How to rationalise 1000/3

Answers

Answer 1

Answer:

Step-by-step explanation:

there is no root in denominator so I think it is rationalised


Related Questions

Find the following, giving your answers
to 1 decimal place.
10 cm/
6 cm
8 cm
a) The volume of the cone.
b) The curved surface area of the cone.

Answers

Answer:

  a) 301.6 cm³

  b) 188.5 cm²

Step-by-step explanation:

The volume and lateral surface area of the cone can be found using the given dimensions with the given formulas. All that is needed is to substitute the appropriate values and do the arithmetic.

__

a) volume

The volume is given by the formula ...

  V = 1/3πr²h

The dimensions are given on the diagram: r = 6 cm, h = 8 cm. Using these values in the formula, we find the volume to be ...

  V = 1/3π(6 cm)²(8 cm) = 96π cm³ ≈ 301.6 cm³

The volume of the cone is about 301.6 cm³.

__

b) area

The lateral area of the cone is given by the formula ...

  A = πrl

The dimensions are given on the diagram: r = 6 cm, l = 10 cm (the slant height). Using these values in the formula, we find the area to be ...

  A = π(6 cm)(10 cm) = 60π cm² ≈ 188.5 cm²

The area of the curved surface is about 188.5 cm².

What is the slope of the linear relationship shown in this table of values?​

Answers

The equation is
The difference of y/ the difference of x
If you want further help ask

Answer:

B

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, - 1) and (x₂, y₂ ) = (- 4, 11) ← 2 ordered pairs from the table

m = [tex]\frac{11-(-1)}{-4-2}[/tex] = [tex]\frac{11+1}{-6}[/tex] = [tex]\frac{12}{-6}[/tex] = - 2

Find the value of x.
5
X
11
y

Answers

The value of the variable is 4√5. Then the correct option is C.

What is the triangle?

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The similar triangles are shown in the diagram.

16 / x = x / 5

    x² = 16 × 5

      x = 4 √5

Then the value of the variable is 4√5.

Then the correct option is C.

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A test is worth of 150 points and contains 70 questions. Some questions are worth 2 points, and some are worth 4 points

2x + 4y = 150

Answers

Answer:

65 2 point questions, 5 4 point questions

Step-by-step explanation:

write a system of equations:

let x be the number of 2 point questions and y be the number of 4 point questions

2x + 4y = 150

x + y = 70 (since there are 70 total questions)

x + y = 70

subtract x from both sides

y = -x + 70

substitute y = -x + 70 into 2x + 4y = 150

2x + 4(-x + 70) = 150

2x - 4x + 280 = 150

-2x = -130

x = 65

substitute x = 65 into x + y = 70

65 + y = 70

subtract 65 from both sides

y = 5

umm.. i fr don’t know how to do this … help pls

Answers

Answer:

2 solutions: ( -4,0 )

( -6,0 )

2 Non solution: ( 2,0 )

( 4,0 )

Answers:

Refer to the graph below

Two solution points are (-5,-4) and (-4,-3)

Non solution points are (0,3) and (1,4)

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

Explanation:

The boundary line for [tex]y \ge 3x+3[/tex] is [tex]y = 3x+3[/tex]

This linear equation has a y intercept of (0,3) and another point on the line is (1,6). Plot these two points and draw a straight line through them. This line is a solid boundary line because of the "or equal to" as part of the inequality sign. This means points on the boundary adjacent to the shaded region area part of the solution set.

Because of the "greater than" portion, we'll shade above the solid boundary line. This only works because y is isolated.

Keep in mind that we're also told that [tex]y < -2[/tex] which means we'll also shade the region below the boundary line [tex]y = -2[/tex]. This is a dashed line through -2 on the y axis. A dashed line does not include points on the boundary as part of the solution.

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

To summarize: We shade above y = 3x+3 (solid) but below y = -2 (dashed).

Refer to the diagram below to see what's going on.

The entire southwest region is shaded.

That blue shaded region represents all (x,y) points that make the system true.

For example, the point (-5,-4) is in the blue region.

Notice how plugging the coordinates into the first inequality gets us...

[tex]y \ge 3x+3\\\\-4 \ge 3(-5)+3\\\\-4 \ge -15+3\\\\-4 \ge -12\\\\[/tex]

which is a true statement. If you plugged y = -4 into [tex]y < -2[/tex], you would also get another true statement.

Both inequalities are true for (x,y) = (-5,-4) which confirms it to be a solution point.

You should also find that a point like (-4,-3) is another solution in the blue region following similar steps. There are infinitely many solution points to pick from. Feel free to choose others.

Non-solution points are such that they aren't in the shaded region. We could also pick points on the dashed boundary line as non-solutions.

Side note: you can pick points on the solid boundary as solution points, but those points must be adjacent to the shaded region. The point (0,3) is NOT a solution even though it's on the solid boundary line.

Round 2
5. A Cadillac Escalade gasoline tank has a capacity of 24
gallons. The car uses approximately 1 gallon for every 25
miles it drives. If the tank starts full, write an equation that
describes the amount of gas, g, left in the tank after it has
been driven for m miles.

Answers

Answer:

g = 24 - 1/25m

Step-by-step explanation:

Since the Cadillac Escalade can travel 25 miles per gallon, each mile the Escalade travels is 1/25th of a gallon of gas.

This means that every mile the Escalade travels, 1/25th of a gallon is subtracted from the gas tank. Since the gas tank has a capacity of 24 gallons, the value of the gas tank is 24.

This leads us to the equation:

g = 24 - 1/25m

where g is the amount of gas left, and m is the number of miles driven.

PLEASE HELP ME WITH THIS ASAP

Answers

Answer:

x=46

Step-by-step explanation:

4(x+1)-3x=50

first you gotta take care of the () so multiple by 4

(4x+4) -3x=50

combine like terms, subtract 4-3 to get 1 so you have 1x left

4 + x = 50

and then solve for x

x=46

( i checked it to make sure it was right so dw)

what is the equation of x2 + 6x + 8 + 0 algebraically

Answers

Answer:

x = - 4 , x = - 2

Step-by-step explanation:

x² + 6x + 8 = 0

consider the factors of the constant term (+ 8) which sum to give the coefficient of the x- term (+ 6)

the factors are + 4 and + 2 , since

4 × 2 = 8 and 4 + 2 = 6 , then

(x + 4)(x + 2) = 0 ← in factored form

equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x + 2 = 0 ⇒ x = - 2

Look at pictures attached for question and answer choices

Answers

The answers are a rhombus, bisect a pair of opposite angles, and SAS congruency postulate respectively.

What is a rhombus?

A rhombus is a two-dimensional shape having four parallel opposite pairs of straight, equal sides. This shape resembles a diamond and is what you'd find on a deck of cards to represent the diamond suit. Rhombuses can be encountered in a variety of common situations.

We have a rhombus shown in the picture.

The intersection point is P

From the definition of the rhombus: JK ≅ KM

According to the SAS congruency postulate, two triangles are congruent if a triangle has two sides and an included angle that are congruent to the two sides and an included angle of another triangle.

Thus, the answers are a rhombus, bisect a pair of opposite angles, and SAS congruency postulate respectively.

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Matt is trying to measure the height of a tree using
trigonometry. He is having trouble because of the
terrain around the tree. The horizontal distance
from the tree to Matt's eyes is 120 feet. The angle
of depression from the horizontal is 30°. Matt's
angle of sight to the top of the tree is 23°. What is
the height of the tree? (Round to the nearest foot.)

Answers

The height of the tree will be 18.35 feet.

What is a right-angle triangle?

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Matt is trying to measure the height of a tree using trigonometry.

He is having trouble because of the terrain around the tree.

The horizontal distance from the tree to Matt's eyes is 120 feet.

The angle of depression from the horizontal is 30°.

Matt's angle of sight to the top of the tree is 23°.

The diagram is given below.

Let x be the height of tree and AM be h.

The value of (h + x) will be

tan 30° = (x + h) / 120

   x + h = 69.288

Then the value of h will be

tan 23° = h / 120

        h = 50.94 feet

Then the height of the tree will be

⇒ h + x – h

⇒ 69.29 - 50.94.

⇒ 18.35 feet

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In a school, the number of girls is 70 more than boys. the total number of students is 1280. find the number of girls and boys

Answers

Answer:

Step-by-step explanation:

Conditions

Let the girls = g

Let the boys = b

Equations

g + b = 1280

g = b + 70

Solution

Put the value for the girls (second equation) into the first equation.

b + 70 + b = 1280                           Subtract 70 from both sides

b + 70 - 70 + b = 1280 -70             Combine

2b = 1210                                        Divide both sides by 2

2b/2 = 1210/2  

b = 605                                          Substitute this value into the top equation

g + 605 = 1280                              Subtract 605 from both sides

g + 605 - 605 = 1280 - 605

g = 675

Answer

# boys = 605

# girls = 675

C
2
1
3
A. 21
B. 23
C.24
D. 25
b7
#
5
4
In the figure, which angle has the same measure as /2?

Answers

Answer:

the angle that has the same measure as /2 is A

I think its 2c but am not sure

The list price of a commodity is RM420 and the percentage profit is 40%. If the commodity is sold at a discount of 10%, the profit is____.​

Answers

Answer:

56

Step-by-step explanation:

you first had to get the marked price so t you can get the profit.

just as illustrated in the picture above.

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the equation.

Answers

Answer 1.p= 15/x
2.x=-3

1. Working
px+1=16

xp=16-1
xp=15
p=15/x

2. 4(-5x+1)=64
-5x+1=16
-5x=16-1
-5x=15 ,
x=-3
I hope this helps^^

What is the volume of a cylinder, in cubic feet, with a height of 13 feet and a base
diameter of 4 feet? Round to the nearest tenths place.

Answers

Answer:

163.3

Step-by-step explanation:

3.14*r^2*h

h=13

4/2 = 2

r=2

2^2 = 4

3.14*4 = 12.56

12.56*13 = 163.28

Rounded = 163.3

I believe the answer is 163.3

how to say i like chees burgers without saying that like how to say im not gonna date you while i still will im just dum what is 1+1

Answers

Answer:

2

I believe that the answer my friend

Which is a rational function?
A. Y=5
B. Y=√x-3
C. Y=x²-3x+5
D.Y = x-5/x

Answers

B…………. is the answer

what is the principle value of sin^-1(1)

Answers

The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. The principal value of sin⁻¹(1) is 90°.

What is Sine (Sinθ)?

The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,

Sin(θ) = Perpendicular/Hypotenuse

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The hypotenuse is the longest side of the triangle.

The principal value of sin⁻¹(1) is,

θ = Sin⁻¹(1)

θ = 90°

Hence, the principal value of sin⁻¹(1) is 90°.

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what is the inverse of f(x)=(-2x+2)/(x+7)?

Answers

By applying the concept of the inverse of a function and algebraic handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).

How to find the inverse of a function

In this question we have a rational function f(x) and finding its inverse consists in clearing x in terms of f(x). Prior any algebraic handling, we need to apply the following substitutions:

[tex]x \to y[/tex]

[tex]f(x) \to x[/tex]

[tex]x = \frac{-2\cdot y + 2}{y+7}[/tex]

x · (y + 7) = - 2 · y + 2

x · y + 7 · x = - 2 · y + 2

2 · y + x · y = - 7 · x + 2

y · (2 + x) = - 7 · x + 2

[tex]g(x) = \frac{- 7\cdot x + 2}{x + 2}[/tex]

By applying the concept of the inverse of a function and algebraic handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).

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I’m having trouble understanding how to solve this someone please help ASAP thank you!

Use the Law of Cosines to solve the problem. You must solve for BC first. Solve this problem in order.

A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173 miles from its original position. To the nearest tenth of a degree, how many degrees north of west (x) did it

turn when it changed direction? Show your work.


Answers

I’m not very good at it myself but it should be abt 40 degrees

Which function can be used to represent the graphed geometric sequence?

f(x) = 80(One-fourth) Superscript x minus 1
f(x) = 320(One-fourth) Superscript x minus 1
f(x) = 80(4)x – 1
f(x) = 320(4)x – 1

Answers

The function which is used to represent the graphed geometric sequence is

[tex]f(x) = 80{( \frac{1}{4}) }^{x - 1} [/tex]

Let a be first term and r common ratio of the Geometric progression.

The Geometric sequence is of the form a,ar,ar^2, ...

The common ratio will be ar/a.

From the graph, we can find out the sequence as 80,20,5, ...

Here we can see that the sequence is in Geometric Progression.

First term a=80

Common ratio r= ar/a

= 20/80

=1/4

General term of Geometric sequence is

[tex]f(x) = a {r}^{x - 1} [/tex]

Substituting the value a = 80 and r = 1/4,

we get,

[tex]f(x) =80 { (\frac{1}{4} )}^{x - 1} [/tex]

Hence, the correct answer is

[tex]f(x) =80 { (\frac{1}{4} )}^{x - 1} [/tex]

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On a number line, 2.5 would be located ______. Choose all answers that make a true statement.

2.5
《----|----|----|----|----|----|----|----|----|----|----》


A. to the right of 2.52
B. between 2.45 and 2.55
C. to the left of 2.3
D. between of 2.4 and 2.6

Answers

Answer:

It is both answers B and D

if the unit rate is 30 miles per hour , then how much miles is traveled in 9 hours

Answers

Answer:

270 miles

Step-by-step explanation:

Since the unit rate is 30 miles per hour, the miles on 9 hours will be:

= 30 × 9

= 270 miles.

Carl is making a garden that is twice as long as it is wide. he wants to cover 271
square feet with the garden. which equation best represents the situation if x
represents the length of the garden?

Answers

The equation which best represents the scenario is, x²/2=271

Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

Perimeter is a length of the boundary surrounding the area

Area of rectangle=length x Breadth

Perimeter=2(length+breadth)

length=x

breadth=x/2

Area=271ft²

Area=length x breadth

So, using the given value we can write

271=x²/2

⇒x=√542

      =23.28ft

Therefore, the equation which best represents the scenario is, x²/2=271

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Select the correct answer.
Which calculation correctly uses prime factorization to write √48 In simplest form?
OA √48 = √2-2-2-2-3-2√12
OB. √48√4 - 12 = 2√12
OC. √48 = √2-2-2-2-3= 4√3
OD. √48 =√16-3 = 4√3

Answers

D. √48 =√16*3 = 4√3

Simplify the radical by breaking the radicand up into a product of known factors.

16*3 = 48

this means that √48 = √16*3, but this can be simplified.

√16 = 4, √3 = √3 because it cannot be simplified farther

making the most simplified answer 4√3

A circle representing a pool is graphed with a center at the origin. Grant enters the pool at point A and swims over to a friend who is located at point B.

Answers

Grant would swim three the middles of the pool (just doing this for the points)

What are the first 10 digits after the decimal point (technically the hexadecimal point...) when the fraction frac17 is written in base 16?

Answers

We happen to have

[tex]\dfrac17 = \dfrac18 + \dfrac1{8^2} + \dfrac1{8^3} + \cdots[/tex]

which is to say, the base-8 representation of 1/7 is

[tex]\dfrac17 \equiv 0.111\ldots_8[/tex]

This follows from the well-known result on geometric series,

[tex]\displaystyle \sum_{n=1}^\infty ar^{n-1} = \frac a{1-r}[/tex]

if [tex]|r|<1[/tex]. With [tex]a=1[/tex] and [tex]r=\frac18[/tex], we have

[tex]\displaystyle \sum_{n=1}^\infty \frac1{8^{n-1}} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac1{1-\frac18} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac87 = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac17 = \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots[/tex]

Uniformly multiplying each term on the right by an appropriate power of 2, we have

[tex]\dfrac17 = \dfrac2{16} + \dfrac{2^2}{16^2} + \dfrac{2^3}{16^3} + \dfrac{2^4}{16^4} + \dfrac{2^5}{16^5} + \dfrac{2^6}{16^6} + \cdots[/tex]

Now observe that for [tex]n\ge4[/tex], each numerator on the right side side will contain a factor of 16 that can be eliminated.

[tex]\dfrac{2^n}{16^n} = \dfrac{2^4\times2^{n-4}}{16^n} = \dfrac{2^{n-4}}{16^{n-1}}[/tex]

That is,

[tex]\dfrac{2^4}{16^4} = \dfrac1{16^3}[/tex]

[tex]\dfrac{2^5}{16^5} = \dfrac2{16^4}[/tex]

[tex]\dfrac{2^6}{16^6} = \dfrac4{16^5}[/tex]

etc. so that

[tex]\dfrac17 = \dfrac2{16} + \dfrac4{16^2} + \dfrac9{16^3} + \dfrac2{16^4} + \dfrac4{16^5} + \dfrac9{16^6} + \cdots[/tex]

and thus the base-16 representation of 1/7 is

[tex]\dfrac17 \equiv 0.249249249\ldots_{16}[/tex]

and the first 10 digits after the (hexa)decimal point are {2, 4, 9, 2, 4, 9, 2, 4, 9, 2}.

Which of the following is equal to m

Answers

Answer: tan^-1 (c/a)

Step-by-step explanation: An angle C ∈ ℝ such that angle C > 0 can be defined by the trigonometric ratio Arctangent (or rather tan^-1) where side "c" divided by side "a" ≠ 0.

Karl’s math class is playing a number game. Each student is given a number card containing the numbers 1 to 6. The rules of the game are that each student must put a cross through two numbers on the card and hand it in to the teacher. The teacher has a bag containing six balls numbered 1 to 6. When all the number cards have been handed in the teacher draws out two balls from the bag. Every student who had chosen the same two numbers shown on the balls wins a prize. If there are 30 students in Karl’s class, how many students are likely to win a prize? Describe your reasoning

Answers

By finding the probability, we can expect that 2 out of the 30 students will win the prize.

How many of the 30 students will win the prize?

First, we should get the probability of winning this game.

Here the students select two numbers out of 6, just to make the calculations let's say that these numbers are 1 and 2.

Now, we need to get these two numbers in two balls. The probability of getting the ball with the number 1 out of the 6 balls is:

p = 1/6

The probability of getting the ball with the number 2 out of the remaining 5 balls (because we already got one) is:

q = 1/5

The joint probability is then:

P = 2*(1/6)*(1/5) = 1/15.

Where the factor 2 comes to take in account the permutations, for the case where we first draw the number 2 and then the number 1.

Then the expected number of students that will win is equal to the probability times the total number of students:

(1/15)*30 = 2

So out of the 30 students, we can expect that 2 will win.

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Points
Find f(−2)
given f(x)=−x3−3x2+8

Answers

Answer:

12 :D

Step-by-step explanation:

First we substitute all x's for -2 :)

f(-2)=−-2^3−3(-2)^2+8

Now we solve :)

f(-2)=−-2^3−3(-2)^2+8

f(-2)=− -8 −3(-2)^2 + 8

f(-2) = -8 - 3(-4) + 8

f(-2) = - 8 + 12 + 8

f(-2) = 4 + 8

f(-2) = 12 :)

f will equal 12 :)

Have an amazing day!!

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