Solve the proportion for x. When applicable, simplify all radicals and show all of your
3/X = x/4

Answers

Answer 1

The simplified radical for the given equation is 2√3.

The given equation is [tex]\frac{3}{x} =\frac{x}{4}[/tex].

What are radicals?

Radical of any number is the same as the root of the number. The root can be a square root, cube root, or in general, it is nth root. Thus, any expression or number that uses a root is known as a radical.

To compute for the values of x given the proportion, we can cross-multiply both sides of the equation as follows:

[tex]\frac{3}{x} =\frac{x}{4}[/tex]

⇒x×x=3×4

⇒x²=12

⇒x=±√12

From this, we can see that the solutions for the equation are the positive and negative roots of 12.

By simplifying the radical, we get √12 = √(2² x 3) = 2√3

Therefore, the simplified radical for the given equation is 2√3.

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Related Questions

Find the slope of the line that passes
through these two points.
Point 1
(4,0)
Point 2
(6,2)

Answers

Answer:

1

Step-by-step explanation:

(2-0) / (6-4)

2/2

xxxxxxxx

Answer:

1

Step-by-step explanation:

I need help explanation if possible

Answers

Step-by-step explanation:

tan x = sin x / cos x

[tex]tan \: x \: = \frac{ \frac{7}{15} }{ \frac{4 \sqrt{11} }{15} } = \frac{7}{4 \sqrt{11} } [/tex]

Marcy and her sister watched a cartoon movie that was 2 hours and 18 minutes long. after the movie, they played a card game for 34 minutes and then played soccer for 1 hour and 12 minutes. when they came in from playing soccer, it was 5:28 p.m. what time did marcy and her sister start watching the movie?

Answers

Answer:

1:24pm

Step-by-step explanation:

Couple of ways to solve this. Here is one method
Convert all times to minutes and find the total number of minutes they spent on all 3 activities. Then convert to hours and minutes and subtract from the end time of 5;28 to get the start time of all activities which is also the start time of watching the movie (first activity)

So time spent:

Movie: 2 hours 18 minutes = 2 * 60 + 18 = 120 + 18 = 138 minutes
Card game: 34 minutes
Soccer: 1 hour 12 minutes = 1 * 60 + 12 = 72 minutes

Total time spent = 138 + 34 + 72 = 244 minutes = 4 hours and 04 minutes

Subtract 4:04 from 5:28 to get 1:24pm

Check
Movie watch starts at 4:04, ends at 1:24 + 2:18 or 3:42pm
Card game starts at 3:42pm ends at 3:42+0:34 ==> 4:16pm
Soccer starts at 4:16pm ends at 4:16pm + 1:12 ==> 5;28pm

which graph correctly represents 3x+y > 7

Answers

Answer:

What graph? add a photo?

PLEASE ANSWER ASAP!!!!!!!!

A Ferris wheel completes 7 revolutions in 14 minutes. The radius of the Ferris wheel is 30 feet.


What is the linear velocity of the Ferris wheel in inches per second?


Enter your answer, rounded to the nearest tenth, in the box.

Answers

The linear velocity of the Ferris wheel in inches per second is 18.9 inches/second.

What is the speed of an object?

The speed of an object is the ratio of the total distance covered by the object and the total time taken by the object to complete that distance.

Here, the radius of the Ferris wheel is (r) = 30 feet.

The circumference of the wheel is

C= 2πr

C= 2 × π × 30 feet

C= 60π feet

Here, the Ferris wheel completes 7 revolutions.

Therefore, it covers the linear distance of

D= 7 × circumference of the wheel

D= 7 × 60π feet

D= 420π feet

Now, the Ferris wheel took 14 minutes to complete 420π feet.

Therefore, the speed of the wheel is

S= (420π/14) feet/minute

S= 30π feet/minute

S= (30π × 12)/60 inches/second

S= 6π inches/second

S= 18.9 inches/second

Therefore the linear velocity of the object will be 18.9 inches/second

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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)

Larry likes skeet shooting. a clay disc is shot into the air and the participant tries to shoot it. he rarely misses, because he knows that the flight of the disc can be modeled by a quadratic function. the discs are released from a firing mechanism that sits at ground level and shoots the disc on average a horizontal distance of 120m. the average maximum vertical height that the disc reaches is 40 m.

Answers

a)The functions that represent the flight of the clay disc in Factored Form will be,[tex]\rm y = - \frac{1}{90} (x-60)^2+40[/tex]

b)The function in its standard form is,[tex]\rm y =- \frac{1}{90} x^3 + \frac{4}{3} x[/tex].

c) The domain and range of the quadratic function with the context provided will be [0,120] and [0,40] respectively.

What exactly is a function?

A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.

The given points represent on the graph is;

x = 0 , y = 0

x = 120 , y = 0

x = 60 , y = 40

The standard equation is;

[tex]\rm y = a(x-h)^2 +k \\\\ y = a(x-60)^2 +40 \\\\ 0 = sA(120-60) +40\\\\ 0= a \times 3600 + 40 \\\\ 3600 a = -40 \\\\ a = - \farc{1}{90}[/tex]

Substitute the value as;

[tex]\rm y = - \frac{1}{90} (x-60)^2+40[/tex]

b)

The above equation  in the standard form is found as;

[tex]\rm y = \frac{-1}{90}(x^2 +3600 -120 x )+40 \\\\ y =- \frac{1}{90}(x^2 -40 + \frac{4}{3}x +40 \\\\ y = \frac{-1}{90} x^2 + \frac{4}{3}x[/tex]

c)The domain and range of the quadratic function with the context provided will be [0,120] and [0,40] respectively.

Hence, the functions that represent the flight of the clay disc in the factored form will be,[tex]\rm y = - \frac{1}{90} (x-60)^2+40[/tex]

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Trout Street and Salmon Street are the same distance from the boardwalk to the intersection of 1st Street, Trout Street, and Salmon Street as shown in the diagram. Abby walks down 1st Street and stops when she reaches the boardwalk.

How far of a walk does she have to get to Trout Street?

Abby's walk to Trout Street is _______ yards.

Answers

Answer:

800

Step-by-step explanation:

I did it on the test

Answer:

800

Step-by-step explanation:

I just fifnished test


Each car on the lot at a car dealership has 4 tires and 2 headlights. Which pair correctly describes tires and headlights?

Answers

Answer: 4 : 2

Step-by-step explanation:

I am going to assume you want a ratio between number of tires to headlights which is

4 : 2

Probably 4:2

Explanation: just guessing‍♀️

Distribute to create an equivalent expression with the fewest symbols possible.
4(5+y)

Answers

Answer:

20 + 4y

Step-by-step explanation:

To have to fewest symbols possible, we must simplify the expression by multiplying 4 into the numbers within the parenthesis. Doing so we get:

[tex]4(5+y) = 4 * 5 + 4 * y = 20 + 4y[/tex]

Answer: 20+4y

Step-by-step explanation:

Hi, let me help you.

What we should do to simplify this expression is to "distribute" 4.

The parentheses around 5+y tell us to multiply 4 times both 5 and y. This is shown below.

[tex]\multimap\quad \tt 4\cdot5+4\cdot y[/tex]

[tex]\multimap\quad\tt 20+4y[/tex] is what we obtain upon multiplying

________________

Hope I helped. Best wishes.

Reach far. Aim high. Dream big.

____________________

What is the probability that a random chosen male voter is a registered Democrat? Round your answer to the nearest tenth of a percent.

Answers

50 percent because the total is the same

The slope of the line below is -2. Write the equation of the line in point-slope
form, using the coordinates of the labeled point. Do not use parenthesis on
the y side.
(-2,1)

Answers

Answer:

y - 1 = -2(x + 2)  

Step-by-step explanation:

The general structure of an equation in point-slope form is:

y - y₁ = m(x - x₁)

In this form, "x" and "y" stand for the values of one point and "x₁" and "y₁" stand for the values of another point. The variable "m" represents the value of the slope. You have been given the values of one point and the slope. When you plug them into the general form, you get this answer:

Point: (-2, 1)

m = -2

y - y₁ = m(x - x₁)                    <----- Point-slope form

y - y₁ = -2(x - x₁)                    <----- Plug -2 in "m"

y - 1 = -2(x - (-2))                   <----- Plug in values from point

y - 1 = -2(x + 2)                    <----- Simplify

The presence of a midpoint will result in what type of segments?

Answers

Answer: two congruent segments.

Step-by-step explanation:

idlk im not smart

The price of a computer at an electronics store is $1200. If the store gives an "End of the year Sale"
discount of 20%, how much Mark needs to pay to buy the computer?

Answers

Answer
$960

Explanation
1,200 × 20 ÷ 100 = 240
1,200 - 240 = 960

Answer:

$960

Step-by-step explanation:

The discount is 20%, so we need to find 80% of the original price:

[tex].80 \times 1200 = 960[/tex]

Write an equation of the line that passes through the point P (2,-2) and is parallel to the line
-2x+y=-3

Answers

Step-by-step explanation:

Solution:

The slope of the line -2x+y = -3 is m1 =

- coefficient of x ÷ coefficient of y

= -(-2) ÷1

=2

Then, according to the question ;

It is stated that the lines are parallel

i.e.

m1=m2

or, 2 = m2

Hence, m2 =2

Again,

The required equation of the line passing through the point P(2,-2) = (x1,y1) is

y-y1 = m2(x- x1)

or, y-(-2) = 2(x-2)

or, y+2 = 2x-4

or, 2+4 = 2x-y

or, 2x-y = 6

Therefore; 2x-y = 6.

]Which statements are true? Check all that apply.

The equation |–x – 4| = 8 will have two solutions.
The equation 3.4|0.5x – 42.1| = –20.6 will have one solution.
The equation StartAbsoluteValue StartFraction one-half EndFraction x minus StartFraction 3 Over 4 EndFraction EndAbsoluteValue equals 0. = 0 will have no solutions.
The equation |2x – 10| = –20 will have two solutions.
The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions.
The equation StartAbsoluteValue StartFraction 1 Over 8 EndFraction x minus 1. EndAbsoluteValue equals 5. = 5 will have infinitely many solutions.

Answers

The correct answers are:

1. The equation |-x -4| = 8 will have two solutions. (True)

5. The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions. (True)

What is Equation?

An equation is a mathematical statement with an 'equal to =' symbol between two expressions that have equal values.

1. The equation |-x -4| = 8 will have two solutions. (True)

|-x - 4| = 8

-x -4 = ±8

-x -4 = 8 and -x -4 = -8

-x = 8 + 4 and -x = -8 + 4

-x = 12 and -x = -4

x = -12 and x = 4

Therefore, it has two solutions x ∈ {-12, 4}

2. The equation 3.4|0.5x - 42.1| = -20.6 will have one solution. (False)

Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.

3. The equation |1/2x - 3/4| = 0 will have no solutions. (False)

|(1/2)x - 3/4| = 0

(1/2)x - 3/4 = ±0

Since ±0 is the same

(1/2)x = 3/4

x = 2X3/4

x = 3/2

Therefore, it has one solution x = 3/2

4. The equation |2x – 10| = –20 will have two solutions. (False)

Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.

5. The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions. (True)

|0.5x – 0.75| + 4.6 = 0.25

|0.5x – 0.75| = 0.25 - 4.6

|0.5x – 0.75| = -4.35

Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.

6. The equation |(1/8)x - 1| = 5 will have infinitely many solutions. (False)

|(1/8)x - 1| = 5

(1/8)x - 1 = ±5

(1/8)x - 1 = 5 and (1/8)x - 1 = -5

(1/8)x = 5 + 1 and (1/8)x = -5 + 1

(1/8)x = 6 and (1/8)x = -4

x = 6X8 and x = -4X8

x = 48 and x = -32

Thus, it has two solutions x ∈ {48, -32}

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find area of shape below to 1 dp

Answers

The shape will have a surface area of 189.25 cm². There are two distinct pieces to the figure: a rectangle and a semicircle.

What is the area?

The space filled by a flat form or the surface of an item is known as the area.

The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.

The figure is divided into two parts one is a rectangle and the second is a semicircle.

Area of figure = Area of rectangle + Area of a semicircle

Area of figure = L × B + (πr²/2)

A = 10 cm × 15 cm + (3.14 ×(5)^2/2)

A= 189.25 cm²

Hence the area of the shape will be 189.25 cm²

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Two-thirds of the tokens in the box are red and 2/5 of the remaining tokens are blue.
If the remaining 24 tokens are green, how many tokens are there in the box?

Answers

Answer:

After solving this question I got and 120 tokens

Which of the following does the function [tex]y=-4cos(3x)-9[/tex] not have?
a) horizontal translation
b)vertical translation
c)horizontal compression
d)reflection

Answers

Answer:

horizontal translation    ( this would require an  x - k   or x+k   type of a factor)

Step-by-step explanation:

It DOES have :

    vertical    due to the -9

    horizontal compression due to the  3x

    reflection due to the   -4

what is the slimpelst form for ratio 21:28

Answers

Answer:

3:4

Step-by-step explanation:

We know this because the GCD of 21 and 28 is 7

so we divide both numbers by 7 and get 3 and 4

so the answer is 3:4

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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Please help very urgent I’m on a time limit and I need the answer this is a test

Answers

An isosceles triangle is one with two equal-length sides. The value of l is 8 ft.

What is an isosceles triangle?

An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.


In the given image it can be observed except 140° angle, the other two angles are congruent to each other which means the triangle is an isosceles triangle.

As per the base angle theorem in an isosceles triangle the sides opposite to the congruent triangle are equal therefore, the length of side l will be 8 ft as well.

Hence, the value of l is 8 ft.

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Based on an architectural drawing, a roof slopes to a drain along the function represented in the table that defines the edge of slope, where x is the horizontal distance in feet and f(x) is the vertical distance in feet.



If the drain is at the minimum point, how far is it from the wall defined by the y-axis?

0 feet
8 feet
80 feet
160 feet

Answers

The distance from the wall defined by the y-axis will be 8 feet. Then the correct option is B.

What is the equation of line?

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

The table is given below.

Then the equation of the line will be

(y – 8) = [(8 – 6) / (0 – 20)](x – 0)

       y = -0.1x + 8

If the drain is at the minimum point.

Then the distance from the wall defined by the y-axis will be 8 feet.

Then the correct option is B.

The complete question is given below.

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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

Answers

The correct simplified inequality is - 6x + 15 < 10 - 5x and the number line representation is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right".

The given inequality is -3(2x - 5) < 5(2 - x)

We need to simplify the inequality.

What is inequality?

In mathematics, inequality is a statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.

Consider LHS and simplify -3(2x - 5) = -3(2x)-5(-3)

⇒ -3(2x - 5) = - 6x + 15 [∵(-)(-) = (+)]

Consider RHS and simplify 5(2 - x) = 5(2) + 5(-x)

⇒5(2 - x) = 10 - 5x [∵(+)(-) = (-)]

Now, - 6x + 15 < 10 - 5x

By subtracting 15 from both sides, we get

- 6x < -5 - 5x

By adding 5x to both sides, we get - x < - 5

The coefficient of x is -1. So, divide both sides by -1

Then we get x > 5

Hence, the correct simplified inequality is - 6x + 15 < 10 - 5x and the number line representation is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right".

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Damek has five number cards lying on the table. There are two number cards with digit 1, two number cards with digit 2 and one number card with 0. How many different three-digit numbers can Damek form? (Number cannot being with 0).

(P.S. Is there a way to find the answer without listing all the possibilities?)

Answers

Damek can form 14 three-digit numbers from the given situation. Hence, only 14 possibilities.

There are five number cards on the table.

2- digit 1 card

1- digit 0 card

2- digit 2 card

There is a possibility of putting 1 or 2 in the hundredth place.

If 1 is put in the hundredth place then there are 3 possibilities for tenth place 1,0,2

If 1 is put there then there is a possibility of 2 numbers 0,2 in ones place

If 2 is put then there is a possibility of 3 numbers 0,1,2 in ones place

If 0 is put then there is a possibility of 2 numbers 1,2 in ones place.

So, there are 7=(2+3+2) possibilities that the hundredth place is filled by 1.

Similarly, there will be 7 possibilities that the hundredth place is filled by 2.

Hence, there are 14 possibilities as required by the problem.

So, the possibilities of 3-digit numbers are (given the number cannot start with 0) 14.

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The graphs below have the same shape. What is the equation of the blue
graph?

Answers

Answer:

The equation of the blue graph is g(x)=(x-3)^{2} +1g(x)=(x−3)

2

+1 . Below is the explanation

Step-by-step explanation:

Given:

The graph of f(x)=x^{2}x

2

To find:

The equation of the transformed graph g(x).

The red graph f(x) is moved right 3 units and up 1 unit to get g(x).

When graph is moved right 3 units , 3 should be subtracted with x.

When graph is moved up 1 unit, 1 is added at the end.

So, our g(x)=(x-3)^{2} +1(x−3)

2

+1

The equation of the blue graph is g(x)=(x-3)^{2} +1g(x)=(x−3)

2

+1

Can you solve this question and explain it for me? Thank you

Answers

Answer:

This is the answer to your question

Martin uses of a gallon of paint to cover of a wall. What is the unit rate at which Martin paints in walls per gallon?

Answers

The unit rate at which Martin paints in walls per gallon is 1 7/25 walls per gallon

Unit rate

Unit rate of paint per gallon = Quantity of wall / gallon of paint

= 4/5 ÷ 5/8

= 4/5 × 8/5

= (4 × 8) / (5 × 5)

= 32/25

= 1 7/25 walls per gallon

Complete question:

Martin uses 5/8 of a gallon of paint to cover4/5 of a wall. What is the unit rate at which Martin paints in walls per gallon

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Please help!

Find m<1

1
60°
63°

Answers

Answer:

i think 150 degrees

Step-by-step explanation:

the 30° angle and ∠1 are a linear pair, and are supplementary. therefore they add up to 180°
∠1 + 30° = 180°

This is from the last question

Answers

Answer:

huh

Step-by-step explanation:

what are you trying to figure out-

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