What is the simplified form of 20 times x to the sixth power over 15 times y to the fifth power times the fraction 5 times y squared over 6 times x to the fourth power ?

a. 9 x squared over 10 y cubed
b. 9 x cubed over 10 y squared
c. 10 x cubed over 9 y squared
d. 10 x squared over 9 y cubed

The missing step in the proof is;

The correct answer choice is option C.

Alternate angle theorem states that when two parallel lines are cut by a transversal, the resulting alternate interior or exterior angles are congruent.

It is used to prove that alternate interior angles are equal if two parallel lines are cut by a transversal,

Hence, angle 1 is congruent to angle 4 and angle 3 is congruent to angle 5.

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5v+7(2.85)=28.70

5v+19.95 = 28.70

5v = 8.75

v = 1.75

Answer:  The correct option is (D). ACB.

Step-by-step explanation:  We are given to identify a semi-circle that contains the point 'C'.

As shown in the figure, AB is the diameter of the circle with center 'O'.

So, there are two congruent semi-circles made by the diameter AB.

The point 'C' lies on the upper semi-circle made by the diameter AB.

Since the upper semi-circle contains the point 'C', so it is named as the semi-circle ACB.

Thus, the semi-circle ACB contains the point 'C'.

Option (D) is correct.

Answer:

Step-by-step explanation:

[tex](5+5-5:5)\cdot5\\\\\text{Use PEMDAS}\\\\\text{P Parentheses first}\\\text{E Exponents}\\\text{MD Multiplication and Division (left-to-right)}\\\text{AS Addition and Subtraction (left-to-right)}\\\\=(5+5-1)\cdot5\\\\=(10-1)\cdot5\\\\=9\cdot5\\\\=45[/tex]

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

Let

x-------> the pressure in PSI

y------> the volume of the gas in cubic inches

In this problem we have the point [tex](30,600)[/tex]

so

[tex]x=30\ psi\\y=600\ in^{3}[/tex]

Find the constant k

[tex]y*x=k[/tex]

substitute the values of x and y

[tex]600*30=k[/tex]

[tex]k=18,000\ lb*in[/tex]

the equation is

[tex]y=18,000/x[/tex]

therefore

the answer is

[tex]y=18,000/x[/tex]

Answer:

[tex]y=\frac{18000}{x}[/tex]

Step-by-step explanation:

Let the volume of gas be y

Let the pressure be x

Since we are given that the volume of the gas is inversely proportional to its pressure.

⇒[tex]y \propto \frac{1}{x}[/tex]

Let the proportionality be k

So, [tex]y=\frac{k}{x}[/tex]  ---A

Now we are given that At a pressure of 30 pounds per square inch (psi), a gas has a volume of 600 cubic inches

So, substitute x = 30

y = 600

[tex]600=\frac{k}{30}[/tex]

[tex]600 \times 30=k[/tex]

[tex]18000 =k[/tex]

Substitute the value of k in A

So,  [tex]y=\frac{18000}{x}[/tex]

Hence  function can be used to model the volume of the gas y, in cubic inches, when the pressure is x psi is    [tex]y=\frac{18000}{x}[/tex]

Answer: False

Martin is asked to find the probability of getting one head and three tails on for coin tosses this is a simple event.

A. True

B. False

Answer: A. 6

A. 4.3%

Step-by-step explanation:

The total number of singers = 4

To choose singers = 2

The number of ways to choose 2 singers from 4= [tex]^4C_2=\frac{4!}{2!(4-2)!}=3\times2=6[/tex]

Hence, A is the right option.

The total number of water purifiers  T= 280

The number of defective purifiers D= 12

The probability that a water purifier chosen at random will be defective (in percent)=[tex]\frac{\text{T}}{\text{D}}\times100[/tex]

[tex]=\frac{12}{280}\times100\\=0.042857\times100\\=4.2857\%\approx4.3\%[/tex]

Hence, A is the right option.

To find the radius of the circle inscribed in the isosceles triangle, we can use the formula for the inradius of a triangle. The inradius is given by the formula: inradius = (area of the triangle) / (semiperimeter of the triangle). First, we need to find the area and semiperimeter of the triangle. Then, we can calculate the inradius and find the radius of the circle.

To find the radius of the circle inscribed in the isosceles triangle, we can use the formula for the inradius of a triangle. The inradius is given by the formula:

inradius = (area of the triangle) / (semiperimeter of the triangle)

First, we need to find the area of the triangle. Since it is an isosceles triangle with equal sides of 5 inches, we can split it into two congruent right triangles. The height of each right triangle can be found using the Pythagorean theorem:

height = sqrt(5^2 - (6/2)^2) = sqrt(25 - 9) = sqrt(16) = 4 inches

Now, we can find the area of the triangle:

area = (1/2) * base * height = (1/2) * 6 * 4 = 12 square inches

Next, we need to find the semiperimeter of the triangle:

semiperimeter = (5 + 5 + 6) / 2 = 16 inches

Finally, we can calculate the inradius:

inradius = 12 / 16 = 3/4 inches

Therefore, the radius of the circle is 3/4 inches.

To get rid of an exponent on a variable, apply the inverse operation of the exponent such as division or root operations.

To get rid of an exponent on a variable, you need to apply the inverse operation of the exponent. If the exponent is multiplication, you use division, and if the exponent is an exponentiation, you use a root operation. For example, to get rid of a squared variable, you take the square root of the variable. If you have a variable raised to the third power, you take the cube root of the variable.

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Answer:

So basically sqrt of 2...

Step-by-step explanation:

Because point C is the centroid of the triangle, therefore:

Segments PZ = ZR;  RY = YQ; QX = XP

A.
If CY = 10, then

PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answers:     

PC = 20     

PY = 30

B.
If QC = 10, then

ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answers:     

ZC = 5       

ZQ = 15

C.
If PX = 20
because the median RX bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer:      

PQ = 40

x+y=12

x*y =36

8+4=12, so make the digits 84, reverse to make it 48

84-48=36

 the numbers are 8 & 4

Answer: [tex]a^{12}+8[/tex]

Step-by-step explanation:

let's check all the expressions

1. [tex]a^3+18[/tex]

here 18 is not a perfect cube.

2. [tex]a^6+9[/tex]

here 9 is not a perfect cube.

3.[tex]a^9+16[/tex]

here 16 is not a perfect cube.

4.[tex]a^{12}+8[/tex]

here 8 is a perfect cube, thus we can write above expression by using laws of exponents as

[tex](a^4)^3+2^3[/tex]

Thus, [tex]a^{12}+8[/tex] is a sum of cubes.

The required value of x is 7.

A linear equation only has one or two variables. No variables in a linear equation is raised to power greater than 1 or used as denominator of a fraction.

Now the given statement is,

Three times the difference of a number x and seven is twenty-three minus the sum of three times a number x and two.

So converting them into numerical form,

the difference of a number x and seven = x - 7

∴ Three times the difference of a number x and seven = 3(x - 7)

Similarly,

the sum of three times a number x and two = 3x + 2

∴ Twenty-three minus the sum of three times a number x = 23 - (3x + 2)

Therefore, the required equation is,

3(x - 7) = 23 - (3x + 2)

Expanding the brackets we get,

3x - 21 = 23 - 3x - 2

or, 3x - 21 = 21 - 3x

Taking alike terms together,

3x + 3x = 21 + 21

or, 6x = 42

Dividing both side by 6 we get,

x = 7

which is the required value of x.

Thus, The required value of x is 7.

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Since the new machine is three times faster, it takes (12 hours) / 3 = 4 hours for the new machine to make 10,000 cans alone.

Let's denote the time it takes the older machine to make 10,000 cans as "t" hours.

The new machine can make 10,000 cans three times faster than the older machine, which means it takes "t/3" hours for the new machine to make 10,000 cans.

When both machines are working together, they can make 10,000 cans in 9 hours.

Now, we can set up an equation based on the work rates of the two machines:

Work rate of the older machine + Work rate of the new machine = Combined work rate

The work rate is the amount of work (number of cans made) per unit of time (hours).

For the older machine:

Work rate of the older machine = 10,000 cans / t hours

For the new machine:

Work rate of the new machine = 10,000 cans / (t/3) hours

Combined work rate when both machines work together:

Combined work rate = 10,000 cans / 9 hours

Now, the equation becomes:

10,000 cans / t hours + 10,000 cans / (t/3) hours = 10,000 cans / 9 hours

To solve for "t," we can start by finding a common denominator for the fractions on the left side of the equation:

t/3 is the same as (1/3)t. So the equation becomes:

10,000 cans / t hours + 10,000 cans / (1/3)t hours = 10,000 cans / 9 hours

Now, to combine the fractions, we find the common denominator, which is 3t:

(3t * 10,000 cans) / (3t * t hours) + (t * 10,000 cans) / (3t * t hours) = 10,000 cans / 9 hours

(30,000t + 10,000t) / (3t^2 hours) = 10,000 cans / 9 hours

Combine the terms on the left side of the equation:

40,000t / (3t^2 hours) = 10,000 cans / 9 hours

Now, cross-multiply to solve for "t":

40,000t * 9 hours = 10,000 cans * 3t^2 hours

360,000t hours = 30,000t^2 hours

Now, rearrange the equation:

30,000t^2 - 360,000t hours = 0

Divide by 30,000t to simplify the equation:

t - 12 = 0

Now, solve for "t":

t = 12 hours

Therefore, it takes the older machine 12 hours to make 10,000 cans.

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