :

The roots are : - 2.886 ; 1.386

The positive solution rounded to the nearest hundredth is : 1.39

Answer:

SU , UT , ST

Step-by-step explanation:

Answer:

its a black screen

Step-by-step explanation:

Answer:

c = 5/Cos 35

Step-by-step explanation:

We are given the following

m<ACB = 90degrees

m<ABC = 35degrees

The side opposite to m<ABC is AC

BA = hypotenuse

CB = adjacent = 5inches

Required

Equation to solve BA which is c

Using the Pythagoras theorem;

Cos theta = Adjacent/Hypotenuse

Cos m<ABC = CB/BA

Cos m<ABC = 5/c

c = 5/cosm<ABC

c = 5/Cos 35

Hence the equation that can be used to solve for c is c = 5/Cos 35

Answer:

Two 1/6 pieces

Step-by-step explanation:

Two 1/6 pieces equals 1/3 of the apple

Answer:

10

Step-by-step explanation:

because it shows where the line is

Answer:

answer

Step-by-step explanation:

=convert 3.8 into mixed number

=3 4/5

=1 3/10+3 4/5

=5.1 in mixed fraction

=5 1/10

if i got it wrong i am seriously sorry!

Answer:

60 cm^3

Step-by-step explanation:

Answer:

I think its 33

Step-by-step explanation:

i may be wrong

Answer:

choice 2) 90

Step-by-step explanation:

-3xy = ?

x=5 and y= -6

-3(5)(-6) = 90

Answer:

Add all of them together. 1/5 + 2/4 + 4/3 + 3/2 = 53/15 miles

Step-by-step explanation:

1/5 + 2(1/4) + 4(1/3) + 3(1/2)

Answer:

Im pretty sure its 11 because if you look at 145 mark its at between 10 and 12, Hopefully that helps!

Step-by-step explanation:

Answer:

its 31

Step-by-step explanation: